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Ionic size effects are significant in many biological systems. Mean-field descriptions of such effects can be efficient but also challenging. When ionic sizes are different, explicit formulas in such descriptions are not available for the dependence of the ionic concentrations on the electrostatic potential, that is, there is no explicit Boltzmann-type(More)
Central in the variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett.2006, 96, 087802 and J. Chem. Phys.2006, 124, 084905] of molecular solvation is a mean-field free-energy functional of all possible solute-solvent interfaces or dielectric boundaries. Such a functional can be minimized numerically by a level-set method(More)
A level-set method is developed for the numerical minimization of a class of Had-wiger valuations with a potential on a set of three-dimensional bodies. Such valuations are linear combinations of the volume, surface area, and surface integral of mean curvature. The potential increases rapidly as the body shrinks beyond a critical size. The combination of(More)
A model nanometer-sized hydrophobic receptor-ligand system in aqueous solution is studied by the recently developed level-set variational implicit solvent model (VISM). This approach is compared to all-atom computer simulations. The simulations reveal complex hydration effects within the (concave) receptor pocket, sensitive to the distance of the (convex)(More)
Reconfigurable SRAM-based FPGAs are highly susceptible to radiation induced single-event upsets (SEUs) in space applications. The bit flip in FPGAs configuration memory may alter user circuit permanently without proper bitstream reparation, which is a completely different phenomenon from upsets in traditional memory devices. It is important to find the(More)
We present a field space based level set method for computing multi-valued solutions to one-dimensional Euler-Poisson equations. The system of these equations has many applications, and in particular arises in semiclassical approximations of the Schrödinger-Poisson equation. The proposed approach involves an implicit Eulerian formulation in an augmented(More)
A novel Bloch band based level set method is proposed for computing the semiclassical limit of Schrödinger equations in periodic media. For the underlying equation, subject to a highly oscillatory initial data, a hybrid of the WKB approximation and homogenization leads to the Bloch eigenvalue problem and an associated Hamilton–Jacobi system for the phase in(More)
The weakly coupled WKB system captures high frequency wave dynamics in many applications. For such a system a level set method framework has been recently developed to compute multi-valued solutions to the Hamilton-Jacobi equation and evaluate position density accordingly. In this paper we propose two approaches for computing multi-valued quantities related(More)
We study a reduced Poisson-Nernst-Planck (PNP) system for a charged spherical solute immersed in a solvent with multiple ionic or molecular species that are electrostatically neutralized in the far field. Some of these species are assumed to be in equilibrium. The concentrations of such species are described by the Boltzmann distributions that are further(More)
Gas-particle and other dispersed-phase flows can be described by a kinetic equation containing terms for spatial transport, acceleration, and particle processes (such as evaporation or collisions). However, computing the dispersed velocity is a challenging task due to the large number of independent variables. A level set approach for computing dilute(More)