Large Deviations from a Stationary Measure for a Class of Dissipative PDEs with Random Kicks

We study a class of dissipative PDEs perturbed by a bounded random kick force. It is assumed that the random force is nondegenerate, so that the Markov process obtained by the restriction of solutions to integer times has a unique stationary measure. The main result of the paper is a large deviations principle for occupation measures of the Markov process in question. The proof is based on Kifer's large‐deviation criterion, a coupling argument for Markov processes, and an abstract result on large‐time asymptotic for generalized Markov semigroups.© 2015 Wiley Periodicals, Inc.     

Estimation of the surface energetic heterogeneity of fillers by inverse gas chromatography

The surface properties of the fillers are determining for obtaining high performance filled polymers. Yet, their determination is most difficult. This paper proposes to use inverse gas chromatography, either at infinite dilution or finite concentration conditions, to estimate surface energy and nanomorphological characteristics, but also surface heterogeneity of different clays, talcs of various origins and ground muscovites.     

13C and 1H NMR analysis of structural defects in PVC: Application to the production of defects at various polymerization stages

High resolution ¹H and ¹³C NMR data were obtained on PVC and PVC reduced with Bu₃SnH. The reduction is never complete and CH₂Cl groups preferentially remain. It causes almost complete formation of cyclopentane structures from both internal and chain end unsaturation. ¹H NMR gives total unsaturation as well as chain end unsaturation except if there are interferences with initiator residues; in that case, its combination with ¹³ C NMR of reduced PVC gives the chain end unsaturation. By the last method short branches and long ends are determined. Residual primary chlorine in all kinds of branches (methyl, ethyl, butyl, long ends) is taken into account. Long end contents are to be corrected (factor around 1.5), due to incomplete relaxation in standard analysis conditions. ¹H NMR of reduced PVC can be used to get the total non-reduced structures, both -CH₂Cl and -CHCl-. PVC was prepared by suspension or solution (trichlorobenzene) polymerization at 55° C, using dicetyl peroxydicarbonate as an initiator. The initiator residue content is higher in suspension PVC at very low conversion, and then levels off at a low value; in solution polymerization, it chiefly depends on the monomer/initiator ratio. At low conversion, more chain end and less short branches are present in suspension polymerization. Otherwise, only the butyl branch content shows a definite trend to increase with conversion. In solution polymerization, the number of defects is chiefly dependent on the initial monomer concentration; it is generally much higher than in suspension, except for the chloromethyl branches where both processes give about the same results.     

Exact maximal height distribution of fluctuating interfaces

We present an exact solution for the distribution P(h(m),L) of the maximal height h(m) (measured with respect to the average spatial height) in the steady state of a fluctuating Edwards-Wilkinson interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h(m),L)=L(-1/2)f(h(m)L(-1/2)) for all L>0, where the function f(x) is the Airy distribution function that describes the probability density of the area under a Brownian excursion over a unit interval. For the free boundary case, the same scaling holds, but the scaling function is different from that of the periodic case. Numerical simulations are in excellent agreement with our analytical results. Our results provide an exactly solvable case for the distribution of extremum of a set of strongly correlated random variables.     

Persistence of zero velocity fronts in reaction diffusion systems

Steady, nonpropagating, fronts in reaction diffusion systems usually exist only for special sets of control parameters. When varying one control parameter, the front velocity may become zero only at isolated values (where the Maxwell condition is satisfied, for potential systems). The experimental observation of fronts with a zero velocity over a finite interval of parameters, e.g., in catalytic experiments [Barelko et al., Chem. Eng. Sci., 33, 805 (1978)], therefore, seems paradoxical. We show that the velocity dependence on the control parameter may be such that velocity is very small over a finite interval, and much larger outside. This happens in a class of reaction diffusion systems with two components, with the extra assumptions that (i) the two diffusion coefficients are very different, and that (ii) the slowly diffusing variables has two stable states over a control parameter range. The ratio of the two velocity scales vanishes when the smallest diffusion coefficient goes to zero. A complete study of the effect is carried out in a model of catalytic reaction. (c) 2000 American Institute of Physics.     

Chaotic behavior of channeling particles

Channeling describes the collimated motion of energetic charged particles along the lattice plane or axis in a crystal. The energetic particles are steered through the channels formed by strings of atomic constituents in the lattice. In the case of planar channeling, the motion of a charged particle between the atomic planes can be periodic or quasiperiodic, such as a simple oscillatory motion in the transverse direction. In practice, however, the periodic motion of the channeling particles can be accompanied by an irregular, chaotic behavior. In this paper, the Moliere potential, which is considered as a good analytical approximation for the interaction of channeling particles with the rows of atoms in the lattice, is used to simulate the channeling behavior of positively charged particles in a tungsten (100) crystal plane. By appropriate selection of channeling parameters, such as the projectile energy E(0) and incident angle psi(0), the transition of channeling particles from regular to chaotic motion is demonstrated. It is argued that the fine structures that appear in the angular scan channeling experiments are due to the particles' chaotic motion.     

Transfer processes in fractal media

An irreversible process in fractal media involves coupling relation between the space and the time. The present note displays how the fractional derivation has to be introduced to describe this effect. As a result the law of the chemical diffusion to a fractal is given.     

Long Time Behavior of the Cahn-Hilliard Equation with Irregular Potentials and Dynamic Boundary Conditions

The Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions is considered.The existence of the global attractor is proved and the long time behavior of the trajectories,namely,the convergence to steady states,is studied.     

Measure space automorphisms,the normalizers of their full groups,and approximate finiteness

We deal with the normalizer $\text{N}$[T] of the full group [T] of a nonsingular transformation T of a Lebesgue measure space in the group of all nonsingular transformations. We solve the conjugacy problem in $\text{N}$[T]/[T] for a measure preserving and ergodic T. Our results show that a locally finite extension of a solvable group is approximately finite.