Expressions for the computer-evaluation of the four kernel functions for line formation with Doppler and Lorentz profiles

Rational approximations for the kernel functions K₁(τ), K₂(τ), M₁(τ) and M₂(τ) that describe the transfer of radiation scattered with complete redistribution over Doppler and Lorentz profiles have been obtained from their series and asymptotic expressions by the techniques of Padé approximants with a maximum relative error of less than 10^-4.     

Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. III. Localization Properties

In this paper, we study the asymptotic localization properties with high probability of the Kth eigenfunction (associated with the Kth largest eigenvalue, K?1 fixed) of the multidimensional Anderson Hamiltonian in torus V increasing to the whole of lattice. Denote by z _K,V ∈V the site at which the Kth largest value of potential is attained. It is well-known that if the tails of potential distribution are heavier than the double exponential function and satisfies additional regularity and continuity conditions at infinity, then the Kth eigenfunction is asymptotically delta-function at the site z _τ(K),V (localization centre) for some random τ(K)=τ _V (K)?1. We study the asymptotic behavior of the index τ _V (K) by distinguishing between three cases of the tails of potential distribution: (i) for the “heavy tails” (including Gaussian), τ _V (K) is asymptotically bounded; (ii) for the light tails, but heavier than the double exponential, the index τ _V (K) unboundedly increases like |V|^o(1); (iii) finally, for the double exponential tails with high disorder, the index τ _V (K) behaves like a power of |V|. For Weibull’s and fractional-double exponential types distributions associated with the case (ii), we obtain the first order expansion formulas for logτ _V (K).     

Physical mechanisms responsible for the relaxation time distribution in disordered dielectrics

The relaxation time distribution function F(τ) is calculated in the framework of the random-field theory. The function F(τ) is expressed through the distribution function f(E) of a random electric field E with due regard for the derived dependence of the relaxation time τ on the electric field. The distribution function F(τ) is calculated in terms of the statistical theory within the random-field approximation. The nonlinear random-field contributions and spatial effects of correlations between randomly distributed electric dipoles are taken into account. The calculations are performed for a mixed ferroelectric glassy phase in which the short-range and long-range polar orders coexist. It is demonstrated that the inclusion of nonlinear contributions of the random field leads to an asymmetric relaxation time distribution function F(τ), whereas allowance made only for the linear random-field contributions results in a symmetric function F(τ). A comparison of the calculated functions F(τ) with empirical functions derived from the Cole-Cole (CC), Davidson-Cole (DC), Kohlrausch-Williams-Watts (KWW), and Havriliak-Negami (HN) laws for the dielectric response shows that these laws correspond to disordered systems in which the long-range and short-range orders coexist. Different forms of the function F(τ) are determined by either linear (the CC law) or nonlinear (the DC, KWW, and HN laws) contributions of the random field.     

Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(S_α(t)), 0<α<1, here dX(τ)=μX(τ)(dτ)^2H+σX(τ)dB_H(τ), as a model of asset prices, which captures the subdiffusive characteristic of financial markets. We find the corresponding subdiffusive Black-Scholes equation and the Black-Scholes formula for the fair prices of European option, the turnover and transaction costs of replicating strategies. We also give the total transaction costs.     

Fluctuation pressure of membrane between walls

We prove that a tensionless membrane, fluctuating harmonically with free ends between two parallel plates of spacing 2d. generates a pressure of the functional form p = (T/Ad)τa(τ), where τ is the dimensionless variable τ ≠ (T/κ)A/d², κ is th curvature elastic constant, and A the area of the plates. For large A, a(τ) becomes a constant which we determine by Monte Carlo simulation to be a_∞ = 0.060±0.003.     

Effects of time delay and non-Gaussian noise on the dynamics of a perceptual bistability

In this paper, we investigate the effects of time delay and non-Gaussian noise on the dynamics properties of the attractor network model of perceptual bistability. Using delay Fokker–Planck equation and projection operator method, the stationary probability distribution P_st(x), the associated relaxation time T_c, and the normalized correlation function C(s) for perceptual bistability are obtained, respectively. Research results show that: (i) the time delay τ and the correlation time τ₀ from non-Gaussian noise can induce the change of the peaks in the P_st(x), i.e., the transition of the system appears; (ii) there exhibits an optimal value of the τ₀ or τ by which the T_c or C(s) is maximum, this maximum shows the τ₀ or τ first reduces the stability of the attractor network model of perceptual bistability in the steady state, and then enhances it; and (iii) the noise intensity P or departure q from the Gaussian noise only enhances the stability of the attractor network model of perceptual bistability in the steady state.     

Hypersurfaces Satisfying <Emphasis Type="BoldItalic">τ</Emphasis><Subscript><Emphasis Type="BoldItalic">2</Emphasis></Subscript><Emphasis Type="BoldItalic">(ϕ) = ητ(ϕ)</Emphasis> in Pseudo-Riemannian Space Forms

In this paper, we derived the equations for the hypersurface \({M^{n}_{r}}\) of a pseudo-Riemannian space form \(N^{n+1}_{q}(c)\) to satisfy τ ₂(?) = η τ(?) (η a constant) with τ(?) and τ ₂(?) be the tension and bitension fields of \({M^{n}_{r}}\). As applications, we prove that a hypersurface \({M^{n}_{r}}\) satisfying τ ₂(?) = η τ(?) in \(N^{n+1}_{q}(c)\) has constant mean curvature, under the assumption that \({M^{n}_{r}}\) has diagonalizable shape operator with at most three distinct principal curvatures. Then, using this result, we classify partially such hypersurface. We also make a preliminary study of hypersurfaces satisfying τ ₂(?) = f τ(?) with f be function.     

Gamma decay of low-lying states in S and Ar

Decay modes and lifetimes of low-lying levels in ³⁰S and ³⁴Ar were investigated by the Doppler-shift attenuation method using the ²⁸Si(³He, n)³⁰S and ³²S(³He, n)³⁴Ar reactions. The lifetimes measured in ³⁰S were (in fs): τ_m(2210) = 310 ± 75, τ_m(3402) = 160 ± 45 and τ_m(3664) > 1400; and in ³⁴Ar: τ_m(2090) = 150 ± 50, τ_m(3286) = 120 ± 65 and τ_m(4513) = 300 ± 80, also in fs. These results are compared with theoretical calculations. A comparison of the E2 decay strengths in masses 30 and 34 is also made to test the isospin dependence of electro-magnetic transitions.     

τ-decay and second-class currents

Second-class currents exists if the following decays of the new heavy lepton τ±(1.9 GeV) are observed: τ^± → B(1228) + ν^?τ and/or τ± → δ ±(976) + ν^?τ.     

Lifetimes of some highly excited levels in the Pb-I spectrum measured by the hanle method

Natural lifetimes of some highly excited levels in the Pb-I spectrum have been measured by the zero field level crossing (Hanle) method. The levels were reached by optical excitation from the metastable 6p ^{2 3} P ₂ and 6p ^{2 3} P ₁ states, were a considerable population had been created by means of adc discharge in a Pb atomic beam. An atomic beam source producing atoms in metastable states is described. For the lifetimes τ of the investigated levels we find:τ(6p(1/2)6d ³ D ₁)=3.74(28) ns,τ(6p(1/2)6d ³ F ₂)=25.8(1.3) ns,τ(6p(1/2)6d ³ D ₂)=4.17_(?31) ^(?49) ns,τ(6p(1/2)6d ³ F ₃)=6.08(26) ns,τ(6p(3/2)7s)³ P ₂=5.85(27) ns. These results are compared with lifetimes derived from oscillator strengths given in the literature.     

Vibrational relaxation time measurements in CH4 and CH4-rare gas mixtures

With a spectrophone vibrational relaxation times in CH₄ and in mixtures of CH₄ with rare gases were measured. Both the amplitude and the phase method were used. The two infrared active modes of CH₄ (ν₄ and ν₃) were investigated separately. The relaxation times, at one atmosphere, after exciting the lowest mode ν₄, were found to be: τ(CH₄-CH₄) = 1.65 μs; τ(CH₄-He) = 1.97 μs; τ(CH₄-Ne) = 8.6 μs; τ(CH₄-Ar) = 12 μs and τ(CH₄-Kr) ≈ 60 μs. From these values one may in that vibrational-rotational (V-R) energy transfer is the dominant relaxation mechanics. By exciting the higher mode the first step in the deactivation of ν₃ was found to be a V-V transfer to the lowest modes ν₄, ν₂.     

A continuous model of human dynamics

Ideas and tools from statistical physics have recently been applied to the investigation of human dynamics. The timing of human activities, in particular, has been studied both experimentally and analytically. Empirical data show that, in many different situations, the time interval separating two consecutive tasks executed by an individual follows a heavy-tailed probability distribution rather than Poisson statistics. To account for this data, human behaviour has been viewed as a decision-based queuing system where individuals select and execute tasks belonging to a finite list of items as an increasing function of a task priority parameter. It is then possible to obtain analytically the empirical result P(τ)∼1/τ, where P(τ) is the waiting time probability distribution.Here a continuous model of human dynamics is introduced using instead an infinite queuing list. In contrast with the results obtained by other models in the finite case we find a waiting time distribution explicitly depending on the priority distribution density function ρ. The power-law scaling P(τ)∼1/τ is then recovered when ρ is exponentially distributed.     

On the characterization of periodic signals using third-order statistical functions

In this paper the theoretical errors involved in the determination of a parameter by measuring g(³)(T,τ,τ') and n⁽³⁾(T) are pointed out. The values of this errors are calculated and compared with those obtained by measuring g(²)(T,τ) for a particular case.     

Spectral analysis by the method of consistent constraints

Two major challenges of numeric analytic continuation—restoring the spectral density, s(ω), from corresponding Matsubara correlator, g(τ)-are (i) producing the most smooth/featureless answer for s(ω), without compromising the error bars on g(τ), and (ii) quantifying possible deviations of the produced result from the actual answer. We introduce the method of consistent constraints that solves both problems.     

Effect of particle size distribution and dynamics on the performance of two-dimensional packing

Extensive computer simulation is used to revisit and to generalize two classical problems: (i) the random car-parking dynamics of A. Rényi and (ii) the irreversible random sequential adsorption (RSA) of parallel squares of same size on a planar substrate of area L². In this paper, differently from the classical RSA, the squares obey the size distribution n(a)=n(1)a^−τ, where a=1,2,3,… is the area of the squares. Using this scaling distribution and three classes of packing dynamics we study the final packing fraction of particles, ?(τ,L), and in particular its thermodynamic limit L→∞. We show that the efficiency to attain a high/low packing density of particles on the substrate is strongly dependent on the value of the exponent τ and on the characteristics of the dynamics.     

Random walks in a simple percolation model with two jump frequencies

We consider transport properties of the system in which the good-conducting bonds lie in parallel planes linked by poor-conducting bonds and the concentration p of good-conducting bonds is close to the two-dimensional percolation threshold p_c. The diffusion coefficient D(τ) which describes the random walking in directions along the planes is calculated as a function of variable τ = p − p_c. For τ → 0 the asymptotic relation D(τ)/D(0) − 1 | ∼ |τ|^α is found w α = 2ν − s. Here s is the superconductivity exponent and ν is the correlation length exponent. It is argued that such behavior is to be expected also for more general models.     

Friedmann universes containing wave fields

In this paper the Friedmann universes containing(i) a massless real scalar field,(ii) a massive real scalar field,(iii) electromagnetic fields,(iv) the combined massive complex scalar and electromagnetic fields are investigated. In(i) the field has to be either purely spatial or else purely temporal and the latter case is completely solved. Similarly in(ii) the purely time-dependent case has been reduced to a single fourth order ordinary differential equation. In this case graphs of the numerical solutions have been exhibited. In(iii) as expected, no non-trivial solution exists. In(iv) all possible cases are studied. In case the complex wave function is a product of two non-constant functions, i.e. ψ=ξ(r)τ(t), there exists no solution. In the subcase gx(r)=ξ^*(r)=constant, ¦τ(t)¦=constant the problem is completely solved. In the subcase ξ(r)=ξ^*(r)=constant and ¦τ(t)¦ is non-constant, the system of equations boil down to the same fourth order ordinary differential equation as mentioned before. In the last two sub-cases, the time-dependent wave field carries electric charge density which, strangely enough, is decoupled from the electromagnetic fields.     

Coevolutionary extremal dynamics on gasket fractal

We considered a Bak-Sneppen model on a Sierpinski gasket fractal. We calculated the avalanche size distribution and the distribution of distances between subsequent minimal sites. To observe the temporal correlations of the avalanche, we estimated the return time distribution, the first-return time, and the all-return time distribution. The avalanche size distribution follows the power law, P(s)∼s−τ, with the exponent τ=1.004(7). The distribution of jumping sites also follows the power law, P(r)∼r−π, with the critical exponent π=4.12(4). We observe the periodic oscillation of the distribution of the jumping distances which originated from the jumps of the level when the minimal site crosses the stage of the fractal. The first-return time distribution shows the power law, Pf(t)∼t−τf, with the critical exponent τf=1.418(7). The all-return time distribution is also characterized by the power law, Pa(t)∼t−τa, with the exponent τa=0.522(4). The exponents of the return time satisfy the scaling relation τf+τa=2 for τf?2.     

Detection of collective motions in dielectric spectra and the meaning of the generalized Vogel-Fulcher-Tamman equation

Based on the reduction property of dielectric spectra associated with the power-law function [∼(jωτ)^±ν] that appears in the frequency domain, one can develop an effective procedure for detection of different reduced motions (described by the corresponding power-law exponents) in temperature domain. If the power-law exponent ν is related to characteristic relaxation time τ by the relationship ν=ν₀ ln(τ/τ_s)/ln(τ/τ₀) (here τ_s, τ₀ are the characteristic times characterizing a movement over fractal cluster that is defined in Ref. [Ya.E. Ryabov, Yu. Feldman, J. Chem. Phys. 116 (2002) 8610]) and the simple temperature dependence of τ(T)=τ_A exp(E/T) obeys the traditional Arrhenius relationship, then one can prove that any extreme point figuring in the complex permittivity ε(jω) spectra (characterized by the values [ω_m, y(ω_m)]) obeys the generalized Vogel-Fulcher-Tamman (VFT) equation. This important statement confirms the existence of the ‘universal’ response (UR) (discovered and classified by Jonscher in frequency domain) and opens new possibilities in the detection of the ‘hidden’ collective motions in temperature region for self-similar (heterogeneous) systems. It gives also the extended interpretation of the VFT equation and allows one to differentiate collective motions passing through an extreme point. This differentiation, in turn, allows one to select the proper fitting function containing one or two (at least) relaxation times for the fitting of the complex permittivity function ε(jω) in the limited frequency domain. This conclusion can allow for the classification of dielectric spectroscopy as the spectroscopy of the reduced (collective) motions, which are described by different power-law exponents on the mesoscale region. The verification of this approach on available DS data (poly(ethylene glycol)-based-single-ion conductors) completely confirms the basic statements of this theory and opens new possibilities in general classification of different motions that can be detected in the analysis of the different dielectric permittivity spectra.     

Analysis of low intensity square wave modulated light beams by measuring the Laplace or squared cosine transform of the time-interval probability

In this paper we study the possibility of analyzing a low-intensity light signal modulated by a square wave by measuring the Laplace or the squared cosine transform of the time interval probability. The error in the determination of the period of the signal is studied and compared with that obtained from the correlation function g⁽²⁾ (τ). We conclude that measurement of the squared cosine transform is a more advantageous method than measurement of g⁽²⁾ (τ) for low intensity light beams, the advantage increasing as the intensity of the light beam decreases. This technique can, for instance, be applied to the fields of laser Doppler velocimetry and optical communications.