A mathematical model of the vertical dual-mass hydroimpulsive mechanism

In this paper, the model of a hydroimpulsive mechanism for boring machines was presented. Differential equations describing the processes occurring in the mechanism were derived

Quasi-Elastic Scattering, Random Fields and phonon-coupling effects in PbMg1/3Nb2/3O3

The low-energy part of the vibration spectrum in PbMg$_{1/3}$Nb$_{2/3}$O$_3$ (PMN) relaxor ferroelectric has been studied by neutron scattering above and below the Burns temperature, T$_d$. The transverse acoustic and the lowest transverse optic phonons are strongly coupled and we have obtained a model for this coupling. We observe that the lowest optic branch is always underdamped. A resolution-limited central peak and quasi-elastic scattering appear in the vicinity of the Burns temperature. It is shown that it is unlikely that the quasi-elastic scattering originates from the combined effects of coupling between TA and TO phonons with an increase of the damping of the TO phonon below T$_d$. The quasi-elastic scattering has a peak as a function of temperature close to the peak in the dielectric constant while the intensity of the central peak scattering increases strongly below this temperature. These results are discussed in terms of a random field model for relaxors

Stationary Kolmogorov Solutions of the Smoluchowski Aggregation Equation with a Source Term

In this paper we show how the method of Zakharov transformations may be used to analyze the stationary solutions of the Smoluchowski aggregation equation for arbitrary homogeneous kernel. The resulting massdistributions are of Kolmogorov type in the sense that they carry a constant flux of mass from small masses to large. We derive a ``locality criterion'', expressed in terms of the asymptotic properties of the kernel, that must be satisfied in order for the Kolmogorov spectrum to be an admissiblesolution. Whether a given kernel leads to a gelation transition or not can be determined by computing the mass capacity of the Kolmogorov spectrum. As an example, we compute the exact stationary state for the family of kernels,$K_\zeta(m_1,m_2)=(m_1m_2)^{\zeta/2}$ which includes both gelling and non-gelling cases, reproducing the known solution in the case $\zeta=0$. Surprisingly, the Kolmogorov constant is the same for all kernels in this family.Comment: This article is an expanded version of a talk given at IHP workshop "Dynamics, Growth and Singularities of Continuous Media", Paris July 2003. Updated 01/04/04. Revised version with additional discussion, references added, several typographical errors corrected. Revised version accepted for publication by Phys. Rev.

Absorption of Soluble Gases by Atmospheric Nanoaerosols

We investigate mass transfer during absorption of atmospheric trace soluble gases by a single droplet whose size is comparable to the molecular mean free path in air at normal conditions. It is assumed that the trace reactant diffuses to the droplet surface and then reacts with the substances inside the droplet according to the first order rate law. Our analysis applies a flux-matching theory of transport processes in gases and assumes constant thermophysical properties of the gases and liquids. We derive an integral equation of Volterra type for the transient molecular flux density to a liquid droplet and solve it numerically. Numerical calculations are performed for absorption of sulfur dioxide (SO2), dinitrogen trioxide (N2O3) and chlorine (Cl2) by liquid nanoaerosols accompanied by chemical dissociation reaction. It is shown that during gas absorption by nanoaerosols the kinetic effects play significant role, and neglecting kinetic effects leads to significant overestimation of the soluble gas flux into a droplet during all the period of gas absorption.Comment: 9 pages, 9 figure

Strong Collapse Turbulence in Quintic Nonlinear Schr\"odinger Equation

We consider the quintic one dimensional nonlinear Schr\"odinger equation with forcing and both linear and nonlinear dissipation. Quintic nonlinearity results in multiple collapse events randomly distributed in space and time forming forced turbulence. Without dissipation each of these collapses produces finite time singularity but dissipative terms prevents actual formation of singularity. In statistical steady state of the developed turbulence the spatial correlation function has a universal form with the correlation length determined by the modulational instability scale. The amplitude fluctuations at that scale are nearly-Gaussian while the large amplitude tail of probability density function (PDF) is strongly non-Gaussian with power-like behavior. The small amplitude nearly-Gaussian fluctuations seed formation of large collapse events. The universal spatio-temporal form of these events together with the PDF for their maximum amplitudes define the power-like tail of PDF for large amplitude fluctuations, i.e., the intermittency of strong turbulence.Comment: 14 pages, 17 figure

Concentration for One and Two Species One-Dimensional Reaction-Diffusion Systems

We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The coagulation (A + A -> A) or the annihilation (A + A -> 0) models can be mapped onto systems in which both processes are allowed. With the help of the coagulation-decoagulation model results for some death-decoagulation and annihilation-creation systems are given. We also find a reaction-diffusion system which is equivalent to the two species annihilation model (A + B ->0). Besides we present numerical results of Monte Carlo simulations. An accurate description of the effects of the reaction rates on the concentration in one-species diffusion-annihilation model is made. The asymptotic behavior of the concentration in the two species annihilation system (A + B -> 0) with symmetric initial conditions is studied.Comment: 20 pages latex, uuencoded figures at the en

Solution of classical stochastic one dimensional many-body systems

We propose a simple method that allows, in one dimension, to solve exactly a wide class of classical stochastic many-body systems far from equilibrium. For the sake of illustration and without loss of generality, we focus on a model that describes the asymmetric diffusion of hard core particles in the presence of an external source and instantaneous annihilation. Starting from a Master equation formulation of the problem we show that the density and multi-point correlation functions obey a closed set of integro-differential equations which in turn can be solved numerically and/or analyticallyComment: 2 figure

How much laser power can propagate through fusion plasma?

Propagation of intense laser beams is crucial for inertial confinement fusion, which requires precise beam control to achieve the compression and heating necessary to ignite the fusion reaction. The National Ignition Facility (NIF), where fusion will be attempted, is now under construction. Control of intense beam propagation may be ruined by laser beam self-focusing. We have identified the maximum laser beam power that can propagate through fusion plasma without significant self-focusing and have found excellent agreement with recent experimental data, and suggest a way to increase that maximum by appropriate choice of plasma composition with implication for NIF designs. Our theory also leads to the prediction of anti-correlation between beam spray and backscatter and suggests the indirect control of backscatter through manipulation of plasma ionization state or acoustic damping.Comment: 15 pages, 4 figures, submitted to Plasma Physics and Controlled Fusio

EQUIVALENCES BETWEEN STOCHASTIC SYSTEMS

Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and between stochastic and soluble {\em non-stochastic} models. The results agree with experiments on one-dimensional annihilation-coagulation processes.Comment: 15 pages, Latex. Some corrections made and an appendix adde

Dynamics of cubic-tetragonal phase transition in KNbO3_3 perovskite

The low-energy part of the vibration spectrum in KNbO$_3$ was studied by cold neutron inelastic scattering in the cubic phase. In addition to acoustic phonons, we observe strong diffuse scattering, which consists of two components. The first one is quasi-static and has a temperature-independent intensity. The second component appears as quasi-elastic scattering in the neutron spectrum indicating a dynamic origin. From analysis of the inelastic data we conclude that the quasi-elastic component and the acoustic phonon are mutually coupled. The susceptibility associated with the quasi-elastic component grows as the temperature approaches T$_C$