Diffusing particles with electrostatic repulsion

Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE. Received: 5 August 1996 / In revised form: 17 October 1996     

The effect of radiofrequency modulation of 57Fe hyperfine interaction by rotating magnetic field

The effect of ⁵⁷Fe hyperfine interaction radiofrequency (rf) modulation by external rotating magnetic field was studied in thin Permalloy foil by means of Mössbauer spectroscopy. The rf effect was investigated as a function of intensity for several rf field frequencies. The experiments show that the external rotating rf field causes considerable changes in the hyperfine pattern. The obtained spectra are in disagreement with those obtained by Perlow [Phys. Rev. 172 (1968) 319]. They also are inconsistent with magnetostriction hypothesis. Proceeding from the Mössbauer spectrum analysis one may conclude that the magnetization of investigated foil changes its direction in a complex manner. However, the undertaken experiments show that the essential number of Mössbauer nuclei experience the rotating magnetic field influence.     

Investigation of microbial—mineral interactions by Mössbauer spectroscopy

Mössbauer spectroscopy was used to investigate the reactions of microbes with iron minerals in aqueous solutions and as components of rocks in banded iron formations and granite. A microbial biofilm that formed on a wall of an excavated granite vault in a deep underground laboratory initiated this research. At the aerobic face of the biofilm, iron was found in a form of ferrihydrite; in the anaerobic face against the rock, iron was found as very small siderite particles. Laboratory incubations of the biofilm microbial consortium showed different mineral species could be formed. When the microbial consortium from the biofilm was incubated with magnetite grains, up to about 10% of the iron was altered in three weeks to hematite. The ability of the consortium to precipitate iron both as Fe²⁺ and Fe³⁺ in close proximity may have a bearing on the deposition of banded iron formations. These reactions could also be important in microbially induced corrosion.     

Parallel Algorithm for Unconstrained Optimization Based on Decomposition Techniques

We present a numerical implementation of the parallel gradient distribution (PGD) method for the solution of large-scale unconstrained optimization problems. The proposed parallel algorithm is characterized by a parallel phase which exploits the portions of the gradient of the objective function assigned to each processor; then, a coordination phase follows which, by a synchronous interaction scheme, optimizes over the partial results obtained by the parallel phase. The parallel and coordination phases are implemented using a quasi-Newton limited-memory BFGS approach. The computational experiments, carried out on a network of UNIX workstations by using the parallel software tool PVM, show that parallelization efficiency was problem dependent and ranged between 0.15 and 8.75. For the 150 problems solved by PGD on more than one processor, 85 cases had parallelization efficiency below 1, while 65 cases had a parallelization efficiency above 1.     

A Method for Establishing Optimality Conditions for a Nonsmooth Vector-Valued Minimax Problem

Using a method of uniform approximations, necessary and sufficient conditions for a nonsmooth constrained vector-valued minimax problem are established in terms of Mordukhovich subdifferentials.