22 citations · 202 across the 36 of their papers we have counts for
36 papers
Phase-Field Models, Sharp Interface Limits, and Numerical Schemes for Contact Line Dynamics
Guosheng Fu, Yuan Gao, Jian-Guo Liu
We study phase-field and sharp-interface models for contact line dynamics of a liquid droplet on a solid substrate within a unified variational framework. The motion of the contact…
Optimal control formulation of transition path problems for Markov Jump Processes
Yuan Gao, Jian-Guo Liu, Oliver Tse
We formulate the transition path problem for Markov jump processes as a stochastic optimal control problem on path space. Transitions between metastable sets are induced by an unbo…
Master equations for finite state mean field games with nonlinear activations
Yuan Gao, Wuchen Li, Jian-Guo Liu
We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled contin…
A selection principle for weak KAM solutions via Freidlin-Wentzell large deviation principle of invariant measures
Yuan Gao, Jian-Guo Liu
This paper reinterprets Freidlin-Wentzell's variational construction of the rate function in the large deviation principle for invariant measures from the weak KAM perspective. Thr…
Large deviation principle and thermodynamic limit of chemical master equation via nonlinear semigroup
Yuan Gao, Jian-Guo Liu
Chemical reactions can be modeled by a random time-changed Poisson process on countable states. The macroscopic behaviors, such as large fluctuations, can be studied via the WKB re…
Asymptotic stability for diffusion with dynamic boundary reaction from Ginzburg-Landau energy
Yuan Gao, Jean-Michel Roquejoffre
The nonequilibrium process in dislocation dynamics and its relaxation to the metastable transition profile is crucial for understanding the plastic deformation caused by line defec…
Physarum Inspired Dynamics to Solve Semi-Definite Programs
Yuan Gao, Hamidreza Kamkari, Andreas Karrenbauer +2
Physarum Polycephalum is a slime mold that can solve shortest path problems. A mathematical model based on Physarum's behavior, known as the Physarum Directed Dynamics, can solve p…
Revisit of macroscopic dynamics for some non-equilibrium chemical reactions from a Hamiltonian viewpoint
Yuan Gao, Jian-Guo Liu
Most biochemical reactions in living cells are open systems interacting with environment through chemostats to exchange both energy and materials. At a mesoscopic scale, the number…
Random walk approximation for irreversible drift-diffusion process on manifold: ergodicity, unconditional stability and convergence
Yuan Gao, Jian-Guo Liu
Irreversible drift-diffusion processes are very common in biochemical reactions. They have a non-equilibrium stationary state (invariant measure) which does not satisfy detailed ba…
Surfactant-dependent contact line dynamics and droplet spreading on textured substrates: derivations and computations
Yuan Gao, Jian-Guo Liu
We study spreading of a droplet, with insoluble surfactant covering its capillary surface, on a textured substrate. In this process, the surfactant-dependent surface tension domina…
Lagrangian correspondences and the generalized Viterbo restriction functor
Yuan Gao
We study two kinds of functors of wrapped Fukaya categories: 1) the Viterbo restriction functor for an inclusion of a Liouville sub-domain; 2) the Lagrangian correspondence functor…
Transition path theory for Langevin dynamics on manifold: optimal control and data-driven solver
Yuan Gao, Tiejun Li, Xiaoguang Li +1
We present a data-driven point of view for rare events, which represent conformational transitions in biochemical reactions modeled by over-damped Langevin dynamics on manifolds in…
Existence and rigidity of the Peierls-Nabarro model for dislocations in high dimensions
Yuan Gao, Jian-Guo Liu, Zibu Liu
We focus on existence and rigidity problems of the vectorial Peierls-Nabarro (PN) model for dislocations. Under the assumption that the misfit potential on the slip plane only depe…
Inbetweening auto-animation via Fokker-Planck dynamics and thresholding
Yuan Gao, Guangzhen Jin, Jian-Guo Liu
We propose an equilibrium-driven deformation algorithm (EDDA) to simulate the inbetweening transformations starting from an initial image to an equilibrium image, which covers imag…
Data-driven Efficient Solvers for Langevin Dynamics on Manifold in High Dimensions
Yuan Gao, Jian-Guo Liu, Nan Wu
We study the Langevin dynamics of a physical system with manifold structure based on collected sample points $\{\mathsf{x}_i\}_{i=1}^n \subset \mat…
Projection method for droplet dynamics on groove-textured surface with merging and splitting
Yuan Gao, Jian-Guo Liu
The geometric motion of small droplets placed on an impermeable textured substrate is mainly driven by the capillary effect, the competition among surface tensions of three phases…
Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects
Yuan Gao, Xin Yang Lu, Chong Wang
We study a nonlocal 4th order degenerate equation deriving from the epitaxial growth on crystalline materials. We first prove the global existence of evolution variational inequali…
Existence and uniqueness of bounded stable solutions to the Peierls-Nabarro model for curved dislocations
Hongjie Dong, Yuan Gao
We study the well-posedness of the vector-field Peierls-Nabarro model for curved dislocations with a double well potential and a bi-states limit at far field. Using the Dirichlet t…
Analysis of a fourth order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates
Yuan Gao, Anya E. Katsevich, Jian-Guo Liu +2
We analytically and numerically study a fourth order PDE modeling rough crystal surface diffusion on the macroscopic level. We discuss existence of solutions globally in time and l…
Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface
Yuan Gao, Jian-Guo Liu
We study the dynamics of a droplet moving on an inclined rough surface in the absence of inertial and viscous stress effects. In this case, the dynamics of the droplet is a purely…
Mathematical validation of the Peierls--Nabarro model for edge dislocations
Yuan Gao, Jian-Guo Liu, Tao Luo +1
In this paper, we perform mathematical validation of the Peierls--Nabarro (PN) models, which are multiscale models of dislocations that incorporate the detailed dislocation core st…
Long time behavior of dynamic solution to Peierls--Nabarro dislocation model
Yuan Gao, Jian-Guo Liu
In this paper we study the relaxation process of Peierls-Nabarro dislocation model, which is a gradient flow with singular nonlocal energy and double well potential describing how…
Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects
Yuan Gao, Jian-Guo Liu, Jianfeng Lu +1
We study a th order PDE with a nd order correction that is a modification of one suggested by Peter Smereka using the tools of Krug et al (Z. Phys. B., 1994). First, we provi…
Global Strong Solution With BV Derivatives to Singular Solid-on-Solid model With Exponential Nonlinearity
Yuan Gao
In this work, we consider the one dimensional very singular fourth-order equation for solid-on-solid model in attachment-detachment-limit regime with exponential nonlinearity $$h_t…