相关论文: Refining and classifying finite-time Lyapunov expo…

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…

We develop a powerful and general method to provide rigorous and accurate upper and lower bounds for Lyapunov exponents of stochastic flows. Our approach is based on computer-assisted tools, the adjoint method and established results on the…

Recent work has introduced the concept of finite-time scaling to characterize bifurcation diagrams at finite times in deterministic discrete dynamical systems, drawing an analogy with finite-size scaling used to study critical behavior in…

We study the probability densities of finite-time or \local Lyapunov exponents (LLEs) in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are…

Domain decomposition has been shown to be a computationally efficient distributed method for solving large scale entropic optimal transport problems. However, a naive implementation of the algorithm can freeze in the limit of very fine…

We propose and analyze a class of second-order dynamical systems for continuous-time optimization that incorporate fractional-order gradient terms. The system is given by \begin{equation} \ddot{x}(t) + \frac{\alpha}{t}\dot{x}(t) +…

Using finite difference method, time evolution of a typical metal molecule metal system is studied by introducing a new method to solve general related Volterra integro differential equation (IDE). Discretization in time domain is applied…

Most neural methods for Vehicle Routing Problems (VRPs) are limited to Euclidean settings or simple graphs. In this work, we instead consider multigraphs, where parallel edges represent distinct travel options with varying trade-offs (e.g.,…

Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled…

This paper presents an improved Matlab routine, FO_LE, for the numerical computation of Lyapunov exponents of fractional-order systems modeled by Caputo's derivative. It is conceived as an enhanced version of the former FO_Lyapunov and…

This article introduces the structure flow field; a flow field that can provide high-speed robo-centric motion information for motion control of highly dynamic robotic devices and autonomous vehicles. Structure flow is the angular 3D…

This note is about a drift-diffusion process $X$ with a time-independent, divergence-free drift $b$, where $b$ is a smooth Gaussian field that decorrelates over large scales. In two space dimensions, this just fails to fall into the…

We develop a Lyapunov-based analysis of Korpelevich's extragradient method and show that it achieves an $o(1/k)$ last-iterate convergence rate of the constructed Lyapunov function. This Lyapunov function simultaneously upper bounds several…

In this paper, a second-order accurate method was developed for calculating fluid flows in complex geometries. This method uses cut-Cartesian cell mesh in finite volume framework. Calculus is employed to relate fluxes and gradients along…

Hybrid Reynolds-averaged Navier Stokes large eddy simulation (RANS LES) methods have become popular for simulation of massively separated flows at high Reynolds numbers due to their reduced computational cost and good accuracy. The current…

Effective field theories of two-dimensional lattice models of fluctuating loops are constructed by mapping them onto random surfaces whose large scale fluctuations are described by a Liouville field theory. This provides a geometrical view…

Remote sensing (RS) image-text retrieval plays a critical role in understanding massive RS imagery. However, the dense multi-object distribution and complex backgrounds in RS imagery make it difficult to simultaneously achieve fine-grained…

We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a…

Two different types of perturbations of the Lorenz 63 dynamical system for Rayleigh-Benard convection by multiplicative noise -- called stochastic advection by Lie transport (SALT) noise and fluctuation-dissipation (FD) noise -- are found…

Ridge regression (RR) is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using RR is the need to set a hyperparameter ($\alpha$) that controls the amount of…