Relaxation system based sub-grid scale modelling for large eddy simulation of Burgers' equation

An implicit sub-grid scale model for large eddy simulation is presented by utilising the concept of a relaxation system for one dimensional Burgers' equation in a novel way. The Burgers' equation is solved for three different unsteady flow situations by varying the ratio of relaxation parameter (epsilon) to time step. The coarse mesh results obtained with a relaxation scheme are compared with the filtered DNS solution of the same problem on a fine mesh using a fourth-order CWENO discretisation in space and third-order TVD Runge-Kutta discretisation in time. The numerical solutions obtained through the relaxation system have the same order of accuracy in space and time and they closely match with the filtered DNS solutions.

Solvation dynamics in a Brownian dipolar lattice. Comparison between computer simulation and various molecular theories of solvation dynamics

Several recent theoretical and computer simulation studies have considered solvation dynamics in a Brownian dipolar lattice which provides a simple model solvent for which detailed calculations can be carried out. In this article a fully microscopic calculation of the solvation dynamics of an ion in a Brownian dipolar lattice is presented. The calculation is based on the non‐Markovian molecular hydrodynamic theory developed recently. The main assumption of the present calculation is that the two‐particle orientational correlation functions of the solid can be replaced by those of the liquid state. It is shown that such a calculation provides an excellent agreement with the computer simulation results. More importantly, the present calculations clearly demonstrate that the frequency‐dependent dielectric friction plays an important role in the long time decay of the solvation time correlation function. We also find that the present calculation provides somewhat better agreement than either the dynamic mean spherical approximation (DMSA) or the Fried–Mukamel theory which use the simulated frequency‐dependent dielectric function. It is found that the dissipative kernels used in the molecular hydrodynamic approach and in the Fried–Mukamel theory are vastly different, especially at short times. However, in spite of this disagreement, the two theories still lead to comparable results in good agreement with computer simulation, which suggests that even a semiquantitatively accurate dissipative kernel may be sufficient to obtain a reliable solvation time correlation function. A new wave vector and frequency‐dependent dissipative kernel (or memory function) is proposed which correctly goes over to the appropriate expressions in both the single particle and the collective limits. This form is expected to lead to better results than all the existing descriptions.

A simple method for potential flow simulation of cascades

A simple method using a combination of conformal mapping and vortex panel method to simulate potential flow in cascades is presented. The cascade is first transformed to a single body using a conformal mapping, and the potential flow over this body is solved using a simple higher order vortex panel method. The advantage of this method over existing methodologies is that it enables the use of higher order panel methods, as are used to solve flow past an isolated airfoil, to solve the cascade problem without the need for any numerical integrations or iterations. The fluid loading on the blades, such as the normal force and pitching moment, may be easily calculated from the resultant velocity field. The coefficient of pressure on cascade blades calculated with this methodology shows good agreement with previous numerical and experimental results.

Analysis of Hydrogen Bonding and Stability of Protein Secondary Structures in Molecular Dynamics Simulation

Molecular Dynamics (MD) simulations provide an atomic level account of the molecular motions and have proven to be immensely useful in the investigation of the dynamical structure of proteins. Once an MD trajectory is obtained, specific interactions at the molecular level can be directly studied by setting up appropriate combinations of distance and angle monitors. However, if a study of the dynamical behavior of secondary structures in proteins becomes important, this approach can become unwieldy. We present herein a method to study the dynamical stability of secondary structures in proteins, based on a relatively simple analysis of backbone hydrogen bonds. The method was developed for studying the thermal unfolding of beta-lactamases, but can be extended to other systems and adapted to study relevant properties.

Design, modelling and simulation of vibratory micromachined gyroscopes

Among various MEMS sensors, a rate gyroscope is one of the most complex sensors from the design point of view. The gyro normally consists of a proof mass suspended by an elaborate assembly of beams that allow the system to vibrate in two transverse modes. The structure is normally analysed and designed using commercial FEM packages such as ANSYS or MEMS specific commercial tools such as Coventor or Intellisuite. In either case, the complexity in analysis rises manyfolds when one considers the etch hole topography and the associated fluid flow calculation for damping. In most cases, the FEM analysis becomes prohibitive and one resorts to equivalent electrical circuit simulations using tools like SABER in Coventor. Here, we present a simplified lumped parameter model of the tuning fork gyro and show how easily it can be implemented using a generic tool like SIMULINK. The results obtained are compared with those obtained from more elaborate and intense simulations in Coventor. The comparison shows that lumped parameter SIMULINK model gives equally good results with fractional effort in modelling and computation. Next, the performance of a symmetric and decoupled vibratory gyroscope structure is also evaluated using this approach and a few modifications are made in this design to enhance the sensitivity of the device.

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.

Ultrafast underdamped solvation: Agreement between computer simulation and various theories of solvation dynamics

A theoretical analysis of the three currently popular microscopic theories of solvation dynamics, namely, the dynamic mean spherical approximation (DMSA), the molecular hydrodynamic theory (MHT), and the memory function theory (MFT) is carried out. It is shown that in the underdamped limit of momentum relaxation, all three theories lead to nearly identical results when the translational motions of both the solute ion and the solvent molecules are neglected. In this limit, the theoretical prediction is in almost perfect agreement with the computer simulation results of solvation dynamics in the model Stockmayer liquid. However, the situation changes significantly in the presence of the translational motion of the solvent molecules. In this case, DMSA breaks down but the other two theories correctly predict the acceleration of solvation in agreement with the simulation results. We find that the translational motion of a light solute ion can play an important role in its own solvation. None of the existing theories describe this aspect. A generalization of the extended hydrodynamic theory is presented which, for the first time, includes the contribution of solute motion towards its own solvation dynamics. The extended theory gives excellent agreement with the simulations where solute motion is allowed. It is further shown that in the absence of translation, the memory function theory of Fried and Mukamel can be recovered from the hydrodynamic equations if the wave vector dependent dissipative kernel in the hydrodynamic description is replaced by its long wavelength value. We suggest a convenient memory kernel which is superior to the limiting forms used in earlier descriptions. We also present an alternate, quite general, statistical mechanical expression for the time dependent solvation energy of an ion. This expression has remarkable similarity with that for the translational dielectric friction on a moving ion.

Applicability of Butler's equation in interpreting the thermodynamic behavior of surfaces and adsorption in Fe-S-O melts

Expressions for various second-order derivatives of surface tension with respect to composition at infinite dilution in terms of the interaction parameters of the surface and those of the bulk phases of dilute ternary melts have been presented. A method of deducing the parameters, which consists of repeated differentiation of Butler's equations with subsequent application of the appropriate boundary conditions, has been developed. The present investigation calculates the surface tension and adsorption functions of the Fe-S-O melts at 1873 and 1923 K using the modified form of Butler's equations and the derived values for the surface interaction parameters of the system. The calculated values are found to be in good agreement with those of the experimental data of the system. The present analysis indicates that the energetics of the surface phase are considerably different from those of the bulk phase. The present research investigates a critical compositional range beyond which the surface tension increases with temperature. The observed increase in adsorption of sulfur with consequent desorption of oxygen as a function of temperature above the critical compositional range has been ascribed to the increase of activity ratios of oxygen to sulfur in the surface relative to those in the bulk phase of the system.

Effect of phosphate adsorption on the permeability of clays

In this paper, the effect of phosphate anion adsorption on the permeability values of homoionized kaolinite and montmorillonite clays is presented. The homoionized sodium, calcium and hydrogen clays are prepared by repeatedly washing the clays with 2N solutions of corresponding chlorides. Phosphate adsorption was induced by treating homoionized clays with phosphoric acids for different periods varying upto 1000 hrs. The coefficient of permeability of the clays was determined from one dimensional consolidation test results. The decrease in the permeability of kaolinite clays on phosphate adsorption has been explained on the fabric changes. For montmorillonite, both cation exchange and phosphate adsorption causes significant changes which are explained based on variation in the thickness of diffuse double layer.

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.