A study on the statistics of sonic images

The statistics of sonic images obtained by an image sonar is ana-lysed.The results show that the statistics of the sonic images is different fromthat of common TV images and,therefore,the processing methods for thesonic images possibly are different from that used for common TV images.     

Probing the statistics of transport in the Hénon Map

The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their transport properties. The boundary is composed of invariant “boundary circles.” We briefly report recent results of the distribution of rotation numbers of boundary circles for the Hénon quadratic map and show that the probability of occurrence of small integer entries of their continued fraction expansions is larger than would be expected for a number chosen at random. However, large integer entries occur with probabilities distributed proportionally to the random case. The probability distributions of ratios of fluxes through island chains is reported as well. These island chains are neighbours in the sense of the Meiss-Ott Markov-tree model. Two distinct universality families are found. The distributions of the ratio between the flux and orbital period are also presented. All of these results have implications for models of transport in mixed phase space.     

Dependence of the intensities of ultrasonic sidebands in the Mössbauer spectrum on the statistics of the acoustic field

The acoustic modulation of quanta is analyzed with regard for dissipation of the energy of the excited mode through resonance (having the acoustic frequency) modes. Given definite assumptions, the Rayleigh-Rice distribution function previously introduced phenomenologically is obtained for the oscillation amplitudes. It is proposed that the intensities of the ultrasonic sidebands be expressed in terms of the parameters m and , which are valid for any degree of sound coherence. The results of numerical computations are given.Translated from Izvestiya Vysshikh Uchebrnykh Zavedenii, Fizika, No. 7, pp. 54–57, July, 1979.In conclusion, the authors express their gratitude to Prof. Sh. Sh. Bashkirov for valuable comments.     

On the effect of backscattering of γ quanta and statistics in positron-annihilation lifetime measurements

The contribution of backscattered, 1.27-MeV quanta to the coincidence counts in positron-annihilation lifetime measurements has been investigated. Depending on the energy window settings and geometry, as much as 20% of the coincidence counts was found to arise from backscattered events. Computer analysis of such spectra leads to erroneous results. Analysis of computer-generated lifetime spectra shows that good statistics is more important than good resolution power for the quality of the analysis.On leave of absence at Danfoss, DK-6430 Nordborg, Denmark     

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

Speckle fields are the random light wave distributions produced when the light fields are scattered from random surfaces or a random medium. They appear in many optical phenomena that are related to light propagations[1,2] and have found wide appli-cations in a variety of scientific and technical fields. The examples of the recent impor-tant applications of speckles include the analysis of the movement of the granules[3], the three-dimensional imaging for the microstructures of metal nanocryst…     

An interpretation of the She-Lévêque model based on order statistics

We present an interpretation of the She-Lévêque model in fully developed turbulence based on order statistics. Turbulent behavior at large values of the Reynolds number is often studied through the scaling behavior of moments of the distribution of the velocity differences and of the energy dissipation. The present interpretation leads to a derivation of the scaling exponents ζ_p and τ_p of these moments, without any postulate about a universal relation over the fluctuation structures such as the one used by She and Lévêque. The interpretation is based on the fact that the hierarchy of fluctuation structures imposes statistical constraints, whereupon the order p itself is seen as a random variable. As proposed by She and Lévêque, the hierarchy of the structures is such that the structures of larger order affect locally lower order structures through an entrainment process. This phenomenon leads to the Fisher-Tippett law, one of three asymptotic distributions for the extreme value of a random sample as the size of the sample grows to infinity.     

Dimer statistics on the Möbius strip and the Klein bottle

Closed-form expressions are obtained for the generating function of close-packed dimers on a 2M×2N simple quartic lattice embedded on a Möbius strip and a Klein bottle. Finite-size corrections are also analyzed and compared with those under cylindrical and free boundary conditions. Particularly, it is found that, for large lattices of the same size and with a square symmetry, the number of dimer configurations on a Möbius strip is 70.2% of that on a cylinder. We also establish two identities relating dimer generating functions for Möbius strips and cylinders.     

A generalization of Haldane's state-counting procedure and π-deformations of statistics

We consider the generalization of Haldane's state-counting procedure to describe all possible types of exclusion statistics which are linear in the deformation parameter g. The statistics are parametrized by elements of the symmetric group of the particles in question. For several specific cases we determine the form of the distribution functions which generalizes results obtained by Wu. Using them we analyze the low-temperature behavior and thermodynamic properties of these systems and compare our results with previous studies of the thermodynamics of a gas of g-ons. Various possible physical applications of these constructions are discussed.     

Lévy statistics of emission from a novel random amplifying medium: an optical realization of the Arrhenius cascade

We report the observation of Lévy-like statistical configuration-to-configuration fluctuations in the intensity of emission from a novel system, the fiber-random amplifying medium, where active fiber segments are embedded randomly in a bulk of pointlike passive scatterers. Some rare configurations of fibers provide long, guided amplifying paths for the photons, leading to high jumps in the intensity, and thus to Lévy statistics. This system provides an optical realization of the Arrhenius cascade.     

Effect of electron interaction on statistics of conductance oscillations in open quantum dots: does the dephasing time saturate?

We perform self-consistent quantum transport calculations in open quantum dots taking into account the effect of electron interaction. We demonstrate that, in the regime of the ultralow temperatures 2 pi kappa BT < or = delta (delta being the mean-level spacing), the electron interaction strongly smears the conductance oscillations and thus significantly affects their statistics. Our calculations are in good quantitative agreement with the observed ultralow temperature statistics of Huibers et al. [Phys. Rev. Lett. 81, 1917 (1998)]. Our findings question a conventional interpretation of the ultralow temperature saturation of the coherence time in open dots which is based on the noninteracting theories, where the agreement with the experiment is achieved by introducing additional phenomenological channels of dephasing.     

Universal record statistics of random walks and Lévy flights

It is shown that statistics of records for time series generated by random walks are independent of the details of the jump distribution, as long as the latter is continuous and symmetric. In N steps, the mean of the record distribution grows as the sqrt[4N/pi] while the standard deviation grows as sqrt[(2-4/pi)N], so the distribution is non-self-averaging. The mean shortest and longest duration records grow as sqrt[N/pi] and 0.626 508...N, respectively. The case of a discrete random walker is also studied, and similar asymptotic behavior is found.     

Saturation of nuclear partons: Fermi statistics or nuclear opacity?

We derive the two-plateau momentum distribution of final state (FS) quarks produced in deep inelastic scattering (DIS) off nuclei in the saturation regime. The diffractive plateau, which dominates for small p, measures precisely the momentum distribution of quarks in the beam photon; the role of the nucleus is simply to provide an opacity. The plateau for truly inelastic DIS exhibits a substantial nuclear broadening of the FS momentum distribution. We discuss the relationship between the FS quark densities and the properly defined initial state (IS) nuclear quark densities. The Weizsäcker-Williams glue of a nucleus exhibits a substantial nuclear dilution, still soft IS nuclear sea saturates because of the anti-collinear splitting of gluons into sea quarks.     

Lévy statistics of vibrational mode fluctuations of single molecules from surface-enhanced Raman scattering

Surface-enhanced Raman spectra of a single Fe-protoporphyrin IX molecule display drastic fluctuations in frequency and intensity. When analyzed in their temporal evolution, the vibrational modes of the molecule undergo an on-off switching behavior that is shown to follow a Lévy statistics. Such a time dependent process may encode both the dynamics of the molecule-environment interactions and the intrinsic gating or activation of the mode emission mechanism.     

Local statistics of laminar expanding flames subjected to Darrieus–Landau instability

We, herein, report an experimental study to investigate the role of local flamefront dynamics on the propagation and acceleration of cellularly unstable premixed expanding laminar flames. Using simultaneous Mie-scattering imaging and Particle Image Velocimetry, we measured the flame edge location and its adjacent flow field, which were subsequently processed to quantify the evolution of the probability density functions (pdfs) of flow velocities, curvature, normal strain rate and tangential strain rate. We showed that appropriate normalizaton of the measured quantities can unify the data from different pressures when identified with the corresponding Peclet number, defined as the ratio of the flame radius to the flame thickness. Since the flamefront is stable and smooth at lower Peclet numbers, the flame-induced flow field and stretch rates are almost uniform over the flamefront, resulting in narrow pdfs. At higher Peclet numbers, however, the flame becomes progressively more wrinkled and hence the variations in the local quantities increase leading to wider pdfs. Furthermore, while the mean curvature was found to be inversely proportional to the mean flame radius and insensitive to the cellular structure, the mean normal strain rate was strongly influenced by the cellular structure.     

Investigation of the Spectral Line Intensities of the ν9 Band of the Trans-Conformer of Ethylene

Russian Physics Journal - The intensities of 740 vibrational-rotational lines of the ν9 fundamental band in the IR spectrum of the trans-C2H2D2 molecule are first analyzed. The...