In simulating charged systems, it is often useful to treat some ionic components of the system at the mean-field level and solve the Poisson-Boltzmann (PB) equation to get their respective density profiles. The numerically intensive task of solving the PB equation at each step of the simulation can be bypassed using variational methods that treat the electrostatic potential as a dynamic variabl...

Four methods for deriving partial atomic charges from the Ž quantum chemical electrostatic potential CHELP, CHELPG, Merz-Kollman, and . RESP have been compared and critically evaluated. It is shown the charges strongly depend on how and where the potential points are selected. Two alternative methods are suggested to avoid the arbitrariness in the point-selection schemes and van der Waals exclu...

The equilibrium measure of a compact plane set gives the steady state distribution of charges on the conductor. We show that certain moments of this equilibrium measure, when taken about the electrostatic centroid and depending only on the real coordinate, are extremal for an interval centered at the origin. This has consequences for means of zeros of polynomials, and for means of critical poin...

A suitable arrangement of biased conductors @1# leads to an electrostatic field of zero magnitude at a central location that grows to tens of kV/cm away from the center. Such a field has allowed polar molecules to be confined in far deeper potential wells than may be realized with magnetic traps @2,3#. The neutral particles we consider do not move in a potential proportional to the electrostati...

Abstract. The paper deals with the diffusion approximation of the Boltzmann equation for semiconductors in the presence of spatially oscillating electrostatic potential. When the oscillation period is of the same order of magnitude as the mean free path, the asymptotics leads to the Drift-Diffusion equation with a homogenized electrostatic potential and a diffusion matrix involving the small sc...

A new noninvasive method for determining the surface electrostatic potential and surface charge density of microscopic particles using second harmonic generation (SHG) is described. The surface electrostatic properties of 1.05 μm polystyrene sulfate spheres in aqueous solution and that of 0.22 μm oil droplets in aqueous emulsions are obtained. Comparisons of the surface potentials obtained from...

Let u be the equilibrium potential of a compact set K in R. An electrostatic skeleton of K is a positive measure μ such that the closed support S of μ has connected complement and no interior, and the Newtonian (or logarithmic, when n = 2) potential of μ is equal to u near infinity. We prove the existence of an electrostatic skeleton for every convex polytope. Our proof raises several interesti...

Photons are carriers of the electromagnetic force and propagate the electrostatic and magnetic vector potentials. While the electrostatic potential ( ) is agreed to be related to the work needed to move a unit charge in an electrostatic field, the meaning of the magnetic vector potential ( ) has been enigmatic. Here I show that the product of the time derivative of the magnetic vector potential...

The potential theory comes from mathematical physics, in particular, from electrostatic and gravitational problems and finds their applications in the probability theory, scattering theory, biological systems and many other branches of science. During the last century the classical potential theory and the non-linear potential theory has occupied an important place in mathematics. We present th...