Related papers: An Application of Reversible Entropic Dynamics on …
Inspired by "quantum graphity" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very…
We study stable conditional measures for a certain equilibrium measure for hyperbolic endomorphisms, on basic sets with overlaps; we show that these conditional measures are geometric probabilities and measures of maximal stable dimension.…
In this work we propose a novel method to ensure important entropy inequalities are satisfied semi-discretely when constructing reduced order models (ROMs) on nonlinear reduced manifolds. We are in particular interested in ROMs of systems…
Decaying electron magnetohydrodynamic (EMHD) turbulence in three dimensions is studied via high-resolution numerical simulations. The resulting energy spectra asymptotically approach a k^{-2} law with increasing R_B, the ratio of the…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that…
The paper provides results for a non-standard, hyperbolic, 1-D, nonlinear traffic flow model on a bounded domain. The model consists of two first-order PDEs with a dynamic boundary condition that involves the time derivative of the…
The behavior of an elastic curve bound to a surface will reflect the geometry of its environment. This may occur in an obvious way: the curve may deform freely along directions tangent to the surface, but not along the surface normal.…
We show that the rainbow state, which has volume law entanglement entropy for most choices of bipartitions, can be embedded in a many-body localized spectrum. For a broad range of disorder strengths in the resulting model, we numerically…
Computational Fluid Dynamics (CFD) simulations using turbulence models are commonly used in engineering design. Of the different turbulence modeling approaches that are available, eddy viscosity based models are the most common for their…
In this work, we developed a nonlinear System Identification (SID) method that we called Entropic Regression. Our method adopts an information-theoretic measure for the data-driven discovery of the underlying dynamics. Our method shows…
Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate…
We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…
This paper develops entropy stable (ES) adaptive moving mesh schemes for the 2D and 3D special relativistic hydrodynamic (RHD) equations. They are built on the ES finite volume approximation of the RHD equations in curvilinear coordinates,…
Information geometry is a mathematical framework that elucidates the manifold structure of the probability distribution space (p-space), providing a systematic approach to transforming probability distributions (PDs). In this study, we…
Earlier, Chicone, Latushkin and Montgomery-Smith [Comm Math Phys (1997)] have proved the existence of a fast dynamo operator, in compact two-dimensional manifold, as long as its Riemannian curvature be constant and negative. More recently…
The streamwise roll and streak structure (RSS) is prominent in observations of the planetary boundary layer in the atmosphere and ocean and in unstratified wall-bounded shear flows. Although the RSS in these systems is structurally similar,…
The study of incompressible magnetohydrodynamic (MHD) turbulence gives useful insights on many astrophysical problems. We describe a pseudo-spectral MHD code suitable for the study of incompressible turbulence. We review our recent works on…
The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the…
The mobility edge, as a central concept in disordered models for localization-delocalization transitions, has rarely been discussed in the context of random matrix theory (RMT). Here we report a new class of random matrix model by direct…