Nonlinear Dynamics of Beams with Stochastic Parameter Variations

The aim of this paper is to investigate the steady state response of beams under the action of random support motions. The study is of relevance in the context of earthquake response of extended land based structures such as pipelines and long span bridges, and, secondary systems such as piping networks in nuclear power plant installations. The following complicating features are accounted for in the response analysis: (a) differential support motions: this is characterized in terms of cross power spectral density functions associated with distinct support motions, (b) nonlinear support conditions, and (c) stochastically inhomogeneous stiffness and mass variations of the beam structure; questions on non-Gaussian models for these variations are considered. The method of stochastic finite elements is combined with equivalent linearization technique and Monte Carlo simulations to obtain response moments.

Synthesis, structural characterization, thermal studies and chain dynamics of poly(methacrylonitrile peroxide) by NMR spectroscopy

Poly(methacrylonitrile peroxide) (PMNP) has been synthesized from methacrylonitrile by free radical initiated oxidative polymerization and characterized by different spectroscopic methods. NMR spectroscopy confirmed the alternating copolymer structure with labile peroxy bonds in the main chain. The extreme instability of PMNP was noted from FTIR spectroscopy. Thermal degradation studies by using differential scanning calorimetry and thermogravimetry have revealed that PMNP degrades highly exothermically and the heat of degradation, 42.5 kcal mol−1, is of the same order as that reported for other vinyl polyperoxides. Mass spectral fragmentation pattern under electron impact (EI) condition has also been investigated. The mechanism of the primary exothermic degradation has been substantiated by thermochemical calculations. The chain dynamics of the polyperoxide chain has been studied by means of 13C spin–lattice relaxation times (T1) of the main chain as well as the side chain carbons. The temperature dependence of the spin–lattice relaxation times shows that the PMNP is more flexible compared to the analogous poly(styrene peroxide).

Understanding glassy dynamics from the free-energy landscape

Many interesting features of the dynamics of simple liquids near the glass transition may be understood in terms of properties of the free-energy landscape obtained from numerical studies of a model free-energy functional. Main results obtained from this approach are summarized and a list of references to relevant publications is provided. (C) 2002 Elsevier Science B.V. All rights reserved.

On the dynamics of activation of mammalian X chromosomes

We have investigated a mathematical model of the process of activation of the X chromosomes in eutherian mammals. The model assumes that the activation is brought about over some definite time interval T by the complete saturation of N receptor sites on an X chromosome by M activating molecules (or multiples of M). The probability λ of a first hit on the receptor site is considered to be very much lower than that of subsequent hits; that is, we assume strong co-operative binding. Assuming further that an incomplete saturation of receptor sites is malfunctional, we can show that for proper activation of X chromosomes in normal diploid males and females, we must have λMT ≥ 3 and 0·96 ≤ N/M ≤ 1. An extension of this analysis for the triploid cases shows that under these conditions, we cannot explain the activation of two X's if the number of activating molecules is fixed at M. This suggests that there must be two classes of triploid embryos differing from each other in a step-wise manner in the number of activating molecules. In other words, triploids with two active X chromosomes would require 2M activating molecules as opposed to M molecules in triploids with a single active X. This interpretation of the two classes of triploids would be consistent with differing imprinting histories of the parental contributions to the triploid zygote.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 2. The fluctuating-force model

A fluctuating-force model is developed for representing the effect of the turbulent fluid velocity fluctuations on the particle phase in a turbulent gas–solid suspension in the limit of high Stokes number, where the particle relaxation time is large compared with the correlation time for the fluid velocity fluctuations. In the model, a fluctuating force is incorporated in the equation of motion for the particles, and the force distribution is assumed to be an anisotropic Gaussian white noise. It is shown that this is equivalent to incorporating a diffusion term in the Boltzmann equation for the particle velocity distribution functions. The variance of the force distribution, or equivalently the diffusion coefficient in the Boltzmann equation, is related to the time correlation functions for the fluid velocity fluctuations. The fluctuating-force model is applied to the specific case of a Couette flow of a turbulent particle–gas suspension, for which both the fluid and particle velocity distributions were evaluated using direct numerical simulations by Goswami & Kumaran (2010). It is found that the fluctuating-force simulation is able to quantitatively predict the concentration, mean velocity profiles and the mean square velocities, both at relatively low volume fractions, where the viscous relaxation time is small compared with the time between collisions, and at higher volume fractions, where the time between collisions is small compared with the viscous relaxation time. The simulations are also able to predict the velocity distributions in the centre of the Couette, even in cases in which the velocity distribution is very different from a Gaussian distribution.

The collective dynamics of self-propelled particles

We propose a method for the dynamic simulation of a collection of self-propelled particles in a viscous Newtonian fluid. We restrict attention to particles whose size and velocity are small enough that the fluid motion is in the creeping flow regime. We propose a simple model for a self-propelled particle, and extended the Stokesian Dynamics method to conduct dynamic simulations of a collection of such particles. In our description, each particle is treated as a sphere with an orientation vector p, whose locomotion is driven by the action of a force dipole Sp of constant magnitude S0 at a point slightly displaced from its centre. To simplify the calculation, we place the dipole at the centre of the particle, and introduce a virtual propulsion force Fp to effect propulsion. The magnitude F0 of this force is proportional to S0. The directions of Sp and Fp are determined by p. In isolation, a self-propelled particle moves at a constant velocity u0 p, with the speed u0 determined by S0. When it coexists with many such particles, its hydrodynamic interaction with the other particles alters its velocity and, more importantly, its orientation. As a result, the motion of the particle is chaotic. Our simulations are not restricted to low particle concentration, as we implement the full hydrodynamic interactions between the particles, but we restrict the motion of particles to two dimensions to reduce computation. We have studied the statistical properties of a suspension of self-propelled particles for a range of the particle concentration, quantified by the area fraction φa. We find several interesting features in the microstructure and statistics. We find that particles tend to swim in clusters wherein they are in close proximity. Consequently, incorporating the finite size of the particles and the near-field hydrodynamic interactions is of the essence. There is a continuous process of breakage and formation of the clusters. We find that the distributions of particle velocity at low and high φa are qualitatively different; it is close to the normal distribution at high φa, in agreement with experimental measurements. The motion of the particles is diffusive at long time, and the self-diffusivity decreases with increasing φa. The pair correlation function shows a large anisotropic build-up near contact, which decays rapidly with separation. There is also an anisotropic orientation correlation near contact, which decays more slowly with separation. Movies are available with the online version of the paper.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 1. Velocity and acceleration distributions

The effect of fluid velocity fluctuations on the dynamics of the particles in a turbulent gas–solid suspension is analysed in the low-Reynolds-number and high Stokes number limits, where the particle relaxation time is long compared with the correlation time for the fluid velocity fluctuations, and the drag force on the particles due to the fluid can be expressed by the modified Stokes law. The direct numerical simulation procedure is used for solving the Navier–Stokes equations for the fluid, the particles are modelled as hard spheres which undergo elastic collisions and a one-way coupling algorithm is used where the force exerted by the fluid on the particles is incorporated, but not the reverse force exerted by the particles on the fluid. The particle mean and root-mean-square (RMS) fluctuating velocities, as well as the probability distribution function for the particle velocity fluctuations and the distribution of acceleration of the particles in the central region of the Couette (where the velocity profile is linear and the RMS velocities are nearly constant), are examined. It is found that the distribution of particle velocities is very different from a Gaussian, especially in the spanwise and wall-normal directions. However, the distribution of the acceleration fluctuation on the particles is found to be close to a Gaussian, though the distribution is highly anisotropic and there is a correlation between the fluctuations in the flow and gradient directions. The non-Gaussian nature of the particle velocity fluctuations is found to be due to inter-particle collisions induced by the large particle velocity fluctuations in the flow direction. It is also found that the acceleration distribution on the particles is in very good agreement with the distribution that is calculated from the velocity fluctuations in the fluid, using the Stokes drag law, indicating that there is very little correlation between the fluid velocity fluctuations and the particle velocity fluctuations in the presence of one-way coupling. All of these results indicate that the effect of the turbulent fluid velocity fluctuations can be accurately represented by an anisotropic Gaussian white noise.

Dynamics and transport properties of Kondo insulators

A many-body theory of paramagnetic Kondo insulators is described, focusing specifically on single-particle dynamics, scattering rates, dc transport and optical conductivities. This is achieved by development of a non-perturbative local moment approach to the symmetric periodic Anderson model within the framework of dynamical mean-field theory. Our natural focus is the strong-coupling, Kondo lattice regime, in particular the resultant 'universal' scaling behaviour in terms of the single, exponentially small low-energy scale characteristic of the problem. Dynamics/transport on all relevant (ω, T)-scales are considered, from the gapped/activated behaviour characteristic of the low-temperature insulator through to explicit connection to single-impurity physics at high ω and/or T; and for optical conductivities emphasis is given to the nature of the optical gap, the temperature scale responsible for its destruction and the consequent clear distinction between indirect and direct gap scales. Using scaling, explicit comparison is also made to experimental results for dc transport and optical conductivities of Ce3Bi4Pt3, SmB6 and YbB12. Good agreement is found, even quantitatively; and a mutually consistent picture of transport and optics results.

Dynamics of bound dyes in a nonpolymeric aqueous gel derived from a tripodal bile salt

Rotational dynamics of polarity sensitive fluorescent dyes (ANS and DPH) in a nonpolymertic aqueous gel derived from tripodal cholamide I was studied using ultrafast time-resolved fluorescence technique. Results were compared with that of naturally occurring di- and trihydroxy bile salts. ANS in the gel showed two rotational correlation time (phi) components, 13.2 ns (bound to the hydrophobic region of the gel) and 1.0 ns (free aqueous ANS), whereas DPH showed only one component (4.8 ns). In the sol state, faster rotational motion was observed, both for ANS and DPH. Our data revealed that dyes get encapsulated more tightly in the gel network when compared to the micellar aggregates. ANS has more restrained rotation compared to DPH. This was attributed to the interaction of the sulfonate group of ANS with water molecules and hydrophilic parts of the gelator molecule. No restricted rotation was observed for DPH in the gel state unlike when it is in the gel phase of lipid bilayer.

Dynamics of pulsed flow in an elastic tube

Internal haemorrhage, often leading to cardio-vascular arrest happens to be one of the prime sources of high fatality rates in mammals. We propose a simplistic model of fluid flow in our attempt to specify the location of the haemorrhagic spot, which, if located accurately, could possibly be operated leading to an instant cure. The model we employ for the purpose is basically fluid mechanical in origin and consists of a viscous fluid, pumped by a periodic force and flowing through an elastic tube. The analogy is with that of blood, pumped from the heart and flowing through an artery or vein. Our results, aided by graphical illustrations, match reasonably well with experimental observations.

Dynamics of water at the interface of a small protein, enterotoxin

Fully atomistic molecular dynamics simulations have been carried out to investigate the correlation of biological activity with dynamics of water molecules in an aqueous protein solution of the toxic domain of enterotoxin (PDB ID: 1ETN). This is a small protein of 13 amino acid residues. Our study of this water soluble protein clearly reveals that water dynamics slows down in the hydration layer. Despite this general slowing down, water molecules in the vicinity of the second beta turn of this protein exhibit faster dynamics than those near other regions of the protein. Since this beta turn is believed to play a critical role in the receptor binding of this protein, the faster dynamics of water near the beta turn m ay have biological significance. The collective orientational dynamics of the water molecules in the protein solution exhibits a characteristic long time component of 27 ps, which agrees well with dielectric relaxation experiments.

Efficient syntheses of benzothiazepines as antagonists for the mitochondrial sodium-calcium exchanger: Potential therapeutics for type II diabetes

Type II diabetes mellitus is a chronic metabolic disorder that can lead to serious cardiovascular, renal, neurologic, and retinal complications. While several drugs are currently prescribed to treat type II diabetes, their efficacy is limited by mechanism-related side effects (weight gain, hypoglycemia, gastrointestinal distress), inadequate efficacy for use as monotherapy, and the development of tolerance to the agents. Consequently, combination therapies are frequently employed to effectively regulate blood glucose levels. We have focused on the mitochondrial sodium-calcium exchanger (mNCE) as a novel target for diabetes drug discovery. We have proposed that inhibition of the mNCE can be used to regulate calcium flux across the mitochondrial membrane, thereby enhancing mitochondrial oxidative metabolism, which in turn enhances glucose-stimulated insulin secretion (GSIS) in the pancreatic beta-cell. In this paper, we report the facile synthesis of benzothiazepines and derivatives by S-alkylation using 2-aminobenzhydrols. The syntheses of other bicyclic analogues based on benzothiazepine, benzothiazecine, benzodiazecine, and benzodiazepine templates are also described. These compounds have been evaluated for their inhibition of mNCE activity, and the results from the structure-activity relationship (SAR) studies are discussed.

Identity, energetics, dynamics and environment of interfacial water molecules in a micellar solution

The structure and energetics of interfacial water molecules in the aqueous micelle of cesium perfluorooctanoate have been investigated, using large-scale atomistic molecular dynamics simulations, with the primary objective of classifying them. The simulations show that the water molecules at the interface fall into two broad classes: bound and free, present in a ratio of 9:1. The bound water molecules can be further categorized on the basis of the number of hydrogen bonds (one or two) that they form with the surfactant headgroups. The hydrogen bonds of the doubly hydrogen-bonded species are found to be, on the average, slightly weaker than those in the singly bonded species. The environment around interfacial water molecules is more ordered than that in the bulk. The surface water molecules have substantially lower potential energy, because of interaction with the micelle. In particular, both forms of bound water have energies that are lower by �2.5-4.0 kcal/ mol. Entropy is found to play an important role in determining the relative concentration of the species.

Study of the dynamics of protein folding through minimalistic models

Starting with the Levinthal paradox, a brief introduction to the protein folding problem is presented. The existing theories of protein folding, including the folding funnel scenario, are discussed. After briefly discussing different simulation studies of model proteins, we discuss our recent work on the dynamics of folding of the model HP-36 (the chicken villin headpiece) protein by using a simplified hydropathy scale. Special attention has been paid to the statics and dynamics of contact formation among the hydrophobic residues. The results obtained from this simple model appear to be surprisingly similar to several features observed in the folding of real proteins. The account concludes with a discussion of future problems.