Distribution of the conductance of a linear chain of tunnel barriers with fractal disorder

Distributions of the conductance G of a long quantum wire with the fractal distribution of barriers have been obtained in the successive incoherent tunneling regime. The asymptotic behavior (in the limit L → ∞) of moments 〈G ^k (L)〉, average power of the shot noise 〈S(L)〉, and Fano factor agree with the results of the work [C. W. J. Beenakker et al., Phys. Rev. B 79, 024204 (2009)], and the distributions themselves describe well the Monte Carlo simulation results. The equation that has been obtained for the distributions of the resistance and conductance agrees with the recent fractional differential generalization of the Dorokhov-Mello-Pereyra-Kumar equation for the quasi-one-dimensional multichannel disordered semiconductors with a self-similar distribution of scatterers.     

Structural ion-sound plasma turbulence as a self-similar random process

It is shown that the experimentally investigated structural ion-sound plasma turbulence is a self-similar stationary random process. The self-similarity parameter is determined by two temporal laws: the nonrandom character of the appearance of nonlinear structures (nonlinear ion-sound solitons) in the plasma, and the nonlinear interaction between them. As the distance from the threshold of the ion-sound current instability increases, the self-similar random process approaches a Gaussian random process, but this limit has not been attained experimentally. The possibility of recording superlong time series of the fluctuations of the signal of the plasma process and processing of the time series by the R/S analysis method has made it possible to prove self-similarity of the plasma structural turbulence. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 203–208 (10 August 1999)     

Estimation of the deformation-potential constant for <Emphasis Type="Italic">p</Emphasis>-type isotropic polycrystalline silicon through the deformation potential of a <Emphasis Type="Italic">p</Emphasis>-type silicon single crystal

A method of calculating the effective deformation-potential constant E ₁ for holes and longitudinal acoustic phonons in isotropic polycrystalline silicon is suggested. The deformation-potential constant E ₁ is estimated through the deformation potentials a, b, and d of the silicon single crystal. The procedure of averaging of the squared modulus of the hole and acoustic phonon interaction Hamiltonian written in the plane wave basis over the polycrystal ensemble provides the basis for calculation of the constant E ₁ . It is demonstrated that for T = 200–600 K, hole concentration p = (5.0–10.0)∙10¹⁹ cm^–3, and crystallite size d = 300–3000 ?, the deformationpotential constant E ₁ is independent of the hole concentration p, temperature T, and crystallite size d.     

Fredholm Modules on P.C.F. Self-Similar Fractals and Their Conformal Geometry

The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct non-trivial Fredholm modules on post critically finite fractals by regular harmonic structures (D, r). The modules are (d _S , ∞)–summable, the summability exponent d _S coinciding with the spectral dimension of the generalized Laplacian operator associated with (D, r). The characteristic tools of the noncommutative infinitesimal calculus allow to define a d _S -energy functional which is shown to be a self-similar conformal invariant. Thiswork has been supported by the project “Teoria ellittica e forme di Dirichlet su spazi frattali” G.N.A.M.P.A. 2008 and by the G.R.E.F.I.-G.E.N.C.O. French-Italian Research Group.     

Stability of Ultraviolet-Cutoff¶Quantum Electrodynamics with Non-Relativistic Matter

We prove that the quantum-mechanical ground state energy of a system consisting of an arbitrary number, M, of static nuclei of atomic number ≤Z and of an arbitrary number, N, of Pauli electrons interacting with the quantized, ultraviolet-cutoff radiation field is bounded below by $-K.M, where K is a finite constant depending on Z, on the finestructure constant α and on the ultraviolet cutoff Λ, with , as , and K' independent of Λ. Received: 4 September 1996/ Accepted: 9 April 1997     

Classification of the FRW universe with a cosmological constant and a perfect fluid of the equation of state <Emphasis Type="Italic">p</Emphasis> = <Emphasis Type="Italic">w</Emphasis><Emphasis Type="Italic">ρ</Emphasis>

We systematically study the evolution of the Friedmann–Robertson–Walker (FRW) universe coupled with a cosmological constant Λ and a perfect fluid that has the equation of state p = w ρ, where p and ρ denote, respectively, the pressure and energy density of the fluid, and w is an arbitrary real constant. Depending on the specific values of w, Λ, and the curvature k of 3-dimensional space, we separate all of the solutions into various cases. In each case the main properties of the evolution are given in detail, including the periods of deceleration and/or acceleration, and the existence of big bang, big crunch, and big rip singularities. In some cases, errors in classification and interpretation appearing in standard textbooks have been corrected.     

Stability,Convergence to Self-Similarity and Elastic Limit for the Boltzmann Equation for Inelastic Hard Spheres

We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients . In the physical regime of a small inelasticity (that is for some constructive ) we prove uniqueness of the self-similar profile for given values of the restitution coefficient , the mass and the momentum; therefore we deduce the uniqueness of the self-similar solution (up to a time translation). Moreover, if the initial datum lies in , and under some smallness condition on depending on the mass, energy and norm of this initial datum, we prove time asymptotic convergence (with polynomial rate) of the solution towards the self-similar solution (the so-called homogeneous cooling state). These uniqueness, stability and convergence results are expressed in the self-similar variables and then translate into corresponding results for the original Boltzmann equation. The proofs are based on the identification of a suitable elastic limit rescaling, and the construction of a smooth path of self-similar profiles connecting to a particular Maxwellian equilibrium in the elastic limit, together with tools from perturbative theory of linear operators. Some universal quantities, such as the “quasi-elastic self-similar temperature” and the rate of convergence towards self-similarity at first order in terms of (1−α), are obtained from our study. These results provide a positive answer and a mathematical proof of the Ernst-Brito conjecture [16] in the case of inelastic hard spheres with small inelasticity.     

Asymptotes of solutions of a perfect fluid coupled with a cosmological constant in four-dimensional spacetime with toroidal symmetry

Asymptotes of solutions of a perfect fluid when coupled with a cosmological constant in four-dimensional spacetime with toroidal symmetry are studied. In particular, it is found that the problem of self-similar solutions of the first kind for a fluid with the equation of state, p = kρ, can be reduced to solving a master equation of the form,

Semilinear PDEs on Self-Similar Fractals

A Laplacian may be defined on self-similar fractal domains in terms of a suitable self-similar Dirichlet form, enabling discussion of elliptic PDEs on such domains. In this context it is shown that that semilinear equations such as Δu+u ^p = 0, with zero Dirichlet boundary conditions, have non-trivial non-negative solutions if 0<ν≤ 2 and p>1, or if ν >2 and 1<p< (ν+ 2)/(ν− 2), where ν is the “intrinsic dimension” or “spectral dimension” of the system. Thus the intrinsic dimension takes the r\^{o}le of the Euclidean dimension in the classical case in determining critical exponents of semilinear problems. Received: 11 December 1998 / Accepted: 22 March 1999     

Higher Dimensional Unified Description of Early Universe with Variable <Emphasis Type="Italic">G</Emphasis> and Λ

A homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model with varying gravitational and cosmological constant is studied in the context of higher dimensional space time. Exact solution of the field equations are obtained by using the “gamma law” equation of state p=(γ−1)ρ, where γ is adiabatic parameter varies continuously as the universe expands. The functional form γ which is assumed to be the function of scale factor R as proposed by Carvalho (1996) is used to analyse the behavior of scale factor R, cosmological constant Λ and the gravitational constant G for two different phases: inflation and radiation. The various physical aspects of the early cosmological models has also been discussed in the framework of higher dimensional space time.     

Strong decays Σ*→Σπ,Λπ and related strong coupling constant

We calculate the strong coupling constant g among the decuplet baryons, the octet baryons and the pseudoscalar mesons in the heavy baryon chiral perturbation theory with the light-cone QCD sum rules, and we study the strong decays Σ ^*→Λ π,Σ π. The numerical value of the strong coupling constant g is consistent with our previous calculation; the central values lead to small SU(3) breaking effects, less than 6%; and no definitive conclusion can be drawn due to the large uncertainties.     

Anisotropic Universe Models with Perfect Fluid and Dark Energy with Time Varying G and Λ

We have investigated general Bianchi type I cosmological models which containing a perfect fluid and dark energy with time varying G and Λ that have been presented. The perfect fluid is taken to be one obeying the equation of state parameter, i.e., p=ωρ; whereas the dark energy density is considered to be either modified polytropic or the Chaplygin gas. Cosmological models admitting both power-law which is explored in the presence of perfect fluid and dark energy too. We reconstruct gravitational parameter G, cosmological term Λ, critical density ρ _c , density parameter Ω, cosmological constant density parameter Ω _Λ and deceleration parameter q for different equation of state. The present study will examine non-linear EOS with a general nonlinear term in the energy density.     

Tutte Polynomials of Two Self-similar Network Models

The Tutte polynomial T(G; x, y) of a graph G, or equivalently the q-state Potts model partition function, is a two-variable polynomial graph invariant of considerable importance in combinatorics and statistical physics. Graph operations have been extensively applied to model complex networks recently. In this paper, we study the Tutte polynomials of the diamond hierarchical lattices and a class of self-similar fractal models which can be constructed through graph operations. Firstly, we find out the behavior of the Tutte polynomial under k-inflation and k-subdivision which are two graph operations. Secondly, we compute and gain the Tutte polynomials of this two self-similar fractal models by using their structure characteristic. Moreover, as an application of the obtained results, some evaluations of their Tutte polynomials are derived, such as the number of spanning trees and the number of spanning forests.

     

Double atomic photoeffect in the relativistic domain: Angular and energy distributions of photoelectrons

We study the double ionization of the atomic K-shell by a single photon in the relativistic energy domain. The differential and total cross sections of the process are calculated. It is shown that the ratio of the cross sections of double and single ionization increases with the photon energy, tending to the limit 0.34/Z ², where Z is the atomic number or the nuclear charge. The formulas are found to be valid for Z≫1 and αZ≪1, where α=1/137 is the fine-structure constant. Zh. éksp. Teor. Fiz. 114, 1537–1554 (November 1998)     

Directional cellular growth of Al-2?wt% Li bulk samples

Al-2 wt% Li alloy was prepared using metals of 99.99% high purity in the vacuum atmosphere. The bulk samples were directionally solidified upward with a constant growth rate, V, (∼8.30 μm/s) and different temperature gradients, G, (3.11–6.06 K/mm) and also with a constant G (6.06 K/mm) and different V (8.3–164.70 μm/s) in the directional solidification apparatus. The cellular spacings, λ, were measured from both transverse and longitudinal section of the specimens and expressed as functions of solidification processing parameters, G and V, by using a linear regression analysis. The effects of the G and V on λ, were investigated. The experimental results were compared with the current theoretical and numerical models, and similar previous experimental results.     

Speedy Motions of a Body Immersed in an Infinitely Extended Medium

We study the motion of a classical point body of mass M, moving under the action of a constant force of intensity E and immersed in a Vlasov fluid of free particles, interacting with the body via a bounded short range potential Ψ. We prove that if its initial velocity is large enough then the body escapes to infinity increasing its speed without any bound (runaway effect). Moreover, the body asymptotically reaches a uniformly accelerated motion with acceleration E/M. We then discuss at a heuristic level the case in which Ψ(r) diverges at short distances like gr ^−α , g,α>0, by showing that the runaway effect still occurs if α<2.     

Next-to-next-leading order correction to 3-jet rate and event-shape distribution

The hadronic events from the e ⁺ e ⁻ annihilation data at the centre-of-mass energies ranging from 60 to 197 GeV were studied. The AMY and OPAL Collaborations offered a unique opportunity to test QCD by measuring the energy dependence of different observables. The coupling constant, α _s, was measured by two different methods: first by employing the three-jet observables. Combining all the data, the value of as at next-to-next leading order (NNLO) was determined to be 0.117 ± 0.004(hard) ± 0.006(theo). Secondly, from the event-shape distributions, the strong coupling constant, α _s, was extracted at NNLO and it’s evaluation was tested with the energy scale. The results were consistent with the running of α _s, expected from QCD predictions. Averaging over different observables, α _s was determined to be 0.115 ± 0.007(hard) ± 0.003(theo).     

QED effective action in a constant electromagnetic field under conditions of possible Lorentz invariance violation in the Dirac equation

This paper is devoted to the calculation of corrections to QED effective action associated with the axial-vector condensate b ^μ, which violate the Lorentz invariance. It was shown that the linear in b ^μ contribution to the 1-loop effective action (Chern-Simons term) is absent in the case of a constant electromagnetic field. The contribution, which is quadratic in b ^μ, was calculated for the cases of both constant magnetic and electric fields. Asymptotic estimates of the quadratic in b ^μ term for strong and weak field strengths were obtained.     

Modeling 1/f noise using moving averages

A model of 1/f noise is considered, based on moving averages of ordern. The coefficientsα _k defining the model are calculated numerically using Seidel iteration which turns out to converge rapidly. The convergence is independent ofn which seems to be caused by the fact that the nonlinear problem solved is defined by a self-similar matrix. The coefficientsα _k appear to approach, with indefinitely growingn, valuesα _k =1/√k and thus the model has a kind of Fourier invariance. Physical interpretation of the invariance is suggested as well as of coefficientsα _k describing long-range correlations. Fractal sets of dimensiond=2.5 are proposed to play certain role in explaining the latter. This work was partly supported by the Scientific Grant Agency of the Ministry of Education of Slovak Republic (VEGA) under the Grant No. 1/3143/96 and by the Slovak Literary Fund.