Stochastic Approximation Algorithms for Constrained Optimization via Simulation

We develop four algorithms for simulation-based optimization under multiple inequality constraints. Both the cost and the constraint functions are considered to be long-run averages of certain state-dependent single-stage functions. We pose the problem in the simulation optimization framework by using the Lagrange multiplier method. Two of our algorithms estimate only the gradient of the Lagrangian, while the other two estimate both the gradient and the Hessian of it. In the process, we also develop various new estimators for the gradient and Hessian. All our algorithms use two simulations each. Two of these algorithms are based on the smoothed functional (SF) technique, while the other two are based on the simultaneous perturbation stochastic approximation (SPSA) method. We prove the convergence of our algorithms and show numerical experiments on a setting involving an open Jackson network. The Newton-based SF algorithm is seen to show the best overall performance.

Digital simulation of galvanostatic current-potential data for gas-diffusion electrodes and estimation of electrodekinetic parameters

A computerized non-linear-least-squares regression procedure to analyse the galvanostatic current-potential data for kinetically hindered reactions on porous gas-diffusion electrodes is reported. The simulated data fit well with the corresponding measured values. The analytical estimates of electrode-kinetic parameters and uncompensated resistance are found to be in good agreement with their respective values obtained from Tafel plots and the current-interrupter method. The procedure circumvents the need to collect the data in the limiting-current region where the polarization values are usually prone to errors. The polarization data for two typical cases, namely, methanol oxidation on a carbon-supported platinum-tin electrode and oxygen reduction on a Nafion-coated platinized carbon electrode, are successfully analysed.

Microscopic theory of vortex dynamics

An approach to vortex dynamics is outlined, a new form being obtained for the pair potential forces on a vortex. A microscopic calculation of the vortex inertial mass is presented. Quantum effects on vortex lattice melting are briefly discussed.

Microscopic Mechanism of 1/f Noise in Graphene: Role of Energy Band Dispersion

A distinctive feature of single-layer graphene is the linearly dispersive energy bands, which in the case of multilayer graphene become parabolic. A simple electrical transport-based probe to differentiate between these two band structures will be immensely valuable, particularly when quantum Hall measurements are difficult, such as in chemically synthesized graphene nanoribbons. Here we show that the flicker noise, or the 1/f noise, in electrical resistance is a sensitive and robust probe to the band structure of graphene. At low temperatures, the dependence of noise magnitude on the carrier density was found to be opposite for the linear and parabolic bands. We explain our data with a comprehensive theoretical model that clarifies several puzzling issues concerning the microscopic origin of flicker noise in graphene field-effect transistors (GraFET).

Microscopic theory of vortex dynamics

An approach to vortex dynamics is outlined, a new form being obtained for the pair potential forces on a vortex. A microscopic calculation of the vortex inertial mass is presented. Quantum effects on vortex lattice melting are briefly discussed.

Solvation dynamics, energy distribution and trapping of a light solute ion

In the theoretical treatments of the dynamics of solvation of a newly created ion in a dipolar solvent, the self-motion of the solute is usually ignored. Recently, it has been shown that for a light ion the translational motion of the ion can significantly enhance its own rate of solvation. Therefore, solvation itself may not be the rate determining step in the equilibration. Instead, the rate determining step is the search of the low energy configuration which serves to localize the light ion. In this article a microscopic calculation of the probability distribution of the interaction energy of the nascent charge with the dipolar solvent molecules is presented in order to address this problem of solute trapping. It is found that to a good approximation, this distribution is Gaussian and the second moment of this distribution is exactly equal to the half of its own solvation energy. It is shown that this is in excellent agreement with the simulation results that are available for the model Brownian dipolar lattice and for liquid acetonitrile. If the distortion of the solvent by the ion is negligible then the same relation gives the energy distribution for the solvated ion, with the average centered at the final equilibrium solvation energy. These results are expected to be useful in understanding various chemical processes in dipolar liquids. Another interesting outcome of the present study is a simple dynamic argument that supports Onsager's ''inverse snow-ball'' conjecture of solvation of a light ion. A simple derivation of the semi-phenomenological relation between the solvation time correlation function and the single particle orientation, reported recently by Maroncelli et al. (J. Phys. Chem. 97 (1993) 13), is also presented.

Brownian dynamics simulation of dense binary colloidal mixtures. I. Structural evolution and dynamics

We have carried out Brownian dynamics simulations of binary mixtures of charged colloidal suspensions of two different diameter particles with varying volume fractions phi and charged impurity concentrations n(i). For a given phi, the effective temperature is lowered in many steps by reducing n(i) to see how structure and dynamics evolve. The structural quantities studied are the partial and total pair distribution functions g(tau), the static structure factors, the time average g(<(tau)over bar>), and the Wendt-Abraham parameter. The dynamic quantity is the temporal evolution of the total meansquared displacement (MSD). All these parameters show that by lowering the effective temperature at phi = 0.2, liquid freezes into a body-centered-cubic crystal whereas at phi = 0.3, a glassy state is formed. The MSD at intermediate times shows significant subdiffusive behavior whose time span increases with a reduction in the effective temperature. The mean-squared displacements for the supercooled liquid with phi = 0.3 show staircase behavior indicating a strongly cooperative jump motion of the particles.

Brownian dynamics simulation of dense binary colloidal mixtures. II. Translational and bond-orientational order

We report the Brownian dynamics simulation results on the translational and bond-angle-orientational correlations for charged colloidal binary suspensions as the interparticle interactions are increased to form a crystalline (for a volume fraction phi = 0.2) or a glassy (phi = 0.3) state. The translational order is quantified in terms of the two- and four-point density autocorrelation functions whose comparisons show that there is no growing correlation length near the glass transition. The nearest-neighbor orientational order is determined in terms of the quadratic rotational invariant Q(l) and the bond-orientational correlation functions g(l)(t). The l dependence of Q(l) indicates that icosahedral (l = 6) order predominates at the cost of the cubic order (l = 4) near the glass as well as the crystal transition. The density and orientational correlation functions for a supercooled liquid freezing towards a glass fit well to the streched-exponential form exp[-(t/tau)(beta)]. The average relaxation times extracted from the fitted stretched-exponential functions as a function of effective temperatures T* obey the Arrhenius law for liquids freezing to a crystal whereas these obey the Vogel-Tamman-Fulcher law exp[AT(0)*/(T* - T-0*)] for supercooled Liquids tending towards a glassy state. The value of the parameter A suggests that the colloidal suspensions are ''fragile'' glass formers like the organic and molecular liquids.

Monte Carlo simulation of low temperature phase diagrams of YBa2Cu3O6+x

We report the results of Monte Carlo simulation of oxygen ordering in the oxygen deficient portion (x<0.5) of YBa2Cu3O6+x at low temperatures. We find qualitative agreement among cluster - variation, Monte Carlo and transfer matrix methods. However, low temperature and ground state simulations clearly indicate the presence of a tetragonal phase. There is also evidence for two second order phase transition lines separating the tetragonal and the �double cell� ortho II phase. The effect of decreasing the inter-chain repulsion on oxygen ordering has also been investigated.

Microscopic origin of the chirality driven morphologies of the amphiphilic monolayers and bilayers

It is widely known that the compressed monolayers and bilayers of chiral lipids or fatty acids form helical morphologies, while the corresponding racemic modification gives only flat platelets without twist. No molecular explanation of this phenomenon is yet available, although subtle interactions at the chiral centers have often been proposed as the driving force behind the morphology of the aggregate to form a particular shape. In the present study, the morphologies of the chiral amphiphilic assemblies have been predicted on the basis of an effective pair potential between the molecules, which depends on the relative sizes of the groups attached to the chiral centers, the orientation of the amphiphilic molecules and also on the distance between them. It is shown that fur a pair of same kind of enantiomers, the minimum energy conformation favours a twist angle between them. This twist between the neighbouring molecules gives rise to the helicity of the aggregate. The present theory also shows from the molecular considerations that for a pair of mirror-image isomers (i.e. the racemic modification) the minimum energy conformation corresponds to the zero angle between the molecules, thus giving rise to flat platelets as observed in experiments. Another fascinating aspect of such chirality driven helical structures is that the sense (or the handedness) of the helix is highly specific about the chirality of the monomer concerned. The molecular theory shows, for the first time, that the sense of the helical structures in many cases is determined by the sizes of the groups attached to the chiral centers and the effective potential between them. The predicted senses of the helical structures are in complete agreement with the experimental results.

Collective Effects on Single Particle Orientational Relaxation in Slow Dipolar Liquids

Theoretical and computer simulation studies of orientational relaxation in dense molecular liquids are presented. The emphasis of the study is to understand the effects of collective orientational relaxation on the single-particle orientational dynamics. The theoretical analysis is based on a recently developed molecular hydrodynamic theory which allows a self-consistent description of both the collective and the single-particle orientational relaxation. The molecular hydrodynamic theory can be used to derive a relation between the memory function for the collective orientational correlation function and the frequency-dependent dielectric function. A novel feature of the present work is the demonstration that this collective memory function is significantly different from the single-particle rotational friction. However, a microscopic expression for the single-particle rotational friction can be derived from the molecular hydrodynamic theory where the collective memory function can be used to obtain the single-particle orientational friction. This procedure allows, us to calculate the single-particle orientational correlation function near the alpha-beta transition in the supercooled liquid. The calculated correlation function shows an interesting bimodal decay below the bifurcation temperature as the glass transition is approached from above. Brownian dynamics simulations have been carried out to check the validity of the above procedure of translating the memory function from the dielectric relaxation data. We have also investigated the following two issues important in understanding the orientational relaxation in slow liquids. First, we present an analysis of the ''orientational caging'' of translational motion. The value of the translational friction is found to be altered significantly by the orientational caging. Second, we address the question of the rank dependence of the dielectric friction using both simulation and the molecular hydrodynamic theory.

Monte Carlo simulation of network formation based on structural fragments in epoxy-anhydride systems

A method combining the Monte Carlo technique and the simple fragment approach has been developed for simulating network formation in amine-catalysed epoxy-anhydride systems. The method affords a detailed insight into the nature and composition of the network, showing the distribution of various fragments. It has been used to characterize the network formation in the reaction of the diglycidyl ester of isophthalic acid with hexahydrophthalic anhydride, catalysed by benzyldimethylamine. Pre-gel properties like number and weight distributions and average molecular weights have been calculated as a function of epoxy conversion, leading to a prediction of the gel-point conversion. Analysis of the simulated network further yields other characteristic properties such as concentration of crosslink points, distribution and concentration of elastically active chains, average molecular weight between crosslinks, sol content and mass fraction of pendent chains. A comparison has been made of the properties obtained through simulation with those predicted by the fragment approach alone, which, however, gives only average properties. The Monte Carlo simulation results clearly show that loops and other cyclic structures occur in the gel. This may account for the differences observed between the results of the simulation and the fragment model in the post-gel phase. Copyright (C) 1996 Elsevier Science Ltd.

Self-consistent microscopic treatment of the effects of self-motion of the probe on ionic and dipolar solvation dynamics

A simple but self-consistent microscopic theory for the time dependent solvation energy of both ions and dipoles is presented which includes, for the first time, the details of the self-motion of the probe on its own solvation dynamics. The theory leads to several interesting predictions. The most important of them is that, for dipolar solvation, both the rotational and the translational motions of the dipolar solute probe can significantly accelerate the rate of solvation. In addition, the rotational self-motion of the solute can also give rise to an additional mechanism of nonexponentiality in solvation time correlation functions in otherwise slow liquids. A comparison between the present theoretical predictions and the recent experimental studies of Maroncelli et al. on solvation dynamics of aniline in l-propanol seems to indicate that the said experiments have missed the initial solvent response up to about 45 ps. After mapping the experimental results on the redefined time scale, the theoretical results can explain the experimental results for solvation of aniline in 1-propanol very well. For ionic solvation, the translational motion is significant for light solutes only. For example, for Li+ in water, translational motion speeds up the solvation by about 20%. The present theory demonstrates that in dipolar solvation the partial quenching of the self-motion due to the presence of specific solute-solvent interactions (such as H-bonding) may lead to a much slower solvation than that when the self-motion is present. This point has been discussed. In addition, we present the theoretical results for solvation of aniline in propylene carbonate, Here, the solvation is predicted to be complete within 15-20 ps.

The mean and turbulence structure simulation of the monsoon trough boundary layer using a one-dimensional model with e-l and e-epsilon closures

An attempt has been made here to study the sensitivity of the mean and the turbulence structure of the monsoon trough boundary layer to the choice of the constants in the dissipation equation for two stations Delhi and Calcutta, using one-dimensional atmospheric boundary layer model with e-epsilon turbulence closure. An analytical discussion of the problems associated with the constants of the dissipation equation is presented. It is shown here that the choice of the constants in the dissipation equation is quite crucial and the turbulence structure is very sensitive to these constants. The modification of the dissipation equation adopted by earlier studies, that is, approximating the Tke generation (due to shear and buoyancy production) in the epsilon-equation by max (shear production, shear + buoyancy production), can be avoided by a suitable choice of the constants suggested here. The observed turbulence structure is better simulated with these constants. The turbulence structure simulation with the constants recommended by Aupoix et al (1989) (which are interactive in time) for the monsoon region is shown to be qualitatively similar to the simulation obtained with the constants suggested here, thus implying that no universal constants exist to regulate dissipation rate. Simulations of the mean structure show little sensitivity to the type of the closure parameterization between e-l and e-epsilon closures. However the turbulence structure simulation with e-epsilon closure is far better compared to the e-l model simulations. The model simulations of temperature profiles compare quite well with the observations whenever the boundary layer is well mixed (neutral) or unstable. However the models are not able to simulate the nocturnal boundary layer (stable) temperature profiles. Moisture profiles are simulated reasonably better. With one-dimensional models, capturing observed wind variations is not up to the mark.