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.

Diffusion and Creep in Silica-Doped Tetragonal Zirconia

Silica segregation at two grain junctions or in amorphous triple junction pockets can influence creep by altering the grain-boundary diffusion coefficient. Although the addition of silica to superplastic yttria-stabilized tetragonal zirconia enhances ductility, differences in reported creep parameters have limited critical identification of rate controlling mechanisms. The present study on a pure 3 mol% yttria-stabilized tetragonal zirconia (3YTZ) and 3YTZ with 0.39 or 3.9 wt% silica involved a detailed characterization of creep over a wide range of experimental conditions and also tracer diffusion measurements. The data broadly show transitions in creep stress exponents from n∼1 to ∼2 to ∼3 with a decrease in the stress. The data at high stresses are consistent with Coble diffusion creep, and creep at lower stresses is attributed to interface-controlled diffusion creep. Measurements indicated that silica does not have any significant influence on grain boundary or lattice diffusion, and this is consistent with the observation that 3YTZ and 3YTZ with 0.39% or 3.9% silica exhibit essentially identical creep behavior in the Coble creep regime. Silica influences the interface control process so that the transitions in stress exponents are pushed to lower stresses with an increase in silica content.

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.

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.

On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rossler system and synchronization of the hyperchaotic Rossler system. (C) 2007 Elsevier B.V. All rights reserved.

Salt diffusion and distribution in meat studied by Na-23 nuclear magnetic resonance imaging and relaxometry

This study introduces the use of combined Na-23 magnetic resonance imaging (MRI) and Na-23 NMR relaxometry for the study of meat curing. The diffusion of sodium ions into the meat was measured using Na-23 MRI on a 1 kg meat sample brined in 10% w/w NaCl for 3-100 h. Calculations revealed a diffusion coefficient of 1 x 10(-5) cm(2)/s after 3 h of curing and subsequently decreasing to 8 x 10(-6) cm(2)/s at longer curing times, suggesting that changes occur in the microscopic structure of the meat during curing. The microscopic mobility and distribution of sodium was measured using Na-23 relaxometry. Two sodium populations were observed, and with increasing length of curing time the relaxation times of these changed, reflecting a salt-induced swelling and increase in myofibrillar pore sizes. Accordingly, the present study demonstrated that pore size and thereby salt-induced swelling in meat can be assessed using Na-23 relaxometry.

Comment on "Local accumulation times for source, diffusion, and degradation models in two and three dimensions" [J. Chem. Phys. 138, 104121 (2013)]

In a recent paper, Gordon, Muratov, and Shvartsman studied a partial differential equation (PDE) model describing radially symmetric diffusion and degradation in two and three dimensions. They paid particular attention to the local accumulation time (LAT), also known in the literature as the mean action time, which is a spatially dependent timescale that can be used to provide an estimate of the time required for the transient solution to effectively reach steady state. They presented exact results for three-dimensional applications and gave approximate results for the two-dimensional analogue. Here we make two generalizations of Gordon, Muratov, and Shvartsman’s work: (i) we present an exact expression for the LAT in any dimension and (ii) we present an exact expression for the variance of the distribution. The variance provides useful information regarding the spread about the mean that is not captured by the LAT. We conclude by describing further extensions of the model that were not considered by Gordon,Muratov, and Shvartsman. We have found that exact expressions for the LAT can also be derived for these important extensions...

The charge effect on the hindrance factors for diffusion and convection of a solute in pores II

The diffusion and convection of a solute suspended in a fluid across porous membranes are known to be reduced compared to those in a bulk solution, owing to the fluid mechanical interaction between the solute and the pore wall as well as steric restriction. If the solute and the pore wall are electrically charged, the electrostatic interaction between them could affect the hindrance to diffusion and convection. In this study, the transport of charged spherical solutes through charged circular cylindrical pores filled with an electrolyte solution containing small ions was studied numerically by using a fluid mechanical and electrostatic model. Based on a mean field theory, the electrostatic interaction energy between the solute and the pore wall was estimated from the Poisson-Boltzmann equation, and the charge effect on the solute transport was examined for the solute and pore wall of like charge. The results were compared with those obtained from the linearized form of the Poisson-Boltzmann equation, i.e.the Debye-Hückel equation. © 2012 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

Space, diffusion and mobility

Given its origins in traditional dialectology, and given advances in our understanding of the social embedding of language variation, it is paradoxical that space should be one of the categories that has received least attention of all in variationist sociolinguistics. Until recently, space has largely been treated as an empty stage on which sociolinguistic processes are enacted. It has been unexamined, untheorized, and its role in shaping and being shaped by variation and change untested. One function of this chapter, therefore, is to assert that space makes a difference, and to begin, in a very hesitant way, to map out what a geographically informed variation analysis might need to address. It also examines variationist interactions with the related concept of mobility. It might be reasonable to think that human geographers would provide some clues on how to proceed. As we will see, they have engaged in a great deal of soul searching about the goals of their discipline, its very existence as a separate field of enquiry, and the directions it should take. Indeed there are remarkable parallels between the recent history of human geographic thought, and interest in language variation across space. Although space has been undertheorized in variation studies, a number of researchers, from the traditional dialectologists through to those interested in the dialectology of mobility and contact, have, of course, been actively engaged in research on geographical variation and language use. Their work will be contextualized here to highlight both the parallels with theory-building in human geography, but also some of the criticisms of earlier approaches which have fed through to human geography, but remain largely unquestioned in variationist practice. The chapter therefore presents a brief theoretical background to space and mobility, before exemplifying these concepts in variationist research through an examination of, for example, the spatial diffusion of linguistic innovations, the spatial configuration of linguistic boundaries and initial steps to examine the consequences of mobility for variationist research.