Isomerization dynamics in viscous liquids: Microscopic investigation of the coupling and decoupling of the rate to and from solvent viscosity and dependence on the intermolecular potential

A detailed investigation of viscosity dependence of the isomerization rate is carried out for continuous potentials by using a fully microscopic, self-consistent mode-coupling theory calculation of both the friction on the reactant and the viscosity of the medium. In this calculation we avoid approximating the short time response by the Enskog limit, which overestimates the friction at high frequencies. The isomerization rate is obtained by using the Grote-Hynes formula. The viscosity dependence of the rate has been investigated for a large number of thermodynamic state points. Since the activated barrier crossing dynamics probes the high-frequency frictional response of the liquid, the barrier crossing rate is found to be sensitive to the nature of the reactant-solvent interaction potential. When the solute-solvent interaction is modeled by a 6-12 Lennard-Jones potential, we find that over a large variation of viscosity (eta), the rate (k) can indeed be fitted very well to a fractional viscosity dependence: (k similar to eta(-alpha)), with the exponent alpha in the range 1 greater than or equal to alpha >0. The calculated values of the exponent appear to be in very good agreement with many experimental results. In particular, the theory, for the first time, explains the experimentally observed high value of alpha even at the barrier frequency, omega(b). similar or equal to 9 X 10(12) s(-1) for the isomerization reaction of 2-(2'-propenyl)anthracene in liquid eta-alkanes. The present study can also explain the reason for the very low value of vb observed in another study for the isomerization reaction of trans-stilbene in liquid n-alkanes. For omega(b) greater than or equal to 2.0 X 10(13) s(-1), we obtain alpha similar or equal to 0, which implies that the barrier crossing rate becomes identical to the transition-state theory predictions. A careful analysis of isomerization reaction dynamics involving large amplitude motion suggests that the barrier crossing dynamics itself may become irrelevant in highly viscous liquids and the rate might again be coupled directly to the viscosity. This crossover is predicted to be strongly temperature dependent and could be studied by changing the solvent viscosity by the application of pressure. (C) 1999 American Institute of Physics. [S0021-9606(9950514-X].

Modelling electricity demand with representative load curves

Models for electricity planning require inclusion of demand. Depending on the type of planning, the demand is usually represented as an annual demand for electricity (GWh), a peak demand (MW) or in the form of annual load-duration curves. The demand for electricity varies with the seasons, economic activities, etc. Existing schemes do not capture the dynamics of demand variations that are important for planning. For this purpose, we introduce the concept of representative load curves (RLCs). Advantages of RLCs are demonstrated in a case study for the state of Karnataka in India. Multiple discriminant analysis is used to cluster the 365 daily load curves for 1993-94 into nine RLCs. Further analyses of these RLCs help to identify important factors, namely, seasonal, industrial, agricultural, and residential (water heating and air-cooling) demand variations besides rationing by the utility. (C) 1999 Elsevier Science Ltd. All rights reserved.

Structural characterization and chain dynamics of poly(alpha-methylstyrene peroxide) by NMR spectroscopy

Poly(alpha-methylstyrene peroxide) has been synthesized and characterized spectroscopically. The H-1 and C-13 NMR spectra are shown to reveal the stereochemical features and the endgroups in the peroxide chain. The preliminary studies on the chain dynamics of the polyperoxide chain has been done by measuring the spin-lattice relaxation times (T-1) of the main chain as well as the side chain carbons. It has been shown from the dependence of the spin-lattice relaxation times that the polyperoxide chain is more flexible compared to the corresponding hydrocarbon-backbone analog.

Nonlinear dynamics and chaotic motions in feedback-controlled two- and three-degree-of-freedom robots

The dynamics of a feedback-controlled rigid robot is most commonly described by a set of nonlinear ordinary differential equations. In this paper we analyze these equations, representing the feedback-controlled motion of two- and three-degrees-of-freedom rigid robots with revolute (R) and prismatic (P) joints in the absence of compliance, friction, and potential energy, for the possibility of chaotic motions. We first study the unforced or inertial motions of the robots, and show that when the Gaussian or Riemannian curvature of the configuration space of a robot is negative, the robot equations can exhibit chaos. If the curvature is zero or positive, then the robot equations cannot exhibit chaos. We show that among the two-degrees-of-freedom robots, the PP and the PR robot have zero Gaussian curvature while the RP and RR robots have negative Gaussian curvatures. For the three-degrees-of-freedom robots, we analyze the two well-known RRP and RRR configurations of the Stanford arm and the PUMA manipulator respectively, and derive the conditions for negative curvature and possible chaotic motions. The criteria of negative curvature cannot be used for the forced or feedback-controlled motions. For the forced motion, we resort to the well-known numerical techniques and compute chaos maps, Poincare maps, and bifurcation diagrams. Numerical results are presented for the two-degrees-of-freedom RP and RR robots, and we show that these robot equations can exhibit chaos for low controller gains and for large underestimated models. From the bifurcation diagrams, the route to chaos appears to be through period doubling.

Polar and nonpolar solvation dynamics, ion diffusion, and vibrational relaxation: Role of biphasic solvent response in chemical dynamics

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Solvation dynamics in nonassociated polar solvents

Ultrafast solvation dynamics in three nonassociated polar solvents, namely, acetonitrile, dimethyl sulfoxide, and acetone, have been studied by using the molecular hydrodynamic theory. For solvation in acetonitrile, the solvent memory function required for this study has been obtained from recent dielectric relaxation measurements of Venabales and Schuttenmaer; earlier theoretical studies used only the Kerr relaxation data. As the latter provides only an indirect information regarding the polar dynamical response of the dipolar liquid, it fails to provide a fully quantitative description of the solvation time correlation function, S(t). The present study with full dielectric data, on the other hand, gives excellent agreement with the experimental results. The theory shows that the ultrafast part of the solvation dynamics originates almost entirely from the high-frequency component of dielectric relaxation (with time constant 0.177 ps), although the latter represents only a small part of the latter. For DMSO and acetone, however, the present theory predicts a decay slower than the experimental observation. It is proposed that for these two solvents specific chromophore-solvent interactions might be responsible for the-large discrepancy. On the basis of the theory, two experimental studies have also been proposed.

Solvation dynamics of a quadrupolar solute in dipolar liquids

A microscopic calculation of solvation dynamics of dipolar and quadrupolar solutes in liquid water and acetonitrile is presented. The solvation is found to he biphasic. The calculated solvation time correlation function of ionic quadrupolar solute (K+) in water is in good agreement with re cent computer simulation results. Present study reveals some interesting aspects of quadrupolar solvation dynamics which differ significantly from that of ionic and dipolar solvation.

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.

Structural characterisation of a uracil containing hairpin DNA by NMR and molecular dynamics

Three-dimensional (3D) structure of a hairpin DNA d-CTAGAGGATCCTTTUGGATCCT (22mer; abbreviated as U4-hairpin), which has a uracil nucleotide unit at the fourth position from the 5' end of the tetra-loop has been solved by NMR spectroscopy. The H-1 resonances of this hairpin have been assigned almost completely. NMR restrained molecular dynamics and energy minimisation procedures have been used to describe the 3D structure of the U4 hairpin. This study establishes that the stem of the hairpin adopts a right handed B-DNA conformation while the T-12 and U-15 nucleotide stack upon 3' and 5' ends of the stem, respectively. Further, T-14 stacks upon both T-12 and U-15 while T-13 partially stacks upon T-14. Very weak stacking interaction is observed between T-13 and T-12. All the individual nucleotide bases adopt 'anti' conformation with respect to their sugar moiety. The turning phosphate in the loop is located between T-13 and T-14. The stereochemistry of U-15 mimics the situation where uracil would stack in a B-DNA conformation. This could be the reason as to why the U4-hairpin is found to be the best substrate for its interaction with uracil DNA glycosylase (UDG) compared to the other substrates in which the uracil is at the first, second and third positions of the tetra-loop from its 5' end, as reported previously.

Subquadratic quantum number dependence and other anomalies of vibrational dephasing in liquid nitrogen: Molecular dynamics simulation study from the triple point to the critical point and beyond

Vibrational phase relaxation near gas-liquid and liquid-solid phase coexistence has been studied by molecular dynamics simulations of N-N stretch in N-2. Experimentally observed pronounced insensitivity of phase relaxation from the triple point to beyond the boiling point is found to originate from a competition between density relaxation and resonant-energy transfer terms. The sharp rise in relaxation rate near the critical point (CP) can be attributed at least partly to the sharp, rise in vibration-rotation coupling contribution. Substantial subquadratic quantum number dependence of overtone dephasing rate is found near the CP and in supercritical fluids. [S0031-9007 (99)09318-7].

Algal Photosynthetic Dynamics in Urban Lakes under Stress Conditions

Urban lakes form vital ecosystems supporting livelihood with social, economic and aesthetic benefits that are essential for quality life. This depends on the biotic and abiotic components in an ecosystem. The structure of an ecosystem forms a decisive factor in sustaining its functional abilities which include nutrient cycling, oxygen production, etc. A community assemblage of primary producers (algae) plays a crucial role in maintaining the balance as they form the base of energy pyramid in the ecosystem. Algae assimilate carbon in the environment via photosynthetic activities and releases oxygen for the next level of biotic elements in an ecosystem. Besides these, algal cells rich in protein serve as food and feed, used as manure and for production of biofuels. Understanding algal photosynthetic dynamics helps in assessing the level of dissolved oxygen (DO), food (fish, etc.), waste assimilation, etc. Algal chlorophyll content, algal biomass, primary productivity and algal photosynthetic quotient are some of the parameters that help in assessing the status of urban lakes. Chlorophyll content gives a measure of the growth, spread and quantity of algae. Unplanned rapid urbanization in Bangalore in recent times has resulted in either disappearance of lake ecosystems or deteriorated the lake water quality impairing the ecological processes. This paper computes algal growth, community structure, primary productivity and composition for three major lakes (T G Halli, Bellandur and Varthur lakes) under contrast levels of anthropogenic influences.

The molecular dynamics study of lithium ion conduction in phosphate glasses and the role of non-bridging oxygen

Molecular dynamics (MD) simulation of lithium phosphate (Li2O-P2O5) glasses with varying Li2O content has been carried out. Two different P-O distances corresponding to phosphorus coordination with bridging oxygen (BO) and non-bridging oxygen (NBO) were identified in the simulated glasses. NBO-BO interconversion or bond switching was noted, which results in a dynamic equilibration of the tetrahedral phosphate units (P-n, n = 1,3 indicates the number of bridging oxygen atoms in the coordination of phosphorus). The NBO-BO bond switching is mildly activated with an effective activation barrier of 0.03-0.05 eV. Lithium ion jumps do not appear to be strongly coupled to bond switching. But the number of Li+ ions coordinated to an optimum number of NBOs and the number of Li+ ions jumping out of their sites appear to be correlated. Detailed analysis was made of the dynamics of P-n species and new insights have been obtained regarding ion migration in network-modified phosphate glasses.

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.

Comparison of the ultrafast to slow time scale dynamics of three liquid crystals in the isotropic phase

The dynamics of three liquid crystals, 4'(pentyloxy)-4-biphenylcarbonitrile (5-OCB), 4'-pentyl-4-biphenylcarbonitrile (5-CB), and 1-isothiocyanato-(4-propylcyclohexyl)benzene (3-CHBT), are investigated from very short time (similar to1 ps) to very long time (>100 ns) as a function of temperature using optical heterodyne detected optical Kerr effect experiments. For all three liquid crystals, the data decay exponentially only on the longest time scale (> several ns). The temperature dependence of the long time scale exponential decays is described well by the Landau-de Gennes theory of the randomization of pseudonematic domains that exist in the isotropic phase of liquid crystals near the isotropic to nematic phase transition. At short time, all three liquid crystals display power law decays. Over the full range of times, the data for all three liquid crystals are fit with a model function that contains a short time power law. The power law exponents for the three liquid crystals range between 0.63 and 0.76, and the power law exponents are temperature independent over a wide range of temperatures. Integration of the fitting function gives the empirical polarizability-polarizability (orientational) correlation function. A preliminary theoretical treatment of collective motions yields a correlation function that indicates that the data can decay as a power law at short times. The power law component of the decay reflects intradomain dynamics. (C) 2002 American Institute of Physics.

Topological phases, Majorana modes and quench dynamics in a spin ladder system

We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections between spin phases and topologically non-trivial phases of non-interacting fermionic systems, demonstrating the equivalence between the spontaneous breaking of global Z(2) symmetry in spin systems and the existence of isolated Majorana modes. In the Kitaev ladder, we investigate topological properties of the system in different sectors characterized by the presence or absence of a vortex in each plaquette of the ladder. We show that vortex patterns can yield a rich parameter space for tuning into topologically non-trivial phases. We introduce and employ a new topological invariant for explicitly determining the presence of zero energy Majorana modes at the boundaries of such phases. Finally, we discuss dynamic quenching between topologically non-trivial phases in the Kitaev ladder and, in particular, the post-quench dynamics governed by tuning through a quantum critical point.