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Pustam | पुस्तम | পুস্তম🇳🇵Convection–diffusion equation The convection-diffusion equation is a more general version of the scalar transport equation. It is a combination of the diffusion and convection (advection) equations. It describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. \[\dfrac{\partial c}{\partial t} = \mathbf{\nabla} \cdot (D \mathbf{\nabla} c - \mathbf{v} c) + R\]\[\dfrac{\partial c}{\partial t} = \underbrace{\mathbf{\nabla} \cdot (D \mathbf{\nabla} c)}_{\text{diffusion}}-\overbrace{\underbrace{\mathbf{\nabla}\cdot (\mathbf{v} c)}_{\text{advection}}}^\text{convection} + \overbrace{\underbrace{R}_\text{destruction}}^\text{creation}\] \(\mathbf{\nabla} \cdot (D \mathbf{\nabla} c)\) is the contribution of diffusion. \(- \mathbf{\nabla}\cdot (\mathbf{v} c)\) is the contribution of convection or advection. \(R\) describes the creation or destruction of the quantity.where \(c\) is the variable of interest. \(D\) is the diffusivity. \(\mathbf{v}\) is the velocity field, and \(R\) is the sources or sinks of the quantity \(c\).<a href="https://mathstodon.xyz/tags/Convection" class="mention hashtag" rel="tag">#Convection</a> <a href="https://mathstodon.xyz/tags/Diffusion" class="mention hashtag" rel="tag">#Diffusion</a> <a href="https://mathstodon.xyz/tags/Transport" class="mention hashtag" rel="tag">#Transport</a> <a href="https://mathstodon.xyz/tags/Advection" class="mention hashtag" rel="tag">#Advection</a> <a href="https://mathstodon.xyz/tags/Equation" class="mention hashtag" rel="tag">#Equation</a> <a href="https://mathstodon.xyz/tags/ConvectionDiffusionEquation" class="mention hashtag" rel="tag">#ConvectionDiffusionEquation</a> <a href="https://mathstodon.xyz/tags/DifferentialEquations" class="mention hashtag" rel="tag">#DifferentialEquations</a> <a href="https://mathstodon.xyz/tags/AdvectionEquation" class="mention hashtag" rel="tag">#AdvectionEquation</a> <a href="https://mathstodon.xyz/tags/DiffusionEquation" class="mention hashtag" rel="tag">#DiffusionEquation</a> <a href="https://mathstodon.xyz/tags/TransportEquation" class="mention hashtag" rel="tag">#TransportEquation</a> <a href="https://mathstodon.xyz/tags/ConvectionEquation" class="mention hashtag" rel="tag">#ConvectionEquation</a>

Lukasz KaczmarczykAn example of an error indicator is driven non-conforming mesh adaptivity for <a href="https://fosstodon.org/tags/advection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#advection</a> problem using upwind high order <a href="https://fosstodon.org/tags/DG" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DG</a>. Wind velocity is discretised by vector potential function in H1 one space. <a href="https://fosstodon.org/tags/MOFEM" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MOFEM</a> can do very cool things. That technology is implemented for 2d/3d problems. <a href="https://fosstodon.org/tags/FEM" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FEM</a> <a href="https://fosstodon.org/tags/FEA" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FEA</a> <a href="https://fosstodon.org/tags/HPC" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HPC</a> Example <a href="https://fosstodon.org/tags/code" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#code</a> is here: <a href="http://mofem.eng.gla.ac.uk/mofem/html/tutorial_level_set.html" rel="nofollow noopener noreferrer" target="_blank">http://mofem.eng.gla.ac.uk/mofem/html/tutorial_level_set.html</a>

Fernando RacimoOur new paper on modelling the <a href="https://fediscience.org/tags/spatiotemporal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#spatiotemporal</a> dynamics of a beneficial genetic variant is out <a href="https://fediscience.org/@eLife" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@eLife</a>. Muktupavela et al: <a href="https://elifesciences.org/articles/73767" rel="nofollow noopener noreferrer" target="_blank">https://elifesciences.org/articles/73767</a> Plus a digest highlight here: <a href="https://elifesciences.org/digests/73767/evolving-through-time-and-space" rel="nofollow noopener noreferrer" target="_blank">https://elifesciences.org/digests/73767/evolving-through-time-and-space</a>We extend a <a href="https://fediscience.org/tags/diffusion" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#diffusion</a> method for inferring the spread of a strongly selected allele, originally developed by Novembre et al. (<a href="https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.0030339" rel="nofollow noopener noreferrer" target="_blank">https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.0030339</a>). We now incorporate <a href="https://fediscience.org/tags/ancientDNA" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ancientDNA</a> and allow for <a href="https://fediscience.org/tags/advection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#advection</a> dynamics.<a href="https://fediscience.org/tags/EvolutionaryGenetics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#EvolutionaryGenetics</a> <a href="https://fediscience.org/tags/Evolution" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Evolution</a> <a href="https://fediscience.org/tags/Genetics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Genetics</a> <a href="https://fediscience.org/tags/EcoEvo" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#EcoEvo</a> <a href="https://fediscience.org/tags/archaeology" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#archaeology</a> <a href="https://fediscience.org/tags/HumanEvolution" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HumanEvolution</a>

Prof. Tatiana Ilyina<a href="https://wisskomm.social/@MPI_Meteo" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@MPI_Meteo</a> The most computationally expensive part of such models is the transport (by <a href="https://mas.to/tags/advection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#advection</a> and <a href="https://mas.to/tags/diffusion" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#diffusion</a>) of <a href="https://mas.to/tags/biogeochemical" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#biogeochemical</a> <a href="https://mas.to/tags/tracers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tracers</a> (zoo and <a href="https://mas.to/tags/phytoplankton" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#phytoplankton</a> <a href="https://mas.to/tags/nutrients" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#nutrients</a>, organic and inorganic <a href="https://mas.to/tags/carbon" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#carbon</a>, etc) with the <a href="https://mas.to/tags/ocean" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ocean</a> <a href="https://mas.to/tags/flow" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#flow</a>.The more tracers we include to represent the complexity of <a href="https://mas.to/tags/ocean" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ocean</a> biogeochemistry, the slower are the model runs. Same problem arises when the <a href="https://mas.to/tags/spatial" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#spatial</a> <a href="https://mas.to/tags/resolution" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#resolution</a> of an <a href="https://mas.to/tags/ESM" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ESM</a> increases.Biogeochemistry models can become a bottleneck in <a href="https://mas.to/tags/ESM" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ESM</a> computations. 2/

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