Zobrazeno 1 - 10
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pro vyhledávání: '"Tapley, Benjamin K"'
Autor:
Tapley, Benjamin K
We present and analyze a framework for designing symplectic neural networks (SympNets) based on geometric integrators for Hamiltonian differential equations. The SympNets are universal approximators in the space of Hamiltonian diffeomorphisms, interp
Externí odkaz:
http://arxiv.org/abs/2408.09821
We present a method to construct superintegrable $n$-component Lotka-Volterra systems with $3n-2$ parameters. We apply the method to Lotka-Volterra systems with $n$ components for $1 < n < 6$, and present several $n$-dimensional superintegrable famil
Externí odkaz:
http://arxiv.org/abs/2303.00229
Autor:
Tapley, Benjamin K
We present a novel numerical method for solving ODEs while preserving polynomial first integrals. The method is based on introducing multiple quadratic auxiliary variables to reformulate the ODE as an equivalent but higher-dimensional ODE with only q
Externí odkaz:
http://arxiv.org/abs/2108.06548
Autor:
Tapley, Benjamin K
One can elucidate integrability properties of ordinary differential equations (ODEs) by knowing the existence of second integrals (also known as weak integrals or Darboux polynomials for polynomial ODEs). However, little is known about how they are p
Externí odkaz:
http://arxiv.org/abs/2105.10929
We propose a novel integral model describing the motion of curved slender fibers in viscous flow, and develop a numerical method for simulating dynamics of rigid fibers. The model is derived from nonlocal slender body theory (SBT), which approximates
Externí odkaz:
http://arxiv.org/abs/2012.11561
A geometric numerical method for simulating suspensions of spherical and non-spherical particles with Stokes drag is proposed. The method combines divergence-free matrix-valued radial basis function interpolation of the fluid velocity field with a sp
Externí odkaz:
http://arxiv.org/abs/1907.11936
In this paper we consider a computational model for the motion of thin, rigid fibers in viscous flows based on slender body theory. Slender body theory approximates the fluid velocity field about the fiber as the flow due to a distribution of singula
Externí odkaz:
http://arxiv.org/abs/1906.00253
Autor:
Tapley, Benjamin K
We present an novel algorithm for tracking massless solid particles in a divergence-free velocity field that is only available at discrete points in space and time such as those arising from a direct numerical simulation of Navier-Stokes. The algorit
Externí odkaz:
http://arxiv.org/abs/1901.05236
Publikováno v:
Journal of Computational Dynamics, 2018
Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations,...) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifolds equipped with Poisson brackets. The Poisson structure is connected
Externí odkaz:
http://arxiv.org/abs/1810.01627
Publikováno v:
In Journal of Computational Physics 1 January 2022 448