Implicit Update of the Moment Equations for a Multi-Species, Homogeneous BGK Model: Implicit update of the moment equations for a multi-species, homogeneous BGK model

Authors: Evan Habbershaw, Cory D. Hauck, Steven M. Wise

Source: SIAM Journal on Numerical Analysis. 63:881-907

Subject Terms: implicit time stepping strategies, moment equations, rarefied gas dynamics, Kinetic theory of gases in time-dependent statistical mechanics, PDEs in connection with mechanics of particles and systems of particles, FOS: Physical sciences, Numerical Analysis (math.NA), Mathematical Physics (math-ph), Rarefied gas flows, Boltzmann equation in fluid mechanics, 76P05, 47J25, 35Q70, 82C40, 65L04, Iterative procedures involving nonlinear operators, Numerical methods for stiff equations, multi-species BGK, kinetic theory, FOS: Mathematics, Mathematics - Numerical Analysis, fixed point iterative solvers, Mathematical Physics

File Description: application/xml

Access URL: http://arxiv.org/abs/2404.18039

A system of continuity equations with nonlocal interactions of Morse type

Authors: Di Francesco, Marco, Iorio, Valeria

Source: Communications on Pure and Applied Analysis. 24:1381-1405

Subject Terms: Optimal transportation, Primary: 35D30, 35F55, 35Q70. Secondary: 35Q49, 49Q22, PDEs in connection with mechanics of particles and systems of particles, Wasserstein gradient flow, nonlocal interaction, Mathematics - Analysis of PDEs, Transport equations, deterministic particle approximation, Morse potential, multi-agent system, Nonlocal interaction, FOS: Mathematics, Initial value problems for systems of nonlinear first-order PDEs, Weak solutions to PDEs, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2406.18771
https://zbmath.org/8035389
https://doi.org/10.3934/cpaa.2025041

A Fast Offline/Online Forward Solver for Stationary Transport Equation with Multiple Inflow Boundary Conditions and Varying Coefficients: A fast offline/online forward solver for stationary transport equation with multiple inflow boundary conditions and varying coefficients

Authors: Fu, Jingyi, Tang, Min

Source: Communications in Computational Physics. 37:457-497

Subject Terms: Finite difference methods for boundary value problems involving PDEs, radiative transport equation, offline/online decomposition, Boundary-layer theory for compressible fluids and gas dynamics, PDEs in connection with mechanics of particles and systems of particles, tailored finite point method, Mathematics - Numerical Analysis, asymptotic preserving, boundary/interface layer

File Description: application/xml

Access URL: http://arxiv.org/abs/2401.03147
https://zbmath.org/8033883
https://doi.org/10.4208/cicp.oa-2022-0127

A model for slowing particles in random media

Authors: françois golse, valeria ricci, ana jacinta soares

Source: Discrete and Continuous Dynamical Systems. 45:3084-3106

Subject Terms: particle systems, kinetic limit, slowing particles, point measure component, random media, Asymptotic behavior of solutions to PDEs, Probability (math.PR), Kinetic theory of gases in time-dependent statistical mechanics, point measure component, PDEs in connection with mechanics of particles and systems of particles, FOS: Physical sciences, Statistical mechanics of plasmas, kinetic limit, Mathematical Physics (math-ph), 35B40, 35Q49, 82C22, 82D10 (Primary) 35Q70, 82C40, 82D30, Mathematics - Analysis of PDEs, Transport equations, FOS: Mathematics, Interacting particle systems in time-dependent statistical mechanics, slowing particles, particle systems, Mathematical Physics, Mathematics - Probability, Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses), Analysis of PDEs (math.AP)

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2406.05895

Macroscopic limit of a Fokker-Planck model of swarming rigid bodies

Authors: Degond, P, Frouvelle, A

Contributors: Degond, Pierre, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)

Source: European Journal of Applied Mathematics, Vol 36, Pp 349-397 (2025)

Subject Terms: Fokker-Planck operator, Particle model, PDEs in connection with biology, chemistry and other natural sciences, 82C40, macroscopic model, 35Q91, PDEs in connection with mechanics of particles and systems of particles, FOS: Physical sciences, 35Q70, 35Q92, [MATH] Mathematics [math], stochastic differential equation, 01 natural sciences, [PHYS] Physics [physics], self-organized hydrodynamics, 92D50, Weyl group, QA1-939, Applications of Lie groups to the sciences, explicit representations, FOS: Mathematics, 60J65, Interacting particle systems in time-dependent statistical mechanics, generalised collision invariant, [MATH]Mathematics [math], rotation group representations, 0101 mathematics, Diffusion processes, Mathematical Physics, 60J60, [PHYS]Physics [physics], 82C70, Probability (math.PR), Kinetic theory of gases in time-dependent statistical mechanics, Transport processes in time-dependent statistical mechanics, Mathematical Physics (math-ph), maximal torus, particle model, self-organised hydrodynamics, 22E70, PDEs in connection with game theory, economics, social and behavioral sciences, generalized collision invariant, 65C65, 82C22, Brownian motion, Mathematics, Animal behavior, Mathematics - Probability

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2307.15560
https://doaj.org/article/226ab155443741b7872517600f236d36

Geometry of coupled dispersionless equations with Mannheim curves

Authors: Eren Kemal

Source: Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, Vol 31, Iss 3, Pp 111-123 (2023)

Subject Terms: lax pairs, secondary 35q70, primary 53a04, Curves in Euclidean and related spaces, Lax pairs, QA1-939, PDEs in connection with mechanics of particles and systems of particles, coupled dispersionless equations, Mannheim curves, Mathematics, mannheim curves

File Description: application/xml

Access URL: https://zbmath.org/8036495
https://doi.org/10.2478/auom-2023-0034
https://doaj.org/article/b22b11f0a8aa49faa2ca542682a6a295

The Maxwell-Klein-Gordon equation with scattering data

Authors: Dai, Wei, Mei, He, Wei, Dongyi, Yang, Shiwu

Source: Advances in Mathematics. 471:110271

Subject Terms: characteristic initial value problem, Mathematics - Analysis of PDEs, Maxwell equations, 35L05, 35Q61, 35Q70, Maxwell-Klein-Gordon system, scattering, FOS: Mathematics, PDEs in connection with mechanics of particles and systems of particles, 0101 mathematics, 01 natural sciences, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2302.08732
https://zbmath.org/8030759
https://doi.org/10.1016/j.aim.2025.110271

The mean-field approximation for higher-dimensional Coulomb flows in the scaling-critical L ∞ space: The mean-field approximation for higher-dimensional Coulomb flows in the scaling-critical \(L^\infty\) space

Authors: Matthew Rosenzweig

Source: Nonlinearity. 35:2722-2766

Subject Terms: critical function space, Smoothness and regularity of solutions to PDEs, Statistical mechanics of superfluids, PDEs in connection with mechanics of particles and systems of particles, mean field limit, 0101 mathematics, PDEs in connection with fluid mechanics, Weak solutions to PDEs, 01 natural sciences, Statistical mechanics of superconductors, Coulomb systems

File Description: application/xml

Access URL: https://zbmath.org/7539289
https://doi.org/10.1088/1361-6544/ac5fd6

Scattering Map for the Vlasov–Poisson System

Authors: Flynn, Patrick J, Ouyang, Zhimeng, Pausader, Benoit, Widmayer, Klaus

Contributors: University of Zurich

Source: Peking Mathematical Journal. 6:365-392

Subject Terms: 10123 Institute of Mathematics, 510 Mathematics, Mathematics - Analysis of PDEs, Asymptotic behavior of solutions to PDEs 35Q70, FOS: Mathematics, PDEs in connection with mechanics of particles and systems of particles, 101002 Analysis, 0101 mathematics, 01 natural sciences, Vlasov equations 35B40, General Engineering 35Q83, Analysis of PDEs (math.AP)

File Description: ZORA_s42543_021_00041_x.pdf - application/pdf

Access URL: https://link.springer.com/content/pdf/10.1007/s42543-021-00041-x.pdf
http://arxiv.org/abs/2101.01390
https://ucrisportal.univie.ac.at/de/publications/4a1e4588-4674-4477-aa75-dca4539423c2
https://doi.org/10.1007/s42543-021-00041-x
https://link.springer.com/content/pdf/10.1007/s42543-021-00041-x.pdf
https://link.springer.com/article/10.1007/s42543-021-00041-x

Scattering Map for the Vlasov–Poisson System

Authors: Flynn, Patrick J, Ouyang, Zhimeng, Pausader, Benoit, Widmayer, Klaus

Source: Flynn, Patrick J; Ouyang, Zhimeng; Pausader, Benoit; Widmayer, Klaus (2023). Scattering Map for the Vlasov–Poisson System. Peking Mathematical Journal, 6(2):365-392.

Subject Terms: Institute of Mathematics, 510 Mathematics, General Engineering 35Q83 - Vlasov equations 35B40 - Asymptotic behavior of solutions to PDEs 35Q70 - PDEs in connection with mechanics of particles and systems of particles

File Description: application/pdf

Relation: https://www.zora.uzh.ch/id/eprint/235342/1/ZORA_s42543_021_00041_x.pdf; urn:issn:2096-6075

Availability: https://www.zora.uzh.ch/id/eprint/235342/
https://www.zora.uzh.ch/id/eprint/235342/1/ZORA_s42543_021_00041_x.pdf

Challenges in active particles methods: Theory and applications: Challenges in active particles methods: theory and applications

Authors: N Bellomo, F Brezzi

Source: Mathematical models and methods in applied sciences 28 (2018): 1627–1633. doi:10.1142/S0218202518020013
info:cnr-pdr/source/autori:N. Bellomo and F. Brezzi/titolo:Challenges in active particles methods: Theory and applications/doi:10.1142%2FS0218202518020013/rivista:Mathematical models and methods in applied sciences/anno:2018/pagina_da:1627/pagina_a:1633/intervallo_pagine:1627–1633/volume:28

Subject Terms: active particles, PDEs in connection with game theory, economics, social and behavioral sciences, PDEs in connection with biology, chemistry and other natural sciences, Nonlinear parabolic equations, PDEs in connection with mechanics of particles and systems of particles, nonlinear interactions, multicellular systems, Complexity, crowds, swarms, 0101 mathematics, complexity, 01 natural sciences

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/7042907
https://doi.org/10.1142/s0218202518020013
https://www.worldscientific.com/doi/abs/10.1142/S0218202518020013
https://www.worldscientific.com/doi/abs/10.1142/S0218202518020013
https://doi.org/10.1142/S0218202518020013
https://hdl.handle.net/20.500.14243/343816

Scalable Reduction of Elastic Continuum for Boundary Energy Control: Scalable reduction of elastic continuum for boundary energy control

Authors: Daiji Ichishima, Kenji Fujimoto, Gou Nishida

Source: SIAM Journal on Control and Optimization. 53:2424-2448

Subject Terms: 0209 industrial biotechnology, PDEs in connection with mechanics of particles and systems of particles, 02 engineering and technology, Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics, molecular dynamics, renormalization, 3. Good health, Dirac structures, model reduction, partial differential equations, Symmetries, invariants, invariant manifolds, momentum maps, reduction, boundary controls, Hamiltonian systems, Control/observation systems governed by ordinary differential equations

File Description: application/xml

Access URL: https://zbmath.org/6474173
https://doi.org/10.1137/11084529x

Simulation of water entry of a wedge through free fall in three degrees of freedom

Authors: Guoxiong Wu, G.D. Xu, W.Y. Duan

Source: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 466:2219-2239

Subject Terms: PDEs in connection with mechanics of particles and systems of particles, 02 engineering and technology, free fall motion, PDEs in connection with fluid mechanics, 01 natural sciences, boundary element method, 0201 civil engineering, Free motion of a rigid body, auxiliary function method, Boundary element methods applied to problems in fluid mechanics, water entry, 0103 physical sciences, time domain simulation, three degrees of freedom

File Description: application/xml

Access URL: https://zbmath.org/5761647
https://doi.org/10.1098/rspa.2009.0614
https://ui.adsabs.harvard.edu/abs/2010RSPSA.466.2219X/abstract
http://discovery.ucl.ac.uk/1315604/
http://rspa.royalsocietypublishing.org/content/466/2120/2219
https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2009.0614

Kinetic equations of higher order

Authors: Arzhanykh, I. S.

Subject Terms: General models, approaches, and methods in mechanics of particles and systems, PDEs in connection with mechanics of particles and systems of particles, kinetic equations, integrability

File Description: application/xml

Access URL: https://zbmath.org/3220197