48 citations · 131 across the 22 of their papers we have counts for
23 papers
Multiscale retinal flow on a spherical cap of varying aperture
Chang Lin, Zilong Song, Bob Eisenberg +2
Modelling retinal haemodynamics is crucial for understanding retinal microcirculation but is computationally demanding because it involves coupling between the vasculature and surr…
A novel multiscale modelling for the hemodynamics in retinal microcirculation with an analytic solution for the capillary-tissue coupled system
Chang Lin, Zilong Song, Robert Eisenberg +2
Mathematical modelling of the microcirculatory hemodynamics in the retina is an essential tool for understanding various diseases of the retina, yet remains challenging due to the…
Glymphatic Clearance in the Optic Nerve: A Multidomain Electro-osmostic Model
Shanfeng Xiao, Huaxiong Huang, Robert Eisenberg +2
Effective metabolic waste clearance and maintaining ionic homeostasis are essential for the health and normal function of the central nervous system. To understand its mechanism an…
Pump-driven droplet electrohydrodynamics: deformation, pinch-off and recoalescence
Yuzhe Qin, Huaxiong Huang, Zilong Song +1
We investigate pump-driven droplet electrohydrodynamics with an emphasis on deformation, pinch-off, and recoalescence. A thermodynamically consistent phase-field framework is devel…
Proper Orthogonal Decomposition-based Model-Order Reduction for Smoothed Particle Hydrodynamics Simulation -- Mass-Spring-Damper System
Lidong Fang, Zilong Song, Kirk Fraser +1
Model Order Reduction (MOR) based on Proper Orthogonal Decomposition (POD) and Smooth Particle Hydrodynamics (SPH) has proven effective in various applications. Most MOR methods ut…
Proper Orthogonal Decomposition-based Model-Order Reduction for Smoothed Particle Hydrodynamics Simulation
Lidong Fang, Zilong Song, Kirk Fraser +3
In this paper, we present a projection-based model-order reduction (MOR) technique for smoothed particle hydrodynamics (SPH) simulations, which is a mesh-free approach within the L…
Micro-Macro Modeling of Polymeric Fluids with Multi-Bead Polymer Chain
Xuelian Bao, Lidong Fang, Huaxiong Huang +2
This work extends the classical dumbbell (two-bead) model of polymer chains to a more detailed multi-bead representation, where each polymer chain consists of beads connected b…
Multidomain Model for Optic Nerve Potassium Clearance: Roles of Glial Cells and Perivascular Spaces
Shanfeng Xiao, Huaxiong Huang, Robert Eisenberg +2
The accumulation of potassium in the extracellular space surrounding nerve cells is a fundamental aspect of biophysics that has garnered significant attention in recent research. T…
A multi-domain model for microcirculation in optic nerve: blood flow and oxygen transport
Zilong Song, Shixin Xu, Robert Eisenberg +1
Microcirculation of blood and oxygen transport play important roles in biological function of optic nerve and are directly affected by damages or pathologies. This work develops a…
Micro-Macro Modeling of Polymeric Fluids and Shear-Induced Microscopic Behaviors
Xuelian Bao, Huaxiong Huang, Zilong Song +1
This article delves into the micro-macro modeling of polymeric fluids, considering various microscopic potential energies, including the classical Hookean potential, as well as new…
A phase field model for droplets suspended in viscous liquids under the influence of electric fields
Yuzhe Qin, Huaxiong Huang, Zilong Song +1
In this paper, we propose a Poisson-Nernst-Planck-Navier-Stokes-Cahn-Hillard (PNP-NS-CH)model for an electrically charged droplet suspended in a viscous fluid subjected to an exter…
Coupled Chemical Reactions: Effects of Electric Field, Diffusion and Boundary Control
Shixin Xu, Robert Eisenberg, Zilong Song +1
Chemical reactions involve the movement of charges, and this work presents a mathematical model for describing chemical reactions in electrolytes. The model is developed using an e…
Mathematical Model for Chemical Reactions in Electrolyte Applied to Cytochrome Oxidase: an Electro-osmotic Approach
Shixin Xu, Robert Eisenberg, Zilong Song +1
A mathematical model for chemical reactions in electrolytes is developed using an Energy variational method consistent with classical thermodynamics. Electrostatics and chemical re…
A Bubble Model for the Gating of Kv Channels
Zilong Song, Robert Eisenberg, Shixin Xu +1
Voltage-gated Kv channels play fundamental roles in many biological processes, such as the generation of the action potential. The gating mechanism of Kv channels is characterized…
An energy stable finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density
Lingyue Shen, Huaxiong Huang, Ping Lin +2
In this paper, we focus on modeling and simulation of two-phase flow with moving contact lines and variable density. A thermodynamically consistent phase-field model with General N…
Analytical study on phase transition of shape memory alloy wire under uniaxial tension
Zilong Song
This paper considers the stress-induced phase transitions of shape memory alloy slender cylinder, and analytically studies the phase transition process and the associated instabili…
On the selectivity of KcsA potassium channel: asymptotic analysis and computation
Zilong Song, Xiulei Cao, Tzyy-Leng Horng +1
Potassium (K) channels regulate the flux of K ions through cell membranes and plays significant roles in many physiological functions. This work studies the KcsA potassium…
Electro-Neutral Models for dynamic Poisson-Nernst-Planck System: 2D Case
Zilong Song, Xiulei Cao, Huaxiong Huang
The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layer…
Osmosis through a Semi-permeable Membrane: a Consistent Approach to Interactions
Shixin Xu, Bob Eisenberg, Zilong Song +1
The movement of ionic solutions is an essential part of biology and technology. Fluidics, from nano- to micro- to microfluidics, is a burgeoning area of technology which is all abo…
What Current Flows Through a Resistor?
Bob Eisenberg, Nathan Gold, Zilong Song +1
Our digital technology depends on mathematics to compute current flow and design its devices. Mathematics describes current flow by an idealization, Kirchhoff's current law. All th…
Electro-Neutral Models for Dynamic Poisson-Nernst-Planck System
Zilong Song, Xiulei Cao, Huaxiong Huang
The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layer…
On a consistent finite-strain plate theory based on 3-D energy principle
Hui-Hui Dai, Zilong Song
This paper derives a finite-strain plate theory consistent with the principle of stationary three-dimensional (3-D) potential energy under general loadings with a third-order error…
Analytical Solutions for the Equilibrium states of a Swollen Hydrogel Shell and an Extended Method of Matched Asymptotics
Hui-Hui Dai, Zilong Song
A polymer network can imbibe water, forming an aggregate called hydrogel, and undergo large and inhomogeneous deformation with external mechanical constraint. Due to the large defo…