Charge fluctuation model of lattice vibrations

A new phenomenological model is proposed for the lattice dynamics of transition metals. It is based on the microscopic model of Sinha and Harmon and includes the effect of charge fluctuations coupled to atomic motions. The model has been found to reproduce very accurately the phonon dispersion curves for Nb with short-range charge fluctuations and interatomic interactions.     

Fractional-dimensional approach for biexcitons in GaAs/AlxGa1−xAs quantum wells

The energy of a biexciton in a GaAs/Al_xGa_1?xAs quantum well structure with finite barriers is investigated by using the geometrical model of two-dimensional biexcitons proposed by Singh et al. [J. Singh, D. Birkedal, V.G. Layssenko, J.M. Hvam, Phys. Rev. B 53 (1996) 15909; I.-K. Oh, J. Singh, Phys. Rev. B 60 (1999) 2528]. A fractional-dimensional approach is used to obtain the binding energy of the biexciton in both square quantum wells and parabolic quantum wells. Theoretical results show that the binding energy of a biexciton in a finite quantum well exhibits a maximum with increasing well width. The ratio of the binding energy of a biexciton to that of an exciton in a quantum well structure is found to be sensitive to the electron-to-hole mass ratio and larger than that in the three-dimensional system. The results agree fairly well with previous experimental results. The results of our approach are also compared with those of earlier theories.     

Structure factors and phonon dispersion in liquid Li<Subscript>0.61</Subscript>Na<Subscript>0.39</Subscript> alloy

The phonon spectra for liquid Li and Na have been computed through the phenomenological model of Bhatia and Singh for disordered systems like liquids and glasses and the obtained results have been compared with the available data obtained by inelastic neutron scattering (INS) and inelastic X-ray scattering (IXS) experiments. The effective pair potentials and their space derivatives are important ingredients in the computation of the dispersion curves. The pair potentials are obtained using the pseudo-potential theory. The empty core model proposed by Ashcroft is widely used for pseudo-potential calculations for alkali metals. But, it is thought to be unsuitable for Li because of its simple 1s electronic structure. However, it can be used with an additional term known as Born-Mayer (BM) core term. The influence of the BM core term on the phonon dispersion is discussed. The same pseudo-potential formalism has been employed to obtain the dispersion relation in liquid Li_0.61Na_0.39 alloy. Apart from the phonon spectra, the Ashcroft-Langreth structure factors in the alloy are derived in the Percus-Yevick approximation.     

Evaluation of local equivalent methods for treating exchange in elastic proton scattering

We have tested the approximate method devised by Sinha for including knock-on exchange in proton-elastic-scattering calculations by comparing with exact calculations involving the solution of an integro-differential equation. We find that the method works quite well for energies above 60 MeV but there are discrepancies at lower energies which we illustrate. In particular we note a systematic tendency to change rms radii by about 0.15 fm and give erroneous volume integrals. We show how the basic approximation of Sinha can be made to give better results.     

Cover Picture: Contrib. Plasma Phys. 6–7/2017

Change in the normalized terahertz (THz) amplitude with normalized distance and normalized plasma frequency. Figures 3b, 3d of the paper by R.K Singh et al.     

Effects of Uniaxial Stress on X-ray Diffraction Spectra

Uniaxial stress is a typical drawback of solid pressure transmitting medium, at low temperature, which affects experimental spectra by shifting and broadening the diffraction peaks. Corrections to this effects have been proposed in the past only for the systematic shifts. We presented a simple model based on elasticity theory which rationalizes both peak shifts and broadening observed in X-ray diffraction. Our results are compared to the popular Singh model.     

A note on pure bending of a piezoelectric rectangular plate

The problem of pure bending of a piezoelectric rectangular plate is considered in this paper by using the electromagnetic equations of Maxwell and equations of elasticity along with the constitutive equations of a piezoelectric quartz.The author extends his sincere gratitude to Dr. D. K. Sinha of Jadavpur University for his kind help and guidance in the preparation of this paper.     

Mechanical response in a composite free piezoelectric transducer with a time-decaying polarization gradient

This article aims at finding the mechanical response of a composite free piezoelectric transducer with a time decaying polarization gradient when it is subjected to an electric voltage input.The author is grateful to Dr. D. K. Sinha for his immense help and active guidance.     

On mechanical response of a non-uniform piezoelectric transducer under the influence of a body-force

The mechanical response of a non-uniform piezoelectric transducer when there is a body force acting on it has been evaluated using the methods of transform calculus.The author is grateful to Dr. D. K. Sinha of Jadavpur University for his kind help in the preparation of this note.     

On the transient electrical response of a piezoelectric transducer due to shock-loaded stress

The methods of transform calculus are made use of in finding the electrical response in a piezoelectric transducer due to shock-loaded stress. The response is found to be transient in character to a first order of approximation.The author is deeply indebted to Dr. D. K. Sinha for his constant guidance in preparing this paper. He also thanks the referee for his comments and suggestions for improving the paper.     

On non-linear oscillations with slowly varying system parameters

The paper deals with an approximate analysis of non-linear oscillation problems with slowly varying system parameters. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by using the generalized averaging method of Sinha and Srinivasan based on ultraspherical polynomial expansions. The Bogoliubov-Mitropolsky results are given by a particular set of these polynomials. Problems of a single degree of freedom system as well as monofrequency oscillations in systems with multiple degrees of freedom are considered. The approach has been illustrated by an example and the results are compared with the numerical solutions. A close agreement is found.     

Simulations of the effects of 1-d interstitial diffusion on void lattice formation during irradiation

This paper describes the use of simulation techniques to examine some of the processes involved in the alignment of voids under the influence of one-dimensional self interstitial atom (1-d SIA) transport. The work follows the paper of Heinisch and Singh on this topic but a different and simpler methodology is used. Besides repeating the scenarios studied by Heinisch and Singh, the effects of re-nucleation and the influence of vacancies have been introduced. One of the important processes that emerged from the results was the barrier to precise void alignment caused by the SIA-induced coalescence of aligned voids. This appears to prevent the formation of stable void lattices by any 1-d SIA transport mechanism, a point supported by the initial void alignment in the mechanism requiring swelling values well above those found experimentally. A full consideration of the void lattice phenomenon shows that the one-dimensional diffusion of self-interstitials central to the production bias model of irradiation damage cannot be the only mode of anisotropic diffusion available under irradiation.     

Cosmological constant in the Bianchi type-I-modified Brans-Dicke cosmology

In 1961, Brans and Dicke [1] provided an interesting alternative to general relativity based on Mach’s principle. To understand the reasons leading to their field equations, we first consider homogeneous and isotropic cosmological models in the Brans-Dicke theory. Accordingly we start with the Robertson-Walker line element and the energy tensor of a perfect fluid. The scalar field φ is now a function of the cosmic time only. Then we consider spatially homogeneous and anisotropic Bianchi type-I-cosmological solutions of modified Brans-Dicke theory containing barotropic fluid. These have been obtained by imposing a condition on the cosmological parameter Λ(φ). Again we try to focus the meaning of this cosmological term and to relate it to the time coordinate which gives us a collapse singularity or the initial singularity. On the other hand, our solution is a generalization of the solution found by Singh and Singh [2]. As far as we are aware, such solution has not been given earlier.     

Critical examination of isolation system design paradigms for a coupled powertrain and frame: Partial torque roll axis decoupling methods given practical constraints

The torque roll axis motion decoupling concept is analytically and computationally studied in a realistic coupled powertrain and frame system using discrete, proportionally damped linear models. Recently, Hu and Singh (2012 [1]) (Journal of Sound and Vibration 331 (2012) 1498–1518) proposed new paradigms to fully decouple such a system. However, critical examination shows that the derivation does not always lead to a physically realizable system, as each powertrain mount is not referenced to a single location. This deficiency is overcome by deriving mount compatibility conditions to ensure realistic mount positions which are incorporated into proposed decoupling conditions. It is mathematically shown that full decoupling is not possible for a practical system, and therefore partial decoupling paradigms are pursued. Powertrain mount design using only the decoupled powertrain achieves better decoupling than minimizing conditions for the coupled system using a total least squares method. Further decoupling is obtained through frame isolation design using a decoupled frame model such that the torque roll mode is dominant over the frequency range considered. Other methods for limiting frame coupling are also briefly discussed.     

Generalized Quantum Probability and Entanglement Enhancement Witnessing

It has been suggested (cf. Sinha et al. in Science 329:418, 2010) that the Born rule for quantum probability could be violated. It has also been suggested that, in a generalized version of quantum mechanical probability theory such as that proposed by Sorkin (Mod. Phys. Lett. A 9:3119, 1994) there might occur deviations from the predictions of quantum probability in cases where more than two paths are available to a self-interfering system. These would lead to additional contributions to interference. Here, these ideas, some in the theoretical context and some in the experimental context, are briefly reviewed and pragmatically extended to situations involving bipartite systems, so that corresponding interference enhancement due to entanglement might be witnessed.     

Analysis of total reaction cross sections for deuterons on 1p-shell-nuclei

This study aims to analyze the differential cross sections(DCSs) of elastic scattering and total reaction cross sections(TRCSs) of the loosely-bound deuteron projectile impinging on 1 p-shell nuclei, such as9 Be,12 C, and16 O, at incident energies ranging between10.6 and 171 MeV using the continuum discretized coupled channel(CDCC) method. By fitting the experimental data for the DCSs and TRCSs, energy-dependent renormalization factors for the real and imaginary parts of the nucleon-nucleus opticalmodel potentials deduced from the studies proposed by Koning and Delaroche(KD02) and by Watson, Singh, and Segel(WSS),are obtained. It is found that with the WSS potential, which was obtained specifically for 1 p-shell nuclei, the CDCC calculations can simultaneously reproduce both the DCSs and the TRCSs. The results show that it is important to choose appropriate optical potentials to describe deuteron-induced reactions.     

Dynamic behavior in mathematical models of the tryptophan operon

This paper surveys the general theory of operon regulation as first formulated by Goodwin and Griffith, and then goes on to consider in detail models of regulation of tryptophan production by Bliss, Sinha, and Santillan and Mackey, and the interrelationships between them. We further give a linear stability analysis of the Santillan and Mackey model for wild type E. coli as well as three different mutant strains that have been previously studied in the literature. This stability analysis indicates that the tryptophan production systems should be stable, which is in accord with our numerical results. (c) 2001 American Institute of Physics.     

Computing with distributed chaos

We describe and discuss in detail some recent results by Sinha and Ditto [Phys. Rev. Lett. 81, 2156 (1998)] demonstrating the capacity of a lattice of threshold coupled chaotic maps to perform computations. Such systems are shown to emulate logic gates, encode numbers, and perform specific arithmetic operations, such as addition and multiplication, as well as yield more specialized operations such as the calculation of the least common multiplier of a sequence of numbers. Furthermore, we extend the scheme to multidimensional continuous time dynamics, in particular to a system relevant to chaotic lasers.     

A stable numerical inversion of Abel's integral equation using almost Bernstein operational matrix

Many problems in physics like reconstruction of the radially distributed emissivity from the line-of-sight projected intensity, the 3-D image reconstruction from cone-beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel's type integral equation. The aim of this communication is to modify the stable algorithm proposed in [Singh VK, Pandey RK, Singh OP. New stable numerical solution of singular integral equations of Abel type by using normalized Bernstein polynomials. Applied Mathematical Sciences 2009;3(5):241–255] which is based on normalized Bernstein polynomial approximation of the projected intensity profile. So, first we construct an orthonormal family of polynomials of degree 5 from the 5th degree Bernstein polynomials B_i5 and use them as a basis to approximate the projected intensity profile. Then, a 6×6 matrix P, named as almost Bernstein operational matrix of integration is constructed and used to reduce the integral equation to a system of algebraic equation which can be solved easily. The method is quite accurate and stable even though the approximations are performed by polynomials of degree 5, as illustrated by applying the method to intensity data with and without random noise to invert and compare it with those obtained by the other methods or with the known analytical inverse. Thus it is good method for applying to experimental intensities distorted by noise.