Nonlinear effects of electrolyte diodes and transistors in a polymer gel medium

The polarization curve of an acid-base interface in a hydrogel medium has a diode characteristic. Two of each such electrolyte diodes can be combined to give an electrolyte transistor. When a salt is added to the alkaline or to the acidic part of a reverse biased electrolyte diode, the current response is highly nonlinear. If the salt is added to the acidic side, even bistability can be observed. This bistability can generate complex oscillations in a base-acid-base electrolyte transistor. These nonlinear effects are studied experimentally and theoretically. While the nonlinear salt effect can be explained with the Nernst-Planck equations, to understand the bistable behavior further investigations are necessary. (c) 1999 American Institute of Physics.     

Atomistic Simulations of Integranular Fracture in Symmetric-Tilt Grain Boundaries

Fracture experiments on symmetric-tilt grain boundaries in Cu are interpreted using the Peierls-Nabarro continuum model of dislocation nucleation as a starting point. Good agreement is found only when the continuum model is modified according to the results of atomistic simulations. The same experiments are also reproduced by direct Molecular Dynamics simulations of fracture propagation and dislocation emission from a microcrack placed in the interface plane of the symmetric-tilt (221)(221) grain boundary in fcc Cu. Direction-dependent fracture response is observed, namely the microcrack advancing by brittle fracture along the [11 ] direction and being blunted by dislocation emission along the opposite [ 4] direction. Moreover, the simulations allow us to establish important differences with respect to the continuum-model predictions due to the shielding of the stress field at the crack-tip and to the presence of the residual stress at the interface.     

On the measure of the spectrum for the almost Mathieu operator

We obtain partial results on the conjecture that for the almost Mathieu operator at irrational frequency, , the measure of the spectrum,S(, , )=|4–2|. For ||2 we show that if _n is rational and irrational, then .Dedicated to Res Jost and Arthur WightmanResearch partially supported by U.S. NSF grant number DMS-8801918 and by BSF under grant number 88-00325     

Hamilton's equations for constrained dynamical systems

We derive expressions for the conjugate momenta and the Hamiltonian for classical dynamical systems subject to holonomic constraints. We give an algorithm for correcting deviations of the constraints arising in numerical solution of the equations of motion. We obtain an explicit expression for the momentum integral for constrained systems.     

SO(n,1) Wigner rotation as an SL(2,R) problem

We show that the composition of not only two SO(3,1) boosts, but also that of two SO(n,1) boosts for anyn 2, is basically an SO(2,1) problem and hence can be analysed completely using SL(2,R) matrices. By computing the expression for the Thomas/Wigner angle directly using SL(2,R) matrices we show that this approach results in considerable economy of algebra.     

Majorana edge states in interacting one-dimensional systems

We show that one-dimensional electron systems in the proximity of a superconductor that support Majorana edge states are extremely susceptible to electron-electron interactions. Strong interactions generically destroy the induced superconducting gap that stabilizes the Majorana edge states. For weak interactions, the renormalization of the gap is nonuniversal and allows for a regime in which the Majorana edge states persist. We present strategies of how this regime can be reached.     

Persistence and breakdown of Airy beams driven by an initial nonlinearity

We study the behavior of Airy beams propagating from a nonlinear medium to a linear medium. We show that an Airy beam initially driven by a self-defocusing nonlinearity experiences anomalous diffraction and can maintain its shape in subsequent propagation, but its intensity pattern and acceleration cannot persist when driven by a self-focusing nonlinearity. The unusual behavior of Airy beams is examined from their energy flow as well as the Brillouin zone spectrum of self-induced chirped photonic lattices.