Gaussian Property of the Rings R(X) and R〈X〉

The content of a polynomial f over a commutative ring R is the ideal c(f) of R generated by the coefficients of f. A commutative ring R is said to be Gaussian if c(fg) = c(f)c(g) for every polynomials f and g in R[X]. A number of authors have formulated necessary and sufficient conditions for R(X) (respectively, R?X?) to be semihereditary, have weak global dimension at most one, be arithmetical, or be Prüfer. An open question raised by Glaz is to formulate necessary and sufficient conditions that R(X) (respectively, R?X?) have the Gaussian property. We give a necessary and sufficient condition for the rings R(X) and R?X? in terms of the ring R in case the square of the nilradical of R is zero.     

Hysteresis of two interacting magnetic pairs with inequivalent perpendicular anisotropy

We consider a model for magnetic memory that consists of strongly coupled dipolar or antiferromagnetic (AF) pairs with inequivalent perpendicular anisotropy _K1$K_1$ and _K2$K_2$. For appropriate parameter values, determined in this work, they have two inequivalent storage states with zero net magnetic moment. Both analytical and numerical calculations are performed, in some cases yielding different results because of relaxation effects (i.e., a dependence on the damping parameter α$\alpha$). Hysteresis loops for a wide variety of parameter values are obtained, both for the AF case and the dipole case. An Appendix gives analytic results for slightly non-collinear spins in an applied field, which were used to test the numerical results.     

Links between microscopic and macroscopic fluid mechanics

The microscopic and macroscopic versions of fluid mechanics differ qualitatively. Microscopic particles obey time-reversible ordinary differential equations. The resulting particle trajectories {q(t)} may be time-averaged or ensemble-averaged so as to generate field quantities corresponding to macroscopic variables. On the other hand, the macroscopic continuum fields described by fluid mechanics follow irreversible partial differential equations. Smooth particle methods bridge the gap separating these two views of fluids by solving the macroscopic field equations with particle dynamics that resemble molecular dynamics. Recently, nonlinear dynamics have provided some useful tools for understanding the relationship between the microscopic and macroscopic points of view. Chaos and fractals play key roles in this new understanding. Non-equilibrium phase-space averages look very different from their equilibrium counterparts. Away from equilibrium the smooth phase-space distributions are replaced by fractional-dimensional singular distributions that exhibit time irreversibility.     

Long-range many-body polyelectrolyte bridging interactions

We investigate polyelectrolyte bridging interactions mediated by charged, flexible, polyelectrolyte chains between fixed cylindrical macroions of opposite charge in a two-dimensional hexagonal crystalline array. We show that in the asymptotic regime of small macroion density, the polyelectrolyte-mediated attraction is long range, falling off approximately linearly with the macroion array density. We investigate the polyelectrolyte free energy as a function of the macroion density and derive several analytic limiting laws valid in different regimes of the parameter space.     

Universal thermal radiation drag on neutral objects

We compute the force on a small neutral polarizable object moving at velocity v--> relative to a photon gas equilibrated at a temperature T. We find a drag force linear in v-->. Its physical basis is related to that in recent formulations of the dissipative component of the Casimir force, i.e., the change in photon momentum in emission and absorption between the moving body and the stationary thermal bath. We estimate the strength of this universal drag force for different dielectric response functions and comment on its relevance in various contexts, especially to radiation-matter coupling in the cosmos.     

Multicarrier Transport: Batteries, Semiconductors, Mixed Ionic-Electronic Conductors, and Biology

Multicarrier systems, such as car batteries and semiconductors, have surprisingly complex transport properties. Even for steady-state transport, one can find counterexamples to standard assumptions about local electroneutrality, constancy in space of the electric field, linearity in space of the voltage, and the relationship between dissipation, voltage, and current. Moreover, unless recombination processes occur, boundaries impose conditions that can disturb the response far into the bulk to remove memory of the boundaries. Because the demands of the chemical reactions at the electrodes cannot be satisfied by diffusion alone, car batteries are electrically active even when they are neither charging nor discharging. We offer practical advice on battery care for bike-riders, say, who only occasionally use their cars. For semiconductors, recombination does occur, which in transport enables partial currents to adjust from their surface to their bulk values. For mixed ionic electronic conductors, bulk recombination may be essential to an understanding of blocking electrodes. The voltage associated with both current-producing and non-current-producing surface reactions provides a natural explanation for the bioelectric fields observed during root and other growth processes.     

Interfacial three-phonon processes and anomalous interfacial energy transport

Interfacial three-phonon processes require only a moderately strong matrix element $\text{(～ 10}{}^5\text{erg}\text{cm}{}^2\text{)}$ to explain the anomalous energy transport observed at high phonon frequencies across the interface between ordinary and “quantum” materials. This mechanism is qualitatively consitent with a wide variety of experiments, and has a large number of symmetry-allowed couplings with which to explain the details of particular experiments. Near “onset”, this mechanism contributes anomalous reflection and transmission varying as the sixth power of the incident phonon frequency.     

Boundary condition histograms for modulated phases

Boundary conditions strongly affect the results of numerical computations for finite size inhomogeneous or incommensurate structures. We present a method which allows to deal with this problem, both for ground state and for critical properties: it combines fluctuating boundary conditions and specific histogram techniques. Our approach concerns classical systems possessing a continuous symmetry as well as quantum systems. In particular, current-current correlation functions, which probe large scale coherence of the states, can be accurately evaluated. We illustrate our method on a frustrated two dimensional XY model. Received: 9 September 1997 / Revised: 17 October 1997 / Accepted: 3 November 1997