Manifold fluid mechanics - Open Access .click

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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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Globalizing manifold-based reduced models for equations and data [PDF]

Nature Communications
One 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
doaj +2 more sources

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., Lazopoulos Anastasios K. +1 more
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Learning image derived PDE-phenotypes from fMRI data [PDF]

Brain Informatics
Partial differential equations (PDEs) model various physical phenomena, such as electromagnetic fields and fluid mechanics. Methods such as sparse identification of nonlinear dynamics (SINDy) and PDE-Net 2.0 have been developed to identify and model PDEs
Ion Bica +5 more
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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

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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A Data-Driven Space-Time-Parameter Reduced-Order Model with Manifold Learning for Coupled Problems: Application to Deformable Capsules Flowing in Microchannels

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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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
Nyawelo, T. S. +2 more
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Numerical manifold method modeling of coupled processes in fractured geological media at multiple scales

Journal of Rock Mechanics and Geotechnical Engineering, 2020
The greatest challenges of rigorously modeling coupled hydro-mechanical (HM) processes in fractured geological media at different scales are associated with computational geometry.
Mengsu Hu, Jonny Rutqvist
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Data-Driven Stabilization of Unstable Periodic Orbits of the Three-Body Problem

IEEE Access
Many different models of the physical world exhibit chaotic dynamics, from fluid flows and chemical reactions to celestial mechanics. The study of the three-body problem (3BP) and its many different families of unstable periodic orbits (UPOs) has ...
Owen M. Brook +3 more
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Turing complete Navier-Stokes steady states via cosymplectic geometry. [PDF]

PNAS Nexus
Dyhr S +3 more
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