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The mathematical modelling of biological systems has historically followed one of two approaches: comprehensive and minimal. In comprehensive models, the involved biological pathways are modelled independently, then brought together as an…
We study both theoretically and experimentally switching dynamics in surface stabilized ferroelectric liquid crystal cells with asymmetric boundary conditions. In these cells the bounding surfaces are treated differently to produce…
We present a mechanistic model of drug release from a multiple emulsion into an external surrounding fluid. We consider a single multi-layer droplet where the drug kinetics are described by a pure diffusive process through different liquid…
We investigate the time-dependent, coherent, and dissipative dynamics of bound particles in single multilevel quantum dots in the presence of sequential tunnelling transport. We focus on the nonequilibrium regime where several channels are…
The flow behaviors of polymer melt composed of short chains with ten beads between parallel plates are simulated by using a hybrid method of molecular dynamics and computational fluid dynamics. Three problems are solved: creep motion under…
Transition metal dichalcogenides exhibit a wide range of semiconducting, metallic, correlated, and topological electronic states that arise from strong coupling between lattice structure, dimensionality, and electronic degrees of freedom.…
Polymers near the glass transition temperature Tg often exhibit a breakdown of time-temperature-superposition (TTS), with chain relaxation times and viscosity exhibiting a weaker temperature dependence than segmental relaxation times. The…
A novel phase field method is proposed to model the continuous transition of binary fluids exhibiting temperature sensitive miscibility gap, from immiscible state to miscible state via partially miscible states. The model is employed to…
Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical…
We developed and experimentally verified an analytical model to describe diffusion of oligonucleotides from stable hydrogel beads. The synthesized alginate beads are Fe3+-cross-linked as well as polyelectrolyte-doped for uniformity and…
We investigate dynamical heterogeneities in the collective relaxation of a concentrated microgel system, for which the packing fraction can be conveniently varied by changing the temperature. The packing fraction dependent mechanical…
We introduce a three-dimensional model for polyelectrolyte hydrogel filaments operating in a fluid environment under an electric field. The formulation builds on a morphoelastic framework for inextensible and unshearable rods, such that the…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
We present an experimental and numerical study of immiscible two-phase flow in 3-dimensional (3D) porous media to find the relationship between the volumetric flow rate ($Q$) and the total pressure difference ($\Delta P$) in the steady…
The dynamic rheology of a polymer melt composed of short chains with ten beads between rapidly oscillating plates is investigated for various oscillation frequencies by using the hybrid simulation of the molecular dynamics and computational…
Poroelastic materials, consisting of a permeable solid matrix infiltrated with fluid, are ubiquitous in natural and engineering contexts. In poroelastic polymer solids, the elastic matrix swells to equilibrium when immersed in a solvent…
We present an experimentally guided, multi-phase, multi-species polyelectrolyte gel model to make quantitative predictions on the electro-chemical properties of articular cartilage. The mixture theory consists of two different types of…
The hydrodynamics of viscoelastic materials (for example polymer melts and solutions) presents interesting and complex phenomena, for example instabilities and turbulent flow at very low Reynolds numbers due to normal stress effects and the…
Understanding and controlling the rheology of polymeric complex fluids that are pushed out-of-equilibrium is a fundamental problem in both industry and biology. For example, to package, repair, and replicate DNA, cells use enzymes to…
Synthetic turbulence models are a useful tool that provide realistic representations of turbulence, necessary to test theoretical results, to serve as background fields in some numerical simulations, and to test analysis tools. Models of 1D…