A molecular dynamics study of a PbO.SiO2 glass and melt

The structures of a PbO.SiO2 glass and melt have been studied using molecular dynamics simulation employing Born-Mayer-Huggins pair potentials. Various pair distribution functions are presented and discussed. Pb-Pb correlations persist in the melt, in agreement with experimental observations. The calculated and experimental radial distribution functions are compared.

A study of symbolic processing and computational aspects in helicopter dynamics

Even research models of helicopter dynamics often lead to a large number of equations of motion with periodic coefficients; and Floquet theory is a widely used mathematical tool for dynamic analysis. Presently, three approaches are used in generating the equations of motion. These are (1) general-purpose symbolic processors such as REDUCE and MACSYMA, (2) a special-purpose symbolic processor, DEHIM (Dynamic Equations for Helicopter Interpretive Models), and (3) completely numerical approaches. In this paper, comparative aspects of the first two purely algebraic approaches are studied by applying REDUCE and DEHIM to the same set of problems. These problems range from a linear model with one degree of freedom to a mildly non-linear multi-bladed rotor model with several degrees of freedom. Further, computational issues in applying Floquet theory are also studied, which refer to (1) the equilibrium solution for periodic forced response together with the transition matrix for perturbations about that response and (2) a small number of eigenvalues and eigenvectors of the unsymmetric transition matrix. The study showed the following: (1) compared to REDUCE, DEHIM is far more portable and economical, but it is also less user-friendly, particularly during learning phases; (2) the problems of finding the periodic response and eigenvalues are well conditioned.

Time-Dependent Dynamics of a Planar Galaxy Model

Time-dependent models of collisionless stellar systems with harmonic potentials allowing for an essentially exact analytic description have recently been described. These include oscillating spheres and spheroids. This paper extends the analysis to time-dependent elliptic discs. Although restricted to two space dimensions, the systems are richer in that their parameters form a 10-dimensional phase space (in contrast to six for the earlier models). Apart from total energy and angular momentum, two additional conserved quantities emerge naturally. These can be chosen as the areas of extremal sections of the ellipsoidal region of phase space occupied by the system (their product gives the conserved volume). The present paper describes the construction of these models. An application to a tidal encounter is given which allows one to go beyond the impulse approximation and demonstrates the effects of rotation of the perturbed system on energy and angular-momentum transfer. The angular-momentum transfer is shown to scale inversely as the cube of the encounter velocity for an initial configuration of the perturbed galaxy with zero quadrupole moment.

Padé approach to potential transients: Part 1. Electron transfer without and with coupling to first-order homogeneous reactions at planar electrodes

Potential transients are obtained by using “Padé approximants” (an accurate approximation procedure valid globally — not just perturbatively) for all amplitudes of concentration polarization and current densities. This is done for several mechanistic schemes under constant current conditions. We invert the non-linear current-potential relationship in the form (using the Lagrange or the Ramanujan method) of power series appropriate to the two extremes, namely near reversible and near irreversible. Transforming both into the Pad́e expressions, we construct the potential-time profile by retaining whichever is the more accurate of the two. The effectiveness of this method is demonstrated through illustrations which include couplings of homogeneous chemical reactions to the electron-transfer step.

On shock dynamics

This is in continuation of our paper On the propagation of a multi-dimensional shock of arbitrary strength’ published earlier in this journal (Srinivasan and Prasad [9]). We had shown in our paper that Whitham’s shock dynamics, based on intuitive arguments, cannot be relied on for flows other than those involving weak shocks and that too with uniform flow behind the shock. Whitham [12] refers to this as misinterpretation of his approximation and claims that his theory is not only correct but also provides a natural closure of the open system of the equations of Maslov [3]. The main aim of this note is to refute Whitham’s claim with the help of an example and a numerical integration of a problem in gasdynamics.

Temperature dependent free energy surface of polymer folding from equilibrium and quench studies

Langevin dynamics simulation studies have been employed to calculate the temperature dependent free energy surface and folding characteristics of a 500 monomer long linear alkane (polyethylene) chain with a realistic interaction potential. Both equilibrium and temperature quench simulation studies have been carried out. Using the shape anisotropy parameter (S) of the folded molecule as the order parameter, we find a weakly first order phase transition between the high-temperature molten globule and low-temperature rodlike crystalline states separated by a small barrier of the order of k(B)T. Near the melting temperature (580 K), we observe an intriguing intermittent fluctuation with pronounced ``1/f noise characteristics'' between these two states with large difference in shape and structure. We have also studied the possibilities of different pathways of folding to states much below the melting point. At 300 K starting from the all-trans linear configuration, the chain folds stepwise into a very regular fourfold crystallite with very high shape anisotropy. Whereas, when quenched from a high temperature (900 K) random coil regime, we identify a two step transition from the random coiled state to a molten globulelike state and, further, to a anisotropic rodlike state. The trajectory reveals an interesting coupling between the two order parameters, namely, radius of gyration (R-g) and the shape anisotropy parameter (S). The rodlike final state of the quench trajectory is characterized by lower shape anisotropy parameter and significantly larger number of gauche defects as compared to the final state obtained through equilibrium simulation starting from all-trans linear chain. The quench study shows indication of a nucleationlike pathway from the molten globule to the rodlike state involving an underlying rugged energy landscape. (C) 2010 American Institute of Physics. doi:10.1063/1.3509398]

Effects of molecular size in solvation dynamics

The effects of molecular size on the dynamics of polar solvation are studied by using a microscopic theory which includes the translational relaxation modes of the solvent consistently. It is shown that while in the absence of the translational contribution the solvation rate increases with the size of the solute (in agreement with the conclusions of the nonequilibrium MSA theory),a complete reversal of the solute size dependence occurs when translational modes make a significant contribution to the solvent polarization relaxation.

Dynamics of activationless reactions in solution

Recent picosecond and subpicosecond laser spectroscopy experiments have revealed several chemically and biologically important reactions in solution in which the reaction potential surface does not present a barrier to the motion along the reaction coordinate.The dynamics of these reactions display diverse and interesting behavior. They include the dependence of relaxation rate on the solvent viscosity, the solvent polarity, the temperature, and the wavelength of the exciting light. In this article we review the recent developments in the theoretical description of activationless processes in solution and compare them with the available experimental results

Dynamics of charge transfer in the excited amine complexes of the fullerenes C60 and C70.: A picosecond laser flash photolysis study

In benzene solution, C60 and C70 interact weakly in the ground state with amines having favourable oxidation potentials. Picosecond time-resolved absorption measurements show that on photoexcilation, the weak complexes undergo charge separation to produce ion pairs which in turn undergo fast geminate recombination either to produce the triplet state of the fullerenes or give back the ground slate of the complex, depending on the oxidation potential of the amine. Free-ion yield is generally negligible.

Molecular dynamics simulations on parallel and antiparallel C.G*G triplexes

Molecular dynamics (MD) studies have been carried out on the Hoogsteen hydrogen bonded parallel and the reverse Hoogsteen hydrogen banded antiparallel C.G*G triplexes. Earlier, the molecular mechanics studies had shown that the parallel structure was energetically more favourable than the antiparallel structure. To characterize the structural stability of the two triplexes and to investigate whether the antiparallel structure can transit to an energetically more favourable structure, due to the local fluctuations in the structure during the MD simulation, the two structures were subjected to 200ps of constant temperature vacuum MD simulations at 300K. Initially no constraints were applied to the structures and it was observed that for the antiparallel tripler, the structure showed a large root mean square deviation from the starting structure within the first 12ps and the N4-H41-O6 hydrogen bond in the WC duplex got distorted due to a high propeller twist and a moderate increase in the opening angle in the basepairs. Starting from an initial value of 30 degrees, helical twist of the average structure from this simulation had a value of 36 degrees, while the parallel structure stabilized at a twist of 33 degrees. In spite of the hydrogen bond distortions in the antiparallel tripler, it was energetically comparable to the parallel tripler. To examine the structural characteristics of an undistorted structure, another MD simulation was performed on the antiparallel tripler by constraining all the hydrogen bonds. This structure stabilized at an average twist of 33 degrees. In the course of the dynamics though the energy of the molecule - compared to the initial structure - improved, it did not become comparable to the parallel structure. Energy minimization studies performed in the presence of explicit water and counterions also showed the two structures to be equally favourable energetically Together these results indicate that the parallel C.G*G tripler with Hoogsteen hydrogen bonds also represents a stereochemically and energetically favourable structure for this class of triplexes.

Sequence Independent Recombination Triple Helices: A Molecular Dynamics Study

Recent experimental studies have shown that the Rec-A mediated homologous recombination reaction involves a triple helical intermediate, in which the third strand base forms hydrogen bonds with both the bases in the major groove of the Watson-Crick duplex. Such 'mixed' hydrogen bonds allow formation of sequence independent triplexes. DNA triple helices involving 'mixed' hydrogen bonds have been studied, using model building, molecular mechanics (MM) and molecular dynamics (MD). Models were built for a tripler comprising all four possible triplets viz., G.C*C, C.G*G, A.T*T and T.A*A. To check the stability of all the 'mixed' hydrogen bonds in such triplexes and the conformational preferences of such tripler structures, MD studies were carried out starting from two structures with 30 degrees and 36 degrees twist between the basepairs. It was observed that though the two triplexes converged towards a similar structure, the various hydrogen bonds between the WC duplex and the third strand showed differential stabilities. An MD simulation with restrained hydrogen bonds showed that the resulting structure was stable and remained close to the starting structure. These studies help us in defining stable hydrogen bond geometries involving the third strand and the WC duplex. It was observed that in the C.G*G triplets the N7 atom of the second strand is always involved in hydrogen bonding. In the G.C*C triplets, either N3 or O2 in the third strand cytosine can interchangeably act as a hydrogen bond acceptor.

Analysis of the evanescent field coupling between a fiber and a planar waveguide using the explicit finite difference method with a nonuniform mesh (Journal Paper)

We investigate an optical waveguide system consisting of an unclad fiber core suspended at a constant distance parallel to the surface of a planar waveguide. The coupling and propagation of light in the combined system is studied using the three-dimensional explicit finite difference beam propagation method with a nonuniform mesh configuration. The power loss in the fiber and the field distribution in the waveguide are studied as a function of various parameters, such as index changes, index profile, and propagation distance, for the combined system.

Stability of synchronization in a multi-cellular system

Networks of biochemical reactions regulated by positive-and negative-feedback processes underlie functional dynamics in single cells. Synchronization of dynamics in the constituent cells is a hallmark of collective behavior in multi-cellular biological systems. Stability of the synchronized state is required for robust functioning of the multi-cell system in the face of noise and perturbation. Yet, the ability to respond to signals and change functional dynamics are also important features during development, disease, and evolution in living systems. In this paper, using a coupled multi-cell system model, we investigate the role of system size, coupling strength and its topology on the synchronization of the collective dynamics and its stability. Even though different coupling topologies lead to synchronization of collective dynamics, diffusive coupling through the end product of the pathway does not confer stability to the synchronized state. The results are discussed with a view to their prevalence in biological systems. Copyright (C) EPLA, 2010