Open Access Published by De Gruyter Open Access

Volume 11 Issue 8

August 2013

Issue of Open Physics

Submit manuscript

Contents
Journal Overview

Open Access October 23, 2013

Is gravitational mass of a composite quantum body equivalent to its energy?

Andrei Lebed

Page range: 969-976

More Download PDF

Abstract

We define passive gravitational mass operator of a hydrogen atom in the post-Newtonian approximation of general relativity and show that it does not commute with energy operator, taken in the absence of gravitational field. Nevertheless, the equivalence between the expectation values of passive gravitational mass and energy is shown to survive for stationary quantum states. Inequivalence between passive gravitational mass and energy at a macroscopic level results in time dependent oscillations of the expectation values of passive gravitational mass for superpositions of stationary quantum states, where the equivalence restores after averaging over time. Inequivalence between gravitational mass and energy at a microscopic level reveals itself as unusual electromagnetic radiation, emitted by the atoms, supported and moved in the Earth gravitational field with constant velocity using spacecraft or satellite, which can be experimentally measured.

Open Access October 23, 2013

A class of exactly solvable models for the Schrödinger equation

Charles Downing

Page range: 977-983

More Download PDF

Abstract

We present a class of confining potentials which allow one to reduce the one-dimensional Schrödinger equation to a named equation of mathematical physics, namely either Bessel’s or Whittaker’s differential equation. In all cases, we provide closed form expressions for both the symmetric and antisymmetric wavefunction solutions, each along with an associated transcendental equation for allowed eigenvalues. The class of potentials considered contains an example of both cusp-like single wells and a double-well.

Open Access October 23, 2013

Conservation laws and associated Lie point symmetries admitted by the transient heat conduction problem for heat transfer in straight fins

Partner Ndlovu, Rasselo Moitsheki

Page range: 984-994

More Download PDF

Abstract

Some new conservation laws for the transient heat conduction problem for heat transfer in a straight fin are constructed. The thermal conductivity is given by a power law in one case and by a linear function of temperature in the other. Conservation laws are derived using the direct method when thermal conductivity is given by the power law and the multiplier method when thermal conductivity is given as a linear function of temperature. The heat transfer coefficient is assumed to be given by the power law function of temperature. Furthermore, we determine the Lie point symmetries associated with the conserved vectors for the model with power law thermal conductivity.

Open Access October 23, 2013

Conditions governing the generalisation of threshold bound states by N attractive delta potentials in one and three dimensions

Marappan Dharani, Basudeb Sahu, Chakrakodi Shastry

Page range: 995-1005

More Download PDF

Abstract

This paper proves that for N attractive delta function potentials the number of bound states (Nb) satisfies 1 ≤ N b ≤ N in one dimension (1D), and is 0 ≤ N b ≤ N in three dimensions (3D). Algebraic equations are obtained to evaluate the bound states generated by N attractive delta potentials. In particular, in the case of N attractive delta function potentials having same separation a between adjacent wells and having the same strength λV, the parameter g=λVa governs the number of bound states. For a given N in the range 1–7, both in 1D and 3D cases the numerical values of gn, where n=1,2,..N are obtained. When g=gn, Nb ≤ n where Nb includes one threshold energy bound state. Furthermore, gn are the roots of the Nth order polynomial equations with integer coefficients. Based on our numerical calculations up to N=40, even when N becomes large, 0 ≤ g n ≤ 4 and $\frac{{\Sigma g_n }} {N} \simeq 2 $ and this result is expected to be generally valid. Thus, for g > 4 there will be no threshold or zero energy bound state, and if g≈ 2 for a given large N, the number of bound states will be approximately N/2. The empirical formula gn = 4/[1+exp((N 0 − n)/β)] gives a good description of the variation of gn as a function of n. This formula is useful in estimating the number of bound states for any N and g both in 1D and 3D cases.

Open Access October 23, 2013

Relativistic oscillator model with spin for nucleon resonances

Dmitry Kulikov, Ivan Uvarov, Arkadiy Yaroshenko

Page range: 1006-1015

More Download PDF

Abstract

The relativistic three-body problem is approached via the extension of the SL(2, C) group to the Sp(4, C) one. In terms of Sp(4, C) spinors, a Dirac-like equation with three-body kinematics is composed. After introducing the linear in coordinates interaction, it describes the spin-1/2 oscillator. For this system, the exact energy spectrum is derived and then applied to fit the Regge trajectories of baryon N-resonances in the (E 2, J) plane. The model predicts linear trajectories at high total energy E with some form of nonlinearity at low E.

Open Access October 23, 2013

Kinetics of the maintenance of the epidermis

Vladimir Zhdanov, Nam-Joon Cho

Page range: 1016-1023

More Download PDF

Abstract

The epidermis is the outermost layer of skin. It is comprised of keratin-containing cells called keratinocytes. Functionally, the epidermis serves as a physical barrier that can prevent infection and regulate body hydration. Maintenance and repair of the epidermis are important for human health. Mechanistically, these processes occur primarily via proliferation and differentiation of stem cells located in the basal monolayer. These processes are believed to depend on cell-cell communication and spatial constraints but existing kinetic models focus mainly on proliferation and differentiation. To address this issue, we present a mean-field kinetic model that takes these additional factors into account and describes the epidermis at a biosystem level. The corresponding equations operate with the populations of stem cells and differentiated cells in the basal layer. The keratinocytes located above the basal layer are treated at a more coarse-grained level by considering the thickness of the epidermis. The model clarifies the likely role of various negative feedbacks that may control the epidermis and, accordingly, provides insight into the cellular mechanisms underlying complex biological phenomena such as wound healing.

Open Access October 23, 2013

Surface relief grating formation in luminescent dye doped photochromic polymer containing azobenzene side groups

Lech Sznitko, Pawel Karpinski, Stanislaw Bartkiewicz, Andrzej Miniewicz, Jaroslaw Mysliwiec

Page range: 1024-1029

More Download PDF

Abstract

We study the formation of a surface relief grating and photoluminescence in a thin layers of a photochromic polymer doped with the luminescent dyes 3-(1,1-dicyanoethenyl)-1-phenyl-4,5-dihydro-1H-pyrazole and Rhodamine 6G. Surface topography measurements via Atomic Force Microscopy confirmed the existence of a surface relief grating with amplitudes as high as 650 nm both for doped and undoped photochromic polymers. Spectroscopic measurements carried out for polymers containing luminescent dyes have shown efficient photoluminescence and amplified spontaneous emission which is characteristic for gain media.

Open Access October 23, 2013

Effective protocol for preparation of three-atom Greenberger-Horne-Zeilinger state and W state with the help of cross-Kerr nonlinearity

Yi-Hao Kang, Yan Xia, Pei-Min Lu

Page range: 1030-1035

More Download PDF

Abstract

We propose a protocol to generate a Greenberger-Horne-Zeilinger (GHZ) state andWstate by using simple linear elements and quantum nondemolition detectors (QNDs). With the help of cross-Kerr nonlinearity, our protocol can generate the intended states with only one setup, and the probability of getting a W state is greatly increased when compared with previous schemes [Phys. Rev. A 75 (2007) 044301]. Also, our proposed protocol is realizable in experiments.

Open Access October 23, 2013

Scattering of longitudinal waves (sound) by defects in fluids. Rough surface

Bogdan Apostol

Page range: 1036-1044

More Download PDF

Abstract

The classical theory of scattering of longitudinal waves (sound) by small inhomogeneities (scatterers) in an ideal fluid is generalized to a distribution of scatterers and such as to include the effect of the inhomogeneities on the elastic properties of the fluid. The results are obtained by a new method of solving the wave equation with spatial restrictions (caused by the presence of the scatterers), which can also be applied to other types of inhomogeneities (like surface roughness, for instance). A coherent forward scattering is identified for a uniform distribution of scatterers (practically equivalent with a mean-field approach), which is due to the fact that our treatment does not include multiple scattering. The reflected wave is obtained for a half-space (semi-infinite fluid) of uniformly distributed scatterers, as well as the field diffracted by a perfect lattice of scatterers. The same method is applied to a (inhomogeneous) rough surface of a semi-infinite ideal fluid. A perturbation-theoretical scheme is devised, with the roughness function as a perturbation parameter, for computing the waves scattered by the surface roughness. The waves scattered by the rough surface are both waves localized (and propagating only) on the surface (two-dimensional waves) and waves reflected back in the fluid. They exhibit directional effects, slowness, attenuation or resonance phenomena, depending on the spatial characteristics of the roughness function. The reflection coefficients and the energy carried on by these waves are calculated both for fixed and free surfaces. In some cases, the surface roughness may generate waves confined to the surface (damped, rough-surface waves).

Open Access October 23, 2013

Estimating the varying topology of discrete-time dynamical networks with noise

Chengyi Tu, Yuhua Cheng, Kai Chen

Page range: 1045-1055

More Download PDF

Abstract

We propose an improved method to estimate the varying topology of discrete-time dynamical networks using autosynchronization. The networks considered in this paper can be weighted or unweighted and directed or undirected, and the dynamics of each node can be nonuniform. Furthermore, we suggest using a moving-average filter to suppress the influence of noise on parameter estimation. Finally, several examples are illustrated to verify the theoretical results by numerical simulation.

About this journal

Open Physics (PHYS) is a peer-reviewed, open access, electronic journal devoted to the publication of fundamental research results in all fields of physics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, no space constraints and immediate publication.

Aims and Scope

The journal publishes research and review articles, rapid and short communications, comments and replies that cover the following areas of physical sciences:

Acoustics

Astrophysics,

Atomic and Molecular Physics,

Biological and Medical Physics,

Complex Networks, Socio- and Econophysics,

Computational Physics,

Condensed Matter Physics,

Cosmology and Gravitation,

Fluid Mechanics,

Geophysics,

Nanophysics,

Optics and Lasers,

Particle and Nuclear Physics,

Plasma Physics,

Statistical and Nonlinear Physics,

Surface Physics,

Theoretical and Mathematical Physics.