Transport processes in one component plasmas using Landau equation

A system of transport equations have been obtained for plasma of electrons and having a background of positive ions in the presence of an electric and magnetic field. The starting kinetic equation is the well-known Landau kinetic equation. The distribution function of the kinetic equation has been expanded in powers of generalized Hermite polynomials and following Grad, a consistent set of transport equations have been obtained. The expressions for viscosity and heat conductivity have been deduced from the transport equation.

Particle dynamics in the channel flow of a turbulent particle-gas suspension at high Stokes number. Part 1. DNS and fluctuating force model

The fluctuating force model is developed and applied to the turbulent flow of a gas-particle suspension in a channel in the limit of high Stokes number, where the particle relaxation time is large compared to the fluid correlation time, and low particle Reynolds number where the Stokes drag law can be used to describe the interaction between the particles and fluid. In contrast to the Couette flow, the fluid velocity variances in the different directions in the channel are highly non-homogeneous, and they exhibit significant variation across the channel. First, we analyse the fluctuating particle velocity and acceleration distributions at different locations across the channel. The distributions are found to be non-Gaussian near the centre of the channel, and they exhibit significant skewness and flatness. However, acceleration distributions are closer to Gaussian at locations away from the channel centre, especially in regions where the variances of the fluid velocity fluctuations are at a maximum. The time correlations for the fluid velocity fluctuations and particle acceleration fluctuations are evaluated, and it is found that the time correlation of the particle acceleration fluctuations is close to the time correlations of the fluid velocity in a `moving Eulerian' reference, moving with the mean fluid velocity. The variances of the fluctuating force distributions in the Langevin simulations are determined from the time correlations of the fluid velocity fluctuations and the results are compared with direct numerical simulations. Quantitative agreement between the two simulations are obtained provided the particle viscous relaxation time is at least five times larger than the fluid integral time.

Particle dynamics in the channel flow of a turbulent particle-gas suspension at high Stokes number. Part 2. Comparison of fluctuating force simulations and experiments

The particle and fluid velocity fluctuations in a turbulent gas-particle suspension are studied experimentally using two-dimensional particle image velocimetry with the objective of comparing the experiments with the predictions of fluctuating force simulations. Since the fluctuating force simulations employ force distributions which do not incorporate the modification of fluid turbulence due to the particles, it is of importance to quantify the turbulence modification in the experiments. For experiments carried out at a low volume fraction of 9.15 x 10(-5) (mass loading is 0.19), where the viscous relaxation time is small compared with the time between collisions, it is found that the gas-phase turbulence is not significantly modified by the presence of particles. Owing to this, quantitative agreement is obtained between the results of experiments and fluctuating force simulations for the mean velocity and the root mean square of the fluctuating velocity, provided that the polydispersity in the particle size is incorporated in the simulations. This is because the polydispersity results in a variation in the terminal velocity of the particles which could induce collisions and generate fluctuations; this mechanism is absent if all of the particles are of equal size. It is found that there is some variation in the particle mean velocity very close to the wall depending on the wall-collision model used in the simulations, and agreement with experiments is obtained only when the tangential wall-particle coefficient of restitution is 0.7. The mean particle velocity is in quantitative agreement for locations more than 10 wall units from the wall of the channel. However, there are systematic differences between the simulations and theory for the particle concentrations, possibly due to inadequate control over the particle feeding at the entrance. The particle velocity distributions are compared both at the centre of the channel and near the wall, and the shape of the distribution function near the wall obtained in experiments is accurately predicted by the simulations. At the centre, there is some discrepancy between simulations and experiment for the distribution of the fluctuating velocity in the flow direction, where the simulations predict a bi-modal distribution whereas only a single maximum is observed in the experiments, although both distributions are skewed towards negative fluctuating velocities. At a much higher particle mass loading of 1.7, where the time between collisions is smaller than the viscous relaxation time, there is a significant increase in the turbulent velocity fluctuations by similar to 1-2 orders of magnitude. Therefore, it becomes necessary to incorporate the modified fluid-phase intensity in the fluctuating force simulation; with this modification, the mean and mean-square fluctuating velocities are within 20-30% of the experimental values.

Group Actions and Elementary Number Theory

Abstract | In this article the shuffling of cards is studied by using the concept of a group action. We use some fundamental results in Elementary Number Theory to obtain formulas for the orders of some special shufflings, namely the Faro and Monge shufflings and give necessary and sufficient conditions for the Monge shuffling to be a cycle. In the final section we extend the considerations to the shuffling of multisets.

Males, but not females, mate with multiple partners: a laboratory study of a primitively eusocial wasp Ropalidia marginata

The intense interest in social Hymenoptera, on account of their elaborate sociality and the paradox of altruism, has often suffered from considerable gender imbalance. This is partly due to the fact that worker behaviour and altruism are restricted to the females and partly because males often live off the nest. Yet, understanding the males, especially in the context of mating biology is essential even for understanding the evolution of sociality. Mating patterns have a direct bearing on the levels of intra-colony genetic relatedness, which in turn, along with the associated costs and benefits of worker behaviour, are central to our understanding of the evolution of sociality. Although mating takes place away from the nest in natural colonies of the primitively eusocial wasp Ropalidia marginata, mating can be observed in the laboratory if a male and a female are placed in a transparent, aerated plastic container, and both wasps are in the range of 5-20 days of age. Here, we use this setup and show that males, but not females, mate serially with multiple partners. The multiple mating behaviour of the males is not surprising because in nature males have to mate with a number of females, only a few of whom will go on to lay eggs. The reluctance of R. marginata females to mate with multiple partners is consistent with the expectation of monogamy in primitively eusocial species with totipotent females, although the apparent discrepancy with a previous work with allozyme markers in natural colonies suggesting that females may sometimes mate with two or three different males remains to be resolved.

Mathematical Model of Viral Kinetics In Vitro Estimates the Number of E2-CD81 Complexes Necessary for Hepatitis C Virus Entry

Interaction between the hepatitis C virus (HCV) envelope protein E2 and the host receptor CD81 is essential for HCV entry into target cells. The number of E2-CD81 complexes necessary for HCV entry has remained difficult to estimate experimentally. Using the recently developed cell culture systems that allow persistent HCV infection in vitro, the dependence of HCV entry and kinetics on CD81 expression has been measured. We reasoned that analysis of the latter experiments using a mathematical model of viral kinetics may yield estimates of the number of E2-CD81 complexes necessary for HCV entry. Here, we constructed a mathematical model of HCV viral kinetics in vitro, in which we accounted explicitly for the dependence of HCV entry on CD81 expression. Model predictions of viral kinetics are in quantitative agreement with experimental observations. Specifically, our model predicts triphasic viral kinetics in vitro, where the first phase is characterized by cell proliferation, the second by the infection of susceptible cells and the third by the growth of cells refractory to infection. By fitting model predictions to the above data, we were able to estimate the threshold number of E2-CD81 complexes necessary for HCV entry into human hepatoma-derived cells. We found that depending on the E2-CD81 binding affinity, between 1 and 13 E2-CD81 complexes are necessary for HCV entry. With this estimate, our model captured data from independent experiments that employed different HCV clones and cells with distinct CD81 expression levels, indicating that the estimate is robust. Our study thus quantifies the molecular requirements of HCV entry and suggests guidelines for intervention strategies that target the E2-CD81 interaction. Further, our model presents a framework for quantitative analyses of cell culture studies now extensively employed to investigate HCV infection.

Rainbow Connection Number and Connectivity

The rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges, so that every pair of vertices is connected by at least one path in which no two edges are colored the same. Our main result is that rc(G) <= inverted right perpendicularn/2inverted left perpendicular for any 2-connected graph with at least three vertices. We conjecture that rc(G) <= n/kappa + C for a kappa-connected graph G of order n, where C is a constant, and prove the conjecture for certain classes of graphs. We also prove that rc(G) < (2 + epsilon)n/kappa + 23/epsilon(2) for any epsilon > 0.

Selective double quantum resolved correlation experiment for the complete separation of entire proton NMR spectra of enantiomers

The present study reports a two dimensional NMR experiment which separates single quantum spectra of enantiomers from that of a racemic mixture. This is a blend of selective double quantum refocusing, for resolving couplings and chemical shift interactions along two dimensions followed by correlation of the selectively excited protons to the entire coupled spin network. The concept is solely based on the presence of distinct intra methyl dipolar couplings of different enantiomers when dissolved in chiral orienting media. The analysis of single enantiomer spectrum obtained from respective F-2 cross sections yield all the spectral information. (C) 2011 Elsevier Inc. All rights reserved.

An inverse problem for Helmholtz equation

This article is concerned with subsurface material identification for the 2-D Helmholtz equation. The algorithm is iterative in nature. It assumes an initial guess for the unknown function and obtains corrections to the guessed value. It linearizes the otherwise nonlinear problem around the background field. The background field is the field variable generated using the guessed value of the unknown function at each iteration. Numerical results indicate that the algorithm can recover a close estimate of the unknown function based on the measurements collected at the boundary.

Real-time monitoring of critical nodes with minimal number of Phasor Measurement Units

This paper presents a method for placement of Phasor Measurement Units, ensuring the monitoring of vulnerable buses which are obtained based on transient stability analysis of the overall system. Real-time monitoring of phase angles across different nodes, which indicates the proximity to instability, the very purpose will be well defined if the PMUs are placed at buses which are more vulnerable. The issue is to identify the key buses where the PMUs should be placed when the transient stability prediction is taken into account considering various disturbances. Integer Linear Programming technique with equality and inequality constraints is used to find out the optimal placement set with key buses identified from transient stability analysis. Results on IEEE-14 bus system are presented to illustrate the proposed approach.

GINZBURG-LANDAU LIKE THEORY OF HIGH TEMPERATURE SUPERCONDUCTIVITY IN THE CUPRATES: EMERGENT d-WAVE ORDER

High temperature superconductivity in the cuprates remains one of the most widely investigated, constantly surprising and poorly understood phenomena in physics. Here, we describe briefly a new phenomenological theory inspired by the celebrated description of superconductivity due to Ginzburg and Landau and believed to describe its essence. This posits a free energy functional for the superconductor in terms of a complex order parameter characterizing it. We propose that there is, for superconducting cuprates, a similar functional of the complex, in plane, nearest neighbor spin singlet bond (or Cooper) pair amplitude psi(ij). Further, we suggest that a crucial part of it is a (short range) positive interaction between nearest neighbor bond pairs, of strength J'. Such an interaction leads to nonzero long wavelength phase stiffness or superconductive long range order, with the observed d-wave symmetry, below a temperature T-c similar to zJ' where z is the number of nearest neighbors; d-wave superconductivity is thus an emergent, collective consequence. Using the functional, we calculate a large range of properties, e. g., the pseudogap transition temperature T* as a function of hole doping x, the transition curve T-c(x), the superfluid stiffness rho(s)(x, T), the specific heat (without and with a magnetic field) due to the fluctuating pair degrees of freedom and the zero temperature vortex structure. We find remarkable agreement with experiment. We also calculate the self-energy of electrons hopping on the square cuprate lattice and coupled to electrons of nearly opposite momenta via inevitable long wavelength Cooper pair fluctuations formed of these electrons. The ensuing results for electron spectral density are successfully compared with recent experimental results for angle resolved photo emission spectroscopy (ARPES), and comprehensively explain strange features such as temperature dependent Fermi arcs above T-c and the ``bending'' of the superconducting gap below T-c.

On the Presumed Kinetic Consequences of Pre-equilibrium. Implications for the Michaelis-Menten Equation

The overall rate equation for a reaction sequence consisting of a pre-equilibrium and rate-determining steps should not be derived on the basis of the concentration of the intermediate product (X). This is apparently indicated by transition state theory (as the path followed to reach the highest energy transition state is irrelevant), but also proved by a straight-forward mathematical approach. The thesis is further supported by the equations of concurrent reactions as applied to the partitioning of X between the two competing routes (reversal of the pre-equilibrium and formation of product). The rate equation may only be derived rigorously on the basis of the law of mass action. It is proposed that the reactants acquire the overall activation energy prior to the pre-equilibrium, thus forming X in a high-energy state en route to the rate-determining transition state. (It is argued that conventional energy profile diagrams are misleading and need to be reinterpreted.) Also, these arguments invalidate the Michaelis-Menten equation of enzyme kinetics, and necessitate a fundamental revision of our present understanding of enzyme catalysis. (The observed ``saturation kinetics'' possibly arises from weak binding of a second molecule of substrate at the active site; analogous conclusions apply to reactions at surfaces).

Thermoluminescence and EPR studies of nanocrystalline Nd2O3:Ni2+ phosphor

Nanocrystalline Nd2O3:Ni2+ (2 mol%) phosphor has been prepared by a low temperature (similar to 400 degrees C) solution combustion method, in a very short time (<5 min). Powder X-ray diffraction results confirm the single hexagonal phase of nanopowders. Scanning electron micrographs show that nanophosphor has porous nature and the particles are agglomerated. Transmission electron microscopy confirms the nanosize (20-25 nm) of the crystallites. The electron paramagnetic resonance (EPR) spectrum exhibits a symmetric absorption at g approximate to 2.77 which suggests that the site symmetry around Ni2+ ions is predominantly octahedral. The number of spins participating in resonance (N) and the paramagnetic susceptibility (chi) has been evaluated. Raman study show major peaks, which are assigned to F-g and combination of A(g) + E-g modes. Thermoluminescence (TL) studies reveal well resolved glow peaks at 169 degrees C along with shoulder peak at around 236 degrees C. The activation energy (E in eV), order of kinetics (b) and frequency factor (s) were estimated using glow peak shape method. It is observed that the glow peak intensity at 169 degrees C increases linearly with gamma-dose which suggest that Nd2O3:Ni2+ is suitable for radiation dosimetry applications. (C) 2012 Elsevier B.V. All rights reserved.

Two-dimensional flow past circular cylinders using finite volume lattice Boltzmann formulation

In this article, an extension to the total variation diminishing finite volume formulation of the lattice Boltzmann equation method on unstructured meshes was presented. The quadratic least squares procedure is used for the estimation of first-order and second-order spatial gradients of the particle distribution functions. The distribution functions were extrapolated quadratically to the virtual upwind node. The time integration was performed using the fourth-order RungeKutta procedure. A grid convergence study was performed in order to demonstrate the order of accuracy of the present scheme. The formulation was validated for the benchmark two-dimensional, laminar, and unsteady flow past a single circular cylinder. These computations were then investigated for the low Mach number simulations. Further validation was performed for flow past two circular cylinders arranged in tandem and side-by-side. Results of these simulations were extensively compared with the previous numerical data. Copyright (C) 2011 John Wiley & Sons, Ltd.

Mass of highly magnetized white dwarfs exceeding the Chandrasekhar limit: An analytical view

In recent years a number of white dwarfs have been observed with very high surface magnetic fields. We can expect that the magnetic field in the core of these stars would be much higher (similar to 10(14) G). In this paper, we analytically study the effect of high magnetic field on relativistic cold electron, and hence its effect on the stability and the mass-radius relation of a magnetic white dwarf. In strong magnetic fields, the equation of state of the Fermi gas is modified and Landau quantization comes into play. For relatively very high magnetic fields (with respect to the average energy density of matter) the number of Landau levels is restricted to one or two. We analyze the equation of states for magnetized electron degenerate gas analytically and attempt to understand the conditions in which transitions from the zeroth Landau level to first Landau level occurs. We also find the effect of the strong magnetic field on the star collapsing to a white dwarf, and the mass-radius relation of the resulting star. We obtain an interesting theoretical result that it is possible to have white dwarfs with mass more than the mass set by Chandrasekhar limit.