THERMODYNAMIC AND PARTICLE-DYNAMIC STUDIES ON SYNTHESIS OF SILICA NANOPARTICLES USING MICROWAVE-INDUCED PLASMA CVD

1. Introduction1.1 Silica nanoparticles and synthesis methods Silica (SiO2) nanoparticles are widely used in industry asan active filler for polymer reinforcement, a rheologicaladditive in fluids, a free flow agent in powders, and anagent for chemical mechanical polishing during IC (inte-grated circuit) fabrication (Sniegowski & de Boer, 2000).Silica powder is also used for producing silicon carbide(Koc & Cattamanchi, 1998) or opaque silica aerosols (Leeet al., 1995). Many methods can …     

On the Von Neumann Paradox of Weak Mach Reflection*

Recent experimental and numerical studies of weak Mach reflections are examined. It is shown that the fundamental reason for the von Neumann paradox is that his theory of Mach reflection is based on the assumption that the flow downstream of the reflected wave and the Mach shock near the wave triple point is uniform. The assumption is shown to be valid for strong Mach reflection which agrees with experiment, but invalid for weak Mach reflection which does not agree with experiment. It is also shown that viscous effects are dominant when the incident shock is within about 100 mean free path lengths of the corner, but not otherwise. The analytical theory of the entire subsonic region supports these conclusions.     

Modelling of dynamical crack propagation using time-domain boundary integral equations

We study dynamic antiplane cracks in the time domain by the boundary integral equation method (BIEM) based on the integral equation for displacement discontinuity (or crack opening displacement, COD) as a function of stress on the crack. This displacement discontinuity formulation presents the advantage, with respect to methods developed by Das and others in seismology, that it has to be solved only inside the crack. This BIEM is, however, difficult to implement numerically because of the hypersingularity of the kernel of the integral equation. Hence it is rewritten into a weakly singular form using a regularization technique proposed by Bonnet. The first step, following a method due to Sladek and Sladek, consists in converting the hypersingular integral equation for the displacement discontinuity into an integral equation for the displacement discontinuity and its tangential derivatives (dislocation density distribution); the latter involves a Cauchy type singular kernel. The second step is based on the observation that the hypersingularity is related to the static component of the kernel; the static singularity is then isolated and can be expressed in terms of weakly singular integrals using a result due to Bonnet. Although numerical applications discussed in this paper are all for the antiplane problem, the technique can be applied as well to in-plane crack dynamics.

The BIEM is implemented numerically using continuous linear space-time base functions to model the COD on the crack. In the present scheme the COD gradient interpolation is discontinuous at the element nodes while the integral equations are collocated at the element midpoints. This leads to an overdetermined discrete problem which is solved by standard least-squares methods. We use the dynamic BIEM to study a set of problems that appear in earthquake source dynamics, including the spontaneous dynamic crack propagation for a very simple rupture criterion. The numerical results compare favorably with the few exact solutions that are available. Then we demonstrate that difficulties experienced with finite difference simulations of spontaneous crack dynamics can be removed with the use of BIEM. The results are improved by the use of singular crack tip elements.     

Wave propagation with tunneling in a highly discontinuous layered medium

An impulsive plane wave traverses a stratified medium consisting of a large number N of homogeneous isotropic perfectly elastic layers. The directly transmitted wave is greatly reduced by the cumulative effect of scattering loss at each of the many interfaces. However, close to the arrival of the direct wave is a broad pulse, arising from multiple scattering; this pulse does not decay as rapidly as the direct wave and ultimately appears to diffuse about a moving center. The latter process, which is determined by the medium statistics, leads to time delays, effective anisotropy, and apparent attenuation.

The present work may be regarded as an extension of that described by Burridge, White and Papanicolaou (1988) and Burridge and Chang (1989) to allow for tunneling P waves for S-wave incidence beyond the critical angle.

When the reflection coefficients at the interfaces are scaled as 1/√N while N → ∞, and when time is measured in units of vertical travel time across an average layer, numerical solutions of the exact problem show that the shape of the broad transmitted pulse approaches the limiting form given as the solution of a certain integrodifferential equation in accordance with our asymptotic theory.     

Groups with the Weak Maximal Condition on Non-permutable Subgroups

Let G be a group with the weak maximal condition on non-permutable subgroups. We prove that if G is a generalized radical group then G is either quasihamiltonian or a soluble-by-finite minimax group.     

Schur operators and domination problem

In this paper we are concerned with developing generalizing concepts of Dunford–Pettis operators analogous to the generalization of compact operators by strictly singular operators. Also, we give some new results concerning the domination problem in the setting of positive operators between Banach lattices.     

Log-Convexity of Counting Processes Evaluated at a Random end of Observation Time with Applications to Queueing Models

We consider a counting processes with independent inter-arrival times evaluated at a random end of observation time T, independent of the process. For instance, this situation can arise in a queueing model when we evaluate the number of arrivals after a random period which can depend on the process of service times. Provided that T has log-convex density, we give conditions for the inter-arrival times in the counting process so that the observed number of arrivals inherits this property. For exponential inter-arrival times (pure-birth processes) we provide necessary and sufficient conditions. As an application, we give conditions such that the stationary number of customers waiting in a queue is a log-convex random variable. We also study bounds in the approximation of log-convex discrete random variables by a geometric distribution.     

Moment convergence of <Emphasis Type="Italic">Z</Emphasis>-estimators

The problem to establish the asymptotic distribution of statistical estimators as well as the moment convergence of such estimators has been recognized as an important issue in advanced theories of statistics. This problem has been deeply studied for M-estimators for a wide range of models by many authors. The purpose of this paper is to present an alternative and apparently simple theory to derive the moment convergence of Z-estimators. In the proposed approach the cases of parameters with different rate of convergence can be treated easily and smoothly and any large deviation type inequalities necessary for the same result for M-estimators do not appear in this approach. Applications to the model of i.i.d. observation, Cox’s regression model as well as some diffusion process are discussed.     

On Eigenvalues of the Transition Matrix of Some Count-Data Markov Chains

We analyze the eigenstructure of count-data Markov chains. Our main focus is on so-called CLAR(1) models, which are characterized by having a linear conditional mean, and also on the case of a finite range, where the second largest eigenvalue determines the speed of convergence of the forecasting distributions. We derive a lower bound for the second largest eigenvalue, which often (but not always) even equals this eigenvalue. This becomes clear by deriving the complete set of eigenvalues for several specific cases of CLAR(1) models.