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math.AP2022
Asymptotic preserving schemes for nonlinear kinetic equations leading to volume-exclusion chemotaxis in the diffusive limit
Gissell Estrada-Rodriguez, Diane Peurichard, Xinran Ruan
In this work we first prove, by formal arguments, that the diffusion limit of nonlinear kinetic equations, where both the transport term and the turning operator are density-depend…
math.AP2018
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…
math.AP2017
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 $…