Spatial dependence of correlation functions in the decay problem for a passive scalar in a large-scale velocity field

Statistical characteristics of a passive scalar advected by a turbulent velocity field are considered in the decay problem with a low scalar diffusivity κ (large Prandtl number v/κ, where v is kinematic viscosity). A regime in which the scalar correlation length remains smaller than the velocity correlation length is analyzed. The equal-time correlation functions of the scalar field are found to vary according to power laws and have angular singularities reflecting locally layered distribution of the scalar in space.     

Upper bounds on neutrino masses

Using a recent experimental bound on τ decay into three charged leptons and a weak assumption concerning a general “see-saw” mechanism for neutrino masses, we show that both v_μ and v_τ must be lighter than 65 eV. If the “see-saw” is driven by a right-handed W boson or by a “horizontal” gauge boson, they must be heavier than 50 PeV.     

Qualitative theory of three-dimensional rotator model

The 3-dimensional planar rotator (PR) model with short-range interaction is studied in the “harmonic” approximation where spin wave and vortex loop (VL) system decouple. The phase transition (PT) occuring in the PR-model is studied via the correlation and stability properties of the VL-system for which a tentative phase diagram is set up. Under the assumption that the PT of the PR-model is continuous an ansatz for the “dielectric” function ?_q of the VL-system is made which leads at criticality simultaneously to scaling of the VL-system and of the PR-model. Physical arguments are given to justify the dimensional properties of ?_q which led to this result. The critical exponents for the VL-system in usual notation are η_L=1, and γ_L=v_L=0. The latter represent logarithmic singularities, i.e., ?₀～–ln|τ|^z_γ, and κ～–1/ln|τ|^z_v. The critical expon ents of the PR-model can be expressed in terms of those of the VL-system. The low and high-temperature correlation functions are given. It is shown that only in the presence of an anisotropy field, e.g., a magnetic field, the low temperature correlation function decays exponentially. The relation between the PR-model, and the melting of crystals is briefly discussed.     

Finite-size scaling of correlation functions in finite systems

We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a ddimensional finite system of size L,the correlation function can be written as the product of|r|~(-(d-2+η))and a finite-size scaling function of the variables r/L and tL~(1/ν),where t=(T-T_c)/T_c,ηis the critical exponent of correlation function,andνis the critical exponent of correlation length.The correlation function only has a sigificant directional dependence when|r|is compariable to L.We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations.We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponentη.     

Overall railway noise impact in the U.K.

As part of a British Rail (BR) “Environmental and Social Impact” study in 1975, an attempt at assessing the relative noise impact of rail and road transport was made; 24 hour L_eq in dB(A) units was adopted for the noise measure, as this appeared to give good correlation with “dissatisfaction” and permitted simple estimation of levels from traffic and location data. Five train types were defined, two classes of line, three regions of population density and three standard topographies. The base L_eq value for each traffic mix, line and population region could be established from BR survey data, and the propagation from topography and population (house) densities, to give the population subjected to each L_eq. The percentage “dissatisfied” at each L_eq was then applied to arrive at the total population “dissatisfied”, which was found to be 106 000. A similar approach applied to motorways and principal “A” roads gave 4480 000 “dissatisfied”.     

Collision induced resonant four-photon parametric generation as a method of nonlinear spectroscopy

Generation of the combination tone ω_v = 2ω₀ ? ω_μ in the case where the nonlinear process is possible only in the presence of coherent reorienting collisions, is considered. A simple measurement method of the cross-section difference between “orientation” and “alignment” destruction is proposed.     

Completely analytical interactions: Constructive description

An interactionU is called a completely analytical (CA) interaction, if it satisfies one of 12 given conditions formulated in terms of analyticity properties of the partition functions Z_v(u), or correlation decay, or truncated correlation bounds, or asymptotic behavior of ln Z_v(u), v→∞. The 12 conditions are presented, together with part of the proof of their equivalence. The main result of the paper is that each condition is constructive in the following sense: instead of checking it in all finite volumesv??^v, it is enough to consider only (a finite amount of) volumes with restricted size. In particular, the partition functions Z _v (u+?) for the complex perturbationsu+? ofu do not vanish for all V? ^v and all ? with ∥?∥<?, provided this is true only forv with diam v?C(?) and ∥?∥<?′ (but with?<?′).     

Correlations in inhomogeneous Ising models

Using general methods developed in a previous treatment we study correlations in inhomogeneous Ising models on a square lattice. The nearest neighbour couplings can vary both in strength and sign such that the coupling distribution is translationally invariant in diagonal direction. We calculate correlations parallel to the layering in the diagonally layered model with periodv=2, the so-called “general square lattice” model (GS). If the model has a finite critical temperature,T _c>0, we have a spontaneous magnetization belowT _c vanishing atT _c with the Ising exponent β=1/8. AtT _c correlations decay algebraically with critical exponnet η=1/4 and exponentially forT>T _c. In the frustrated case we have oscillatory behaviour superposed on the exponential decay where the wavevector of the oscillations changes at some “disorder temperature”T _D(>T _c) from commensurate to temperature-dependent in commensurate periods. If the critical temperature vanishes,T _c=0 we always have exponential decay at finite temperatures, while atT=T _c=0 we encounter either long-range order or algebraic decay with critical index η=1/2, i.e.T=0 is thus a critical point.     

Surface-enhanced Raman spectroscopy of electrochemically characterized interfaces; potential dependence of Raman spectra for thiocyanate at silver electrodes

Surface-Enhanced Raman Spectra have been obtained for thiocyanate anions at silver electrodes following an oxidation-reduction cycle (ORC) as a function of electrode potential and electrolyte composition and compared with the extent of thiocyanate adsorption determined under the same conditions from differential capacitance-potential data. A spectrograph equipped with an optical multichannel analyzer (OMA) detector and a scanning spectrometer were used to make the Raman measurements. Spectra were obtained over the frequency range 100–2200 cm^?1, where all three normal vibrations, CN stretching (v_CN, 2090–2120 cm^?1), CS stretching (v_CN, 735 cm^?1), NCS angle bending (δ_NCS, 450 cm^?1) occur, along with a low frequency vibration attributed to a metal-ligand stretching mode (v_ml, 200–215 cm^?1) arising from a silver-sulfur surface bond. Both v_CN and v_ML decreased in frequency as well as intensity as the potential was made more negative in the region ?100 to ?700 mV versus Ag/AgCl for bulk thiocyanate concentrations of one millimolar and above, even though the thiocyanate surface concentration remained close to a monolayer throughout. By means of rapid time-resolved spectral measurements following potential steps using the OMA, the decrease of the intensity and frequency of the v_CN mode with increasing negative electrode potential was separated into a rapid “reversible” component and a slower “irreversible” decay. The latter component is attributed to the decay of Raman-active sites associated with the dissipation of metastable silver clusters formed during the ORC, that are prevented from rearranging at more positive potentials due to the presence of surrounding anionic adsorbate.     

Intermittency in the atmospheric surface layer: Unresolved or slowly varying?

We present streamwise velocity structure functions 〈δv_L(τ)〉=〈|v(t+τ)−v(t)|^p〉 (with p=1:5) obtained in the near neutral atmospheric surface layer at the Utah SLTEST site at the highest terrestrial Reynolds number Re_τ=O(10⁶). We show that the occurrence of very large scale coherent oscillations in the streamwise velocity throughout the wall region, interpreted as genuine structural features of the canonical turbulent boundary layer, affects the scaling exponents of the p>3 order structure functions. This results in a slight alteration of the intermittent behavior of the velocity field. It was found that for positive (fast) large scale oscillation of the low-pass filtered velocity signal, deviations from the Kolmogorov K41 prediction (absence of multiscaling) are more marked, as compared to negative (slow) excursion. The results are discussed in terms of convergence of statistics from atmospheric boundary layer measurements.     

A study of Fe-doped Bi-Sr-Ca-Cu superconductors

We have substituted 1.5% of Fe for Cu in several “2212” and “2223” Bi-Sr-Ca-Cu superconductors. All of the samples show a reduction ofT _c about 13 K due to the Fe impurities. Mössbauer measurements at room temperature reveal the structural characteristics such as stacking faults and intergrowth of different phases in these Bi-based compounds on the microscopic scale. The susceptibility ofT _c to Fe-doping in the Bi-“2212” or “2223” system is comparable to that of the “123” system but much smaller than that of the “214” system. The interplanar correlation existing in the “123” and the Bi-“2212” and “2223” systems seems to play an important role in sustaining the high temperature superconductivity and weakening the detrimental effect of impurity elements on superconductivity in these two systems.     

Sound velocity in single crystals of synthetic opals

The [111] longitudinal sound velocity (v _L) in a single-crystal synthetic opal has been measured at a frequency of 10 MHz in the temperature range 4.2–300 K. At 300 K, v _L=2.1×10⁵ cm/s. The quantity dv _L/v _{300 K}(T) (where v _T,K?v_{300 K}) in the ranges 4.2–200 and 200–300 K behaves in the way typical of amorphous and crystalline solids, respectively.     

Förster resonance energy transfer in hybrid associates of colloidal Ag<Subscript>2</Subscript>S quantum dots with thionine molecules

Nonradiative resonance energy transfer in hydrophilic hybrid associates of thionine molecules (TH⁺) with colloidal Ag₂S quantum dots (QDs) with average diameter of 3.5 nm was studied. Photoluminescence spectra and its decay shown that for these systems the supplemental photosensitization of recombination luminescence of Ag₂S QDs (1200 nm) from the region of TH⁺ fluorescence (618 nm) is possible. It was found that the average lifetime of TH⁺ molecules luminescence is shortened during their association with Ag₂S QDs. Approximation of luminescence decay by stretched exponent with value of parameter β =?0.5 indicates on the inductive-resonance dipole-dipole (Förster) mechanism of nonradiative energy transfer (FRET). The efficiency of FRET was 0.29–0.41.     

The estimates of correlations in two-dimensional Ising model

We investigate the correlation inequalities and the decay of correlations of stochastic Ising model in a rectangle with side length 2L×K(LlnL)^1/2, where K is some positive constant. With different boundary conditions, at inverse temperature β>β_c or β<β_c and zero external field, we show some estimates of the correlation functions for the two-dimensional Ising model.     

The velocity autocorrelation function and self-diffusion coefficient of fluids with steeply repulsive potentials

We consider the velocity autocorrelation function, vacf, or C_v(t) and self-diffusion coefficients, D, of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, ? (r) = ?(σ/r)ⁿ. The C_v(t) are calculated numerically by molecular dynamics simulations. Accurate expressions for the short time expansion of C_v(t) to order O(t⁴) for n large are derived for this fluid. We propose novel expressions for C_v (t) that, for n large, spans the transition from the short time regime (expandable in even powers of time) and the longer time exponential-like regime characteristic of hard spheres. Inter alia we introduce relaxation times that characterize the duration of a collision and the decay of the velocity correlation within the mean-collision or Enskog-like relaxation time, T_E.     

Effects of finite size and shape on scattering and thermodynamic quantities at 2D Ising critical points

Using recent results by Cardy based on the conformal invariance of critical correlation functions we calculate universal results for scattering functions S(k), susceptibilities, correlation lengths and specific heat correction terms for finite Ising systems in two dimensions with circular and rectangular shapes and free boundary conditions. Our results specify the effect of shape on these quantities at the critical point. In particular, the half-width and lineshape of the scattering function is found to be strongly influenced by geometry. For a circle, S(k) follows the infinite system behavior 1/k^2−η, η = 0.25 only for very large k. For a substantial range of intermediate k values it is well represented by 1/k^2−η_app, with an “apparent” exponent η_app. We also discuss the probable influence of end, edge and domain wall effects on the correlation lengths, susceptibilities and specific heat correction terms. The application of our results to experimental systems and other theoretical models is considered.