Linear Quadratic Gaussian Homing for Markov Processes with Regime Switching and Applications to Controlled Population Growth/Decay

Methodology and Computing in Applied Probability - The problem of optimally controlling one-dimensional diffusion processes until they enter a given stopping set is extended to include Markov...     

Critical branching in a highly fluctuating random medium

Summary A model of one-dimensional critical branching (superprocess) is constructed in a random medium fluctuating both in time and space. The medium describes a moving system of point catalysts, and branching occurs only in the presence of these catalysts. Although the medium has an infinite overall density, the clumping features of the branching model can be exhibited by rescaling time, space, and mass by an exactly calculated scaling power which is stronger than in the constant medium case. The main technique used is the asymptotic analysis of a generalized diffusion-reaction equation in the space-time random medium, which (given the medium) prescribes the evolution of the Laplace transition functional of the Markov branching process.     

Intrinsic echolocation capability of Hector's dolphin, Cephalorhynchus hectori.

A sonar system's echolocation capabilities can be inferred from the ambiguity distribution (defined here in terms of the conventional signal response function) of each of its transmitted signals. Several records of sounds emitted by Hector's dolphin are analyzed. The computed ambiguity distributions indicate that the sonar clicks of Hector's dolphins should be capable of resolving the ranges of targets as close together as 2 cm apart, but that target velocities cannot be resolved to any useful degree from a single echo.     

A thermoanalytical study of the formation and activation of novel copper-carbon catalysts

Simultaneous DSC-TG and DTA-TG were used to investigate the calatytic effect of the metal on the thermal decomposition of a cellulose matrix containing small copper particles. The techniques were also used to demonstrate the effect of the metal particles on the subsequent activation of the carbon matrix, a process which develops the pore structure necessary to expose the metal particles to the gas phase. Temperature programmed desorption was used to study the initial mass loss found on activation. To quantify the catalytic effect of the copper particles on the activation process an estimate was made of the activation energy of the catalysed and uncatalysed reactions. The work gives valuable information on the processes involved in the preparation of a new range of metal-carbon catalysts. In celebration of the 60^th birthday of Dr. Andrew K. Galwey     

Theoretical and experimental approaches to kinetics at the collapse transition of a homopolymer

Summary We discuss some recent theoretical studies of the kinetics of the collapse transition in homopolymers. An isolated polymer is modelled using computer simulation, and a time-dependent mean-field theory. The mean-field theory is analysed analytically for early stages, and for short polymers the equations are studied numerically. The results of simulation and theory are compared yielding, we argue, a consistent physical picture. Quantitative comparisons are not yet given, but seem relatively promising. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4– 1994.     

Surface enhanced Raman scattering from mildly roughened surfaces: variation of signal with metal grain size

The intensity of surface enhanced Raman scattering from benzoic acid derivatives on mildly roughened, thermally evaporated Ag films shows a remarkably strong dependence on metal grain size. Large grained (slowly deposited) films give a superior response, by up to a factor of 10, to small grained (quickly deposited) films, with films of intermediate grain size yielding intermediate results. The optical field amplification underlying the enhancement mechanism is due to the excitation of surface plasmon polaritons (SPPs). Since surface roughness characteristics, as determined by STM, remain relatively constant as a function of deposition rate, it is argued that the contrast in Raman scattering is due to differences in elastic grain boundary scattering of SPPs (leading to different degrees of internal SPP damping), rather than differences in the interaction of SPPs with surface inhomogeneities.     

Dynamics of muons in the ferroelectric material KDP

Muon spin relaxation in zero field and longitudinal field was measured in single crystal samples of KH₂PO₄ (KDP) and KD₂PO₄ (DKDP) over a temperature range of 5 K to 300 K. At low temperatures, diamagnetic muons and muon substituted radicals with nuclear hyperfine coupling can be observed. For both KDP and DKDP, a minor change was observed in the dynamics of the muon below 140 K. Above 140 K, the mobility of the muon appears to increase and the diffusion rate becomes faster with increasing temperature. Only a small increase in the relaxation rate is observed in KDP due to the presence of theH ⁺, suggesting that the relaxation effects probably originate from the³¹P.     

Generalized solutions of a class of nuclear-space-valued stochastic evolution equations

Generalized solutions are defined for stochastic evolution equations of the formdY _t =A ^* Y _t dt + dZ _t on the nuclear triplel(R ^d ) L²(R ^d ) l(R ^d ), whereA does not mapl(R ^d ) into itself. One case which is treated in detail involvesA = –(–) ^/2 ,0 < < 2. This example arises as the Langevin equation for the fluctuation limit of a system of particles migrating according to a symmetric stable process and undergoing critical branching in a random medium.The research of D. A. Dawson was supported by the Natural Sciences and Engineering Research Council of Canada. L. G. Gorostiza's research was supported in part by CONACyT Grants PCEXCNA-040319 and 140102 G203-006, Mexico.