Bifurcation in a reaction diffusion system

The bifurcation and nonlinear stability properties of the Meinhardt-Gierer model for biochemical pattern formation are studied. Analyses are carried out in parameter ranges where the linearized system about a trivial solution loses stability through one to three eigenfunctions, yielding both time independent and periodic final states. Solution branches are obtained that exhibit secondary bifurcation and imperfection sensitivity and that appear, disappear, or detach themselves from other branches.

TRANSIENT SCANNING ELECTRON BEAM ANNEALING METHODS USED TO STUDY DIFFUSION AND DEFECTS IN IMPLANTED SILICON.

Rapid thermal annealing of arsenic and boron difluoride implants, such as those used for source/drain regions in CMOS, has been carried out using a scanning electron beam annealer, as part of a study of transient diffusion effects. Three types of e-beam anneal have been performed, with peak temperatures in the range 900 -1200 degree C; the normal isothermal e-beam anneals, together with sub-second fast anneals and 'dual-pulse' anneals, in which the sample undergoes an isothermal pre-anneal followed by rapid heating to the required anneal temperature is less than 0. 5s. The diffusion occuring during these anneal cycles has been modelled using SPS-1D, an implant and diffusion modelling program developed by one of the authors. This has been modified to incorporate simulated temperature vs. time cycles for the anneals. Results are presented applying the usual equilibrium clustering model, a transient point-defect enhancement to the diffusivity proposed recently by Fair and a new dynamic clustering model for arsenic. Good agreement with SIMS measurements is obtained using the dynamic clustering model, without recourse to a transient defect model.

Creation and suppression of point defects through a kick-out substitution process of Fe in InP

Indium antisite defect In-P-related photoluminescence has been observed in Fe-diffused semi-insulating (SI) InP. Compared to annealed undoped or Fe-predoped SI InP, there are fewer defects in SI InP obtained by long-duration, high-temperature Fe diffusion. The suppression of the formation of point defects in Fe-diffused SI InP can be explained in terms of the complete occupation by Fe at indium vacancy. The In-P defect is enhanced by the indium interstitial that is caused by the kick out of In and the substitution at the indium site of Fe in the diffusion process. Through these Fe-diffusion results, the nature of the defects in annealed undoped SI InP is better understood. (C) 2002 American Institute of Physics.

High power red-light GaInP/AlGaInP laser diodes with nonabsorbing windows based on Zn diffusion-induced quantum well intermixing

The layer structure of GaInP/AlGaInP quantum well laser diodes (LDs) was grown on GaAs substrate using low-pressure metalorganic chemical vapor deposition (LP-MOCVD) technique. In order to improve the catastrophic optical damage (COD) level of devices, a nonabsorbing window (NAW), which was based on Zn diffusion-induced quantum well intermixing, was fabricated near the both ends of the cavities. Zn diffusions were respectively carried out at 480, 500, 520, 540, and 580 Celsius degree for 20 minutes. The largest energy blue shift of 189.1 meV was observed in the window regions at 580 Celsius degree. When the blue shift was 24.7 meV at 480 Celsius degree, the COD power for the window LD was 86.7% higher than the conventional LD.

Neutron and proton diffusion in fusion reactions for the synthesis of superheavy nuclei

The restriction of the one dimensional (1D) master equation (ME) with the mass number of the projectile-like fragment as a variable is studied, and a two-dimensional (2D) master equation with the neutron and proton numbers as independent variables is set up, and solved numerically. Our study showed that the 2D ME can describe the fusion process well in all projectile-target combinations. Therefore the possible channels to synthesize super-heavy nuclei can be studied correctly in wider possibilities. The available condition for employing 1D ME is pointed out.

Characterization of structure and diffusion behaviour of Ca-alginate beads prepared with external or internal calcium sources

Ca-alginate beads were prepared with either external or internal calcium sources. The structures of both beads were investigated with the aid of scanning electron microscopy (SEM) and confocal microscopy. It was shown that the beads with internal calcium source had a looser structure and bigger pore size than those with external calcium source. The attempts to interpret the difference were carried out by determining the Ca content within the beads at various times, which indicated that it was the different gelation mechanisms that caused the difference of structures of both beads. Furthermore, it was also found that the diffusion rate of haemoglobin (Hb) within the beads with an internal calcium source was faster than that of the beads with an external one, which was consistent with the observation of their structures.

CHRONOAMPEROMETRIC STUDIES ON MIGRATION AND DIFFUSION OF COUNTERION IN POLY(3-METHYLTHIOPHENE)

Small amplitude potential step experiments were carried out to study the counterion transfer process in oxidized poly(3-methylthiophene) (PMT) film. The results demonstrate that anion transfer process in PMT film is migration rather than diffusion. A porous metal electrode model-single hole model, which takes into account both the ionic resistance of the film and the uncompensated solution resistance, was found suitable to describe the potential step experiments. According to this model, the ionic resistivity of oxidized PMT film was calculated to be 5.0 x 10(4) OMEGA.cm, and, in turn, the diffusion coefficent of ClO4- ion in PMT film 3.7 x 10(-9) cm2/s.

Turbulent diffusion and mixing in interstellar dark clouds with adsorption onto grains

This paper reports the results of models of dark cloud chemistry incorporating a depth dependent density distribution with diffusive mixing and adsorption onto grains. The model is based on the approach taken by Xie et al. (1995), with the addition of grain accretion effects. Without diffusion, the central regions of the cloud freeze out in less than 10(7) years. Freeze-out time is dependent on density, so the diffuse outer region of the cloud remains abundant in gas for about an order of magnitude longer. We find that fairly small amounts of diffusive mixing can delay freeze-out at the centre of the model cloud for a time up to an order of magnitude greater than without diffusion, due to material diffusing inward from the edges of the cloud. The gas-phase lifetime of the cloud core can thus be increased by up to an order of magnitude or more by this process. We have run three different grain models with various diffusion coefficients to investigate the effects of changing the sticking parameters.

Dissolved Argon Changes the Rate of Diffusion in Room Temperature Ionic Liquids: Effect of the Presence and Absence of Argon and Nitrogen on the Voltammetry of Ferrocene

This work explores the effects of argon and nitrogen, two electrochemically and chemically inert gases frequently used in sample preparation of room temperature ionic liquid (RTIL) solutions, on the eelectrochemical characterization of ferrocene (Fc) dissolved in the RTIL 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([C(2)mim][NTf2]). Remarkably, chronoamperometrically determined diffusion coefficients of Fc in [C(2)mim][NTf2] are found to increase from 4.8 (+/- 0.2) x 10(-11) m(2) s(-1) under vacuum conditions to 6.6 (+/- 0.5) x 10(-11) m(2) s(-1) in an atmosphere of 1 atm Ar. In contrast, exposing a vacuum-purified sample to an atmosphere of 1 atm N-2 resulted in no significant change in the measured diffusion coefficient of Fc. The effect of dissolved argon on diffusion transport is unexpected and has implications in electrochemistry and elsewhere. Fc was found to volatilize under vacuum conditions. We propose, however, that evacuation of the cell by vacuum prior to electrochemical measurements being carried out is the only way to ensure that no contamination of the sample occurs, and use of an in situ method of determining the diffusion coefficient and concentration of Fc dispells,any ambiguity associated with Fc depletion by vacuum.

How to measure the phase diffusion dynamics in the micromaser

We propose a realistic scheme for measuring the micromaser linewidth by monitoring the phase diffusion dynamics of the cavity field. Our strategy consists of exciting an initial coherent state with the same photon number distribution as the micromaser steady-state field, singling out a purely diffusive process in the system dynamics. After the injection of a counterfield, measurements of the population statistics of a probe atom allow us to derive the micromaser linewidth in all ranges of the relevant parameters, establishing experimentally the distinctive features of the micromaser spectrum due to the discreteness of the electromagnetic field.

The characteristic time of glucose diffusion measured for muscle tissue at optical clearing

The study of agent diffusion in biological tissues is very important to understand and characterize the optical clearing effects and mechanisms involved: tissue dehydration and refractive index matching. From measurements made to study the optical clearing, it is obvious that light scattering is reduced and that the optical properties of the tissue are controlled in the process. On the other hand, optical measurements do not allow direct determination of the diffusion properties of the agent in the tissue and some calculations are necessary to estimate those properties. This fact is imposed by the occurrence of two fluxes at optical clearing: water typically directed out of and agent directed into the tissue. When the water content in the immersion solution is approximately the same as the free water content of the tissue, a balance is established for water and the agent flux dominates. To prove this concept experimentally, we have measured the collimated transmittance of skeletal muscle samples under treatment with aqueous solutions containing different concentrations of glucose. After estimating the mean diffusion time values for each of the treatments we have represented those values as a function of glucose concentration in solution. Such a representation presents a maximum diffusion time for a water content in solution equal to the tissue free water content. Such a maximum represents the real diffusion time of glucose in the muscle and with this value we could calculate the corresponding diffusion coefficient.

Application of laser beam deflection technique to study the diffusion process in electrolyte solutions

A simple method based on laser beam deflection to study the variation of diffusion coefficient with concentration in a solution is presented. When a properly fanned out laser beam is passed through a rectangular cell filled with solution having concentration gradient, the emergent beam traces out a curved pattern on a screen. By taking measurements on the pattern at different concentrations, the variation of diffusion coefficient with concentration can be determined.

Studies on Heat Diffusion in Selected Conducting Polymers using Probe Beam Deflection and Photoacoustic Techniques

In the present study, radio frequency plasma polymerization technique is used to prepare thin films of polyaniline, polypyrrole, poly N-methyl pyrrole and polythiophene. The thermal characterization of these films is carried out using transverse probe beam deflection method. Electrical conductivity and band gaps are also determined. The effect of iodine doping on electrical conductivity and the rate of heat diffusion is explored.Bulk samples of poyaniline and polypyrrole in powder form are synthesized by chemical route. Open photoacoustic cell configuration is employed for the thermal characterization of these samples. The effect of acid doping on heat diffusion in these bulk samples of polyaniline is also investigated. The variation of electrical conductivity of doped polyaniline and polypyrrole with temperature is also studied for drawing conclusion on the nature of conduction in these samples. In order to improve the processability of polyaniline and polypyrrole, these polymers are incorporated into a host matrix of poly vinyl chloride. Measurements of thermal diffusivity and electrical conductivity of these samples are carried out to investigate the variation of these quantities as a function of the content of polyvinyl chloride.

Analytical Studies on Diffusion and lntermittency in Chaotic Maps

The study of simple chaotic maps for non-equilibrium processes in statistical physics has been one of the central themes in the theory of chaotic dynamical systems. Recently, many works have been carried out on deterministic diffusion in spatially extended one-dimensional maps This can be related to real physical systems such as Josephson junctions in the presence of microwave radiation and parametrically driven oscillators. Transport due to chaos is an important problem in Hamiltonian dynamics also. A recent approach is to evaluate the exact diffusion coefficient in terms of the periodic orbits of the system in the form of cycle expansions. But the fact is that the chaotic motion in such spatially extended maps has two complementary aspects- - diffusion and interrnittency. These are related to the time evolution of the probability density function which is approximately Gaussian by central limit theorem. It is noticed that the characteristic function method introduced by Fujisaka and his co-workers is a very powerful tool for analysing both these aspects of chaotic motion. The theory based on characteristic function actually provides a thermodynamic formalism for chaotic systems It can be applied to other types of chaos-induced diffusion also, such as the one arising in statistics of trajectory separation. It was noted that there is a close connection between cycle expansion technique and characteristic function method. It was found that this connection can be exploited to enhance the applicability of the cycle expansion technique. In this way, we found that cycle expansion can be used to analyse the probability density function in chaotic maps. In our research studies we have successfully applied the characteristic function method and cycle expansion technique for analysing some chaotic maps. We introduced in this connection, two classes of chaotic maps with variable shape by generalizing two types of maps well known in literature.

Resource allocation analysis of the stochastic diffusion search

The Stochastic Diffusion Search (SDS) was developed as a solution to the best-fit search problem. Thus, as a special case it is capable of solving the transform invariant pattern recognition problem. SDS is efficient and, although inherently probabilistic, produces very reliable solutions in widely ranging search conditions. However, to date a systematic formal investigation of its properties has not been carried out. This thesis addresses this problem. The thesis reports results pertaining to the global convergence of SDS as well as characterising its time complexity. However, the main emphasis of the work, reports on the resource allocation aspect of the Stochastic Diffusion Search operations. The thesis introduces a novel model of the algorithm, generalising an Ehrenfest Urn Model from statistical physics. This approach makes it possible to obtain a thorough characterisation of the response of the algorithm in terms of the parameters describing the search conditions in case of a unique best-fit pattern in the search space. This model is further generalised in order to account for different search conditions: two solutions in the search space and search for a unique solution in a noisy search space. Also an approximate solution in the case of two alternative solutions is proposed and compared with predictions of the extended Ehrenfest Urn model. The analysis performed enabled a quantitative characterisation of the Stochastic Diffusion Search in terms of exploration and exploitation of the search space. It appeared that SDS is biased towards the latter mode of operation. This novel perspective on the Stochastic Diffusion Search lead to an investigation of extensions of the standard SDS, which would strike a different balance between these two modes of search space processing. Thus, two novel algorithms were derived from the standard Stochastic Diffusion Search, ‘context-free’ and ‘context-sensitive’ SDS, and their properties were analysed with respect to resource allocation. It appeared that they shared some of the desired features of their predecessor but also possessed some properties not present in the classic SDS. The theory developed in the thesis was illustrated throughout with carefully chosen simulations of a best-fit search for a string pattern, a simple but representative domain, enabling careful control of search conditions.