Reaching the minimum ideal in a finite semigroup

We introduce the depth parameters of a finite semigroup, which measure how hard it is to produce an element in the minimum ideal when we consider generating sets satisfying some minimality conditions. We estimate such parameters for some families of finite semigroups, and we obtain an upper bound for wreath products and direct products of two finite (transformation) monoids. Keywords: semigroup, generating set, minimum ideal, A-depth of a semigroupComment: 29 page

A Local Condensation Analysis Representing Two-phase Annular Flow in Condenser/radiator Capillary Tubes

NASA's effort for the thermal environmental control of the Space Station Freedom is directed towards the design, analysis, and development of an Active Thermal Control System (ATCS). A two phase, flow through condenser/radiator concept was baselined, as a part of the ATCS, for the radiation of space station thermal load into space. The proposed condenser rejects heat through direct condensation of ATCS working fluid (ammonia) in the small diameter radiator tubes. Analysis of the condensation process and design of condenser tubes are based on the available two phase flow models for the prediction of flow regimes, heat transfer, and pressure drops. The prediction formulas use the existing empirical relationships of friction factor at gas-liquid interface. An attempt is made to study the stability of interfacial waves in two phase annular flow. The formulation is presented of a stability problem in cylindrical coordinates. The contribution of fluid viscosity, surface tension, and transverse radius of curvature to the interfacial surface is included. A solution is obtained for Kelvin-Helmholtz instability problem which can be used to determine the critical and most dangerous wavelengths for interfacial waves

Optical Modulation by Conducting Interfaces

We analyze the interaction of a propagating guided electromagnetic wave with a quantum well embedded in a dielectric slab waveguide. First, we design a quantum well based on InAlGaAs compounds with the transition energy of 0.8eV corresponding to a wavelength of 1.55um. By exploiting the envelope function approximation, we derive the eigenstates of electrons and holes and the transition dipole moments, through solution of the Luttinger Hamiltonian. Next, we calculate the electrical susceptibility of a three-level quantum system (as a model for the two-dimensional electron gas trapped in the waveguide), by using phenomenological optical Bloch equations. We show that the two-dimensional electron gas behaves as a conducting interface, whose conductivity can be modified by controlling the populations of electrons and holes the energy levels. Finally, we design a slab waveguide in which a guided wave with the wavelength of 1.55um experiences a strong coupling to the conducting interface. We calculate the propagation constant of the wave in the waveguide subject to the conducting interface, by exploiting the modified transfer matrix method, and establish it linear dependence on the interface conductivity. By presenting a method for controlling the populations of electrons and holes, we design a compact optical modulator with an overall length of around 60um