Related papers: Scenery flow, conical densities, and rectifiabilit…
We explicitly construct parameter transformations between gradient flows in metric spaces, called curves of maximal slope, having different exponents when the associated function satisfies a suitable convexity condition. These…
Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous application focused on two-dimensional homogeneous fluid, this study examines the geometric…
This paper presents a geometric microcanonical ensemble perspective on two-dimensional Truncated Euler flows, which contain a finite number of (Fourier) modes and conserve energy and enstrophy. We explicitly perform phase space volume…
A pseudorandom point in an ergodic dynamical system over a computable metric space is a point which is computable but its dynamics has the same statistical behavior as a typical point of the system. It was proved in [Avigad et al. 2010,…
This is the first of a series of papers devoted to a thorough analysis of the class of gradient flows in a metric space $(X,\mathsf{d})$ that can be characterized by Evolution Variational Inequalities. We present new results concerning the…
We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…
After an introductory chapter on the quantum supersymmetric string, in which particular attention will be devoted to the techniques via which phenomenologically viable models can be obtained from the ultraviolet microscopic degrees of…
The optical flow of natural scenes is a combination of the motion of the observer and the independent motion of objects. Existing algorithms typically focus on either recovering motion and structure under the assumption of a purely static…
Using viscous relativistic hydrodynamics we show that systematic studies of the impact parameter dependence of the eccentricity scaled elliptic flow can distinguish between different models for the calculation of the initial source…
We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…
We study the problem of sinking particles in a realistic oceanic flow, with major energetic structures in the mesoscale, focussing in the range of particle sizes and densities appropriate for marine biogenic particles. Our aim is to unify…
We give a surface for which the Ricci Flow applied to the metric will increase the topological entropy of the geodesic flow. Specifically, we first adapt the Melnikov method to apply to a Ricci Flow perturbation and then we construct a…
A recent paper [CGT] studies the evolution of star-shaped mean convex hypersurfaces of the Euclidean space by a class of nonhomogeneous expanding curvature flows. In the present paper we consider the same problem in the real, complex and…
We conduct a numerical study of relativistic viscous fluid dynamics in the Density Frame for one-dimensional fluid flows. The Density Frame is a formulation of relativistic viscous hydrodynamics that is first-order in time, requires no…
Many generative models originally developed in finite-dimensional Euclidean space have functional generalizations in infinite-dimensional settings. However, the extension of rectified flow to infinite-dimensional spaces remains unexplored.…
We study a mathematical model of a perturbed stratified shear mean flow in the presence of eddy coefficients of turbulent viscosity. We adopt the standard Boussinesq approximation in the natural convection of the buoyancy-driven flow and…
In this article we investigate the dynamical properties of the geodesic flow for a proper metric space endowed with a proper action by isometries of a group with a contracting element. We show that the existence of a contracting isometry is…
We reframe scene flow as the task of estimating a continuous space-time ODE that describes motion for an entire observation sequence, represented with a neural prior. Our method, EulerFlow, optimizes this neural prior estimate against…
We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include…
We consider geometric flows of hypersurfaces expanding by a function of the extrinsic curvature and we show that the homothethic sphere is the unique solution of the flow which converges to a point at the initial time. The result does not…