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		<id>http://www.dyco.fr/index.php?action=history&amp;feed=atom&amp;title=PACS%2FPlant_response_to_stress_%26_Biological_Networks</id>
		<title>PACS/Plant response to stress &amp; Biological Networks - Revision history</title>
		<link rel="self" type="application/atom+xml" href="http://www.dyco.fr/index.php?action=history&amp;feed=atom&amp;title=PACS%2FPlant_response_to_stress_%26_Biological_Networks"/>
		<link rel="alternate" type="text/html" href="http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;action=history"/>
		<updated>2026-04-19T19:58:15Z</updated>
		<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=539&amp;oldid=prev</id>
		<title>Yd: /* The Lechatelier-Braun principle */</title>
		<link rel="alternate" type="text/html" href="http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=539&amp;oldid=prev"/>
				<updated>2016-04-11T12:47:03Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;The Lechatelier-Braun principle&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 12:47, 11 April 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l26&quot; &gt;Line 26:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 26:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;====''The Lechatelier-Braun principle''====&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;====''The Lechatelier-Braun principle''====&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;According to the Lechatelier-Braun principle all the &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;thermodanymic &lt;/del&gt;potentials are connected.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;According to the Lechatelier-Braun principle all the &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;thermodynamic &lt;/ins&gt;potentials are connected.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;For instance, the hydraulic and electric responses of plant are known to be highly correlated (Mancuso 1999) revealing the underlying coupling between P and &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;μ&lt;/del&gt;. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;For instance, the hydraulic and electric responses of plant are known to be highly correlated (Mancuso 1999) revealing the underlying coupling between &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt; &amp;lt;math&amp;gt;&lt;/ins&gt;P&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;/math&amp;gt; &lt;/ins&gt;and &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;&lt;/ins&gt;. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Similar observations of coupling between &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;μ &lt;/del&gt;and T have been reported from vegetal thermoelectric responses. All these thermodynamic-type analyses (cf. also e.g. Demirel &amp;amp; Sandler 2002, or Qian &amp;amp; Beard 2005) would benefit from a description of the energetic &amp;amp; material fluxes in order to build up solid knowledge about a plant metabolism. The dynamics energy budget 􏰀(DEB􏰁) theory is the most popular non-species-specific theory of this kind. However, this now quite standard modeling of biochemical networks neglects the spatial structure and the complex transport and allocation processes in the organism.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Similar observations of coupling between &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt; &lt;/ins&gt;and &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt; &amp;lt;math&amp;gt;&lt;/ins&gt;T&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;/math&amp;gt; &lt;/ins&gt;have been reported from vegetal thermoelectric responses. All these thermodynamic-type analyses (cf. also e.g. Demirel &amp;amp; Sandler 2002, or Qian &amp;amp; Beard 2005) would benefit from a description of the energetic &amp;amp; material fluxes in order to build up solid knowledge about a plant metabolism. The dynamics energy budget 􏰀(DEB􏰁) theory is the most popular non-species-specific theory of this kind. However, this now quite standard modeling of biochemical networks neglects the spatial structure and the complex transport and allocation processes in the organism.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;====''A spatio-temporal nodal approach''====&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;====''A spatio-temporal nodal approach''====&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Yd</name></author>	</entry>

	<entry>
		<id>http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=538&amp;oldid=prev</id>
		<title>Yd: /* Context */</title>
		<link rel="alternate" type="text/html" href="http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=538&amp;oldid=prev"/>
				<updated>2016-04-11T12:44:04Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Context&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 12:44, 11 April 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l4&quot; &gt;Line 4:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 4:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==''Context'' ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==''Context'' ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Global agriculture is facing a serious threat from climate change that compromises&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Global agriculture is facing a serious threat from climate change that compromises&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;global food security and &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;impact &lt;/del&gt;the ecosystem services and biodiversity. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;global food security and &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;impacts &lt;/ins&gt;the ecosystem services and biodiversity. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;High temperatures affect plant development at the level of seed germination which represents the first step of plant establishment and also reduce the plant growth by affecting the shoot net assimilation rates and thus the total dry weight of the plant (Bita et al 2013). It is the first climatic factor capping yields on a global scale for wheat (Lobell et al 2007) and rice (Peng et al 2004). Projections predict a 9-15% decrease in the production of major cereals by 2020 (Hisas et al. 2011). Climate change will increase the negative effect on crop productivity not only due to heat waves, i.e. an increase of several degrees over the seasonal temperature for a sustained period of days (IPCC 2014), but also by exacerbating broad-spectrum stresses such as drought, cold, salinity, flood, submergence and pests (Kole et al 2015). Moreover, recent studies have revealed that the response of plants to combinations of two or more stress conditions is unique and cannot be directly extrapolated from the response of plants to each of the different stresses applied individually. Indeed the responses to the combined stresses are complex and largely controlled by different, and sometimes opposing, signaling pathways that may interact and inhibit each other (Suzuki et al 2014). &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;High temperatures affect plant development at the level of seed germination which represents the first step of plant establishment and also reduce the plant growth by affecting the shoot net assimilation rates and thus the total dry weight of the plant (Bita et al 2013). It is the first climatic factor capping yields on a global scale for wheat (Lobell et al 2007) and rice (Peng et al 2004). Projections predict a 9-15% decrease in the production of major cereals by 2020 (Hisas et al. 2011). Climate change will increase the negative effect on crop productivity not only due to heat waves, i.e. an increase of several degrees over the seasonal temperature for a sustained period of days (IPCC 2014), but also by exacerbating broad-spectrum stresses such as drought, cold, salinity, flood, submergence and pests (Kole et al 2015). Moreover, recent studies have revealed that the response of plants to combinations of two or more stress conditions is unique and cannot be directly extrapolated from the response of plants to each of the different stresses applied individually. Indeed the responses to the combined stresses are complex and largely controlled by different, and sometimes opposing, signaling pathways that may interact and inhibit each other (Suzuki et al 2014). &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Yd</name></author>	</entry>

	<entry>
		<id>http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=501&amp;oldid=prev</id>
		<title>Yd: /* Expected Validations and Outcomes */</title>
		<link rel="alternate" type="text/html" href="http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=501&amp;oldid=prev"/>
				<updated>2016-04-07T07:48:44Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Expected Validations and Outcomes&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 07:48, 7 April 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l41&quot; &gt;Line 41:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 41:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Since the approach is quite versatile, more complex non-homogeneous structures and topologies may also be analyzed, and help possibly encompassing the role of the spatial biological cells distribution for the plant response to stress. Possibly anisotropic, discontinuous transport and thermoelectric properties may also be included, hence mimicking the sharp interface between cells of different kinds. Notice that the numerical strategy is able to enforce the fluxes (of energy, matter, species) continuity at the local (nodal) scale, and at any time. This aspect is of paramount importance, enforcing the compatibility of the numerical modeling with physical first-principles.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Since the approach is quite versatile, more complex non-homogeneous structures and topologies may also be analyzed, and help possibly encompassing the role of the spatial biological cells distribution for the plant response to stress. Possibly anisotropic, discontinuous transport and thermoelectric properties may also be included, hence mimicking the sharp interface between cells of different kinds. Notice that the numerical strategy is able to enforce the fluxes (of energy, matter, species) continuity at the local (nodal) scale, and at any time. This aspect is of paramount importance, enforcing the compatibility of the numerical modeling with physical first-principles.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The aim would be to be able to validate the network modeling against the observed data obtained from experiments,. Once thoroughly validated, &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;ons &lt;/del&gt;should be able to extrapolate the modeling to situations where no data can be measured (because e.g. of too high spatial and/or temporal resolution requirements), or difficult to measure properties. To our knowledge, this would be the very first spatio-temporal network-based thermodynamic-type modeling of the whole plant, in order to reproduce the plant response to different kinds of simultaneous (and hence interacting) stresses.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The aim would be to be able to validate the network modeling against the observed data obtained from experiments,. Once thoroughly validated, &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;one &lt;/ins&gt;should be able to extrapolate the modeling to situations where no data can be measured (because e.g. of too high spatial and/or temporal resolution requirements), or difficult to measure properties. To our knowledge, this would be the very first spatio-temporal network-based thermodynamic-type modeling of the whole plant, in order to reproduce the plant response to different kinds of simultaneous (and hence interacting) stresses.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== ''Participants'' ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== ''Participants'' ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;François Bouteau, Delphine Bonnin,&amp;#160; [https://www.researchgate.net/profile/Hayat_El-Maarouf-Bouteau Hayat El-Maarouf-Bouteau], Patrice Meimoun, [https://www6.rennes.inra.fr/umreva/Annuaire/INFlux/E.-Le-Deunff Erwan Le Deunff], Eric Herbert, Christophe Goupil, Yves D'Angelo.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;François Bouteau, Delphine Bonnin,&amp;#160; [https://www.researchgate.net/profile/Hayat_El-Maarouf-Bouteau Hayat El-Maarouf-Bouteau], Patrice Meimoun, [https://www6.rennes.inra.fr/umreva/Annuaire/INFlux/E.-Le-Deunff Erwan Le Deunff], Eric Herbert, Christophe Goupil, Yves D'Angelo.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Yd</name></author>	</entry>

	<entry>
		<id>http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=497&amp;oldid=prev</id>
		<title>Yd: /* A spatio-temporal nodal approach */</title>
		<link rel="alternate" type="text/html" href="http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=497&amp;oldid=prev"/>
				<updated>2016-04-06T14:12:02Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;A spatio-temporal nodal approach&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 14:12, 6 April 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l36&quot; &gt;Line 36:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 36:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[File:Pacs.png|330 px]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[File:Pacs.png|330 px]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and the vector of potential output/input differences &amp;lt;math&amp;gt;{\&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;bf \delta &lt;/del&gt;\mu}&amp;lt;/math&amp;gt; can be proposed, thank to the introduction of the Onsager matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;{\bf X}= {\bf Z \mu}&amp;lt;/math&amp;gt;. The coefficient of the matrix &amp;lt;math&amp;gt;{\bf Z} &amp;lt;/math&amp;gt; can depend on &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;{\&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;bf &lt;/del&gt;\mu}&amp;lt;/math&amp;gt; (their local value, and possibly their temporal gradient or history).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and the vector of potential output/input differences &amp;lt;math&amp;gt;{\&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;large &lt;/ins&gt;\mu}&amp;lt;/math&amp;gt; can be proposed, thank to the introduction of the Onsager matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;{\bf X}= {\bf Z&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;}{\large &lt;/ins&gt;\mu}&amp;lt;/math&amp;gt;. The coefficient of the matrix &amp;lt;math&amp;gt;{\bf Z} &amp;lt;/math&amp;gt; can depend on &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;{\&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;large &lt;/ins&gt;\mu}&amp;lt;/math&amp;gt; (their local value, and possibly their temporal gradient or history).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;===''Expected Validations and Outcomes''===&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;===''Expected Validations and Outcomes''===&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Yd</name></author>	</entry>

	<entry>
		<id>http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=496&amp;oldid=prev</id>
		<title>Yd: /* Expected Validations */</title>
		<link rel="alternate" type="text/html" href="http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=496&amp;oldid=prev"/>
				<updated>2016-04-06T14:10:42Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Expected Validations&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 14:10, 6 April 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l38&quot; &gt;Line 38:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 38:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and the vector of potential output/input differences &amp;lt;math&amp;gt;{\bf \delta \mu}&amp;lt;/math&amp;gt; can be proposed, thank to the introduction of the Onsager matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;{\bf X}= {\bf Z \mu}&amp;lt;/math&amp;gt;. The coefficient of the matrix &amp;lt;math&amp;gt;{\bf Z} &amp;lt;/math&amp;gt; can depend on &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;{\bf \mu}&amp;lt;/math&amp;gt; (their local value, and possibly their temporal gradient or history).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and the vector of potential output/input differences &amp;lt;math&amp;gt;{\bf \delta \mu}&amp;lt;/math&amp;gt; can be proposed, thank to the introduction of the Onsager matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;{\bf X}= {\bf Z \mu}&amp;lt;/math&amp;gt;. The coefficient of the matrix &amp;lt;math&amp;gt;{\bf Z} &amp;lt;/math&amp;gt; can depend on &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;{\bf \mu}&amp;lt;/math&amp;gt; (their local value, and possibly their temporal gradient or history).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;===''Expected Validations''===&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;===''Expected Validations &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;and Outcomes&lt;/ins&gt;''===&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Since the approach is quite versatile, more complex non-homogeneous structures and topologies may also be analyzed, and help possibly encompassing the role of the spatial biological cells distribution for the plant response to stress. Possibly anisotropic, discontinuous transport and thermoelectric properties may also be included, hence mimicking the sharp interface between cells of different kinds. Notice that the numerical strategy is able to enforce the fluxes (of energy, matter, species) continuity at the local (nodal) scale, and at any time. This aspect is of paramount importance, enforcing the compatibility of the numerical modeling with physical first-principles.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Since the approach is quite versatile, more complex non-homogeneous structures and topologies may also be analyzed, and help possibly encompassing the role of the spatial biological cells distribution for the plant response to stress. Possibly anisotropic, discontinuous transport and thermoelectric properties may also be included, hence mimicking the sharp interface between cells of different kinds. Notice that the numerical strategy is able to enforce the fluxes (of energy, matter, species) continuity at the local (nodal) scale, and at any time. This aspect is of paramount importance, enforcing the compatibility of the numerical modeling with physical first-principles.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Yd</name></author>	</entry>

	<entry>
		<id>http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=495&amp;oldid=prev</id>
		<title>Yd: /* &quot;Validations&quot; */</title>
		<link rel="alternate" type="text/html" href="http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=495&amp;oldid=prev"/>
				<updated>2016-04-06T14:10:09Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;&amp;quot;Validations&amp;quot;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 14:10, 6 April 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l38&quot; &gt;Line 38:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 38:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and the vector of potential output/input differences &amp;lt;math&amp;gt;{\bf \delta \mu}&amp;lt;/math&amp;gt; can be proposed, thank to the introduction of the Onsager matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;{\bf X}= {\bf Z \mu}&amp;lt;/math&amp;gt;. The coefficient of the matrix &amp;lt;math&amp;gt;{\bf Z} &amp;lt;/math&amp;gt; can depend on &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;{\bf \mu}&amp;lt;/math&amp;gt; (their local value, and possibly their temporal gradient or history).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and the vector of potential output/input differences &amp;lt;math&amp;gt;{\bf \delta \mu}&amp;lt;/math&amp;gt; can be proposed, thank to the introduction of the Onsager matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;{\bf X}= {\bf Z \mu}&amp;lt;/math&amp;gt;. The coefficient of the matrix &amp;lt;math&amp;gt;{\bf Z} &amp;lt;/math&amp;gt; can depend on &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;{\bf \mu}&amp;lt;/math&amp;gt; (their local value, and possibly their temporal gradient or history).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;===&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot;&lt;/del&gt;Validations&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot;&lt;/del&gt;===&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;===&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;''Expected &lt;/ins&gt;Validations&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;''&lt;/ins&gt;===&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Since the approach is quite versatile, more complex non-homogeneous structures and topologies may also be analyzed, and help possibly encompassing the role of the spatial biological cells distribution for the plant response to stress. Possibly anisotropic, discontinuous transport and thermoelectric properties may also be included, hence mimicking the sharp interface between cells of different kinds. Notice that the numerical strategy is able to enforce the fluxes (of energy, matter, species) continuity at the local (nodal) scale, and at any time. This aspect is of paramount importance, enforcing the compatibility of the numerical modeling with physical first-principles.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Since the approach is quite versatile, more complex non-homogeneous structures and topologies may also be analyzed, and help possibly encompassing the role of the spatial biological cells distribution for the plant response to stress. Possibly anisotropic, discontinuous transport and thermoelectric properties may also be included, hence mimicking the sharp interface between cells of different kinds. Notice that the numerical strategy is able to enforce the fluxes (of energy, matter, species) continuity at the local (nodal) scale, and at any time. This aspect is of paramount importance, enforcing the compatibility of the numerical modeling with physical first-principles.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Yd</name></author>	</entry>

	<entry>
		<id>http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=494&amp;oldid=prev</id>
		<title>Yd: /* A spatio-temporal nodal approach */</title>
		<link rel="alternate" type="text/html" href="http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=494&amp;oldid=prev"/>
				<updated>2016-04-06T14:09:35Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;A spatio-temporal nodal approach&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 14:09, 6 April 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l34&quot; &gt;Line 34:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 34:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The figure below illustrates the envisaged structure for the elementary building block and the way the blocks can be (physically) connected:&amp;#160; generalized fluxes &amp;lt;math&amp;gt;X_i &amp;lt;/math&amp;gt;and generalized input and output potentials &amp;lt;math&amp;gt;\mu_j^{in}&amp;lt;/math&amp;gt; and&amp;#160; &amp;lt;math&amp;gt;\mu_j^{out}&amp;lt;/math&amp;gt; are inter-connected through a (locally linearized) Onsager-type approach.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The figure below illustrates the envisaged structure for the elementary building block and the way the blocks can be (physically) connected:&amp;#160; generalized fluxes &amp;lt;math&amp;gt;X_i &amp;lt;/math&amp;gt;and generalized input and output potentials &amp;lt;math&amp;gt;\mu_j^{in}&amp;lt;/math&amp;gt; and&amp;#160; &amp;lt;math&amp;gt;\mu_j^{out}&amp;lt;/math&amp;gt; are inter-connected through a (locally linearized) Onsager-type approach.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[File:Pacs.png|330 px]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[&lt;/ins&gt;[File:Pacs.png|330 px&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;]&lt;/ins&gt;]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and the vector of potential output/input differences &amp;lt;math&amp;gt;{\bf \delta \mu}&amp;lt;/math&amp;gt; can be proposed, thank to the introduction of the Onsager matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt;, &lt;del class=&quot;diffchange diffchange-inline&quot;&gt; &lt;/del&gt;&amp;lt;math&amp;gt;{\bf X}&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;/math&amp;gt;&lt;/del&gt;= {\bf Z \mu}&amp;lt;/math&amp;gt;. The coefficient of the matrix &amp;lt;math&amp;gt;{\bf Z &amp;lt;/math&amp;gt; can depend on &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;{\bf \mu}&amp;lt;/math&amp;gt; (their local value, and possibly their temporal gradient or history).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and the vector of potential output/input differences &amp;lt;math&amp;gt;{\bf \delta \mu}&amp;lt;/math&amp;gt; can be proposed, thank to the introduction of the Onsager matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;{\bf X}= {\bf Z \mu}&amp;lt;/math&amp;gt;. The coefficient of the matrix &amp;lt;math&amp;gt;{\bf Z&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;} &lt;/ins&gt;&amp;lt;/math&amp;gt; can depend on &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;{\bf \mu}&amp;lt;/math&amp;gt; (their local value, and possibly their temporal gradient or history).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;===&amp;quot;Validations&amp;quot;===&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;===&amp;quot;Validations&amp;quot;===&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Yd</name></author>	</entry>

	<entry>
		<id>http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=493&amp;oldid=prev</id>
		<title>Yd: /* A spatio-temporal nodal approach */</title>
		<link rel="alternate" type="text/html" href="http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=493&amp;oldid=prev"/>
				<updated>2016-04-06T14:08:04Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;A spatio-temporal nodal approach&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 14:08, 6 April 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l33&quot; &gt;Line 33:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 33:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Coupling the thermal, electric, hydrodynamic and chemical phenomena, the methodology would involve a nodal-type network and should allow for steady, pseudo-unsteady &amp;amp; unsteady simulations. Owing to an Onsager type force-flux approach, an elementary building block trying to mimic the behaviour of a (group of) similar plant (biological) cell(s) can first be designed then connected to others to form a network. More specifically, the inputs/outputs and local features of this building block would be e.g.: chemical composition (like &amp;lt;math&amp;gt;Ca^{++}&amp;lt;/math&amp;gt; concentration), temperature &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt;, electro-chemical potential &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, local sap mass flow-rate and variation of the pressure &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt;. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Coupling the thermal, electric, hydrodynamic and chemical phenomena, the methodology would involve a nodal-type network and should allow for steady, pseudo-unsteady &amp;amp; unsteady simulations. Owing to an Onsager type force-flux approach, an elementary building block trying to mimic the behaviour of a (group of) similar plant (biological) cell(s) can first be designed then connected to others to form a network. More specifically, the inputs/outputs and local features of this building block would be e.g.: chemical composition (like &amp;lt;math&amp;gt;Ca^{++}&amp;lt;/math&amp;gt; concentration), temperature &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt;, electro-chemical potential &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, local sap mass flow-rate and variation of the pressure &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt;. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The figure below illustrates the envisaged structure for the elementary building block and the way the blocks can be (physically) connected:&amp;#160; generalized fluxes &amp;lt;math&amp;gt;X_i &amp;lt;/math&amp;gt;and generalized input and output potentials &amp;lt;math&amp;gt;\mu_j^{in}&amp;lt;/math&amp;gt; and&amp;#160; &amp;lt;math&amp;gt;\mu_j^{out}&amp;lt;/math&amp;gt; are inter-connected through a (locally linearized) Onsager-type approach.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The figure below illustrates the envisaged structure for the elementary building block and the way the blocks can be (physically) connected:&amp;#160; generalized fluxes &amp;lt;math&amp;gt;X_i &amp;lt;/math&amp;gt;and generalized input and output potentials &amp;lt;math&amp;gt;\mu_j^{in}&amp;lt;/math&amp;gt; and&amp;#160; &amp;lt;math&amp;gt;\mu_j^{out}&amp;lt;/math&amp;gt; are inter-connected through a (locally linearized) Onsager-type approach.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{| class=&amp;quot;wikitable&amp;quot;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|[[File:Pacs.png|330 px]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and the vector of potential output/input differences &amp;lt;math&amp;gt;{\bf \delta \mu}&amp;lt;/math&amp;gt; can be proposed, thank to the introduction of the Onsager matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt;,&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt;= {\bf Z \mu}&amp;lt;/math&amp;gt;. The coefficient of the matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt; can depend on &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;{\bf \mu}&amp;lt;/math&amp;gt; (their local value, and possibly their temporal gradient or history).&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Since the approach is quite versatile, more complex non-homogeneous structures and topologies may also be analyzed, and help possibly encompassing the role of the spatial biological cells distribution for the plant response to stress. Possibly anisotropic, discontinuous transport and thermoelectric properties may also be included, hence mimicking the sharp interface between cells of different kinds. Notice that the numerical strategy is able to enforce the fluxes (of energy, matter, species&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;, momentum&lt;/del&gt;) continuity at the local (nodal) scale, and at any time. This aspect is of paramount importance, enforcing the compatibility of the numerical modeling with physical first-principles.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[File:Pacs.png|330 px]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and the vector of potential output/input differences &amp;lt;math&amp;gt;{\bf \delta \mu}&amp;lt;/math&amp;gt; can be proposed, thank to the introduction of the Onsager matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt;,&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt;= {\bf Z \mu}&amp;lt;/math&amp;gt;. The coefficient of the matrix &amp;lt;math&amp;gt;{\bf Z &amp;lt;/math&amp;gt; can depend on &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;{\bf \mu}&amp;lt;/math&amp;gt; (their local value, and possibly their temporal gradient or history).&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;===&amp;quot;Validations&amp;quot;===&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Since the approach is quite versatile, more complex non-homogeneous structures and topologies may also be analyzed, and help possibly encompassing the role of the spatial biological cells distribution for the plant response to stress. Possibly anisotropic, discontinuous transport and thermoelectric properties may also be included, hence mimicking the sharp interface between cells of different kinds. Notice that the numerical strategy is able to enforce the fluxes (of energy, matter, species) continuity at the local (nodal) scale, and at any time. This aspect is of paramount importance, enforcing the compatibility of the numerical modeling with physical first-principles.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The aim would be to be able to validate the network modeling against the observed data obtained from experiments,. Once thoroughly validated, ons should be able to extrapolate the modeling to situations where no data can be measured (because e.g. of too high spatial and/or temporal resolution requirements), or difficult to measure properties. To our knowledge, this would be the very first spatio-temporal network-based thermodynamic-type modeling of the whole plant, in order to reproduce the plant response to different kinds of simultaneous (and hence interacting) stresses.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The aim would be to be able to validate the network modeling against the observed data obtained from experiments,. Once thoroughly validated, ons should be able to extrapolate the modeling to situations where no data can be measured (because e.g. of too high spatial and/or temporal resolution requirements), or difficult to measure properties. To our knowledge, this would be the very first spatio-temporal network-based thermodynamic-type modeling of the whole plant, in order to reproduce the plant response to different kinds of simultaneous (and hence interacting) stresses.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Yd</name></author>	</entry>

	<entry>
		<id>http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=492&amp;oldid=prev</id>
		<title>Yd: /* A spatio-temporal nodal approach */</title>
		<link rel="alternate" type="text/html" href="http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=492&amp;oldid=prev"/>
				<updated>2016-04-06T14:04:56Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;A spatio-temporal nodal approach&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 14:04, 6 April 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l36&quot; &gt;Line 36:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 36:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|[[File:Pacs.png|330 px]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|[[File:Pacs.png|330 px]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; According to the Lechatelier-Braun principle all the thermodynamic potentials are coupled. For instance, the hydraulic and electric responses of plants are known to be highly correlated (Mancuso 1999) revealing the underlying Lechatelier-Braun coupling between P and μ. Similar observations of coupling between &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;&amp;#160; and &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; have also been reported from vegetal thermoelectric responses. &lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and the vector of potential output/input differences &amp;lt;math&amp;gt;{\bf \delta \mu}&amp;lt;/math&amp;gt; can be proposed, thank to the introduction of the Onsager matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt;,&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt;= {\bf Z \mu}&amp;lt;/math&amp;gt;. The coefficient of the matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt; can depend on &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;{\bf \mu}&amp;lt;/math&amp;gt; (their local value, and possibly their temporal gradient or history).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and the vector of potential output/input differences &amp;lt;math&amp;gt;{\bf \delta \mu}&amp;lt;/math&amp;gt; can be proposed, thank to the introduction of the Onsager matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt;,&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt;= {\bf Z \mu}&amp;lt;/math&amp;gt;. The coefficient of the matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt; can depend on &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;{\bf \mu}&amp;lt;/math&amp;gt; (their local value, and possibly their temporal gradient or history).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Yd</name></author>	</entry>

	<entry>
		<id>http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=491&amp;oldid=prev</id>
		<title>Yd: /* A spatio-temporal nodal approach */</title>
		<link rel="alternate" type="text/html" href="http://www.dyco.fr/index.php?title=PACS/Plant_response_to_stress_%26_Biological_Networks&amp;diff=491&amp;oldid=prev"/>
				<updated>2016-04-06T14:04:13Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;A spatio-temporal nodal approach&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 14:04, 6 April 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l31&quot; &gt;Line 31:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 31:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;====''A spatio-temporal nodal approach''====&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;====''A spatio-temporal nodal approach''====&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;Au contraire&lt;/del&gt;, the &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;versatility of &lt;/del&gt;a &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;spatio-temporal &lt;/del&gt;nodal approach &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;would &lt;/del&gt;be &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;able &lt;/del&gt;to &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;handle both local &lt;/del&gt;to &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;global scales (i&lt;/del&gt;.e. &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;from coarse&lt;/del&gt;-&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;grain &lt;/del&gt;to &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;finer tuning&lt;/del&gt;) and also complex non-homogeneous structures and topologies&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;. Moreover&lt;/del&gt;, possibly anisotropic, discontinuous transport and thermoelectric properties may also be included, hence mimicking the sharp interface between cells of different kinds. &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;The properties can also be time or temperature/concentrations/electric potential dependent &lt;/del&gt;and &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;allow for more complex behavior&lt;/del&gt;. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Coupling the thermal, electric, hydrodynamic and chemical phenomena&lt;/ins&gt;, the &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;methodology would involve &lt;/ins&gt;a nodal&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;-type network and should allow for steady, pseudo-unsteady &amp;amp; unsteady simulations. Owing to an Onsager type force-flux &lt;/ins&gt;approach&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, an elementary building block trying to mimic the behaviour of a (group of) similar plant (biological) cell(s) can first &lt;/ins&gt;be &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;designed then connected &lt;/ins&gt;to &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;others &lt;/ins&gt;to &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;form a network&lt;/ins&gt;. &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;More specifically, the inputs/outputs and local features of this building block would be &lt;/ins&gt;e.&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;g.: chemical composition (like &amp;lt;math&amp;gt;Ca^{++}&amp;lt;/math&amp;gt; concentration), temperature &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt;, electro&lt;/ins&gt;-&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;chemical potential &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, local sap mass flow-rate and variation of the pressure &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt;. &lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The aim would be to be able to validate the network modeling against the observed data obtained from &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;the PACS project&lt;/del&gt;, &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;then &lt;/del&gt;to extrapolate the modeling to situations where no data can be measured (because e.g. of too high spatial and/or temporal resolution requirements, or difficult to measure properties.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;The figure below illustrates the envisaged structure for the elementary building block and the way the blocks can be (physically) connected:&amp;#160; generalized fluxes &amp;lt;math&amp;gt;X_i &amp;lt;/math&amp;gt;and generalized input and output potentials &amp;lt;math&amp;gt;\mu_j^{in}&amp;lt;/math&amp;gt; and&amp;#160; &amp;lt;math&amp;gt;\mu_j^{out}&amp;lt;/math&amp;gt; are inter-connected through a (locally linearized) Onsager-type approach.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;{| class=&amp;quot;wikitable&amp;quot;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;|[[File:Pacs.png|330 px]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;|}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt; According &lt;/ins&gt;to &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;the Lechatelier-Braun principle all the thermodynamic potentials are coupled. For instance, the hydraulic and electric responses of plants are known to be highly correlated (Mancuso 1999&lt;/ins&gt;) &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;revealing the underlying Lechatelier-Braun coupling between P &lt;/ins&gt;and &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;μ. Similar observations of coupling between &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;&amp;#160; and &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; have &lt;/ins&gt;also &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;been reported from vegetal thermoelectric responses. &lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and the vector of potential output/input differences &amp;lt;math&amp;gt;{\bf \delta \mu}&amp;lt;/math&amp;gt; can be proposed, thank to the introduction of the Onsager matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt;,&amp;#160; &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt;= {\bf Z \mu}&amp;lt;/math&amp;gt;. The coefficient of the matrix &amp;lt;math&amp;gt;{\bf Z}&amp;lt;/math&amp;gt; can depend on &amp;lt;math&amp;gt;{\bf X}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;{\bf \mu}&amp;lt;/math&amp;gt; (their local value, and possibly their temporal gradient or history).&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Since the approach is quite versatile, more &lt;/ins&gt;complex non-homogeneous structures and topologies &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;may also be analyzed&lt;/ins&gt;, &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;and help &lt;/ins&gt;possibly &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;encompassing the role of the spatial biological cells distribution for the plant response to stress. Possibly &lt;/ins&gt;anisotropic, discontinuous transport and thermoelectric properties may also be included, hence mimicking the sharp interface between cells of different kinds. &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Notice that the numerical strategy is able to enforce the fluxes (of energy, matter, species, momentum) continuity at the local (nodal) scale, &lt;/ins&gt;and &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;at any time&lt;/ins&gt;. &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;This aspect is of paramount importance, enforcing the compatibility of the numerical modeling with physical first-principles.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The aim would be to be able to validate the network modeling against the observed data obtained from &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;experiments&lt;/ins&gt;,&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;. Once thoroughly validated, ons should be able &lt;/ins&gt;to extrapolate the modeling to situations where no data can be measured (because e.g. of too high spatial and/or temporal resolution requirements&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;)&lt;/ins&gt;, or difficult to measure properties&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;. To our knowledge, this would be the very first spatio-temporal network-based thermodynamic-type modeling of the whole plant, in order to reproduce the plant response to different kinds of simultaneous (and hence interacting) stresses&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== ''Participants'' ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== ''Participants'' ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;François Bouteau, Delphine Bonnin,&amp;#160; [https://www.researchgate.net/profile/Hayat_El-Maarouf-Bouteau Hayat El-Maarouf-Bouteau], Patrice Meimoun, [https://www6.rennes.inra.fr/umreva/Annuaire/INFlux/E.-Le-Deunff Erwan Le Deunff], Eric Herbert, Christophe Goupil, Yves D'Angelo.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;François Bouteau, Delphine Bonnin,&amp;#160; [https://www.researchgate.net/profile/Hayat_El-Maarouf-Bouteau Hayat El-Maarouf-Bouteau], Patrice Meimoun, [https://www6.rennes.inra.fr/umreva/Annuaire/INFlux/E.-Le-Deunff Erwan Le Deunff], Eric Herbert, Christophe Goupil, Yves D'Angelo.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Yd</name></author>	</entry>

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