New Submissions to TMLR · @tmlrsub
196 followers · 672 posts · Server sigmoid.social
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs
Yohan John 🤖🧠 · @DrYohanJohn
1337 followers · 1173 posts · Server fediscience.org
Beautiful PDE visualization tool!
Here's a reaction-diffusion system with a pic of Turing himself as the initial condition.
#ODEs #PDEs #differentialequations #mathematics
Published papers at TMLR · @tmlrpub
518 followers · 416 posts · Server sigmoid.social
Learning to correct spectral methods for simulating turbulent flows
Gideon Dresdner, Dmitrii Kochkov, Peter Christian Norgaard et al.
Action editor: Ivan Oseledets.
JMLR · @jmlr
655 followers · 208 posts · Server sigmoid.social
'Neural Operator: Learning Maps Between Function Spaces With Applications to PDEs', by Nikola Kovachki et al.
http://jmlr.org/papers/v24/21-1524.html
#discretization #operators #pdes
#discretization #operators #PDEs
JMLR · @jmlr
657 followers · 205 posts · Server sigmoid.social
'Learning Partial Differential Equations in Reproducing Kernel Hilbert Spaces', by George Stepaniants.
http://jmlr.org/papers/v24/21-1363.html
#regression #pdes #kernel
Erwin Schrödinger Institute · @ESIVienna
115 followers · 47 posts · Server mathstodon.xyz
Are you keen to read about results in #MathematicalPhysics and Analysis of #PDEs? Take a look at the paper of our previous workshop participant! 🧐
#FunctionalAnalysis #SpectralTheory
@univienna
https://arxiv.org/pdf/2303.04527.pdf
#SpectralTheory #FunctionalAnalysis #PDEs #mathematicalphysics
Dom · @freeDomForTooting
47 followers · 127 posts · Server qoto.org
#SoftMatter have just published the results of a project that Renato Assante, Davide Marenduzzo, Alexander Morozov, and I recently worked on together! What did we do and what’s new? Briefly…
#Microswimmer suspensions behave in a similar way to fluids containing kinesin and microtubules. Both systems can be described by the same system of three coupled nonlinear #PDEs.
A #LinearStabilityAnalysis of these equations suggests that variations in concentration across the system don’t significantly affect emergent #phaseBehaviour. How then can we explain #experiments that show visible inhomogeneities in #microtubule–#kinesin mixtures, for instance?
With increasing activity, we move away from the quiescent regime, past the onset of #SpontaneousFlow, and deeper into the active phase, where #nonlinearities become more important. What role do concentration inhomogeneities play here?
We investigated these questions, taking advantage of the #openSource #Dedalus #spectral framework to simulate the full nonlinear time evolution. This led us to predict a #novel regime of #spontaneous #microphaseSeparation into active (nematically ordered) and passive domains.
Active flow arrests macrophase separation in this regime, counteracting domain coarsening due to thermodynamic coupling between active matter concentration and #nematic order. As a result, domains reach a characteristic size that decreases with increasing activity.
This regime is one part of the #PhaseDiagram we mapped out. Along with our other findings, you can read all about it here!
low #ReynoldsNumber #turbulence #ActiveTurbulence #CahnHilliard #ActiveMatter #NavierStokes #BerisEdwards #CondensedMatter #PhaseTransitions #TheoreticalPhysics #BioPhysics #StatisticalPhysics #FluidDynamics #ComputationalPhysics #Simulation #FieldTheory #paperthread #NewPaper #science #research #ActiveGel #activeNematic #analytic #cytoskeleton #hydrodynamics #MPI #theory
#microswimmer #opensource #Dedalus #spectral #novel #spontaneous #microphaseSeparation #nematic #phasediagram #reynoldsnumber #turbulence #ActiveTurbulence #theoreticalphysics #biophysics #science #research #ActiveGel #cytoskeleton #mpi #BerisEdwards #computationalPhysics #simulation #softmatter #PDEs #LinearStabilityAnalysis #phaseBehaviour #experiments #microtubule #kinesin #SpontaneousFlow #nonlinearities #CahnHilliard #activematter #navierstokes #condensedmatter #phasetransitions #statisticalphysics #fluiddynamics #fieldtheory #PaperThread #newpaper #activeNematic #analytic #hydrodynamics #theory
Pustam Raut🇳🇵(पुस्तम राउत) · @pustam_egr
35 followers · 116 posts · Server mathstodon.xyz
How do Maxwell's equations predict that the speed of light is constant?🤔 (photo credit: Fermat's Library)
Maxwell's equations, a set of coupled partial differential equations (PDEs), describe the behaviour of electric and magnetic fields and predict that the speed of light is constant in all reference frames, which is a fundamental principle of the theory of relativity. #Electromagnetism #Relativity #SpeedOfLight #LightSpeed #Light #ElectricField #MagneticField #PDEs #Maxwell #CoupledPDEs
#coupledpdes #maxwell #PDEs #magneticfield #electricfield #light #lightspeed #speedoflight #relativity #electromagnetism
Dom · @freeDomForTooting
44 followers · 125 posts · Server qoto.org
#SoftMatter have just published the results of a project that Renato Assante, Davide Marenduzzo, Alexander Morozov, and I recently worked on together! What did we do and what’s new? Briefly…
The #hydrodynamic behaviour of inhomogeneous #activeNematic gels (such as extensile bundles of #cytoskeletal filaments or suspensions of low #ReynoldsNumber swimmers) can be described by the time evolution of three coupled #PDEs.
Standard #ActiveGel #theory concludes, from a #LinearStabilityAnalysis of these equations, that fluctuations in concentration don’t significantly affect emergent #phaseBehaviour. However, this leaves #experimental #observations of visible inhomogeneities in #microtubule–#kinesin mixtures unexplained. As we move away from the passive (quiescent) regime, past the onset of #SpontaneousFlow, and deeper into the active phase, #nonlinearities become more important. What role do concentration inhomogeneities play here?
Alongside #analytic techniques, we used an in-house #MPI-parallel code developed within the #Dedalus #spectral framework to investigate. We predict a #novel regime of #spontaneous #microphaseSeparation into active (nematically ordered) and passive domains. In this regime, active flow arrests macrophase separation, which is itself driven by the thermodynamic coupling between active matter concentration and #nematic order. As a result, domains do not #coarsen past a typical size, which decreases with increasing activity. This regime is one part of the #PhaseDiagram we mapped out.
Along with our other findings, you can read all about it here!
#CahnHilliard #ActiveMatter #NavierStokes #BerisEdwards #CondensedMatter #PhaseTransitions #TheoreticalPhysics #BioPhysics #StatisticalPhysics #FluidDynamics #ComputationalPhysics #Simulation #FieldTheory #paperthread #NewPaper #science #research
#softmatter #activeNematic #cytoskeletal #reynoldsnumber #phaseBehaviour #experimental #microtubule #navierstokes #BerisEdwards #condensedmatter #phasetransitions #theoreticalphysics #research #PDEs #LinearStabilityAnalysis #spectral #novel #spontaneous #microphaseSeparation #nematic #coarsen #phasediagram #CahnHilliard #activematter #biophysics #statisticalphysics #fluiddynamics #computationalPhysics #simulation #fieldtheory #PaperThread #newpaper #science #hydrodynamic #ActiveGel #theory #observations #kinesin #SpontaneousFlow #nonlinearities #analytic #mpi #Dedalus
Nalini Joshi · @monsoon0
891 followers · 260 posts · Server mathstodon.xyz
Nalini Joshi · @monsoon0
886 followers · 251 posts · Server mathstodon.xyz
TuxRiders · @tuxriders
23 followers · 4 posts · Server fosstodon.org
Mastodon #introduction: TuxRiders is a journey to research experiences using free and #opensource scientific computing programs, which aimed to demonstrate their power for real-world scientific research.
In our #YouTube channel, we regularly talk about #FiniteElement, #EngineeringMath, #PDEs, #NumericalMethods, #FreeFEM, #FEniCS, #ParaView, #C++, #Python, #OpenFOAM, and #Linux.
Check out our YT channel: https://www.youtube.com/TuxRiders
#introduction #opensource #youtube #FiniteElement #engineeringmath #PDEs #numericalmethods #freefem #fenics #paraview #c #python #openfoam #linux
Nalini Joshi · @monsoon0
623 followers · 126 posts · Server mathstodon.xyz
For those interested, here is the poster for the #trilateral meeting on #nonlinear #PDEs in January 2023, in Perth, Western Australia
Nalini Joshi · @monsoon0
604 followers · 121 posts · Server mathstodon.xyzI’ll be in #Perth for the trilateral meeting on #nonlinear #PDEs in January, 2023. Anyone else going to be there?