A White Noise Approach to Stochastic Neumann Boundary-Value Problems

We illustrate the use of white noise analysis in the solution of stochastic partial differential equations by explicitly solving the stochastic Neumann boundary-value problem LU(x)–c(x)U(x)=0, xDR ^d ,(x)U(x)=–W(x), xD, where L is a uniformly elliptic linear partial differential operator and W(x), xR ^d , is d-parameter white noise.     

Large transverse momentum phenomena in a hadronic bremsstrahlung model

We present a bremsstrahlung model which at large transverse momenta p_T leads to an inverse power law for the pion distribution in pp → π^±0 + X. The model predicts particle yields that increase with energy at fixed p_T (breaking Feynman scaling in a definite way) and provides an understanding of the excess of π⁺'s over π^?'s, and of the increase with p_T of the associated multiplicity in the direction opposite to the observed pion; it also accounts for proton to π⁺ ratios of order 1, but in a parameter-dependent way. The recently observed increase of the mean charged multiplicity in pp → p + MM with the transverse momentum of the projectile is also accounted for.     

Near-stoichiometric sodium beta alumina

The preparation of near-stoichiometric sodium beta alumina is described. The activation energy for sodium-ion conduction, 0.62 eV, is significantly larger than for the highly non-stoichiometric starting material.     

First-hit analysis of algorithms for computing quadratic irregularity

The author has previously extended the theory of regular and irregular primes to the setting of arbitrary totally real number fields. It has been conjectured that the Bernoulli numbers, or alternatively the values of the Riemann zeta function at odd negative integers, are uniformly distributed modulo for every . This is the basis of a well-known heuristic, given by Siegel, estimating the frequency of irregular primes. So far, analyses have shown that if is a real quadratic field, then the values of the zeta function at negative odd integers are also distributed as expected modulo for any . We use this heuristic to predict the computational time required to find quadratic analogues of irregular primes with a given order of magnitude. We also discuss alternative ways of collecting large amounts of data to test the heuristic.

     

Comparison of algorithms to calculate quadratic irregularity of prime numbers

In previous work, the author has extended the concept of regular and irregular primes to the setting of arbitrary totally real number fields , using the values of the zeta function at negative integers as our ``higher Bernoulli numbers'. In the case where is a real quadratic field, Siegel presented two formulas for calculating these zeta-values: one using entirely elementary methods and one which is derived from the theory of modular forms. (The author would like to thank Henri Cohen for suggesting an analysis of the second formula.) We briefly discuss several algorithms based on these formulas and compare the running time involved in using them to determine the index of -irregularity (more generally, ``quadratic irregularity') of a prime number.

     

Josephson plasma resonance and phonon anomalies in trilayer Bi2Sr2Ca2Cu3O10

The far-infrared (FIR) c axis conductivity of a Bi2223 crystal has been measured by ellipsometry. Below T(c) a strong absorption band develops near 500 cm(-1), corresponding to a transverse Josephson plasmon. The related increase in FIR spectral weight leads to a giant violation of the Ferrell-Glover-Tinkham sum rule. The gain in c axis kinetic energy accounts for a sizable part of the condensation energy. We also observe phonon anomalies which suggest that the Josephson currents lead to a drastic variation of the local electric field within the block of closely spaced CuO2 planes.     

A class of exact solutions for finite plane strain deformations of a particular elastic material

Summary In this paper we consider plane deformations of an incompressible elastic material and we show that by a suitable choice of strain energy function we can find the class of deformations with constant local rotation angle. Although the form for the strain energy function is chosen in the first place for mathematical convenience it does correspond to physically reasonable behaviour and such a theory may be regarded as a first order theory. The class of solutions obtained are expressed in a parametric form involving an arbitrary function, simple choices of which correspond to the well known exact solutions of finite elasticity.     

Pressure-dependent ion current rectification in conical-shaped glass nanopores

Ion current rectification that occurs in conical-shaped glass nanopores in low ionic strength solutions is shown to be dependent on the rate of pressure-driven electrolyte flow through the nanopore, decreasing with increasing flow rate. The dependence of the i-V response on pressure is due to the disruption of cation and anion distributions at equilibrium within the nanopore. Because the flow rate is proportional to the third power of the nanopore orifice radius, the pressure-driven flow can eliminate rectification in nanopores with radii of ～200 nm but has a negligible influence on rectification in a smaller nanopore with a radius of ～30 nm. The experimental results are in qualitative agreement with predictions based on finite-element simulations used to solve simultaneously the Nernst-Planck, Poisson, and Navier-Stokes equations for ion fluxes in a moving electrolyte within a conical nanopore.