6 papers
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 pressu…
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…