相关论文: Critical trajectories in kinetic geometry

We consider stochastic equations in Hilbert spaces with singular drift in the framework of [Da Prato, R\"ockner, PTRF 2002]. We prove a Harnack inequality (in the sense of [Wang, PTRF 1997]) for its transition semigroup and exploit its…

In this paper we carry out an asymptotic analysis of the proximal-gradient dynamical system \begin{equation*}\left\{ \begin{array}{ll} \dot x(t) +x(t) = \prox_{\gamma f}\big[x(t)-\gamma\nabla\Phi(x(t))-ax(t)-by(t)\big],\\ \dot…

The approximation of fixed points by numerical fixed points was presented in the elegant monograph of Krasnosel'skii et al. (1972). The theory, both in its formulation and implementation, requires a differential operator calculus, so that…

We investigate the critical dynamics of O(N)-symmetric scalar field theories to determine the critical exponents of transport coefficients as a second-order phase transition is approached from the symmetric phase. A set of stochastic…

For rescaled additive functionals of the sine-process, upper bounds are obtained for their speed of convergence to the Gaussian distribution with respect to the Kolmogorov-Smirnov metric. Under scaling with coefficient $R$ the…

We prove the existence of locally distance increasing maps with it controllable small curvatures

I investigate the Kazakov-Migdal (KM) model -- the Hermitean gauge-invariant matrix model on a D-dimensional lattice. I utilize an exact large-N solution of the KM model with a logarithmic potential to examine its critical behavior. I find…

In a recent work, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential - for example, the interatomic potential at short ranges, and the electrostatic potential at long ranges.…

We develop the optimal transportation approach to modified log-Sobolev inequalities and to isoperimetric inequalities. Various sufficient conditions for such inequalities are given. Some of them are new even in the classical log-Sobolev…

The focus of this work is to analyze the trajectories of a point on the ellipsoid $\mathbb{S}_{a_{1},a_{2},a_{3}}^{2}$ while it is under the influence of a Killing vector field $K$. For this purpose, we introduce the generalized Darboux…

This work derives the Navier--Stokes hydrodynamic equations for a model of a confined, quasi-two-dimensional, $s$-component mixture of inelastic, smooth, hard spheres. Using the inelastic version of the revised Enskog theory, macroscopic…

We study vector fields generating a local flow by automorphisms of a parabolic geometry with higher order fixed points. We develop general tools extending the techniques of [1], [2], and [3]. We apply these tools to almost Grassmannian,…

This paper presents an advanced method for addressing the inverse kinematics and optimal path planning challenges in robot manipulators. The inverse kinematics problem involves determining the joint angles for a given position and…

We introduce a new approach for computing curvature of sub-Riemannian manifolds. Curvature is here meant as symplectic invariants of Jacobi curves of geodesics, as introduced by Zelenko and Li. We describe how they can be expressed using a…

Existence, uniqueness and stability of kinetic and entropy solutions to the boundary value problem for the Kolmogorov-type genuinely nonlinear ultra-parabolic equation with a smooth source term is established. After this, we consider the…

Nonholonomic mechanics describes the motion of systems constrained by nonintegrable constraints. One of its most remarkable properties is that the derivation of the nonholonomic equations is not variational in nature. {However, in} this…

For appropriate choices of the coupling constants, the equations of motion of Lovelock gravities up to order n in the Riemann tensor can be factorized such that the theories admits a single (A)dS vacuum. In this paper we construct two…

In $n \geq 1$ spatial dimensions, we study the Cauchy problem for a quasilinear transport equation coupled to a quasilinear symmetric hyperbolic subsystem of a rather general type. For an open set (relative to a suitable Sobolev topology)…

We establish the existence of complete K\"ahler metrics of semi-positive holomorphic sectional curvature with many zeroes in an interesting and natural geometric setting. Specifically, we use Calabi's Ansatz in the form due to Koiso-Sakane…

In this work, the first-order constitutive equations for a relativistic charged gas are obtained based on the Chapman-Enskog expansion of near-equilibrium solutions to the Boltzmann equation by implementing the projection method. To this…