Counting the number of solutions in combustion and reactive flow problems

Summary Computational methods and comparison theory enable, when combined, an enhanced capability for counting the number of solutions in combustion equations. Very good lower bounds for the last turning point reveal a stable high temperature explosion branch for very small positive exothermicity.     

Dynamical symmetry analysis of ionization and harmonic generation of atoms in bichromatic laser pulses

Recently the effect of the relative phase ? in a high‐intensity (～10¹⁴ W/cm²) two‐color (bichromatic) CW laser with frequencies ω and 2ω on the high‐order harmonic generation (HHG) was studied within the framework of the non‐Hermitian quantum mechanics (NHQM) [Phys Rev A 2004, 69, 043404/1]. Here we emphasize the study of symmetries in bichromatic HHG spectra within the framework of the conventional Hermitian QM, and in particular by taking the duration of the laser pulse into consideration (an effect that has not been included in the non‐Hermitian studies due to the time asymmetry problem in NHQM). The phase dependence of HHG and intense‐field ionization probability in a 1D Xe atom with symmetric field‐free potential and symmetric initial wave function were studied numerically and analytically. From simulations based on a single‐particle response it can be seen that the HHG spectra is symmetric with respect to inversion in the relative phase between the two colors ? only if ionization is forbidden in the system and the laser pulse is an adiabatic one. The HHG spectra is symmetric with respect to a π‐shift in ? whenever the laser pulse is an adiabatic one, either for bound or open (ionized) systems. The ionization probability is symmetric both to inversion or π‐shift in ?; the component probabilities (right‐ and left‐ionization probabilities) have the same ?‐dependence, up to a shift of π. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Inverse semigroups on graphs

For each [directed] graph we construct an inverse semigroup. Our main application is a simple proof of the characterization of partially ordered sets ofJ-classes of finite semigroups, and some generalizations; our proof avoids using the inductive construction of the previous method by one of the authors [4]. For a connected graph in which each vertex has index at least two, our construction gives a congruence free inverse semigroup. In the final section we describe how a slight modification bf the construction yields the polycyclic monoids.     

Stationary Non-Newtonian Fluid Flows¶in Channel-like and Pipe-like Domains

This paper is concerned with stationary non-Newtonian fluid in an unbounded domain which geometrically is channel-like in two dimensions or axisymmetric pipe-like in three. The flow satisfies no-slip boundary conditions, and behaves as Poiseuille flow at infinity. Existence and uniqueness are proved under the assumption of a large kinematic viscosity. The results apply to a family of models including second-order, Maxwell and Oldroyd-B fluids. For second-order fluids, the existence and uniqueness results are extended to the case when the boundary has corner points.     

In situ sonochemical hydrolysis and deposition of composite layers of ionic liquid entrapped in colloidal silica network and their application as sensors for various gases

An efficient one-step process for forming uniform solid-like layers of ionic liquid (IL) entrapped in colloidal silica network on interdigitated electrodes (IDE) using ultrasonic deposition is described in this communication. The electrical response of such layers deposited on insulating substrates fitted with interdigitated electrodes was measured upon exposure to different gases (H₂, NO₂, CO, and CH₄) in air demonstrating reversible and sensitive response at 100 °C.     

A free boundary problem for a singular system of differential equations: An application to a model of tumor growth

In this paper we consider a free boundary problem for a nonlinear system of two ordinary differential equations, one of which is singular at some points, including the initial point . Because of the singularity at , the initial value problem has a one-parameter family of solutions. We prove that there exists a unique solution to the free boundary problem. The proof of existence employs two ``shooting' parameters. Analysis of the profiles of solutions of the initial value problem and tools such as comparison theorems and weak limits of solutions play an important role in the proof. The system considered here is motivated by a model in tumor growth, but the methods developed should be applicable to more general systems.

     

Thermo-osmosis of sorbable gases in porous media : Part II. Cascades

The theoretical basis of mixture separation by thermo-osmosis has been developed for two different experimental arrangements. In the first of these two vessels are connected only by a membrane across which a temperature gradient is maintained. Expressions were obtained for the separation factor of binary mixtures in terms of heats of transport, for pressure and composition changes across the membrane, and for determining the heat of transport of each component. In the second arrangement the vessels are connected via the membrane and also by a capillary of appropriate geometry, so that in the steady state there is a constant circulation of each component of the mixture. Expressions have again been derived for the steady state separation factor, and pressure and composition differences for binary mixtures.