Effect of dynamical asymmetry on the viscosity of a random copolymer melt

The variation of the viscosity as a function of the sequence distribution in an A-B random copolymer melt is determined. The parameters that characterize the random copolymer are the fraction of A monomers f, the parameter lambda which determines the correlation in the monomer identities along a chain and the Flory chi parameter chi(F) which determines the strength of the enthalpic repulsion between monomers of type A and B. For lambda>0, there is a greater probability of finding like monomers at adjacent positions along the chain, and for lambda<0 unlike monomers are more likely to be adjacent to each other. The traditional Markov model for the random copolymer melt is altered to remove ultraviolet divergences in the equations for the renormalized viscosity, and the phase diagram for the modified model has a binary fluid type transition for lambda>0 and does not exhibit a phase transition for lambda<0. A mode coupling analysis is used to determine the renormalization of the viscosity due to the dependence of the bare viscosity on the local concentration field. Due to the dissipative nature of the coupling. there are nonlinearities both in the transport equation and in the noise correlation. The concentration dependence of the transport coefficient presents additional difficulties in the formulation due to the Ito-Stratonovich dilemma, and there is some ambiguity about the choice of the concentration to be used while calculating the noise correlation. In the Appendix, it is shown using a diagrammatic perturbation analysis that the Ito prescription for the calculation of the transport coefficient, when coupled with a causal discretization scheme, provides a consistent formulation that satisfies stationarity and the fluctuation dissipation theorem. This functional integral formalism is used in the present analysis, and consistency is verified for the present problem as well. The upper critical dimension for this type of renormaliaation is 2, and so there is no divergence in the viscosity in the vicinity of a critical point. The results indicate that there is a systematic dependence of the viscosity on lambda and chi(F). The fluctuations tend to increase the viscosity for lambda<0, and decrease the viscosity for lambda>0, and an increase in chi(F) tends to decrease the viscosity. (C) 1996 American Institute of Physics.

On generating optimal signal probabilities for random tests: A genetic approach

Genetic Algorithms are robust search and optimization techniques. A Genetic Algorithm based approach for determining the optimal input distributions for generating random test vectors is proposed in the paper. A cost function based on the COP testability measure for determining the efficacy of the input distributions is discussed, A brief overview of Genetic Algorithms (GAs) and the specific details of our implementation are described. Experimental results based on ISCAS-85 benchmark circuits are presented. The performance pf our GA-based approach is compared with previous results. While the GA generates more efficient input distributions than the previous methods which are based on gradient descent search, the overheads of the GA in computing the input distributions are larger. To account for the relatively quick convergence of the gradient descent methods, we analyze the landscape of the COP-based cost function. We prove that the cost function is unimodal in the search space. This feature makes the cost function amenable to optimization by gradient-descent techniques as compared to random search methods such as Genetic Algorithms.

Stability of stochastic Leipholz column with stochastic loading

The Leipholz column which is having the Young modulus and mass per unit length as stochastic processes and also the distributed tangential follower load behaving stochastically is considered. The non self-adjoint differential equation and boundary conditions are considered to have random field coefficients. The standard perturbation method is employed. The non self-adjoint operators are used within the regularity domain. Full covariance structure of the free vibration eigenvalues and critical loads is derived in terms of second order properties of input random fields characterizing the system parameter fluctuations. The mean value of critical load is calculated using the averaged problem and the corresponding eigenvalue statistics are sought. Through the frequency equation a transformation is done to yield load parameter statistics. A numerical study incorporating commonly observed correlation models is reported which illustrates the full potentials of the derived expressions.

Fixed points in a Hopfield model with random asymmetric interactions

We calculate analytically the average number of fixed points in the Hopfield model of associative memory when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. Addition of the antisymmetric part causes an exponential decrease in the total number of fixed points. If the relative strength of the antisymmetric component is small, then its presence does not cause any substantial degradation of the quality of retrieval when the memory loading level is low. We also present results of numerical simulations which provide qualitative (as well as quantitative for some aspects) confirmation of the predictions of the analytic study. Our numerical results suggest that the analytic calculation of the average number of fixed points yields the correct value for the typical number of fixed points.

Theory of electron transfer processes via chemisorbed intermediates: Part II. Current-potential characteristics

Current-potential characteristics are obtained numerically for a lone-adsorbate-mediated anodic charge transfer at the electrode-solution interface. An increase in the overpotential leads to the appearance of maxima in the anodic current-potential plots instead of the extended activationless region (i.e. a saturation current at large positive overpotentials) predicted by the direct heterogeneous outer-sphere anodic charge transfer process. A detailed analysis of the dependence of current-potential profiles and other kinetic parameters on various system parameters is also presented.

Thermodynamics of flow and vaporization processes in long-chain liquids

The flow and vaporization behaviors of long-chain esters of varying molecular weights (300-900) ana branching (linear, Y-shaped, and +-shaped molecules) have been studied. The flow behavior is found to depend on the structure as well as the molecular weight. Below a molecular weight of 600, the molecules flow wholly but above this, segmental motion occurs, and the flow becomes independent of the molecular weight which is explained from the blob model. The blob concept demonstrates that the hole of a size of about 11 angstrom is needed for the flow to occur and it is much less than the size of the molecule. The blob size is observed to slightly decrease along the series linear and Y- and +-branched esters. The heat of vaporization is found to be independent of the molecular structure since the molecules acquire a coiled spherical shape during vaporization and hence depends only on the molecular weight. A significant structural effect is observed for the esters on their glass transition temperature (T(g)). The T(g) vs molecular weight plot displays contrasting trend for linear and +-branched esters, with Y esters showing an intermediate behavior. It is explained from their molecular packing and entanglement as visualized by the blob model.

Some Basic Aspects of Reaction Engineering of Precipitation Processes

Analysis of precipitation reactions is extremely important in the technology of production of fine particles from the liquid phase. The control of composition and particle size in precipitation processes requires careful analysis of the several reactions that comprise the precipitation system. Since precipitation systems involve several, rapid ionic dissociation reactions among other slower ones, the faster reactions may be assumed to be nearly at equilibrium. However, the elimination of species, and the consequent reduction of the system of equations, is an aspect of analysis fraught with the possibility of subtle errors related to the violation of conservation principles. This paper shows how such errors may be avoided systematically by relying on the methods of linear algebra. Applications are demonstrated by analyzing the reactions leading to the precipitation of calcium carbonate in a stirred tank reactor as well as in a single emulsion drop. Sample calculations show that supersaturation dynamics can assume forms that can lead to subsequent dissolution of particles that have once been precipitated.

Structured systems methodology for evaluation of random interruptions in continuous process type manufacturing systems

A structured systems methodology was developed to analyse the problems of production interruptions occurring at random intervals in continuous process type manufacturing systems. At a macro level the methodology focuses on identifying suitable investment policies to reduce interruptions of a total manufacturing system that is a combination of several process plants. An interruption-tree-based simulation model was developed for macroanalysis. At a micro level the methodology focuses on finding the effects of alternative configurations of individual process plants on the overall system performance. A Markov simulation model was developed for microlevel analysis. The methodology was tested with an industry-specific application.

Methods of nonlinear random vibration analysis

The various techniques available for the analysis of nonlinear systems subjected to random excitations are briefly introduced and an overview of the progress which has been made in this area of research is presented. The discussion is mainly focused on the basis, scope and limitations of the solution techniques and not on specific applications.

Lasing in active, sub-mean-free path-sized systems with dense, random, weak scatterers

We report enhanced emission and gain narrowing in Rhodamine 590 perchlorate dye in an aqueous suspension of polystyrene microspheres. A systematic experimental study of the threshold condition for and the gain narrowing of the stimulated emission over a wide range of dye concentrations and scatterer number densities showed several interesting features, even though the transport mean free path far exceeded the system size. The conventional diffusive-reactive approximation to radiative transfer in an inhomogeneously illuminated random amplifying medium, which is valid for a transport mean-free path much smaller than the system size, is clearly inapplicable here. We propose a new probabilistic approach for the present case of dense, random, weak scatterers involving the otherwise rare and ignorable sub-mean-free-path scatterings, now made effective by the high gain in the medium, which is consistent: with experimentally observed features. (C) 1997 Optical Society of America.

Modelling transport processes during microwave heating: A review

The review is concerned with models that analyze transport:processes that occur during microwave heating. Early models on microwave. heating used Lambert's law to describe the microwave power absorption. Over the last decade, models for transport processes have been developed with the microwave power derived from Maxwell's equations. Those models, primarily based on plane waves, have been used for analyzing microwave heating of solids, liquids, emulsions, microwave thawing and drying. The models illustrate phenomena such a resonances, hot spots, edge and runaway heating. The literature on microwave sintering, susceptor heating and microwave assisted synthesis is largely experimental in nature and only key issues are highlighted. To fully appreciate the models for microwave heating, a section on the theory of electromagnetic wave propagation is included, where expressions for the electric field in dielectric slabs and cylinders are presented.

Residence time distribution for a class of Gaussian Markov processes

We study the distribution of residence time or equivalently that of "mean magnetization" for a family of Gaussian Markov processes indexed by a positive parameter alpha. The persistence exponent for these processes is simply given by theta=alpha but the residence time distribution is nontrivial. The shape of this distribution undergoes a qualitative change as theta increases, indicating a sharp change in the ergodic properties of the process. We develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha. For some special values of alpha, we obtain closed form expressions of the distribution function. [S1063-651X(99)03306-1].

Stochastic dynamics modeling of the protein sequence length distribution in genomes: implications for microbial evolution

In this paper, we report an analysis of the protein sequence length distribution for 13 bacteria, four archaea and one eukaryote whose genomes have been completely sequenced, The frequency distribution of protein sequence length for all the 18 organisms are remarkably similar, independent of genome size and can be described in terms of a lognormal probability distribution function. A simple stochastic model based on multiplicative processes has been proposed to explain the sequence length distribution. The stochastic model supports the random-origin hypothesis of protein sequences in genomes. Distributions of large proteins deviate from the overall lognormal behavior. Their cumulative distribution follows a power-law analogous to Pareto's law used to describe the income distribution of the wealthy. The protein sequence length distribution in genomes of organisms has important implications for microbial evolution and applications. (C) 1999 Elsevier Science B.V. All rights reserved.

Biological water: Femtosecond dynamics of macromolecular hydration

The unique features of a macromolecule and water as a solvent make the issue of solvation unconventional, with questions about the static versus dynamic nature of hydration and the, physics of orientational and translational diffusion at the boundary. For proteins, the hydration shell that covers the surface is critical to the stability of its structure and function. Dynamically speaking, the residence time of water at the surface is a signature of its mobility and binding. With femtosecond time resolution it is possible to unravel the shortest residence times which are key for the description of the hydration layer, static or dynamic. In this article we review these issues guided by experimental studies, from this laboratory, of polar hydration dynamics at the surfaces of two proteins (Subtilisin Carlsberg (SC) and Monellin). The natural probe tryptophan amino acid was used for the interrogation of the dynamics, and for direct comparison we also studied the behavior in bulk water - a complete hydration in 1 ps. We develop a theoretical description of solvation and relate the theory to the experimental observations. In this - theoretical approach, we consider the dynamical equilibrium in the hydration shell, defining the rate processes for breaking and making the transient hydrogen bonds, and the effective friction in the layer which is defined by the translational and orientational motions of water molecules. The relationship between the residence time of water molecules and the observed slow component in solvation dynamics is a direct one. For the two proteins studied, we observed a "bimodal decay" for the hydration correlation function, with two primary relaxation times: ultrafast, typically 1 ps or less, and longer, typically 15-40 ps, and both are related to the residence time at the protein surface, depending on the binding energies. We end by making extensions to studies of the denatured state of the protein, random coils, and the biomimetic micelles, and conclude with our thoughts on the relevance of the dynamics of native structures to their functions.