Related papers: Complex variable solution on asymmetrical sequenti…
Under compressive creep, visco-plastic solids experiencing internal mass transfer processes have been recently proposed to accommodate singular cnoidal wave solutions, as material instabilities at the stationary wave limit. These…
We present a path - integral approach to treat a 2D model of a quantum bifurcation. The model potential has two equivalent minima separated by one or two saddle points, depending on the value of a continuous parameter. Tunneling is…
This paper studies the Craig variant of the Golub-Kahan bidiagonalization algorithm as an iterative solver for linear systems with saddle point structure. Such symmetric indefinite systems in 2x2 block form arise in many applications, but…
In this paper, we construct a robust adaptive central-upwind scheme on unstructured triangular grids for two-dimensional shallow water equations with variable density. The method is well-balanced, positivity-preserving, and oscillation-free…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
We design a conservative finite difference scheme for ideal magnetohydrodynamic simulations that attains high-order accuracy, shock-capturing, and divergence-free condition of the magnetic field. The scheme interpolates pointwise physical…
We propose a novel multiple-scale spatial marching method for flows with slow streamwise variation. The key idea is to couple the boundary region equations, which govern large-scale flow evolution, with local exact coherent structures that…
Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme.…
We present an analytical solution for the tunneling process in a piecewise linear and quadratic potential which does not make use of the thin-wall approximation. A quadratic potential allows for smooth attachment of various slopes exiting…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
We study quantum tunneling in an asymmetric double-well potential using a dynamical systems--based approach rooted in the Ehrenfest formalism. In this framework, the time evolution of a Gaussian wave packet is governed by a hierarchy of…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
This paper synthesizes anytime algorithms, in the form of continuous-time dynamical systems, to solve monotone variational inequalities. We introduce three algorithms that solve this problem: the projected monotone flow, the safe monotone…
A combined approach that uses the vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI) method together with the semiclassical instanton theory was developed to study vibrational tunneling spectra of…
A formulation of the shallow water equations adapted to general complex terrains is proposed. Its derivation starts from the observation that the typical approach of depth integrating the Navier-Stokes equations along the direction of…
The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply…
One dimensional (1D) simulations of the flow and flooding of open channels are known to be inaccurate as the flow is multi-dimensional in nature, especially at the flooded regions. However, multi-dimensional simulations, even in two…
Spatially localized structures are key components of turbulence and other spatio-temporally chaotic systems. From a dynamical systems viewpoint, it is desirable to obtain corresponding exact solutions, though their existence is not…
A study of the dynamics of a tunneling particle in a driven bistable potential which is moderately-to-strongly coupled to a bath is presented. Upon restricting the system dynamics to the Hilbert space spanned by the M lowest energy…
Smoothed particle hydrodynamics (SPH) has been extensively studied in computer graphics to animate fluids with versatile effects. However, SPH still suffers from two numerical difficulties: the particle deficiency problem, which will…