From the Boltzmann equation to fluid mechanics on a manifold [PDF]
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2011 We apply the Chapman–Enskog procedure to derive hydrodynamic equations on an arbitrary surface from the Boltzmann equation on the surface.
Love, Peter John, Cianci, Donato, '10
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Relativistic fluid mechanics, Kähler manifolds, and supersymmetry [PDF]
Physical Review D, 2003 We propose an alternative for the Clebsch decomposition of currents in fluid mechanics, in terms of complex potentials taking values in a Kahler manifold. We reformulate classical relativistic fluid mechanics in terms of these complex potentials and rederive the existence of an infinite set of conserved currents. We perform a canonical analysis to find
Tino S. Nyawelo +2 more
semanticscholar +6 more sources
Globalizing manifold-based reduced models for equations and data [PDF]
Nature CommunicationsOne of the very few mathematically rigorous nonlinear model reduction methods is the restriction of a dynamical system to a low-dimensional, sufficiently smooth, attracting invariant manifold.
Bálint Kaszás, George Haller
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A Hierarchy of Probability, Fluid and Generalized Densities for the Eulerian Velocivolumetric Description of Fluid Flow, for New Families of Conservation Laws [PDF]
Entropy, 2022 The Reynolds transport theorem occupies a central place in continuum mechanics, providing a generalized integral conservation equation for the transport of any conserved quantity within a fluid or material volume, which can be connected to its ...
Robert K. Niven
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Fractional vector calculus and fluid mechanics
Journal of the Mechanical Behavior of Materials, 2017 Basic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands.
Lazopoulos Konstantinos A. +1 more
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Linear and nonlinear dimensionality reduction from fluid mechanics to machine learning [PDF]
Measurement science and technology, 2022 Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis.
M. A. Mendez
semanticscholar +1 more source
NOMAD: Nonlinear Manifold Decoders for Operator Learning [PDF]
Neural Information Processing Systems, 2022 Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling.
Jacob H. Seidman +3 more
semanticscholar +1 more source
Diffusion-driven flows in a nonlinear stratified fluid layer [PDF]
Journal of Fluid Mechanics, 2023 Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary.
Lingyun Ding
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Free Boundary Problem for a Gas Bubble in a Liquid, and Exponential Stability of the Manifold of Spherically Symmetric Equilibria [PDF]
Archive for Rational Mechanics and Analysis, 2022 We consider the dynamics of a gas bubble immersed in an incompressible fluid of fixed temperature, and focus on the relaxation of an expanding and contracting spherically symmetric bubble due to thermal effects.
Chen-Chih Lai, M. Weinstein
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Entropy, 2021 An innovative data-driven model-order reduction technique is proposed to model dilute micrometric or nanometric suspensions of microcapsules, i.e., microdrops protected in a thin hyperelastic membrane, which are used in Healthcare as innovative drug ...
Toufik Boubehziz +5 more
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