Relativistic particle models with separable interactions

We present relativistic, classical particle models that possess Poincaré invariance, invariant world lines, particle interaction, and separability.

A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization

While frame-invariant solutions for arbitrarily large rotational deformations have been reported through the orthogonal matrix parametrization, derivation of such solutions purely through a rotation vector parametrization, which uses only three parameters and provides a parsimonious storage of rotations, is novel and constitutes the subject of this paper. In particular, we employ interpolations of relative rotations and a new rotation vector update for a strain-objective finite element formulation in the material framework. We show that the update provides either the desired rotation vector or its complement. This rules out an additive interpolation of total rotation vectors at the nodes. Hence, interpolations of relative rotation vectors are used. Through numerical examples, we show that combining the proposed update with interpolations of relative rotations yields frame-invariant and path-independent numerical solutions. Advantages of the present approach vis-a-vis the updated Lagrangian formulation are also analyzed.

Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Bi-criteria single machine scheduling problem with a learning effect: Aneja-Nair method to obtain the set of optimal sequences

In this paper, we consider the bi-criteria single machine scheduling problem of n jobs with a learning effect. The two objectives considered are the total completion time (TC) and total absolute differences in completion times (TADC). The objective is to find a sequence that performs well with respect to both the objectives: the total completion time and the total absolute differences in completion times. In an earlier study, a method of solving bi-criteria transportation problem is presented. In this paper, we use the methodology of solvin bi-criteria transportation problem, to our bi-criteria single machine scheduling problem with a learning effect, and obtain the set of optimal sequences,. Numerical examples are presented for illustrating the applicability and ease of understanding.

Study of effects of dopants on structure of vitreous semiconductors (GeSe3.5)100-xMx (M = Bi, Sb) using high pressure techniques

An investigation of the problem of controlled doping of amorphous chalcogenide semiconductors utilizing a Bridgman anvil high pressure technique, has been undertaken. Bulk amorphous semiconducting materials (GeSe3.5)100-x doped with M = Bi (x = 2, 4, 10) and M = Sb (x = 10) respectively are studied up to a pressure of 100 kbar down to liquid nitrogen temperature, with a view to observe the impurity induced modifications. Measurement of the electrical conductivity of the doped samples under quasi-hydrostatic pressure reveals that the pressure induced effects in lightly doped (2 at % Bi) and heavily doped (x = 4, 10) semiconductors are markedly different. The pressure effects in Sb-doped semiconductors are quite different from those in Bi-doped material.

Improving Flow-Insensitive Solutions for Non-Separable Dataflow Problems

Flow-insensitive solutions to dataflow problems have been known to be highly scalable; however also hugely imprecise. For non-separable dataflow problems this solution is further degraded due to spurious facts generated as a result of dependence among the dataflow facts. We propose an improvement to the standard flow-insensitive analysis by creating a generalized version of the dominator relation that reduces the number of spurious facts generated. In addition, the solution obtained contains extra information to facilitate the extraction of a better solution at any program point, very close to the flow-sensitive solution. To improve the solution further, we propose the use of an intra-block variable renaming scheme. We illustrate these concepts using two classic non-separable dataflow problems --- points-to analysis and constant propagation.

Novel intramolecular reductive C-C coupling during borohydride reduction of a bi-enone

Borohydride reduction of the bi-enone (1) gave the structurally and mechanistically interesting compounds (4) and (5a-c) resulting from intramolecular carbon-carbon coupling.

A note on non-separable solutions of linear partial differential equation

A method has been presented for constructing non-separable solutions of homogeneous linear partial differential equations of the type F(D, D′)W = 0, where D = ∂/∂x, D′ = ∂/∂y, Image where crs are constants and n stands for the order of the equation. The method has also been extended for equations of the form Φ(D, D′, D″)W = 0, where D = ∂/∂x, D′ = ∂/∂y, D″ = ∂/∂z and Image As illustration, the method has been applied to obtain nonseparable solutions of the two and three dimensional Helmholtz equations.

On a generalized dynamic model of bi-state social interaction processes

A non-linear model, construed as a generalized version of the models put forth earlier for the study of bi-state social interaction processes, is proposed in this study. The feasibility of deriving the dynamics of such processes is demonstrated by establishing equivalence between the non-linear model and a higher order linear model.

Invariant magneto-electric and piezomagnetic coefficients

Invariant magneto-electric coefficients and invariant piezomagnetic coefficients are obtained for all the magnetic crystal classes.

Electrical transport in Bi doped n-type amorphous semiconductors (GeSe3.5)100-xBix at high pressure

Electrical transport in Bi doped amorphous semiconductors (GeSe3.5)100-xBix (x=0,4,10) is studied in a Bridgman anvil system up to a pressure of 90 kbar and down to 77 K. A pressure induced continuous transition from an amorphous semiconductor to a metal-like solid is observed in GeSe3.5. The addition of Bi disturbs significantly the behaviour of resistivity with pressure. The results are discussed in the light of molecular cluster model for GeySe1-y proposed by Phillips.

An analytical approach to the study of a class of bi-state social interaction processes

Sufficient conditions for obtaining an equivalent linear model to classes of non-linear, bi-state, social interaction processes are derived. These parametric constraints, when satisfied, permit analytical determination of the dynamics of the non-linear process of social interaction.

The curvature invariant for a class of homogeneous operators

For an operator T in the class B-n(), introduced by Cowen and Douglas, the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle E-T determine the unitary equivalence class of the operator T. In a subsequent paper, the authors ask if the simultaneous unitary equivalence class of the curvature and these covariant derivatives are necessary to determine the unitary equivalence class of the operator T is an element of B-n(). Here we show that some of the covariant derivatives are necessary. Our examples consist of homogeneous operators in B-n(). For homogeneous operators, the simultaneous unitary equivalence class of the curvature and all its covariant derivatives at any point w in the unit disc are determined from the simultaneous unitary equivalence class at 0. This shows that it is enough to calculate all the invariants and compare them at just one point, say 0. These calculations are then carried out in number of examples. One of our main results is that the curvature along with its covariant derivative of order (0, 1) at 0 determines the equivalence class of generic homogeneous Hermitian holomorphic vector bundles over the unit disc.

Behaviour of Bi-material interface cracks in the presence of material nonlinearity of adherends

The well known features of crack face interpenetration/contact at the tip of an interface crack is re-examined using finite element analysis and assuming material nonlinear properties for the adherends. It was assumed in literature that the crack tips are fully open at all load levels in the presence of material nonlinearity of the adherends. Analysis for the case of remote tension shows that even in the presence of material nonlinearity, crack tip closes at small load levels and opens above a certain load level. Mixed-mode fracture parameters are evaluated for the situation when the crack tips are fully open. Due to the presence of nonlinearity, the mixed-mode fracture parameters are measured with the symmetric and anti-symmetric components of J-integral. The present analysis explains the sequence of events at the interface crack tip with progressively increasing remote tension load for the case of adherends with material nonlinear behaviour.

Evolution of nanocrystalline BaBi2Nb2O9 in Li2B4O7 BaO-Bi(2)O3-Nb2O5 glass system

Transparent glasses and glass nano crystal composites (GNCs) of various compositions in the system (100 - x)Li2B4O7-x (BaO-Bi2O3-Nb2O5) (where x = 10, 20, and 30 in molar ratio) were fabricated via splat-quenching technique. The glassy nature of the as quenched samples was established by differential thermal analyses. X-ray powder diffraction and transmission electron microscopic (TEM) studies confirmed the formation of layered perovskite BBN via a fluorite like phase. TEM studies revealed the presence of 10 nm sized spherical crystallites of fluorite like BaBi2Nb2O9 phase in the glassy matrix of Li2B4O7 (LBO). The influence of composition on the dielectric and the optical properties (transmission, optical band gap) of these samples has been investigated. (c) 2007 Elsevier B.V. All rights reserved.