#differentialequations

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Stefan Wolfrum :mastodon:I could watch forever ... <a href="https://mastodon.social/tags/LorenzAttractor" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LorenzAttractor</a> <a href="https://mastodon.social/tags/ButterflyEffect" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ButterflyEffect</a> <a href="https://mastodon.social/tags/JavaScript" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#JavaScript</a> <a href="https://mastodon.social/tags/p5js" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#p5js</a> <a href="https://mastodon.social/tags/DifferentialEquations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DifferentialEquations</a> <a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mastodon.social/tags/visualization" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#visualization</a> <a href="https://mastodon.social/tags/computergraphics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#computergraphics</a> <a href="https://mastodon.social/tags/dynamicsystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#dynamicsystems</a>

Pustam | पुस्तम | পুস্তম🇳🇵LINEAR TRANSPORT EQUATION The linear transport equation (LTE) models the variation of the concentration of a substance flowing at constant speed and direction. It's one of the simplest partial differential equations (PDEs) and one of the few that admits an analytic solution.Given \(\mathbf{c}\in\mathbb{R}^n\) and \(g:\mathbb{R}^n\to\mathbb{R}\), the following Cauchy problem models a substance flowing at constant speed in the direction \(\mathbf{c}\). \[\begin{cases} u_t+\mathbf{c}\cdot\nabla u=0,\ \mathbf{x}\in\mathbb{R}^n,\ t\in\mathbb{R}\\ u(\mathbf{x},0)=g(\mathbf{x}),\ \mathbf{x}\in\mathbb{R}^n \end{cases}\] If \(g\) is continuously differentiable, then \(\exists u:\mathbb{R}^n\times\mathbb{R}\to\mathbb{R}\) solution of the Cauchy problem, and it is given by \[u(\mathbf{x},t)=g(\mathbf{x}-\mathbf{c}t)\]<a href="https://mathstodon.xyz/tags/LinearTransportEquation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LinearTransportEquation</a> <a href="https://mathstodon.xyz/tags/LinearTransport" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LinearTransport</a> <a href="https://mathstodon.xyz/tags/Cauchy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Cauchy</a> <a href="https://mathstodon.xyz/tags/CauchyProblem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CauchyProblem</a> <a href="https://mathstodon.xyz/tags/PDE" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PDE</a> <a href="https://mathstodon.xyz/tags/PDEs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PDEs</a> <a href="https://mathstodon.xyz/tags/CauchyModel" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CauchyModel</a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Maths</a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematics</a> <a href="https://mathstodon.xyz/tags/Linear" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Linear</a> <a href="https://mathstodon.xyz/tags/LinearPDE" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LinearPDE</a> <a href="https://mathstodon.xyz/tags/TransportEquation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TransportEquation</a> <a href="https://mathstodon.xyz/tags/DifferentialEquations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DifferentialEquations</a>

Big MathsJamIt's almost the end of this year's gathering. Our final session of talks featured Adam Townsend, who showed us how we can use differential equations to make beautiful moving patterns - you can explore them yourselves at <a href="https://visualpde.com" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://visualpde.com</a>. We also heard from Hannah Gray, who was inspired by playing <a href="http://heardledecades.com" rel="nofollow noopener noreferrer" translate="no" target="_blank">http://heardledecades.com</a> to talk about whether men sing more songs (spoiler alert: yes, but it's better now than it was in the 1950s!) Last but absolutely not least, Colin Wright talked about the twist of a Moebius Rollercoaster: <a href="https://en.wikipedia.org/wiki/Grand_National_(roller_coaster)" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://en.wikipedia.org/wiki/Grand_National_(roller_coaster)</a> <a href="https://mathstodon.xyz/tags/mathsjam" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathsjam</a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://mathstodon.xyz/tags/differentialequations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#differentialequations</a> <a href="https://mathstodon.xyz/tags/movingpatterns" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#movingpatterns</a> <a href="https://mathstodon.xyz/tags/skittles" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#skittles</a> <a href="https://mathstodon.xyz/tags/uniqueness" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#uniqueness</a> <a href="https://mathstodon.xyz/tags/moebius" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#moebius</a> <a href="https://mathstodon.xyz/tags/rollercoasters" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#rollercoasters</a> <a href="https://mathstodon.xyz/tags/music" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#music</a> <a href="https://mathstodon.xyz/tags/domensingmore" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#domensingmore</a>

SciHi BlogOn January 15, 1850, Russian mathematician Sofia Kovalevskaya was born. Kovalevskaya was responsible for important original contributions to analysis, partial differential equations and mechanics, and the first woman appointed to a full professorship in Northern Europe.<a href="http://scihi.org/sofia-kovalevskaya-mathematician-writer/" rel="nofollow noopener noreferrer" target="_blank">http://scihi.org/sofia-kovalevskaya-mathematician-writer/</a><a href="https://fedihum.org/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://fedihum.org/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://fedihum.org/tags/analysis" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#analysis</a> <a href="https://fedihum.org/tags/differentialequations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#differentialequations</a> <a href="https://fedihum.org/tags/historyofscience" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#historyofscience</a> <a href="https://fedihum.org/tags/womeninscience" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#womeninscience</a> <a href="https://fedihum.org/tags/womeninstem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#womeninstem</a> <a href="https://fedihum.org/tags/otd" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#otd</a>

Jared DavisHello 👋 my name is Jared. I work in software writing data pipelines in <a href="https://mastodon.online/tags/golang" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#golang</a> . I'm interested in <a href="https://mastodon.online/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> <a href="https://mastodon.online/tags/linearalgebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#linearalgebra</a> <a href="https://mastodon.online/tags/differentialequations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#differentialequations</a> <a href="https://mastodon.online/tags/economics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#economics</a> <a href="https://mastodon.online/tags/literature" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#literature</a> and <a href="https://mastodon.online/tags/philosophy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#philosophy</a> . I never enjoyed Twitter, and I'm hoping that I can find a healthy online community here. <a href="https://mastodon.online/tags/introduction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#introduction</a>

Sarah KavassalisFor my introduction, I’m an <a href="https://climatejustice.social/tags/atmospheric" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#atmospheric</a> <a href="https://climatejustice.social/tags/chemist" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#chemist</a> who builds models of the <a href="https://climatejustice.social/tags/atmosphere" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#atmosphere</a> with lots of different <a href="https://climatejustice.social/tags/computational" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#computational</a> tools (finite state machines, many flavours of <a href="https://climatejustice.social/tags/differentialequations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#differentialequations</a>, and <a href="https://climatejustice.social/tags/machinelearning" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#machinelearning</a>). I also work on cool collaboration with computer scientists and psychologists to try and understand what makes some research more effective at changing <a href="https://climatejustice.social/tags/environmental" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#environmental</a> <a href="https://climatejustice.social/tags/regulations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#regulations</a> than others. A lot of my energy goes into undergraduate <a href="https://climatejustice.social/tags/education" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#education</a> and trying to figure out how we should best <a href="https://climatejustice.social/tags/teach" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#teach</a> climate science (and the modern computational tools behind it) for societal good. Career wise, I’ll be starting as an Assistant <a href="https://climatejustice.social/tags/Professor" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Professor</a> of <a href="https://climatejustice.social/tags/Climate" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Climate</a> and <a href="https://climatejustice.social/tags/Chemistry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Chemistry</a> at Harvey Mudd College next summer.

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