Similarity, attraction and initial conditions in an example of nonlinear diffusion

Similarity solutions play an important role in many fields of science. The recent book of Barenblatt (1996) discusses many examples. Often, outstanding unresolved issues are whether a similarity solution is dynamically attractive, and if it is, to what particular solution does the system evolve. By recasting the dynamic problem in a form to which centre manifold theory may be applied, based upon a transformation by Wayne (1997), we may resolve these issues in many cases. For definiteness we illustrate the principles by discussing the application of centre manifold theory to a particular nonlinear diffusion problem arising in filtration. Theory constructs the similarity solution, confirms its relevance, and determines the correct solution for any compact initial condition. The techniques and results we discuss are applicable to a wide range of similarity problems

Analysis of GaAs and Si solar energy hybrid systems

Various silicon hybrid systems are modeled and compared with a gallium arsenide hybrid system. The hybrid systems modeled produce electric power and also thermal power which can be used for heating or air conditioning. Various performance indices are defined and used to compare the system performance: capital cost per electric power out; capital cost per total power out; capital cost per electric power plus mechanical power; annual cost per annual electric energy; and annual cost per annual electric energy plus annual mechanical work. These performance indices indicate that concentrator hybrid systems can be cost effective when compared with present day energy costs

MEXIT: Maximal un-coupling times for stochastic processes

Classical coupling constructions arrange for copies of the \emph{same} Markov process started at two \emph{different} initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two \emph{different} Markov (or other stochastic) processes to remain equal for as long as possible, when started in the \emph{same} state. We refer to this "un-coupling" or "maximal agreement" construction as \emph{MEXIT}, standing for "maximal exit". After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit \MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of \MEXIT for Brownian motions with two different constant drifts.Comment: 28 page

Fluctuation-induced interactions between dielectrics in general geometries

We study thermal Casimir and quantum non-retarded Lifshitz interactions between dielectrics in general geometries. We map the calculation of the classical partition function onto a determinant which we discretize and evaluate with the help of Cholesky factorization. The quantum partition function is treated by path integral quantization of a set of interacting dipoles and reduces to a product of determinants. We compare the approximations of pairwise additivity and proximity force with our numerical methods. We propose a ``factorization approximation'' which gives rather good numerical results in the geometries that we study

Low-speed flowfield characterization by infrared measurements of surface temperatures

An experimental program was aimed at identifying areas in low speed aerodynamic research where infrared imaging systems can make significant contributions. Implementing a new technique, a long electrically heated wire was placed across a laminar jet. By measuring the temperature distribution along the wire with the IR imaging camera, the flow behavior was identified. Furthermore, using Nusselt number correlations, the velocity distribution could be deduced. The same approach was used to survey wakes behind cylinders in a wind-tunnel. This method is suited to investigate flows with position dependent velocities, e.g., boundary layers, confined flows, jets, wakes, and shear layers. It was found that the IR imaging camera cannot accurately track high gradient temperature fields. A correlation procedure was devised to account for this limitation. Other wind-tunnel experiments included tracking the development of the laminar boundary layer over a warmed flat plate by measuring the chordwise temperature distribution. This technique was applied also to the flow downstream from a rearward facing step. Finally, the IR imaging system was used to study boundary layer behavior over an airfoil at angles of attack from zero up to separation. The results were confirmed with tufts observable both visually and with the IR imaging camera

Desorption From Interstellar Ices

The desorption of molecular species from ice mantles back into the gas phase in molecular clouds results from a variety of very poorly understood processes. We have investigated three mechanisms; desorption resulting from H_2 formation on grains, direct cosmic ray heating and cosmic ray induced photodesorption. Whilst qualitative differences exist between these processes (essentially deriving from the assumptions concerning the species-selectivity of the desorption and the assumed threshold adsorption energies, E_t) all three processes are found to be potentially very significant in dark cloud conditions. It is therefore important that all three mechanisms should be considered in studies of molecular clouds in which freeze-out and desorption are believed to be important. Employing a chemical model of a typical static molecular core and using likely estimates for the quantum yields of the three processes we find that desorption by H_2 formation probably dominates over the other two mechanisms. However, the physics of the desorption processes and the nature of the dust grains and ice mantles are very poorly constrained. We therefore conclude that the best approach is to set empirical constraints on the desorption, based on observed molecular depletions - rather than try to establish the desorption efficiencies from purely theoretical considerations. Applying this method to one such object (L1689B) yields upper limits to the desorption efficiencies that are consistent with our understanding of these mechanisms.Comment: 11 pages, 5 figures, accepted by MNRAS subject to minor revision which has been carried ou

Angular dependence of domain wall resistivity in artificial magnetic domain structures

We exploit the ability to precisely control the magnetic domain structure of perpendicularly magnetized Pt/Co/Pt trilayers to fabricate artificial domain wall arrays and study their transport properties. The scaling behaviour of this model system confirms the intrinsic domain wall origin of the magnetoresistance, and systematic studies using domains patterned at various angles to the current flow are excellently described by an angular-dependent resistivity tensor containing perpendicular and parallel domain wall resistivities. We find that the latter are fully consistent with Levy-Zhang theory, which allows us to estimate the ratio of minority to majority spin carrier resistivities, rho-down/rho-up~5.5, in good agreement with thin film band structure calculations.Comment: 14 pages, 3 figure