MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework [PDF]
, 2020 We propose MeshfreeFlowNet, a novel deep learning-based super-resolution framework to generate continuous (grid-free) spatio-temporal solutions from the low-resolution inputs. While being computationally efficient, MeshfreeFlowNet accurately recovers the
Anandkumar, Anima +8 more
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Steve Smale and Geometric Mechanics [PDF]
, 1993 Thus, one can say-perhaps with only a slight danger of oversimplification- that reduction theory synthesises the work of Smale, Arnold (and their predecesors of course) into a bundle, with Smale as the base and Arnold as the fiber.
Marsden, Jerrold E.
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Weak Continuity and Compactness for Nonlinear Partial Differential Equations [PDF]
, 2015 We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role.
Chen, Gui-Qiang G.
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3+1 formulation of non-ideal hydrodynamics [PDF]
, 1997 The equations governing dissipative relativistic hydrodynamics are formulated within the 3+1 approach for arbitrary spacetimes. Dissipation is accounted for by applying the theory of extended causal thermodynamics (Israel-Stewart theory).
Appl, Stefan, Peitz, Jochen
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Energy preserving model order reduction of the nonlinear Schr\"odinger equation [PDF]
, 2018 An energy preserving reduced order model is developed for two dimensional nonlinear Schr\"odinger equation (NLSE) with plane wave solutions and with an external potential.
Karasözen, Bülent, Uzunca, Murat
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Analysis of the shearing instability in nonlinear convection and magnetoconvection [PDF]
, 1996 Numerical experiments on two-dimensional convection with or without a vertical magnetic field reveal a bewildering variety of periodic and aperiodic oscillations.
A M Rucklidge +41 more
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Multisymplectic formulation of fluid dynamics using the inverse map [PDF]
, 2007 We construct multisymplectic formulations of fluid dynamics using the inverse of the Lagrangian path map. This inverse map, the ‘back-to-labels’ map, gives the initial Lagrangian label of the fluid particle that currently occupies each Eulerian position.
Cotter, CJ, Holm, DD, Hydon, PE
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Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues [PDF]
, 2012 The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to PDE-based continuum methods, although formal relationships between the discrete and continuum frameworks ...
Byrne, H. M. +4 more
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On a hierarchy of nonlinearly dispersive generalized KdV equations
, 2015 We propose a hierarchy of nonlinearly dispersive generalized Korteweg--de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. It is shown that two recent nonlinear
Christov, Ivan C.
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Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations [PDF]
, 2020 We introduce a new method, the Local Monge Parametrizations (LMP) method, to approximate tensor fields on general surfaces given by a collection of local parametrizations, e.g.~as in finite element or NURBS surface representations.
Arroyo, Marino +2 more
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