4 papers
An asymptotic preserving scheme for a tumor growth model of porous medium type
Noemi David, Xinran Ruan
Mechanical models of tumor growth based on a porous medium approach have been attracting a lot of interest both analytically and numerically. In this paper, we study the stability…
Computing ground states of Bose-Einstein Condensates with higher order interaction via a regularized density function formulation
Weizhu Bao, Xinran Ruan
We propose and analyze a new numerical method for computing the ground state of the modified Gross-Pitaevskii equation for modeling the Bose-Einstein condensate with a higher order…
Fundamental Gaps of the Fractional Schrödinger Operator
Weizhu Bao, Xinran Ruan, Jie Shen +1
We study asymptotically and numerically the fundamental gap -- the difference between the first two smallest (and distinct) eigenvalues -- of the fractional Schrödinger operator (F…
Ground states and energy asymptotics of the nonlinear Schrödinger equation
Xinran Ruan
We study analytically the existence and uniqueness of the ground state of the nonlinear Schrödinger equation (NLSE) with a general power nonlinearity described by the power index $…