相关论文: On the convergence of the continuous version of th…

We study the approximation of fixed points of nonexpansive mappings in CAT(k) spaces. We show that the iterative sequence generated by the Moudafi's viscosity type algorithm converges to one of the fixed points of the nonexpansive mapping…

The viscosity and self-diffusion constant of a mesoscale hydrodynamic method, dissipative particle dynamics (DPD), are investigated. The viscosity of DPD with finite time step, including the Lowe-Anderson thermostat, is derived analytically…

In this work we introduce a viscosity-based notion of solution for general approximation schemes associated with partial differential equations, such as dynamic programming principles~(DPPs). A key feature of our approach is that it…

We study the asymptotic behavior of the trajectory of a nonautonomous evolution equation governed by a quasi-nonexpansive operator in Hilbert spaces. We prove the weak convergence of the trajectory to a fixed point of the operator by…

The discrete-dipole approximation (DDA) is a flexible technique for computing scattering and absorption by targets of arbitrary geometry. In this paper we perform systematic study of various non-stationary iterative (conjugate gradient)…

Direct numerical simulations (DNS) of microscale fluid-structure interactions (mFSI) in multicomponent multiphase flows pose many challenges, including the thermodynamic consistency of multiphysics couplings, tracking of moving interfaces,…

In this work, a localized artificial-viscosity/diffusivity method is proposed for accurately capturing discontinuities in compressible flows. There have been numerous efforts to improve the artificial diffusivity formulation in the last two…

Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations (DNS) by solving the equations that govern the statistics themselves. DSS…

In this paper, we study properties of sensitivity, transitivity and chaos for non-autonomous discrete systems(NDS). Firstly, we present some different sufficient conditions for NDS to be chaotic. Then, we relate the transitivity with the…

The Continuum Dislocation Dynamics (CDD) theory and the Discrete Dislocation Dynamics (DDD) method are compared based on concise mathematical formulations of the coarse graining of discrete data. A numerical tool for converting from a…

In this paper we investigate the effectiveness of direct statistical simulation (DSS) for two low-order models of dynamo action. The first model, which is a simple model of solar and stellar dynamo action, is third-order and has cubic…

In this paper we explore the extent to which discretely self-similar (DSS) solutions to the 3D Navier-Stokes equations with rough data almost have the same asymptotics as DSS flows with smoother data. In a previous work, we established…

The direct sampling method (DSM) has been introduced for non-iterative imaging of small inhomogeneities and is known to be fast, robust, and effective for inverse scattering problems. However, to the best of our knowledge, a full analysis…

The inviscid and thin accretion disc is a simple and well understood model system in accretion studies. In this work, modelling such a disc like a dynamical system, we analyse the nature of the fixed points of the stationary solutions of…

Dynamical systems (DSs) provide a framework for high flexibility, robustness, and control reliability and are widely used in motion planning and physical human-robot interaction. The properties of the DS directly determine the robot's…

Recent advances in 3D Gaussian Splatting (3DGS) have enabled visually realistic demonstration generation from a single expert trajectory and a short multi-view scan. However, existing 3DGS-based synthesis pipelines typically generate new…

A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…

Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…

In this article we find explicit formulae for spherically symmetric solutions of the multidimensional zero-pressure gas dynamics system and its adhesion approximation. The asymptotic behaviour of the explicit solutions of the adhesion…

We are interested in a complete characterization of the contact-line singularity of thin-film flows for zero and nonzero contact angles. By treating the model problem of source-type self-similar solutions, we demonstrate that this…