15 citations · 40 across the 17 of their papers we have counts for
20 papers
A positive-conservative Fourier optimization method for ground states of Bose--Einstein condensates with higher-order interactions
Bo Lin, Xinran Ruan
We develop a positive-conservative Fourier optimization (PCFO) method for computing ground states of Bose--Einstein condensates with higher-order interactions. The ground-state pro…
An Onsager Variational Scheme for Pressure-Driven Tumor Growth and Hele-Shaw Limits
Weijie Huang, Xinran Ruan
Pressure-driven tumor growth models describe the coupling between cell proliferation and mechanical pressure and naturally lead to moving free boundary problems. Their numerical ap…
A WKB-based fixed-grid method for capturing trait concentration in a dispersal evolution model
Weijie Huang, Xinran Ruan
The evolution of dispersal traits is a fundamental topic in evolutionary ecology, where natural selection may drive the trait distribution toward concentration in the rare-mutation…
A sharp-interface model for solid-state dewetting with wetting potential
Weijie Huang, Xinran Ruan
We propose a sharp-interface model for solid-state dewetting of thin films with wetting potential, where the wetting effect is incorporated through a thickness-dependent surface en…
Ground states and droplet regimes of the extended Gross-Pitaevskii equation with Lee-Huang-Yang correction
Weijie Huang, Yang Liu, Xinran Ruan
We study the ground states of the extended Gross--Pitaevskii equation with the Lee--Huang--Yang correction from both theoretical and numerical perspectives. Starting from the three…
Mathematical and numerical studies on ground states of trapped unitary Fermi gases
Yongyong Cai, Xinran Ruan, Yanzhi Zhang
We mathematically and numerically study the ground states of unitary Fermi gases. Starting from the three-dimensional nonlinear Schrödinger equation that contains a quantum pressur…
A phenotype-structured reaction-diffusion model of avascular glioma growth
Francesca Ballatore, Xinran Ruan, Chiara Giverso +1
We consider a phenotype-structured reaction-diffusion model of avascular glioma growth. The model describes the interaction dynamics between tumour cells and oxygen, and takes into…
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…
Individual-based and continuum models of phenotypically heterogeneous growing cell populations
Fiona R Macfarlane, Xinran Ruan, Tommaso Lorenzi
Existing studies comparing individual-based models of growing cell populations and their continuum counterparts have mainly focused on homogeneous populations, in which all cells h…
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…
Quantum versus Classical Regime in Circuit Quantum Acoustodynamics
Gang-hui Zeng, Yang Zhang, Aleksey N. Bolgar +8
We experimentally study a circuit quantum acoustodynamics system, which consists of a superconducting artificial atom, coupled to both a two-dimensional surface acoustic wave reson…
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…
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…
A normalized gradient flow method with attractive-repulsive splitting for computing ground states of Bose-Einstein condensates with higher-order interaction
Xinran Ruan
In this paper, we generalize the normalized gradient flow method to compute the ground states of Bose-Einstein condensates (BEC) with higher order interactions (HOI), which is mode…
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 $…
Ground states of Bose-Einstein condensates with higher order interaction
Weizhu Bao, Yongyong Cai, Xinran Ruan
We analyze the ground state of a Bose-Einstein condensate in the presence of higher-order interaction (HOI), modeled by a modified Gross-Pitaevskii equation (MGPE). In fact, due to…
Effects of the non-parabolic kinetic energy on non-equilibrium polariton condensates
Florian Pinsker, Xinran Ruan, Tristram Alexander
In the study of non-equilibrium polariton condensates it is usually assumed that the dispersion relation of polaritons is parabolic in nature. We show that considering the true non…
Fundamental gaps of the Gross-Pitaevskii equation with repulsive interaction
Weizhu Bao, Xinran Ruan
We study asymptotically and numerically the fundamental gaps (i.e. the difference between the first excited state and the ground state) in energy and chemical potential of the Gros…
Mean-field regime and Thomas-Fermi approximations of trapped Bose-Einstein condensates with higher order interactions in one and two dimensions
Xinran Ruan, Yongyong Cai, Weizhu Bao
We derive rigorously one- and two-dimensional mean-field equations for cigar- and pancake-shaped Bose-Einstein condensates (BEC) with higher order interactions (HOI). We show how t…