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...

Potential field methods are rapidly gaining popularity in obstacle avoidance applications for mobile robots. The general principles of potential field path planning are presented first. The electrostatic potential field (EPF) path planner is then combined with a twolayered fuzzy logic inference engine and implemented for mobile robot navigation in a 2-D dynamic environment. The first layer of t...

The effect of the magnetic field on the electrostatic potential of electrons inside and in close vicinity outside the quark surface of the star is studied. Depending on the value of the crust potential and the electron chemical potential at the base of the nuclear crust, we find that the strong surface magnetic field, 1.0 × 1014 ≤ H ≤ 3.0 × 1016 Gauss leads to a considerable reduction of the el...

The mechanism regulating the equilibrium electrostatic potential in the scrape-off layer (SOL) of magnetic confinement devices is elucidated. Based on a generalized Ohm’s law and the boundary conditions at the magnetic presheath entrance, an analytical expression for the equilibrium electrostatic potential is derived. Results imply that the relative importance of the plasma dynamics at the shea...

Magnetic reconnection in the collisionless regime is studied on the Versatile Toroidal Facility (VTF). The detailed evolution of the profiles of plasma density, current density, and electrostatic potential at the onset of driven reconnection is reconstructed experimentally. Despite a constant, externally imposed reconnection drive, we show that the reconnection does not proceed in a steady-stat...

We consider the boundary value problem of calculating the electrostatic potential for a homogeneous conductor containing finitely many small insulating inclusions. We give a new proof of the asymptotic expansion of the electrostatic potential in terms of the background potential, the location of the inhomogeneities and their geometry, as the size of the inhomogeneities tends to zero. Such asymp...