Non-diffusive classical transport in a medium with static randomness

The probability distribution for the displacement x of a particle moving in a one-dimensional continuum is derived exactly for the general case of combined static and dynamic gaussian randomness of the applied force. The dynamics of the particle is governed by the high-friction limit of Brownian motion discussed originally by Einstein and Smoluchowski. In particular, the mean square displacement of the particle varies as t2 for t to infinity . This ballistic motion induced by the disorder does not give rise to a 1/f power spectrum, contrary to recent suggestions based on the above dynamical model.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

Molecular theory of solvation and solvation dynamics of a classical ion in a dipolar liquid

A microscopic theory of equilibrium solvation and solvation dynamics of a classical, polar, solute molecule in dipolar solvent is presented. Density functional theory is used to explicitly calculate the polarization structure around a solvated ion. The calculated solvent polarization structure is different from the continuum model prediction in several respects. The value of the polarization at the surface of the ion is less than the continuum value. The solvent polarization also exhibits small oscillations in space near the ion. We show that, under certain approximations, our linear equilibrium theory reduces to the nonlocal electrostatic theory, with the dielectric function (c(k)) of the liquid now wave vector (k) dependent. It is further shown that the nonlocal electrostatic estimate of solvation energy, with a microscopic c(k), is close to the estimate of linearized equilibrium theories of polar liquids. The study of solvation dynamics is based on a generalized Smoluchowski equation with a mean-field force term to take into account the effects of intermolecular interactions. This study incorporates the local distortion of the solvent structure near the ion and also the effects of the translational modes of the solvent molecules.The latter contribution, if significant, can considerably accelerate the relaxation of solvent polarization and can even give rise to a long time decay that agrees with the continuum model prediction. The significance of these results is discussed.

Freezing of classical fluids in a quenched random potential

The phase diagram of a hard-sphere fluid in the presence of a random pinning potential is studied analytically and numerically. In the analytic work, replicas are introduced for averaging over the quenched disorder, and the hypernetted chain approximation is used to calculate density correlations in the replicated liquid. The freezing transition of the liquid into a nearly crystalline state is studied using a density-functional approach, and the liquid to glass transition is studied using a phenomenological replica symmetry breaking approach. In the numerical work, local minima of a discretized version of the Ramakrishnan-Yussouff free-energy functional are located and the phase diagram in the density-disorder plane is obtained from an analysis of the relative stability of these minima. Both approaches lead to similar results for the phase diagram. The first-order liquid to crystalline solid transition is found to change to a continuous liquid to glass transition as the strength of the disorder is increased above a threshold value.

Classical integrability in the BTZ black hole

Using the fact the BTZ black hole is a quotient of AdS(3) we show that classical string propagation in the BTZ background is integrable. We construct the flat connection and its monodromy matrix which generates the non-local charges. From examining the general behaviour of the eigen values of the monodromy matrix we determine the set of integral equations which constrain them. These equations imply that each classical solution is characterized by a density function in the complex plane. For classical solutions which correspond to geodesics and winding strings we solve for the eigen values of the monodromy matrix explicitly and show that geodesics correspond to zero density in the complex plane. We solve the integral equations for BMN and magnon like solutions and obtain their dispersion relation. We show that the set of integral equations which constrain the eigen values of the monodromy matrix can be identified with the continuum limit of the Bethe equations of a twisted SL(2, R) spin chain at one loop. The Landau-Lifshitz equations from the spin chain can also be identified with the sigma model equations of motion.

Supersymmetry of classical solutions in Chern-Simons higher spin supergravity

We construct and study classical solutions in Chern-Simons supergravity based on the superalgebra sl(N vertical bar N = 1). The algebra for the N = 3 case is written down explicitly using the fact that it arises as the global part of the super conformal W-3 superalgebra. For this case we construct new classical solutions and study their supersymmetry. Using the algebra we write down the Killing spinor equations and explicitly construct the Killing spinor for conical defects and black holes in this theory. We show that for the general sl(N|N - 1) theory the condition for the periodicity of the Killing spinor can be written in terms of the products of the odd roots of the super algebra and the eigenvalues of the holonomy matrix of the background. Thus the supersymmetry of a given background can be stated in terms of gauge invariant and well defined physical observables of the Chern-Simons theory. We then show that for N >= 4, the sl(N|N - 1) theory admits smooth supersymmetric conical defects.

UVB irradiation alters the activities and kinetic properties of the enzymes of energy metabolism in rat lens during aging

Ultraviolet (UV) radiation is one of the major risk factors of cataract (loss of eye-lens transparency). The influence of UVB radiation (300 nm, 100 mu W cm(-2)) on the activity and apparent kinetic constants (K-m and V-max) of rat lens hexokinase (HK;EC2.7.1.1), phosphofructokinase (PFK;EC2.7.1.11), isocitrate dehydrogenase (ICDH;EC1.1.1.41) and malate dehydrogenase (MDH;EC1.1.1.37) of energy metabolism has been investigated by irradiating the lens homogenate of three-and 12-month-old rats. In the three-month-old group specific activities of HK and PFK are reduced by 56 and 43 %, respectively, and there is no change in ICDH and MDH activities after a 24 h exposure. On the other hand, in the 12-month-old group the decreases are 72, 71, 24 and 16 % for HK, PFK. ICDH and MDH, respectively. UVB irradiation increases the apparent K-m of HK and PFK (in both age groups), whereas the K-m of ICDH and MDH is not altered. While the decrease in V-max of these enzymes due to UVB exposure is only marginal in three-month-old rats, it is more pronounced (significant) in 12-month-old rats. A similar decrease in enzyme activities of HK and PFK is also observe upon UVB exposure of the intact rat lens. The photoinduced changes in energy metabolism may in turn have a bearing on lens transparency, particularly at an older age.

Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero —the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial but subtle role of the boundary, we have simulated here the case of a finite but unbounded system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment that now indeed turns out to be non-zero and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.

Non-Abelian monopoles break color. I. Classical mechanics

Monopoles which are sources of non-Abelian magnetic flux are predicted by many models of grand unification. It has been argued elsewhere that a generic transformation of the "unbroken" symmetry group H cannot be globally implemented on such monopoles for reasons of topology. In this paper, we show that similar topological obstructions are encountered in the mechanics of a test particle in the field of these monopoles and that the transformations of H cannot all be globally implemented as canonical transformations. For the SU(5) model, if H is SU(3)C×U(1)em, a consequence is that color multiplets are not globally defined, while if H is SU(3)C×SU(2)WS×U(1)Y, the same is the case for both color and electroweak multiplets. There are, however, several subgroups KT, KT′,… of H which can be globally implemented, with the transformation laws of the observables differing from group to group in a novel way. For H=SU(3)C×U(1)em, a choice for KT is SU(2)C×U(1)em, while for H=SU(3)C×SU(2)WS×U(1)Y, a choice is SU(2)C×U(1)×U(1)×U(1). The paper also develops the differential geometry of monopoles in a form convenient for computations.

Dopamine receptors in human foetal brains:Characterization, regulation and ontogeny of [3H]spiperone binding sites in striatum

Eighteen corpora striata from normal human foetal brains ranging in gestational age from 16 to 40 weeks and five from post natal brains ranging from 23 days to 42 years were analysed for the ontogeny of dopamine receptors using [3H]spiperone as the ligand and 10 mM dopamine hydrochloride was used in blanks. Spiperone binding sites were characterized in a 40-week-old foetal brain to be dopamine receptors by the following criteria: (1) It was localized in a crude mitochondrial pellet that included synaptosomes; (2) binding was saturable at 0.8 nM concentration; (3) dopaminergic antagonists spiperone, haloperidol, pimozide, trifluperazine and chlorpromazine competed for the binding with IC50 values in the range of 0.3–14 nM while agonists—apomorphine and dopamine gave IC50 values of 2.5 and 10 μM, respectively suggesting a D2 type receptor.Epinephrine and norepinephrine inhibited the binding much less efficiently while mianserin at 10 μM and serotonin at 1 mM concentration did not inhibit the binding. Bimolecular association and dissociation rate constants for the reversible binding were 5.7 × 108 M−1 min−1 and 5.0 × 10−2 min−1, respectively. Equilibrium dissociation constant was 87 pM and the KD obtained by saturation binding was 73 pM.During the foetal age 16 to 40 weeks, the receptor concentration remained in the range of 38–60 fmol/mg protein or 570–1080 fmol/g striatum but it increased two-fold postnatally reaching a maximum at 5 years Significantly, at lower foetal ages (16–24 weeks) the [3H]spiperone binding sites exhibited a heterogeneity with a high (KD, 13–85 pM) and a low (KD, 1.2–4.6 nM) affinity component, the former accounting for 13–24% of the total binding sites. This heterogeneity persisted even when sulpiride was used as a displacer. The number of high affinity sites increased from 16 weeks to 24 weeks and after 28 weeks of gestation, all the binding sites showed only a single high affinity.GTP decreased the agonist affinity as observed by dopamine competition of [3H]spiperone binding in 20-week-old foetal striata and at all subsequent ages. GTP increased IC50 values of dopamine 2 to 4.5 fold and Hill coefficients were also increased becoming closer to one suggesting that the dopamine receptor was susceptible to regulation from foetal life onwards.

Characterization of estuarine marine clays for coastal reclamation in Pusan, Korea

Large scale reclamation works in coastal areas of the Nakdong River plain are at various stages of progress, since early 1990's on in-situ soft marine clay deposits. These deposits are of the order of 30 to 40 m thick. A realistic rapid characterization of soft ground would ensure success of any reclamation work in this area. In order to cope with the work carried out with different agencies, it is desirable to evolve a systematic methodology. In this study, engineering properties of clays at three coastal areas, Gadukdo, Noksan and Shinho, have been generated. The analysis of data has been done within the framework of classical developments in soil mechanics. Analysis has also been made by making use of the recent developments in dealing with soft clays. The dominant factors, namely, stress, time, and environment influencing the response of clay to loading are identified.

Describing Hand Postures: Inspirations from Classical Mudras

The objective of this work is to develop a systematic methodology for describing hand postures and grasps which is independent of the kinematics and geometry of the hand model which in turn can be used for developing a universal referencing scheme. It is therefore necessary that the scheme be general enough to describe the continuum of hand poses. Indian traditional classical dance form, “Bharathanatyam”, uses 28 single handed gestures, called “mudras”. A Mudra can be perceived as a hand posture with a specific pattern of finger configurations. Using modifiers, complex mudras could be constructed from relatively simple mudras. An adjacency matrix is constructed to describe the relationship among mudras. Various mudra transitions can be obtained from the graph associated with this matrix. Using this matrix, a hierarchy of the mudras is formed. A set of base mudras and modifiers are used for describing how one simple posture of hand can be transformed into another relatively complex one. A canonical set of predefined hand postures and modifiers can be used in digital human modeling to develop standard hand posture libraries.

Generating string solutions in BTZ

Integrability of classical strings in the BTZ black hole enables the construction and study of classical string propagation in this background. We first apply the dressing method to obtain classical string solutions in the BTZ black hole. We dress time like geodesics in the BTZ black hole and obtain open string solutions which are pinned on the boundary at a single point and whose end points move on time like geodesics. These strings upon regularising their charge and spins have a dispersion relation similar to that of giant magnons. We then dress space like geodesics which start and end on the boundary of the BTZ black hole and obtain minimal surfaces which can penetrate the horizon of the black hole while being pinned at the boundary. Finally we embed the giant gluon solutions in the BTZ background in two different ways. They can be embedded as a spiral which contracts and expands touching the horizon or a spike which originates from the boundary and touches the horizon.

Multiwalled-carbon-nanotube-induced miscibility in near-critical PS/PVME blends: assessment through concentration fluctuations and segmental relaxation

The effects of multiwalled carbon nanotubes (MWNTs) on the concentration fluctuations, interfacial driven elasticity, phase morphology, and local segmental dynamics of chains for near-critical compositions of polystyrene/poly(vinyl to methyl ether) (PS/PVME) blends were systematically investigated using dynamic shear rheology and dielectric spectroscopy. The contribution of the correlation length (xi) of the concentration fluctuations to the evolving stresses was monitored in situ to probe the different stages of demixing in the blends. The classical upturn in the dynamic moduli was taken as the rheological demixing temperature (T-rheo), which was also observed to be in close agreement with those obtained using concentration fluctuation variance, <(delta phi)(2)>, versus temperature curves. Further, Fredrickson and Larson's approach involving the mean-field approximation and the double-reptation self-concentration (DRSC) model was employed to evaluate the spinodal decomposition temperature (T-s). Interestingly, the values of both T-rheo and T-s shifted upward in the blends in the presence of MWNTs, manifesting in molecular-level miscibility. These phenomenal changes were further observed to be a function of the concentration of MWNTs. The evolution of morphology as a function of temperature was studied using polarized optical microscopy (POM). It was observed that PVME, which evolved as an interconnected network during the early stages of demixing, coarsened into a matrix-droplet morphology in the late stages. The preferential wetting of PVME onto MWNTs as a result of physicochemical interactions retained the interconnected network of PVME for longer time scales, as supported by POM and atomic force microscopy (AFM) images. Microscopic heterogeneity in macroscopically miscible systems was studied by dielectric relaxation spectroscopy. The slowing of segmental relaxations in PVME was observed in the presence of both ``frozen'' PS and MWNTs interestingly at temperatures much below the calorimetric glass transition temperature (T-g). This phenomenon was observed to be local rather than global and was addressed by monitoring the evolution of the relaxation spectra near and above the demixing temperature.

Energy loss due to adhesion in longitudinal impact of elastic cylinders

Adhesive interaction between impacting bodies can cause energy loss, even in an otherwise elastic impact. Adhesion force induces tensile stress in the bodies, which modifies the stress wave profile and influences the restitution behavior. We investigate this effect by developing a finite element framework, which incorporates a Lennard-Jones-type potential for modeling the adhesive interaction between volume elements. With this framework, the classical problems in contact mechanics can be revisited without the restrictive surface-force approximation. In this paper, we study the longitudinal impact of an elastic cylinder on a rigid half-space with adhesion. In the absence of adhesion, this problem reduces to the impact between two identical cylinders in which there is no energy loss. Adhesion causes a fraction of energy in the stress waves to remain in the cylinder as residual stress waves. This apparent loss in kinetic energy is shown to be a unique function of maximum tensile strain energy. We have developed a 1-D model in terms of interaction force parameters, velocity and material properties to estimate the tensile stain energy. We show that this model can be used to predict practically important phenomena like capture wherein the impacting bodies stick together. (C) 2013 Elsevier Masson SAS. All rights reserved.