15 citations · 40 across the 17 of their papers we have counts for
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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…
Invasion fronts and adaptive dynamics in a model for the growth of cell populations with heterogeneous mobility
Tommaso Lorenzi, Benoît Perthame, Xinran Ruan
We consider a model for the dynamics of growing cell populations with heterogeneous mobility and proliferation rate. The cell phenotypic state is described by a continuous structur…
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 $…