On Estimates of the Boltzmann Collision Operator with Cut-off

We present new estimates of the Boltzmann collision operator in weighted Lebesgue and Bessel potential spaces. The main focus is put on hard potentials under the assumption that the angular part of the collision kernel fulfills some weighted integrability condition. In addition, the proofs for some previously known -estimates have been considerably shortened and carried out by elementary methods. For a class of metric spaces, the collision integral is seen to be a continuous operator into the same space. Furthermore, we give a new pointwise lower bound as well as asymptotic estimates for the loss term without requiring that the entropy is finite.     

Epitaxy of Binary Compounds and Alloys

The present work aims at constructing a theoretical framework within which to address the issues of morphological instabilities (one-dimensional step bunching and two-dimensional step meandering), alloying, and phase segregation in binary systems in the context of (physical or chemical) vapor deposition. The length scale of interest, although nanoscopic, is sufficiently large that the steps on a vicinal surface can be viewed as smooth curves and, correspondingly, the theory is a continuum one. In a departure from theories inaugurated by Burton, Cabrera, and Frank [The growth of crystals and the equilibrium structure of their surfaces. Phil. Trans. Roy. Soc. A 243 (1951) 299–358] the steps are endowed with a thermodynamic structure whose main ingredients are a step free-energy density and edge species chemical potentials. Moreover, crystal anisotropy, with its altering of the dynamics of steps and the associated morphological instabilities, is accounted for – in a manner consistent with the second law – both in the thermodynamic and kinetic properties of terraces and, more importantly, of steps. Additionally, in contrast with most of the literature on the subject (cf. [J. Krug, Introduction to step dynamics and step instabilities. In: A. Voigt (ed.) Multiscale Modeling in Epitaxial Growth. Birkhäusser, Berlin (2005)]), adsorption–desorption along the steps, bulk atomic diffusion, and chemical reactions (both on the terraces and along the step edges) are incorporated and coupled to the other mechanisms, e.g., terrace adatom diffusion and step attachment–detachment kinetics, whose interplay governs the evolution of steps on vicinal surfaces. Importantly, aided by the concept of configurational forces for which a separate balance law is postulated Configurational Forces as Basic Concepts of Continuum Physics. Springer, Berlin Heidelberg New York (2000)]), the proposed theory allows the steps to evolve away from local equilibrium thus contributing to a general treatment of the dynamics of steps. Finally, a specialization to the epitaxy of binary compounds and alloys is afforded, yielding a generalization of the classical Gibbs–Thomson relation in the former and novel evolution equations for an individual step in the latter.     

Delay equations with fluctuating delay related to the regenerative chatter

The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. In this paper, non-linear delay differential equations with periodic delays which model the machine tool chatter with continuously modulated spindle speed are studied. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state-dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. The reduced bifurcation equation is obtained by making use of Lyapunov-Schmidt Reduction method. By using the reduced bifurcation equations, the periodic solutions are determined to analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions near the new stability boundary.     

A semi-inverse shape optimization problem in linear anti-plane shear

The design of a semi-infinite fillet for efficient stress transmission is considered. The problem is treated within the context of anti-plane shear deformations of a homogeneous, isotropic, linearly elastic solid. Under a remote state of simple shear, it is desired to determine the shape of the traction-free lateral boundaries of a symmetric plane domain so that the shear stress distribution on the finite end is as uniform as possible. A semi-inverse approach for a particular class of semi-infinite profiles is used to examine this issue.     

First- and second-order sensitivities of beams with respect to cross-sectional cracks

This paper deals with a variational formulation for the sensitivity problem of beam systems in the context of deformable solids with cracks. Natural frequencies are defined as state variables involved in the energy functional of the system, while the cracks length and position are treated as system parameters. The hierarchical equation system is formed and solved for the first and second derivatives of the natural frequency functions with respect to the cracks length and position. An analytical procedure for calculations of the second-order sensitivities of natural frequencies is proposed for the non-symmetrical equation system operator. Numerical algorithms are worked out and implemented computationally. Analytical and numerical aspects of the problem are discussed in detail through a number of illustrative results.The support of this work by the State Committee for Scientific Research (KBN) under Grant No. 4-050-0148/17-98-00 is gratefully acknowledged.     

On a principle of virtual work for thermo-elastic bodies

A principle of virtual work is proposed for thermo-elastic bodies. From it are derived the equations of motion, the Cauchy stress principle and the Gibbs relations. The principle is also used to analyse the response of internally constrained bodies.     

On the macroscopic dynamics induced by a model wave-particle collision operator

The macroscopic dynamics of a kinetic equation involving a model wave-particle collision operator of plasma physics is investigated. The Chapman-Enskog asymptotics is first considered in the framework of a hydrodynamic scaling. The obtained macroscopic model still involves a kinetic variable, the particle energy in the rest frame of the fluid, but shares similarities with the compressible Navier-Stokes equation of gas dynamics. Then a diffusive scaling is examined under the hypothesis of small perturbations of a global equilibrium. In this case, the macroscopic model couples the usual incompressible Navier-Stokes with a diffusion equation for the energy distribution function of the particles, constrained by an extended version of the Boussinesq relation. In both cases, the effect of a Lorentz force term is developed, in the perspective of plasma physical modelling. Received June 16, 1997     

The Hydrotrope Action of Vitamin C

The effects of vitamin C are determined in the oil-in-water(0/ W) and water-in-oil(W/ 0) microemulsion regions of CTAB/ pentanol/ p-xylene/ H20 system. The addition of Vc joins the O/ W and W/ O areas in the phase diagram and expands the bicontinous region by reducing the lamellar liquid crystal one. The results show that the “ coupling action” of Vc is in fact a structural transition from lamellar crystal to isotropic phase with W/ O, O/ W and bicontinous structure.     

Effect of Emulsification Method on the Properties of Lecithin‐ and PGPR‐Stabilized Water‐in‐Oil‐Emulsions

Water‐in‐oil (w/o) emulsions were prepared with phosphatidylcholine‐depleted lecithin or polyglycerol polyricinoleate (PGPR) as emulsifying agents. The effect of different laboratory emulsification devices and the effect of sodium chloride on particle size distribution, coalescence stability, and water droplet sedimentation were investigated. The properties of lecithin‐stabilized w/o emulsions were found to depend more strongly on the emulsifying method than those prepared with PGPR. The rotor‐stator system was not suitable for preparing stable w/o emulsions with lecithin. Whereas the addition of salt was essential to achieve coalescence‐stable emulsions prepared with PGPR, the presence of NaCl favored the coalescence of water droplets and phase separation in emulsions containing lecithin.     

Prediction of CL-20 chemical degradation pathways,theoretical and experimental evidence for dependence on competing modes of reaction

Highest occupied and lowest unoccupied molecular orbital energies, formation energies, bond lengths and FTIR spectra all suggest competing CL-20 degradation mechanisms. This second of two studies investigates recalcitrant, toxic, aromatic CL-20 intermediates that absorb from 370 to 430?nm. Our earlier study (Struct. Chem., 15, 2004) revealed that these intermediates were formed at high OH^? concentrations via the chemically preferred pathway of breaking the C–C bond between the two cyclopentanes, thereby eliminating nitro groups, forming conjugated π bonds, and resulting in a pyrazine three-ring aromatic intermediate. In attempting to find and make dominant a more benign CL-20 transformation pathway, this current research validates hydroxylation results from both studies and examines CL-20 transformations via photo-induced free radical reactions. This article discusses CL-20 competing modes of degradation revealed through: computational calculation; UV/VIS and SF spectroscopy following alkaline hydrolysis; and photochemical irradiation to degrade CL-20 and its byproducts at their respective wavelengths of maximum absorption.