Poynting Vector Flow in a Circular Circuit

A circuit is considered in the shape of a ring, with a battery of negligible size and a wire of uniform resistance. A linear charge distribution along the wire maintains an electrostatic field and a steady current, which produces a constant magnetic field. Earlier studies of the Poynting vector and the rate of flow of energy considered only idealized geometries in which the Poynting vector was confined to the space within the circuit. But in more realistic cases the Poynting vector is nonzero outside as well as inside the circuit. An expression is obtained for the Poynting vector in terms of products of integrals, which are evaluated numerically to show the energy flow. Limiting expressions are obtained analytically. It is shown that the total power generated by the battery equals the energy flowing into the wire per unit time.Comment: 19 pages, 8 figure

Thin film deposition with time varying temperature

We study the effects of time-dependent substrate/film temperature in the deposition of a mesoscopically thick film using a statistical model that accounts for diffusion of adatoms without lateral neighbors whose coefficients depend on an activation energy and temperature. Dynamic scaling with fixed temperature is extended to predict conditions in which the temperature variation significantly affects surface roughness scaling. It agrees with computer simulation results for deposition of up to ${10}^4$ atomic layers and maximal temperature changes of $30 K$, near or below the room temperature. If the temperature decreases during the growth, the global roughness may have a rapid growth, with effective exponents larger than 1/2 due to the time-decreasing adatom mobility. The local roughness in small box size shows typical evidence of anomalous scaling, with anomaly exponents depending on the particular form of temperature decrease. If the temperature increases during the growth, a non-monotonic evolution of the global roughness may be observed, which is explained by the competition of kinetic roughening and the smoothing effect of increasing diffusion lengths. The extension of the theoretical approach to film deposition with other activation energy barriers shows that similar conditions on temperature variation may lead to the same morphological features. Equivalent results may also be observed by controlling the deposition flux.Comment: 18 pages, 8 figure

The Pauli equation with complex boundary conditions

We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. A special attention is paid to PT-symmetric boundary conditions with the physical choice of the time-reversal operator T.Comment: 16 pages, 4 figure