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A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a…
Continuum simulation is employed to study ion transport and fluid flow through a nanopore in a solid-state membrane under an applied potential drop. Results show the existence of concentration polarization layers on the surfaces of the…
Interfaces are a most common motif in complex systems. To understand how the presence of interfaces affect hydrophobic phenomena, we use molecular simulations and theory to study hydration of solutes at interfaces. The solutes range in size…
The $n$-body problem with a purely repulsive Coulomb interaction is considered. It is shown that for large times $t$ the distance between any two particles grows linearly in $t$. The trajectory of each particle is asymptotically a straight…
Water shapes and defines the properties of biological systems. Therefore, understanding the nature of the mutual interaction between water and biological systems is of primary importance for a proper assessment of biological activity and…
Particles embedded in a fluctuating interface experience forces and torques mediated by the deformations and by the thermal fluctuations of the medium. Considering a system of two cylinders bound to a fluid membrane we show that the…
The thermodynamic and kinetics of the one dimensional lattice gas with repulsive interaction is investigated using transfer matrix technique and Monte Carlo simulations. This simple model is shown to exhibit waterlike anomalies in density,…
Here I introduce the model in an attempt to describe the underlying reasons of attraction and repulsion forces between two physical bodies. Both electrical and gravitational forces are considered. Results are based on the technique…
In this paper we introduce a mesoscale continuum model for membranes made of two different types of amphiphilic lipids. The model extends work by Peletier and the second author [Arch. Ration. Mech. Anal. 193, 2009] for the one-phase case.…
We generalize the predictions for attractions between over-all neutral surfaces induced by charge fluctuations/correlations to non-uniform systems that include dielectric discontinuities, as is the case for mixed charged lipid membranes in…
Four results associated with the diffuse-interface model (DIM) for contact lines are reported in this paper. First, a boundary condition is derived, which states that the fluid near a solid wall must have a certain density $\rho_{0}$…
We examine the effective force between two nanometer scale solutes in water by Molecular Dynamics simulations. Macroscopic considerations predict a strong reduction of the hydrophobic attraction between solutes when the latter are charged.…
We present theory for ion and water transport through reverse osmosis membranes based on a Maxwell-Stefan framework combined with hydrodynamic theory for the reduced motion of particles in thin pores. We include all driving forces and…
Modern theories of the hydrophobic effect highlight its dependence on length scale, emphasizing in particular the importance of interfaces that emerge in the vicinity of sizable hydrophobes. We recently showed that a faithful treatment of…
Thermodynamics and dynamics of a classical two-dimensional system with dipole-like isotropic repulsive interactions are studied systematically using extensive molecular dynamics (MD) simulations supplemented by appropriate theoretical…
We have fabricated and characterized a novel superhydrophobic system, a mesh-like porous superhydrophobic membrane with solid area fraction $\Phi_s$, which can maintain intimate contact with outside air and water reservoirs simultaneously.…
The molecular structure of moving contact lines (MCLs) and the emergence of a corresponding macroscopic dissipation have made the MCL a paradigm of fluid dynamics. Through novel averaging techniques that remove capillary waves smearing we…
We consider an osmotic equilibrium between bulk solutions of polyelectrolyte bounded by semipermeable membranes and separated by a thin film of salt-free liquid. Although the membranes are neutral, the counter-ions of the polyelectrolyte…
We show using theory and experiments that a small particle moving along an elastic membrane through a viscous fluid is repelled from the membrane due to hydro-elastic forces. The viscous stress field produces an elastic disturbance leading…
One of the most promising applications in nanoscience is the design of new materials to improve water permeability and selectivity of nanoporous membranes. Understanding the molecular architecture behind these fascinating structures and how…