Intermittency in galaxy distribution

The method of scaled factorial moments of normalized distribution is used to analyze the galaxy distribution in the Universe. Two types of galaxy subsamples and two ways of dividing the space into cells are considered for CfA catalogue. In all cases we observe strong intermittency in the galaxy distribution. We estimate also the fractal dimensionsD ₂ ...,D ₅.     

The computed force constants and vibrational spectra of cubane

The geometry, complete harmonic force field, and dipole moment derivatives of cubane, C₈H₈, have been calculated at the Hartree-Fock level using a 4–21 Gaussian basis set. The infrared and Raman spectra of cubane and four deuterated derivatives were calculated and compared with previously observed spectra. A set of five scale factors for the calculated force constants was then derived by least-squares fitting of the fundamental vibrational frequencies calculated from the scaled force field to the frequencies obtained by direct experimental measurement. The resulting scaled quantum-mechanical (SQM) force field, containing 73 unique elements, is believed to give an accurate representation of the harmonic vibrational potential of cubane. In most cases, the spectral assignments previously made from purely empirical considerations were confirmed, but a few corrections are proposed. The only major alteration is for an A_2u mode revised to appear at 1030 cm^?1 in the undeuterated molecule. Coriolis constants and approximate infrared intensities are also calculated.     

Performance characteristic of a Stirling refrigeration cycle in micro/nano scale

The aim of the paper is to present the performance characteristics of a Stirling refrigeration cycle in micro/nano scale, in which the working substance of cycle is an ideal Maxwellian gas. Due to the quantum boundary effect on the gas particles confined in the finite domain, the cycle no longer possesses the condition of perfect regeneration. The inherent regenerative losses, the refrigeration heat and coefficient of performance (COP) of the cycle are derived. It is found that, for the micro/nano scaled Stirling refrigeration cycle devices, the refrigeration heat and COP of cycle all depend on the surface area of the system (boundary of cycle) besides the temperature of the heat reservoirs, the volume of system and other parameters, while for the macro scaled refrigeration cycle devices, the refrigeration heat and COP of cycle are independent of the surface area of the system. Variations of the refrigeration heat ratio r_R and the COP ratio r_ε with the temperature ratio τ and volume ratio r_V for the different surface area ratio r_A are examined, which reveals the influence of the boundary of cycle on the performance of a micro/nano scaled Stirling refrigeration cycle. The results are useful for designing of a micro/nano scaled Stirling cycle device and may conduce to confirming experimentally the quantum boundary effect in the micro/nano scaled devices.     

Hard-thermal-loop QCD trace anomaly

In this proceedings I summarize results of QCD trace anomaly from recent three-loop hard-thermal-loop perturbation theory (HTLpt) calculations. I focus on the trace anomaly scaled by T ² for pure-glue and N _f = 3 QCD. The comparison to available lattice data suggests that for pure-glue QCD agreement between HTLpt results and lattice data for the trace anomaly begins at temperatures above 8 T _c while when including quarks (N _f = 3) agreement begins already at temperatures above 2 T _c . The results in both cases indicate that at very high temperatures the T ²-scaled trace anomaly increases with temperature in accordance with the predictions of HTLpt.     

Short- and long-range screening of optical phase singularities and C points

Screening of signed (charged) singularities-phase vortices in scalar fields, C points in vector fields, is discussed for paraxial optical fields with short- and long-range correlations. A circular region of radius R is assumed. Short-range screening is exemplified by a Gaussian field correlator, long-range screening by a J₀ Bessel function. The short-range screening length is obtained analytically; this is found to be in substantial agreement with recent experiments. For long-range screening, an accurate asymptotic formula suitable for quantitative comparison with data (numerical or laboratory) is derived for the variance of the net charge. A J₀ correlation function is not attainable in practice, but it is shown how to generate a pseudo-long-range optical field whose correlation function closely approximates this form; screening in such a field is well described by our theoretical results for J₀. The charge variance can be measured by three different methods: by counting positive and negative singularities inside the region of interest, by counting signed zero crossings on the perimeter of this region; or by measuring phase derivatives along the perimeter. For the first method, the charge variance is calculated by integration over the charge correlation function, for the second (third) by integration over the zero crossing (phase derivative) correlation function. It is proven explicitly that, as expected, all three calculations yield the same result. It is also shown analytically that for short-range screening the zero crossings can be counted along a straight line whose length is 2πR, but that for long-range screening this useful simplification no longer holds; for this case another formula is given that is suitable for data correction. The effects of boundary smoothing are discussed, and a class of generalized exponential smoothing functions is introduced. Analytical (numerical) results are given for the large R limit of the charge variance for the short (long) range case. Finally, it is shown that for realizable optical fields, both for the short and pseudo-long-range cases, for sufficiently small R the charge variance grows as R², whereas for sufficiently large R it grows as R.     

A note on scaled variance ratio estimation of the Hurst exponent with application to agricultural commodity prices

The measure of long-term memory is important for the study of economic and financial time series. This paper estimates the Hurst exponent from a Scaled Variance Ratio model for 17 commodity price series under the efficient market null H₀:H=0.5. The distribution about the estimates of H are obtained from 90%, 95% and 99% confidence intervals generated from 20,000 Monte Carlo replications of a geometric Brownian motion. The results show that the scaled variance ratio provides a very good and stable estimate of the Hurst exponent, but the estimates can be quite different from the measure obtained from rescaled range or R–S analysis. In general commodity prices are consistent with the underlying assumption of a geometric Brownian motion.     

Stochastic processes originating in deterministic microscopic dynamics

We investigate the probability distribution of the scaled trajectory of a test particle moving in an equilibrium fluid according to the laws of classical mechanics, i.e., ifQ(t) is the displacement of the test particle we letQ _A(t) =Q(At)/√A and consider the distribution of the trajectory Q_A(t) in the limit A→∞. The randomness of the motion is due entirely to the randomness of the initial state of the fluid, test particle, or both, and the process is generally non-Markovian. Nevertheless, it can be proven in some cases and we expect it to be true in many more that Q_A (t) looks like Brownian motion in the limit A→∞. Some results for simple model systems are presented.     

456-nm deep-blue laser generation by intracavity frequency doubling of Nd:GdVO4 under 879-nm diode pumping

We report on a simple, compact continuous-wave 456-nm laser by intracavity frequency doubling of an end-pumped Nd:GdVO₄ laser on the ⁴ F _3/2 → ⁴ I _9/2 transition. A 5-mm-long, 0.2-at % Nd:GdVO₄ bulk crystal is employed as the gain medium and the Nd³⁺ ion is directly pumped into the emitting level (⁴ F _3/2) by a novel 879-nm laser diode. Intracavity frequency doubling with a 15-mm-long LBO crystal and a 10-mm-long BiBO crystal in a linear cavity yield 56- and 118-mW single-ended blue outputs at the absorbed pump power of 11.9 W, respectively. The corresponding values are scaled to 286 and 391 mW, respectively, in a V-type cavity, with optical conversion efficiencies of 2.4 and 3.3% versus the absorbed pump power. The fluctuations of the 456-nm output power for both cases are less than 3% at the maximum output level.     

Locally Perturbed Random Walks with Unbounded Jumps

Szász and Telcs (J. Stat. Phys. 26(3), 1981) have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if d≥2. The extension of their result to finite range random walks is straightforward. Here, however, we are interested in the situation when the random walk has unbounded range. Concretely we generalize the statement of Szász and Telcs (J. Stat. Phys. 26(3), 1981) to unbounded random walks whose jump distribution belongs to the domain of attraction of the normal law. We do this first: for diffusively scaled random walks on Z ^d (d≥2) having finite variance; and second: for random walks with distribution belonging to the non-normal domain of attraction of the normal law. This result can be applied to random walks with tail behavior analogous to that of the infinite horizon Lorentz-process; these, in particular, have infinite variance, and convergence to Brownian motion holds with the superdiffusive \(\sqrt{n\log n}\) scaling.     

Dynamics of the one dimensional ideal spin glass

The dynamical susceptibility and relaxational behaviour of the one dimensional ideal spin glass obeying Glauber's model is considered. The dynamics can be found exactly as they are related by a transformation to the dynamics of the Ising model. The susceptibility does not show simple relaxational behaviour, rather it can be scaled by two relaxation timesτ ₁ andτ ₂ , with dynamical exponentsz ₁=2 andz ₂=1, which are just the arithmetic and geometric means of the related ferromagnetic and antiferromagnetic relaxation times. The critical slowing down at lower temperatures will result in an increasingly nearly elastic contribution to diffuse magnetic neutron scattering, while at higher temperatures the susceptibility is dominated by independent spin relaxation.     

The structure of single vortices in type II superconductors

This paper reports the first results of a program for the investigation of the detailed electronic and magnetic structure of type II superconductors. The structure of a single flux bundle or vortex in an infinite superconducting specimen is investigated, assuming weak coupling and a spherical Fermi surface of the material. The equations governing the gap parameterΔ(r) and the vector potentialA(r) are suitably scaled and simplified using the symmetry of the system. These equations can be solved numerically only; for their solution the asymptotics ofΔ(r) andA(r) far from the center of the vortex are required. These asymptotics are derived here by properly linearising the equations; they are found to be of the typer ^?1/2 exp (?r/rin0) wherer ₀ is determined by temperature and material parameters. Implicit equations forr ₀ are derived and discussed. We find that for materials withκ-values less than 1.7 (e.g. pure niobium)r ₀ becomes complex at low temperatures; i.e. the deviation ofΔ(r) andA(r) from their values at infinity is a damped oscillation as function ofr.     

Franck-Condon factors and absolute transition probabilities for the if (B3Π0+-X1Σ+) transition

Improved spectroscopic constants have been used to calculate Rydberg-Klein-Rees (RKR) potentials and Franck-Condon factors for the IF(B³Π₀₊-X¹Σ⁺) transition. The Franck-Condon factors are generally in good agreement with previously calculated values, but differ by as much as 30% for transitions from higher levels of the B-state. Several experimentally measured relative transition moment functions have been evaluated and the best scaled, so that the total transition probability calculated for each B-state vibrational level, A(v'), matched measured values. The scaled function was then used to calculate individual transition probabilities, A(v',v), for the vibronic transitions.     

Surface quantum oscillations in (110) and (111) n-type silicon inversion layers

Shubnikov-de Haas oscillations have been studied for (110) and (111) n-type silicon inversion layers. The measured cyclotron masses m_c = (0.38 ± 0.03)m₀ and m_c = (0.40 ± 0.03)m₀ for (110) and (111) planes, respectively, are larger than theoretically predicted values. The experimental valley degeneracy factor g_v = 2 ± 0.2 for both orientations is also at variance with self consistent calculations. The electronic g-factor depends on the surface carrier concentration and is enhanced over its bulk value. There was no evidence for the occupation of other subbands.     

A pocket model for the surface tension of compressed nuclei

The surface structure of compressed semi-infinite isoscalar nuclear matter is studied starting from a simple energy density functional and adding constraints equivalent to some external pressure. For a wide class of compression modes we derive analytical expressions for the surface tension σ as a function of the (de)compressed bulk density n_c. The σ(n₀) = 0 theorem is verified for all modes. The model is tested with numerical calculations using realistic Skyrme-ETF energy density functionals including spin-orbit and effective mass contributions. They confirm the simple analytical model results almost quantitatively. The mode which leads to an antiscaled density (increasing surface diffuseness with increasing bulk density) leads to minimum values for σ around n₀. The implications of the static model for the compression modes in finite nuclei are discussed.     

About Thinning Invariant Partition Structures

Bernoulli-p thinning has been well-studied for point processes. Here we consider three other cases: (1) sequences (X ₁,X ₂,??); (2) gaps of such sequences (X _n+1?X ₁) _n???; (3) partition structures. For the first case we characterize the distributions which are simultaneously invariant under Bernoulli-p thinning for all p??(0,1]. Based on this, we make conjectures for the latter two cases, and provide a potential approach for proof. We explain the relation to spin glasses, which is complementary to important previous work of Aizenman and Ruzmaikina, Arguin, and Shkolnikov.     

Some observations on Levy stability and intermittency in nucleus-nucleus interactions at SPS energies

The power law relation between higher order and second order scaled factorial moments is studied in one dimensional pseudo-rapidity phase (η) space in the interactions of ³²S beam with CNO, AgBr and Emulsion at incident energy of 200 AGeV. Observation for such a power law may indicate a self similar cascade mechanism in multiparticle production process. The values of slope, β_q are found to be independent of target size. The value of the scaling exponent υ = 1.412 obtained is higher than the critical value υ = 1.304, indicating that no second order phase transition exists in our data. The ratio of anomalous fractal dimensions, d_q/d₂ is found to increase with increase in the order of moments, q. The dependence of d_q/d₂ on q indicates a multifractal structure and the presence of self-similar cascading mechanism in our data. The d_q/d₂ values are well described by the Levy-stable distribution with Levy index μ = 1.562 which is consistent with and lies within the Levy stable region (0 ≤ μ ≤ 2). The multifractal spectrum is concave downward with a maximum at q = 0. The decrease in D_q with increasing q shows that there is a self affine multifractal behaviour in multiparticle production in our data.     

Kβ X-ray emission from He-like ions

Relativistic calculations on the energies and electric dipole rates of K_β X-rays from 1s3p(¹P₁,³P₁)-1s² (¹S₀) transitions for He-like ions in the range Z=14–54 are carried out using multi-configuration Dirac–Fock (MCDF) wave functions in the active space interaction approach. The contributions from Breit interaction and quantum electrodynamics have also been included in the calculation. An attempt has been made to find a scaling expression for Breit energy in terms of Zα .The scaled Breit energies are in good agreement with the earlier accurate relativistic results and this ensures the reliability of our scaling procedure. The behavior of MCDF wavefunctions for a given J in the non-relativistic limit has also been studied. The calculated K_β X-ray energies and rates agree well with other available experimental and theoretical values.