73 citations · 235 across the 26 of their papers we have counts for
27 papers
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…
Optimal allocation to deferred income annuities
F. Habib, H. Huang, A. Mauskopf +2
In this paper we employ a lifecycle model that uses utility of consumption and bequest to determine an optimal Deferred Income Annuity (DIA) purchase policy. We lay out a mathemati…
Multi-objective optimization and explanation for stroke risk assessment in Shanxi province
Jing Ma, Yiyang Sun, Junjie Liu +3
Stroke is the top leading causes of death in China (Zhou et al. The Lancet 2019). A dataset from Shanxi Province is used to identify the risk of each patient's at four states low/m…
Membranes in Optic Nerve Models
Yi Zhu, Shixin Xu, Robert S. Eisenberg +1
Membranes are present in all cells and tissues. Mathematical models of cells and tissues need a compact mathematical description of membranes with a resolution of about 1 nm. Membr…
Analysis and classification of main risk factors causing stroke in Shanxi Province
Junjie Liu, Yiyang Sun, Jing Ma +6
In China, stroke is the first leading cause of death in recent years. It is a major cause of long-term physical and cognitive impairment, which bring great pressure on the National…
A phase field model for mass transport with semi-permeable interfaces
Yuzhe Qin, Huaxiong Huang, Yi Zhu +2
In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted…
Homogenization Theory of Ion Transportation in Multicellular Tissue
Chun Xiao, Xingye Yue, Huaxiong Huang +1
Ion transport in biological tissues is crucial in the study of many biological and pathological problems. Some multi-cellular structures, like smooth muscles on the vessel walls, c…
Optic Nerve Microcirculation: Fluid Flow and Electrodiffusion
Yi Zhu, Shixin Xu, Robert S. Eisenberg +1
Complex fluids flow in complex ways in complex structures. Transport of water and various organic and inorganic molecules in the central nervous system are important in a wide rang…
An Energy Stable C0 Finite Element Scheme for A Phase-Field Model of Vesicle Motion and Deformation
Lingyue Shen, Zhiliang Xu, Ping Lin +2
A thermodynamically consistent phase-field model is introduced for simulating motion and shape transformation of vesicles under flow conditions. In particular, a general slip bound…
A Tridomain Model for Potassium Clearance in Optic Nerve of Necturus
Yi Zhu, Shixin Xu, Robert S. Eisenberg +1
The accumulation of potassium in the narrow space outside nerve cells is a classical subject of biophysics that has received much attention recently. It may be involved in potassiu…
Numerical Method for Parameter Inference of Nonlinear ODEs with Partial Observations
Yu Chen, Jin Cheng, Arvind Gupta +2
Parameter inference of dynamical systems is a challenging task faced by many researchers and practitioners across various fields. In many applications, it is common that only limit…
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…
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…
Retirement spending and biological age
Huaxiong Huang, Moshe A. Milevsky, Thomas S. Salisbury
We solve a lifecycle model in which the consumer's chronological age does not move in lockstep with calendar time. Instead, biological age increases at a stochastic non-linear rate…
A Bidomain Model for Lens Microcirculation
Yi Zhu, Shixin Xu, Robert S. Eisenberg +1
There exists a large body of research on the lens of mammalian eye over the past several decades. The objective of the current work is to provide a link between the most recent com…
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…
A mathematical model of the metabolic and perfusion effects on cortical spreading depression
Joshua C. Chang, K. C. Brennan, Dongdong He +4
Cortical spreading depression (CSD) is a slow-moving ionic and metabolic disturbance that propagates in cortical brain tissue. In addition to massive cellular depolarization, CSD a…
Valuation and hedging of the ruin-contingent life annuity (RCLA)
Huaxiong Huang, Moshe A. Milevsky, Thomas S. Salisbury
This paper analyzes a novel type of mortality contingent-claim called a ruin-contingent life annuity (RCLA). This product fuses together a path-dependent equity put option with a "…