Ultrafast Solvation Dynamics of an Ion in the gamma-Cyclodextrin Cavity: The Role of Restricted Environment

A detailed study of the solvation dynamics of a charged coumarin dye molecule in gamma-cyclodextrin/water has been carried out by using two different theoretical approaches. The first approach is based on a multishell continuum model (MSCM). This model predicts the time scales of the dynamics rather well, provided an accurate description of the frequency-dependent dielectric function is supplied. The reason for this rather surprising agreement is 2-fold. First, there is a cancellation of errors, second, the two-zone model mimics the heterogeneous microenvironment surrounding the ion rather well. The second approach is based on the molecular hydrodynamics theory (MI-IT). In this molecular approach, the solvation dynamics has been studied by restricting the translational motion of the solvent molecules enclosed within the cavity. The results from the molecular theory are also in good agreement with the experimental results. Our study indicates that, in the present case, the restricted environment affects only the long time decay of the solvation time correlation function. The short time dynamics is still governed by the librational (and/or vibrational) modes present in bulk water.

Quest for new materials: Inorganic chemistry plays a crucial role

There is an endless quest for new materials to meet the demands of advancing technology. Thus, we need new magnetic and metallic/semiconducting materials for spintronics, new low-loss dielectrics for telecommunication, new multi-ferroic materials that combine both ferroelectricity and ferromagnetism for memory devices, new piezoelectrics that do not contain lead, new lithium containing solids for application as cathode/anode/electrolyte in lithium batteries, hydrogen storage materials for mobile/transport applications and catalyst materials that can convert, for example, methane to higher hydrocarbons, and the list is endless! Fortunately for us, chemistry - inorganic chemistry in particular - plays a crucial role in this quest. Most of the functional materials mentioned above are inorganic non-molecular solids, while much of the conventional inorganic chemistry deals with isolated molecules or molecular solids. Even so, the basic concepts that we learn in inorganic chemistry, for example, acidity/basicity, oxidation/reduction (potentials), crystal field theory, low spin-high spin/inner sphere-outer sphere complexes, role of d-electrons in transition metal chemistry, electron-transfer reactions, coordination geometries around metal atoms, Jahn-Teller distortion, metal-metal bonds, cation-anion (metal-nonmetal) redox competition in the stabilization of oxidation states - all find crucial application in the design and synthesis of inorganic solids possessing technologically important properties. An attempt has been made here to illustrate the role of inorganic chemistry in this endeavour, drawing examples from the literature its well as from the research work of my group.

Role of conformational dynamics in kinetics of an enzymatic cycle in a nonequilibrium steady state

Enzyme is a dynamic entity with diverse time scales, ranging from picoseconds to seconds or even longer. Here we develop a rate theory for enzyme catalysis that includes conformational dynamics as cycling on a two-dimensional (2D) reaction free energy surface involving an intrinsic reaction coordinate (X) and an enzyme conformational coordinate (Q). The validity of Michaelis-Menten (MM) equation, i.e., substrate concentration dependence of enzymatic velocity, is examined under a nonequilibrium steady state. Under certain conditions, the classic MM equation holds but with generalized microscopic interpretations of kinetic parameters. However, under other conditions, our rate theory predicts either positive (sigmoidal-like) or negative (biphasic-like) kinetic cooperativity due to the modified effective 2D reaction pathway on X-Q surface, which can explain non-MM dependence previously observed on many monomeric enzymes that involve slow or hysteretic conformational transitions. Furthermore, we find that a slow conformational relaxation during product release could retain the enzyme in a favorable configuration, such that enzymatic turnover is dynamically accelerated at high substrate concentrations. The effect of such conformation retainment in a nonequilibrium steady state is evaluated.

On the propagation of a weak shock front: Theory and application

In this paper the kinematics of a weak shock front governed by a hyperbolic system of conservation laws is studied. This is used to develop a method for solving problems, involving the propagation of nonlinear unimodal waves. It consists of first solving the nonlinear wave problem by moving along the bicharacteristics of the system and then fitting the shock into this solution field, so that it satisfies the necessary jump conditions. The kinematics of the shock leads in a natural way to the definition of ldquoshock-raysrdquo, which play the same role as the ldquoraysrdquo in a continuous flow. A special case of a circular cylinder introduced suddenly in a constant streaming flow is studied in detail. The shock fitted in the upstream region propagates with a velocity which is the mean of the velocities of the linear and the nonlinear wave fronts. In the downstream the solution is given by an expansion wave.

A numerical study of the role of the vertical structure of vorticity during tropical cyclone genesis

An eight-level axisymmetric model with simple parameterizations for clouds and the atmospheric boundary layer was developed to examine the evolution of vortices that are precursors to tropical cyclones. The effect of vertical distributions of vorticity, especially that arising from a merger of mid-level vortices, was studied by us to provide support for a new vortex-merger theory of tropical cyclone genesis. The basic model was validated with the analytical results available for the spin-down of axisymmetric vortices. With the inclusion of the cloud and boundary layer parameterizations, the evolution of deep vortices into hurricanes and the subsequent decay are simulated quite well. The effects of several parameters such as the initial vortex strength, radius of maximum winds, sea-surface temperature and latitude (Coriolis parameter) on the evolution were examined. A new finding is the manner in which mid-level vortices of the same strength decay and how, on simulated merger of these mid-level vortices, the resulting vortex amplifies to hurricane strength in a realistic time frame. The importance of sea-surface temperature on the evolution of full vortices was studied and explained. Also it was found that the strength of the surface vortex determines the time taken by the deep vortex to amplify to hurricane strength.

Molecular hydrodynamic theory of non‐Markovian collective orientational relaxation in dense dipolar liquids

A microscopic study of the non‐Markovian (or memory) effects on the collective orientational relaxation in a dense dipolar liquid is carried out by using an extended hydrodynamic approach which provides a reliable description of the dynamical processes occuring at the molecular length scales. Detailed calculations of the wave‐vector dependent orientational correlation functions are presented. The memory effects are found to play an important role; the non‐Markovian results differ considerably from that of the Markovian theory. In particular, a slow long‐time decay of the longitudinal orientational correlation function is observed for dense liquids which becomes weaker in the presence of a sizeable translational contribution to the collective orientational relaxation. This slow decay can be attributed to the intermolecular correlations at the molecular length scales. The longitudinal component of the orientational correlation function becomes oscillatory in the underdamped limit of momenta relaxations and the frequency dependence of the friction reduce the frictional resistance on the collective excitations (commonly known as dipolarons) to make them long lived. The theory predicts that these dipolarons can, therefore, be important in chemical relaxation processes, in contradiction to the claims of some earlier theoretical studies.

A Theory of the Lifted Temperature Minimum on Calm Clear Nights

Numerous reports from several parts of the world have confirmed that on calm clear nights a minimum in air temperature can occur just above ground, at heights of the order of $\frac{1}{2}$ m or less. This phenomenon, first observed by Ramdas & Atmanathan (1932), carries the associated paradox of an apparently unstable layer that sustains itself for several hours, and has not so far been satisfactorily explained. We formulate here a theory that considers energy balance between radiation, conduction and free or forced convection in humid air, with surface temperature, humidity and wind incorporated into an appropriate mathematical model as parameters. A complete numerical solution of the coupled air-soil problem is used to validate an approach that specifies the surface temperature boundary condition through a cooling rate parameter. Utilizing a flux-emissivity scheme for computing radiative transfer, the model is numerically solved for various values of turbulent friction velocity. It is shown that a lifted minimum is predicted by the model for values of ground emissivity not too close to unity, and for sufficiently low surface cooling rates and eddy transport. Agreement with observation for reasonable values of the parameters is demonstrated. A heuristic argument is offered to show that radiation substantially increases the critical Rayleigh number for convection, thus circumventing or weakening Rayleigh-Benard instability. The model highlights the key role played by two parameters generally ignored in explanations of the phenomenon, namely surface emissivity and soil thermal conductivity, and shows that it is unnecessary to invoke the presence of such particulate constituents as haze to produce a lifted minimum.

Quenching across quantum critical points: Role of topological patterns

We introduce a one-dimensional version of the Kitaev model consisting of spins on a two-legged ladder and characterized by Z(2) invariants on the plaquettes of the ladder. We map the model to a fermionic system and identify the topological sectors associated with different Z2 patterns in terms of fermion occupation numbers. Within these different sectors, we investigate the effect of a linear quench across a quantum critical point. We study the dominant behavior of the system by employing a Landau-Zener-type analysis of the effective Hamiltonian in the low-energy subspace for which the effective quenching can sometimes be non-linear. We show that the quenching leads to a residual energy which scales as a power of the quenching rate, and that the power depends on the topological sectors and their symmetry properties in a non-trivial way. This behavior is consistent with the general theory of quantum quenching, but with the correlation length exponent nu being different in different sectors. Copyright (C) EPLA, 2010

Application of scaled particle theory to alkyl-aryl surfactants: a two zone model of micellar core

Scaled Particle Theory (SPT) has been applied to predict the total free energies of micellization of ionic as well as nonionic micellar systems containing an aryl ring. A modification of the previously developed model has been made, proposing a two-zone model of micellar core which corroborates with the structural information available for such systems. The results are in good agreement with experimental data and also confirm the dictating role of cavity forming free energies for such systems

Orientational relaxation in dipolar systems: How much do we understand the role of correlations

Dipolar systems, both liquids and solids, constitute a class of naturally abundant systems that are important in all branches of natural science. The study of orientational relaxation provides a powerful method to understand the microscopic properties of these systems and, fortunately, there are many experimental tools to study orientational relaxation in the condensed phases. However, even after many years of intense research, our understanding of orientational relaxation in dipolar systems has remained largely imperfect. A major hurdle towards achieving a comprehensive understanding is the long range and complex nature of dipolar interactions which also made reliable theoretical study extremely difficult. These difficulties have led to the development of continuum model based theories, which although they provide simple, elegant expressions for quantities of interest, are mostly unsatisfactory as they totally neglect the molecularity of inter-molecular interactions. The situation has improved in recent years because of renewed studies, led by computer simulations. In this review, we shall address some of the recent advances, with emphasis on the work done in our laboratory at Bangalore. The reasons for the failure of the continuum model, as revealed by the recent Brownian dynamics simulations of the dipolar lattice, are discussed. The main reason is that the continuum model predicts too fast a decay of the torque-torque correlation function. On the other hand, a perturbative calculation, based on Zwanzig's projection operator technique, provides a fairly satisfactory description of the single particle orientational dynamics for not too strongly polar dipolar systems. A recently developed molecular hydrodynamic theory that properly includes the effects of intermolecular orientational pair correlations provides an even better description of the single-particle orientational dynamics. We also discuss the rank dependence of the dielectric friction. The other topics reviewed here includes dielectric relaxation and solvation dynamics, as they are intimately connected with orientational relaxation. Recent molecular dynamics simulations of the dipolar lattice are also discussed. The main theme of the present review is to understand the effects of intermolecular interactions on orientational relaxation. The presence of strong orientational pair correlation leads to a strong coupling between the single particle and the collective dynamics. This coupling can lead to rich dynamical properties, some of which are detailed here, while a major part remains yet unexplored.

Light-induced geometric isomerization of 1,2-diphenylcyclopropanes included within Y zeolites: Role of cation-guest binding

Through a systematic study of several diphenylcyclopropane derivatives, we have inferred that the cations present within a zeolite control the excited-state chemistry of these systems. In the parent 1,2-diphenylcylopropane, the cation binds to the two phenyl rings in a sandwich-type arrangement, and such a mode of binding prevents cis-to-trans isomerization. Once an ester or amide group is introduced into the system (derivatives of 2beta,3beta-diphenylcyclopropane-1alpha-carboxylic acid), the cation binds to the carbonyl group present in these chromophores and such a binding has no influence on the cis-trans isomerization process. Cation-reactant structures computed at density functional theory level have been very valuable in rationalizing the observed photochemical behavior of diphenylcyclopropane derivatives included in zeolites. While the parent system, 1,2-diphenyleylopropane, has been extensively investigated in the context of chiral induction in solution, owing to its failure to isomerize from cis to trans, the same could not be investigated in zeolites. However, esters of 2beta,3beta-diphenylcyclopropane-1alpha-carboxylic acid could be studied within zeolites in the context of chiral induction. Chiral induction as high 20% ee and 55% de has been obtained with selected systems. These numbers, although low, are much higher than what has been obtained in solution with the same system or with the parent system by other investigators (maximum similar to10% ee).

Can the viscosity in astrophysical black hole accretion disks be close to its string theory bound?

String theory and gauge/gravity duality suggest the lower bound of shear viscosity (eta) to entropy density (s) for any matter to be mu h/4 pi k(B), when h and k(B) are reduced Planck and Boltzmann constants respectively and mu <= 1. Motivated by this, we explore eta/s in black hole accretion flows, in order to understand if such exotic flows could be a natural site for the lowest eta/s. Accretion flow plays an important role in black hole physics in identifying the existence of the underlying black hole. This is a rotating shear flow with insignificant molecular viscosity, which could however have a significant turbulent viscosity, generating transport, heat and hence entropy in the flow. However, in presence of strong magnetic field, magnetic stresses can help in transporting matter independent of viscosity, via celebrated Blandford-Payne mechanism. In such cases, energy and then entropy produces via Ohmic dissipation. In,addition, certain optically thin, hot, accretion flows, of temperature greater than or similar to 10(9) K, may be favourable for nuclear burning which could generate/absorb huge energy, much higher than that in a star. We find that eta/s in accretion flows appears to be close to the lower bound suggested by theory, if they are embedded by strong magnetic field or producing nuclear energy, when the source of energy is not viscous effects. A lower bound on eta/s also leads to an upper bound on the Reynolds number of the flow.

Sustaining cooperation on networks: an analytical study based on evolutionary game theory

We analytically study the role played by the network topology in sustaining cooperation in a society of myopic agents in an evolutionary setting. In our model, each agent plays the Prisoner's Dilemma (PD) game with its neighbors, as specified by a network. Cooperation is the incumbent strategy, whereas defectors are the mutants. Starting with a population of cooperators, some agents are switched to defection. The agents then play the PD game with their neighbors and compute their fitness. After this, an evolutionary rule, or imitation dynamic is used to update the agent strategy. A defector switches back to cooperation if it has a cooperator neighbor with higher fitness. The network is said to sustain cooperation if almost all defectors switch to cooperation. Earlier work on the sustenance of cooperation has largely consisted of simulation studies, and we seek to complement this body of work by providing analytical insight for the same. We find that in order to sustain cooperation, a network should satisfy some properties such as small average diameter, densification, and irregularity. Real-world networks have been empirically shown to exhibit these properties, and are thus candidates for the sustenance of cooperation. We also analyze some specific graphs to determine whether or not they sustain cooperation. In particular, we find that scale-free graphs belonging to a certain family sustain cooperation, whereas Erdos-Renyi random graphs do not. To the best of our knowledge, ours is the first analytical attempt to determine which networks sustain cooperation in a population of myopic agents in an evolutionary setting.