Related papers: Toda flow with unbounded initial data
The first-order textbook formulations of relativistic viscous hydrodynamics are unstable and acausal. These shortcomings may be rectified by using effective theories which maintain stability and causality. In this dissertation, which is…
Properties of steady compressible flow for which geometric constraints have been placed on the potential function are derived, under hypotheses on the flow density and the singular set. Some related unconstrained problems are also…
Over a given regular domain of independent variables {x,y,z,t}, every covariant vector field of flow can be constructed in terms a differential 1-form of Action. The associated Cartan topology permits the definition of four basic…
In hydrodynamics, the momentum distribution of particles at the end of the evolution is completely determined by initial conditions. We study quantitatively to what extent anisotropic flow is determined by predictors such as the initial…
Let $f:T\longrightarrow T$ be a mapping and $\Omega$ be a subset of $T$ which intersects every (positive) orbit of $f$. Assume that there are given a second dynamical system $\lambda:Y\longrightarrow Y$ and a mapping…
We study the solution of the Toda lattice Cauchy problem with steplike initial data. The initial data are supposed to tend to zero as $n \to +\infty$. By the inverse scattering transform method formulas allowing us to find solution of the…
We consider initial-boundary problems for general linear first-order strictly hyperbolic systems with local or nonlocal nonlinear boundary conditions. While boundary data are supposed to be smooth, initial conditions can contain…
The boundary conditions prescribing the constant traction or the so-called do-nothing conditions are frequently taken on artificial boundaries in the numerical simulations of steady flow of incompressible fluids, despite the fact that they…
Three dimensional unsteady flow of fluids in the Lagrangian description is considered as an autonomous dynamical system in four dimensions. The condition for the existence of a symplectic structure on the extended space is the frozen field…
One of the few accepted dynamical foundations of non-additive "non-extensive") statistical mechanics is that the choice of the appropriate entropy functional describing a system with many degrees of freedom should reflect the rate of growth…
This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…
We associate bicomplexes with the finite Toda lattice and with a finite Toda field theory in such a way that conserved currents and charges are obtained by a simple iterative construction.
Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase…
We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possible for the vertical translation flows on such flat…
In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are usually treated separately in literature. To study complex flows when all three regimes…
We establish conditions for an exponential rate of forgetting of the initial distribution of nonlinear filters in $V$-norm, path-wise along almost all observation sequences. In contrast to previous works, our results allow for unbounded…
We present a novel, conditional generative probabilistic model of set-valued data with a tractable log density. This model is a continuous normalizing flow governed by permutation equivariant dynamics. These dynamics are driven by a…
An excited random walk is a non-Markovian extension of the simple random walk, in which the walk's behavior at time $n$ is impacted by the path it has taken up to time $n$. The properties of an excited random walk are more difficult to…
The latent space of normalizing flows must be of the same dimensionality as their output space. This constraint presents a problem if we want to learn low-dimensional, semantically meaningful representations. Recent work has provided…