General Limit Distributions for Sums of Random Variables with a Matrix Product Representation

The general limit distributions of the sum of random variables described by a finite matrix product ansatz are characterized. Using a mapping to a Hidden Markov Chain formalism, non-standard limit distributions are obtained, and related to a form of ergodicity breaking in the underlying non-homogeneous Hidden Markov Chain. The link between ergodicity and limit distributions is detailed and used to provide a full algorithmic characterization of the general limit distributions.     

激发压缩真空态的相位概率分布

应用Pegg和Barnett提出的相位算符和相位态理论,研究了激发压缩真空态的相位概率分布特性.数值计算结果表明,激发压缩真空态的相位概率分布主要受到相位参量和压缩参量的调节,相位参量使相位概率分布呈峰值结构,压缩参量的变化将影响相位概率分布的峰值强度,此外激发光子数对相位概率分布也有较大的影响.     

Features of the Temperature Distribution in Flat Conductors with Different Configurations

Steady-state temperature distributions in flat conductors of different configurations with direct electric current flowing inside them are investigated. It is shown that the temperature distributions are determined not only by the properties of a material, but also by the characteristic dimensions of a conductor and do not necessarily correlate with the current distributions. Criteria for the similarity between temperature distributions in geometrically identical flat conductors are established.     

Debye Length in a Neutral-beam-heated Plasma

The scale length for an effective shielding of a charged particle in a plasma is the Debye length, which is for Maxwellian velocity distributions determined by the ratio of the temperature to the density. However, fusion plasmas heated by neutral-beam injection (NBI) exhibit highly non-Maxwellian slowing-down velocity distributions. In this case, the evaluation of the characteristic shielding distance from these velocity distributions requires the solution of Fokker-Planck-Poisson equations. In this paper, the effect of NBI slowing-down velocity distributions on the shielding distance are discussed. Analytic expressions for the Debye length of a neutral-beam-heated plasma are given. The results are compared to the Maxwellian case.     

Underlying probability distributions of the canonical ensemble

The canonical distributions are chi-square distributions which are derived from parent distributions for nonconjugate fluctuating thermodynamic variables. The probability distributions are generated by discrete random variables which are the number of degrees of freedom and the number of particles. Randomized sampling of the total number of degrees of freedom and total number of particles gives rise, respectively, to fluctuations in the energy and volume.     

Ternary fission of nuclei in the adiabatic approximation

On the basis of a generalization of integral formulas for nuclear-decay widths to the three-body case, the spontaneous and the low-energy induced ternary fission of nuclei are investigated by using the adiabatic approximation. The properties of energy distributions, of partial fission widths, and of the angular distributions of fission fragments are analyzed for the case of ternary fission. Conditions are found under which the angular distributions of two heavy fragments originating from ternary fission are similar to the analogous distributions of fragments originating from binary fission. The features of angular distributions are investigated, along with the parities and angular momenta of the third (light) ternary-fission fragment.     

Effects of initial electron beam parameters of a linear accelerator on the properties of bremsstrahlung radiation in a radiotherapy setting

The dependence of the initial electron-beam parameters on absorbed dose distributions have been investigated using a CyberKnife radiotherapy accelerator (Accuray, United States). To describe the initial electron-beam characteristics, simulations of the linear electron accelerator are performed and the electron distributions in the beam of a linac output are analyzed. The radial distributions of electrons are assumed exponential, whereas the energy electron distributions are approximated by monoenergetic and rectangular spectra. There is no significant dependence of depth-dose curves in a phantom on the shape of the electron beam. Importantly, a clear dependence of the radiation field profile on the size of the electron beam is observed not just in the penumbra region, but also in the open part.     

Maximal invariants for Lorentz–Wishart models

In this paper we consider two statistical hypotheses for the families of Wishart type distributions. These distributions are analogs of the Wishart distributions defined and parametrized over a Lorentz cone. We test these hypotheses by means of maximal invariant statistics which are explicitly derived in the paper. The testing problems, respectively, concern the hypothesis that parameters are in a sub-Lorentz-cone and the hypothesis that two observations have the same parameter.     

Dislocations and internal length measurement in continuized crystals. II. Closed teleparallelism

The Burgers field responsible for dislocations in a continuized crystal is represented by the torsion tensor of a teleparallel connection, metric with respect to the internal length measurement metric tensor. Lattice lines in a continuized dislocated monocrystal are represented by geodesics of the teleparallel connection, and the internal length measurement along these geodesics is analyzed. The closed teleparallelism responsible for uniformly dense distributions of dislocations is discussed, and equations describing slip surfaces for such distributions of dislocations are formulated. The Galilei-like character of the geometry describing uniformly dense distributions of dislocations is pointed out.     

Size distribution in quantum-dot heterostructures

The size distribution functions for nanoclusters in quantum-dot heterostructures are calculated within the LSW theory. The most common numerical characteristics are calculated for these distributions. The corresponding size distribution functions are selected by means of comparison of the calculated dispersion and mean square deviation with the experimental values obtained for real quantum-dot heterostructures. The regularities of variations of certain numerical characteristics as a function of growth mechanism are shown for different distributions, from the well-known modified Wagner and Lifshitz-Slezov distributions to the distributions proposed in this work. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 59–66, April, 2006.     

Photon path length distributions for an isotropically scattering planar medium

The optical path length concept is employed to determine path length distributions by an approximate numerical inversion of the Laplace transform. Six-term or 13-term closed-form representations of the hemispherical reflectance and transmittance optical path length distributions are presented. The mean path lengths and the distributions integrated over path length are found to be in excellent agreement with known results for a scattering optical depth range of 0.001 to 50.0. Any absorption feature of a medium is easily included in a scattering calculation using the results presented. Internal directional heat flux optical path length distributions are shown to exhibit the effects of higher orders of scattering.     

Retainability of canonical distributions for a Brownian particle controlled by a time-dependent harmonic potential

The retainability of canonical distributions for a Brownian particle controlled by a time-dependent harmonic potential is investigated in the overdamped and underdamped situations, respectively. Because of different time scales, the overdamped and underdamped Langevin equations (as well as the corresponding Fokker-Planck equations) lead to distinctive restrictions on protocols maintaining canonical distributions. Two special cases are analyzed in details: First, a Brownian particle is controlled by a time-dependent harmonic potential and embedded in medium with constant temperature; Second, a Brownian particle is controlled by a timedependent harmonic potential and embedded in a medium whose temperature is tuned together with the potential stiffness to keep a constant effective temperature of the Brownian particle. We find that the canonical distributions are usually retainable for both the overdamped and underdamped situations in the former case. However, the canonical distributions are retainable merely for the overdamped situation in the latter case. We also investigate general time-dependent potentials beyond the harmonic form and find that the retainability of canonical distributions depends sensitively on the specific form of potentials.     

Distributions of ions in a cluster plasma created by a laser pulse

Energy and charge distributions of ions are calculated for a cluster beam irradiated by a high-power ultrashort laser pulse. It is shown that the self-consistent field of a cluster ionized by the laser beam strongly affects the characteristics of the ion distributions obtained after the cluster explodes. The mean concentration of atoms bound into clusters in a beam, the cluster size distribution, and the focal-spot diameter are found to have a weak effect on both energy and charge distributions of the ions, whereas the energy spectrum of the produced ions is determined by the mean cluster size.     

Indirect measurement of AC current distributions in HTS tapes by a pickup coil method

It is necessary to develop HTS conductors with a large current capacity and low AC loss characteristics for practical use of HTS power devices. For large capacity power applications, HTS tapes such as Bi-2223 tapes and YBCO coated conductors are assembled. So, it is important to evaluate the characteristics of current distributions in such assembled HTS tapes. However, an adequate measurement method has not been established. In this study, we have tried the development of an indirect measurement method to evaluate the current distributions in stacked HTS tapes. In this method, the current distributions are indirectly found from the results of the field distributions measured by a pickup coil located around the surface of the sample tapes. To confirm the accuracy and the sensitivity of this method, current distributions in a test conductor made of copper tapes are measured. Numerical and measured current distributions are compared. Using this method, the current distributions in stacked Bi-2223 tapes are measured at room temperature and 77 K. On the basis of the obtained results, the characteristics of the AC current distributions in the HTS tapes are discussed.     

Negative binomial distributions in different pseudorapidity windows in 800 GeV proton-nucleon interactions

Experimental results on multiplicity distributions for full phase space and in different pesudorapidity windows of charged secondary particles produced in proton-nucleon collisions at 800 GeV are presented and discussed. It is found that all these multiplicity distributions are well described by negative binomial distributions. We interpret our results on the basis of clan model. The bin size dependence of multiplicity distribution of charged secondary particles in proton-nucleon interactions is analysed in terms of multifractals. The values of generalised dimensions obtained from fitted distributions show a good agreement with those obtained from the data.     

Multiple returns for some regular and mixing maps

We study the distributions of the number of visits for some noteworthy dynamical systems, considering whether limit laws exist by taking domains that shrink around points of the phase space. It is well known that for highly mixing systems such limit distributions exhibit a Poissonian behavior. We analyze instead a skew integrable map defined on a cylinder that models a shear flow. Since almost all fibers are given by irrational rotations, we at first investigate the distributions of the number of visits for irrational rotations on the circle. In this last case the numerical results strongly suggest the existence of limit laws when the shrinking domain is chosen in a descending chain of renormalization intervals. On the other hand, the numerical analysis performed for the skew map shows that limit distributions exist even if we take domains shrinking in an arbitrary way around a point, and these distributions appear to follow a power law decay of which we propose a theoretical explanation. It is interesting to note that we observe a similar behavior for domains wholly contained in the integrable region of the standard map. We also consider the case of two or more systems coupled together, proving that the distributions of the number of visits for domains intersecting the boundary between different regions are a linear superposition of the distributions characteristic of each region. Using this result we show that the real limit distributions can be hidden by some finite-size effects. In particular, when a chaotic and a regular region are glued together, the limit distributions follow a Poisson-like law, but as long as the measure of the shrinking domain is not zero, the polynomial behavior of the regular component dominates for large times. Such an analysis seems helpful to understand the dynamics in the regions where ergodic and regular motions are intertwined, as it may occur for the standard map. Finally, we study the distributions of the number of visits around generic and periodic points of the dissipative Henon map. Although this map is not uniformly hyperbolic, the distributions computed for generic points show a Poissonian behavior, as usually occurs for systems with highly mixing dynamics, whereas for periodic points the distributions follow a different law that is obtained from the statistics of first return times by assuming that subsequent returns are independent. These results are consistent with a possible rapid decay of the correlations for the Henon map.     

Reconstruction of spatial distributions of sound velocity and absorption in soft biological tissues using model ultrasonic tomographic data

A two-step algorithm is used to reconstruct the spatial distributions of the acoustic characteristics of soft biological tissues-the sound velocity and absorption coefficient. Knowing these distributions is urgent for early detection of benign and malignant neoplasms in biological tissues, primarily in the breast. At the first stage, large-scale distributions are estimated; at the second step, they are refined with a high resolution. Results of reconstruction on the base of model initial data are presented. The principal necessity of preliminary reconstruction of large-scale distributions followed by their being taken into account at the second step is illustrated. The use of CUDA technology for processing makes it possible to obtain final images of 1024 × 1024 samples in only a few minutes.