Welcome to Xinran Ruan's Homepage

W. Huang and X. Ruan^*, An Onsager variational scheme for pressure-driven tumor growth and Hele-Shaw limits, Preprint, (2026).

W. Huang and X. Ruan^*, A WKB-based fixed-grid method for capturing trait concentration in a dispersal evolution model, ArXiv, (2026). [PDF]

W. Huang, Y. Liu and X. Ruan^*, Mathematical and numerical studies on ground states of the extended Gross-Pitaevskii equation with the Lee-Huang-Yang correction, ArXiv, (2026). [PDF]

Y. Cai, X. Ruan^* and Y. Zhang, Mathematical and numerical studies on ground states of trapped unitary Fermi gases, SIAM J. Appl. Math., (2026), accepted. [PDF]

G. Estrada-Rodriguez, D. Peurichard and X. Ruan^*, From a nonlinear kinetic equation to a volume-exclusion chemotaxis model via asymptotic preserving methods, Kinet. Rel. Models, 18 (2025), 989--1015.

F. Ballatore, X. Ruan, C. Giverso and T. Lorenzi, A phenotype-structured reaction-diffusion model of avascular glioma growth, ArXiv, (2025), 1--23. [PDF]

N. David and X. Ruan^*, An asymptotic preserving scheme for a tumor growth model of porous medium type, ESAIM: M2AN, 56 (2022), 121--150. [PDF]

F. R. Macfarlane^*, X. Ruan and T. Lorenzi^*, Individual-based and continuum models of phenotypically heterogeneous growing cell populations, AIMS Bioengineering, 9 (2022), 68--92. [PDF]

L. Almeida, B. Perthame and X. Ruan^*, An asymptotic preserving scheme for capturing concentrations in age-structured models arising in adaptive dynamics, J. Comput. Phys., 464 (2022), 111335. [PDF]

T. Lorenzi, B. Perthame and X. Ruan, Invasion fronts and adaptive dynamics in a model for the growth of cell populations with heterogeneous mobility, Eur. J. Appl. Math., 33 (2022), 766--783. [PDF]

W. Bao and X. Ruan^*, Computing ground states of Bose–Einstein condensates with higher order interaction via a regularized density function formulation, SIAM J. Sci. Comput., 41 (2019), B1284--B1309. [PDF]

W. Bao, Y. Cai^* and X. Ruan, Ground states of Bose–Einstein condensates with higher order interaction, Physica D, 386--387 (2019), 38--48. [PDF]

W. Yi, X. Ruan^* and C. Su, Optimal resolution methods for the Klein–Gordon–Dirac system in the nonrelativistic limit regime, J. Sci. Comput., 79 (2019), 1907--1935. [PDF]

W. Bao, X. Ruan^*, J. Shen and C. Sheng, Fundamental gaps of the Fractional Schrödinger Operator, Commun. Math. Sci., 17 (2019), 447--471. [PDF]

X. Ruan^*, A normalized gradient flow method with attractive-repulsive splitting for computing ground states of Bose-Einstein condensates with higher-order interaction, J. Comput. Phys., 367 (2018), 374--390. [PDF]

X. Ruan and W. Yi^*, Ground states and energy asymptotics of the nonlinear Schrödinger equation with a general power nonlinearity, Commun. Comput. Phys., 24 (2018), 1121--1142. [PDF]

W. Bao and X. Ruan^*, Fundamental gaps of the Gross–Pitaevskii equation with repulsive interaction, Asymp. Anal., 110 (2018), 53--82. [PDF]

F. Pinsker^*, X. Ruan and T. J. Alexander, Effects of the non-parabolic kinetic energy on non-equilibrium polariton condensates, Sci. Rep., 7 (2017), 1891. [PDF]

X. Ruan, Y. Cai^* and W. Bao^*, Mean-field regime and Thomas-Fermi approximations of trapped Bose-Einstein condensates with higher order interactions in one and two dimensions, J. Phys. B: At. Mol. Opt. Phys., 49 (2016), 125304. [PDF]