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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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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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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On Relativistic Generalization of Perelman's W-entropy and Statistical Thermodynamic Description of Gravitational Fields [PDF]
, 2017 Using double 2+2 and 3+1 nonholonomic fibrations on Lorentz manifolds, we extend the concept of W-entropy for gravitational fields in the general relativity, GR, theory.
Ruchin, Vyacheslav +2 more
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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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The adventures of Spacetime [PDF]
, 2006 We discuss how developments in physics often imply in the need that spacetime acquires an increasingly richer and complex structure. General Relativity was the first theory to show us the way to connect space and time with the physical world. Since then,
Bertolami, Orfeu
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The Lie-Poisson Structure of the Euler Equations of an Ideal Fluid [PDF]
, 2005 This paper provides a precise sense in which the time t map for the Euler equations of an ideal fluid in a region in R^n (or a smooth compact n-manifold with boundary) is a Poisson map relative to the Lie-Poisson bracket associated with the group of ...
Marsden, Jerrold E., Vasylkevych, Sergiy
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Continuum Mechanics and Thermodynamics in the Hamilton and the Godunov-type Formulations
, 2017 Continuum mechanics with dislocations, with the Cattaneo type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov type system of the first order, symmetric hyperbolic ...
Grmela, Miroslav +3 more
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Computation of frequency responses for linear time-invariant PDEs on a compact interval
, 2013 We develop mathematical framework and computational tools for calculating frequency responses of linear time-invariant PDEs in which an independent spatial variable belongs to a compact interval.
Jovanović, Mihailo R., Lieu, Binh K.
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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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