Analytic Specific Attenuation Model for Rain for Use in Prediction Methods

Based on the values of k and given by ITU-R for the power-law relationship of specific rain attenuation _R=kR , the analytic expressions for k and are regressed as a function of frequency and are in high agreement with the values tabulated. The specific rain attenuation calculated by the analytic expressions are also in high agreement with those by the values of k and tabulated. Comparisons with other analytic expressions show that the ones in this paper are more accuracy and simple.     

Temperature Dependence of the Gibbs State in the Random Energy Model

We consider the problem of temperature dependence of the Gibbs states in two spin-glass models: Derrida's Random Energy Model and its analogue, where the random variables in the Hamiltonian are replaced by independent standard Brownian motions. For both of them we compute in the thermodynamic limit the overlap distribution ^N _{i=1 i i} /N[–1,1] of two spin configurations , under the product of two Gibbs measures, which are taken at temperatures T,T respectively. If TT are fixed, then at low temperature phase the results are different for these models: for the first one this distribution is D _{0 0}+D _{1 1}, with random weights D ₀, D ₁, while for the second one it is ₀. We compute consequently the overlap distribution for the second model whenever T–T0 at different speeds as N.     

Analytic extrapolation inL ∞-norm: An alternative approach to “QCD Sum Rules”

In view of physical applications (especially to QCD Sum Rules), the following problem, pertaining to analytic extrapolation techniques, is studied. We are considering amplitudes, which are (real) analytic functions in the complex plane cut along=[s ₀, ). A modelF ₀(s) of the amplitude is given through the values ofF ₀(s) on some interval=[s ₂,s ₁] (withs ₁<s ₀) and the values of its discontinuity on. These values are approximate, and are supplemented by prescribed error channels, measured inL -norm (both on and). Investigating the compatibility between these data leads to an extremum problem which is solved up to a point where numerical methods can be implemented.Unité Associée au CNRS n^o040768     

Structural relaxation effects on the low-temperature properties of vitreous silica

Measurements of the low-temperature specific heatC and thermal conductivity of vitreous silica after heat treatment at temperaturesT _a between 900°C and 1,400°C are reported. A decrease ofC and an increase of are observed over the whole temperature range studied (C0.06K<T<6K; 0.5 K<T<20 K). Below 1 K the changes inC and (10%) are attributed to a dependence of the density of tunneling states on the fictive temperature. Measurements of the thermal conductivity show that these changes are reversible, thus strongly supporting the evidence for a connection between the tunneling states and the quasi-equilibrium state which is frozen in when an undercooled liquid drops out of thermal equilibrium. Our results are compared to predictions of the free-volume theory of the glass transition. At higher temperaturesC decreases by roughly the same amount as below 1 K while increases by up to 30%. The dependence ofC and onT _a cannot be explained unambigously in terms of a phonon-fraction crossover in the vibrational density of states. Instead, a recently proposed model of coupled SiO₄ rotations is favored.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Unstable Particles, Gauge Invariance and the Δ++ Resonance Parameters

The elastic and radiative ⁺ p scattering are studied in the framework of an effective Lagrangian model for the ⁺⁺ resonance and its interactions. The finite width effects of this spin-3/2 resonance are introduced in the scattering amplitudes through a complex mass scheme to respect electromagnetic gauge invariance. The resonant pole ( ⁺⁺) and background contributions ( ⁰, , , and neutron states) are separated according to the principles of the analytic S-matrix theory. The mass and width parameters of the ⁺⁺ obtained from a fit to experimental data on the total cross section are in agreement with the results of a model-independent analysis based on the analytic S-matrix approach. The magnetic dipole moment determined from the radiative ⁺ p scattering is nuclear magnetons.     

A one-parameter family of cylindrically symmetric perfect fluid cosmologies

Non-stationary cylindrically symmetric one-parameter solutions to Einstein's equations are given for a perfect fluid. There is a time singularity (t=0) at which the pressurep and density are equal to + throughout the radial coordinate range 0 r < , but the solutions are well behaved fort > 0,p and decreasing steadily to zero asr increases through the range 0r<, or as t increases through the range 0<t<. The motion is irrotational with shear, expansion and acceleration. The family of solutions, of Petrov type I, are generally spatially inhomogeneous, of class B(ii), having two spacelike Killing vectors which are mutually orthogonal and hypersurface orthogonal, associated with an orthogonally transitive groupG ₂. The particular members for which there are equations of statep=/3 andp= are specially considered.     

Computer simulation of driven diffusive systems with exchanges

The field-driven Kawasaki model with a fractionp admixture of Glauber dynamics is studied by computer simulation:p=0 corresponds to the order-parameter-onserving driven diffusive system, whilep=1 is the equilibrium Ising model. Forp=0.1 our best estimates of critical exponents based on a system of size 4096×128 are0.22, ^RS0.45, andv v 1. These exponents differ from both the values predicted by a field-theoretic method forp=0 and those of the equilibrium Ising model. Anisotropic finite-size scaling analyses are carried out, both for subsystems of the large system and for fully periodic systems. The results of the latter, however, are inconsistent, probably due to the complexity of the size effects. This leaves open the possibility that we are in a crossover regime fromp=0 top0 and that our critical exponents are effective ones. Forp=0 our results are consistent with the predictionsv >v .     

Renormalization group equations with several length scales and crossover scaling functions for axial anisotropy

The critical behaviour of axially anisotropicn-vector models is characterized by two distinct length scales, the correlation lengths and for the easy and hard axes. In order to handle the full range of anisotropics from to partial differential renormalization group equations are derived, depending on and . The anisotropicX-Y model is studied in detail near four dimensions. The crossover scaling functions for the susceptibilities are calculated to first order in=4–d. Two distinct crossover regions are found for weak and dominant anisotropy, respectively.     

Band-gap structure of the spectrum of periodic Maxwell operators

We investigate the band-gap structure of some second-order differential operators associated with the propagation of waves in periodic two-component media. Particularly, the operator associated with the Maxwell equations with position-dependent dielectric constant (x),xR ³, is considered. The medium is assumed to consist of two components: the background, where (x) = _b , and the embedded component composed of periodically positioned disjoint cubes, where (x) = _a . We show that the spectrum of the relevant operator has gaps provided some reasonable conditions are imposed on the parameters of the medium. Particularly, we show that one can open up at least one gap in the spectrum at any preassigned point provided that the size of cubesL, the distancel=L betwen them, and the contrast = _b / _a are chosen in such a way thatL ^–2, and quantities ^-1-3/2 and ² are small enough. If these conditions are satisfied, the spectrum is located in a vicinity of widthw(^3/2)^-1 of the set {² L ^-2 k ²:kZ³}. This means, in particular, that any finite number of gaps between the elements of this discrete set can be opened simultaneously, and the corresponding bands of the spectrum can be made arbitrarily narrow. The method developed shows that if the embedded component consists of periodically positioned balls or other domains which cannot pack the space without overlapping, one should expect pseudogaps rather than real gaps in the spectrum.     

A Monomial Basis for the Virasoro Minimal Series M(p,p′) : The Case 1<p′/p<2

Quadratic relations are given explicitly in two cases of chiral conformal field theory, and monomial bases of the representation spaces are constructed by using the Fourier components of the intertwiners. The first case is the (2,1) primary fields for the (p,p)-minimal series M_r,s (1rp–1,1sp–1) for the Virasoro algebra where 1<p/p<2. We restrict ourselves to the case p3, for which the (2,1) primary field exists. The second case is the intertwiners corresponding to the two-dimensional representation for the level k integrable highest weight modules V() (0k) for the affine Lie algebra      

Bianchi V imperfect fluid cosmology

Bianchi V, spatially homogeneous imperfect fluid cosmological models which contain both viscosity and heat flow are investigated. The Einstein field equations are established in the case that the equations of state are given byp-(-1),=o ^m, and=o ⁿ (where, o, o,m andn are constants). The physical constraints on the solutions of the Einstein field equations, and, in particular, the thermodynamical laws and energy conditions that govern such solutions, are discussed in some detail. Simple power law solutions and solutions in which there is no heat conduction are studied first. Exact solutions are then investigated in more generality, and it is shown that there exist two first integrals of the field equations for certain values of the physical parameters, m andn. Finally, it is shown that in a special case of interest (in whichm =n = 1/2) the imperfect fluid Bianchi V field equations can be written as a plane-autonomous system, thus facilitating the qualitative analysis of these cosmological models.     

Critical behavior of the site percolation model on the square lattice in aL×M geometry

Relevant aspects of the critical behavior of the site percolation model in aL×M geometry (LM) are studied. It is shown that this geometry favors the growth of percolating clusters in theL-direction with respect to those growing in theM-direction, causing pronounced finite-size effects on the percolation probabilities. Scaling functions have an additional parameter, namelyM, which introduces a dependence of these functions on the aspect ratioL/M. At criticality, the probability of a site belonging to the percolation clusters (P _L,M ) behaves likeP _L,M L ^/v (L/M) with =5/36 andv=4/3, where is a suitable scaling function. Using scaling arguments it is conjectured and then tested by means of Monte Carlo simulations, the following asymptotic behavior (L/M)(L/M), (L,M, =1), for the leading term. Systematic deviations of the Monte Carlo data from the conjectured behavior are due to second order corrections to the leading term which can also be under-stood on the basis of scaling ideas. Finite-size dependent critical probabilities are also functions ofL/M as it follows from scaling arguments which are corroborated by the simulations.Financially supported by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) de la República Argentina     

Random walk with persistence

The exact analytic result is obtained for the Fourier transform of the generating functionF(R,s)= _n=0 s ⁿ P(R,n), whereP(R,n) is the probability density for the end-to-end distanceR inn steps of a random walk with persistence. The moments R ²(n), R ⁴(n), and R ⁶(n) are calculated and approximate results forP(R,n) and R ^–1(n) are given.     

Structure factor of substitutional sequences

We study the structure factor for a large class of sequences of two elementsa andb such that longer sequences are generated from shorter ones by a simple substitution rulea ₁(a, b) andb ₂(a, b), where the's are some sequences ofa's andb's. Such sequences include periodic and quasiperiodic systems (e.g., the Fibonacci sequence), as well as systems such as the Thue-Morse sequence, which are neither. We show that there are values of the frequency at which the structure factors of these sequences have peaks that scale withL, the size of the system likeL ⁽⁾. For a given sequence a simple one- or two-dimensional dynamical iterative map of the variable can easily be abstracted from the substitution algorithm. The basin of attraction of a given fixed point or limit cycle of this map is a set of values of at which there are peaks of the structure factor all of which share the same value of. Furthermore, only those values of which are in the basin of attraction of the origin can have()=2. All other peaks will grow less rapidly withL. We show how to construct many sequences which, like the Thue-Morse sequence, have noL ² peaks. Other qualitative features of the structure factors are presented. Our approach unifies the treatment of a large class of apparently very diverse systems. Implications for the band structure of these systems as well as for the analysis of sequences with more than two elements are discussed.     

The classification of differential structures on quantum 2-spheres

Exterior algebras of differential forms on quantum 2-spheresS _qc ² ,q[–1, 1]/{0},c[0, ] (c=0 forq=±1), are classified. In the definition of exterior algebras we assume the invariance w.r.t. the action of the quantumSU(2) group and dimensionality conditions (which imply that we deal with two-dimensional manifolds). The exterior algebras exist only forc=0 and are unique in that case. The corresponding generalized directional derivatives are provided.     

Branched polymers in a wedge geometry in three dimensions

We investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and. We show that the growth constant is equal to ^f , where is the self-avoiding walk limit. Thef and (, ) dependences of the corresponding critical exponent _f (, ) are studied using Monte Carlo techniques. In the casef=1, our results are compared with existing predictions obtained from series expansion and renormalization group methods. We have also estimated the amplitudes for the mean square radius of gyration and the mean square end-to-end branch length. Our results for the ratio of the mean square radius of gyration of anf-star to that of a linear polymer of the same degree of polymerization attached in a similar wedge, and the analogous ratio for the mean square end-to-end branch length, are consistent with these ratios being lattice-independent quantities.     

The surfboard Schrödinger equations

We study the large time behavior of solutions of time dependent Schrödinger equationsiu/t=–(1/2)u+t V(x/t)u with bounded potentialV(x). We show that (1) if>–1, all solutions are asymptotically free ast, (2) if–1 a solution becomes asymptotically free if and only if it has the momentum support outside of suppV for large time, (3) if –1 <0 all solutions are still asymptotically modified free ast and that (4) if 0 <2, for each local minimumx ₀ ofV(x), there exist solutions which are asymptotically Gaussians centered atx=tx ₀ and spreading slowly ast.     

Laser-Induced Flourescence Excitation Spectroscopy and Photophysics of Naphthalene Bichromophoric Molecules in Supersonic Jets

We present studies of interchromophore interactions under supersonic jet conditions in a large number of dinaphthyl bichromophoric molecules by measuring their laser-induced fluorescence (LIF) excitation spectra. The molecules are composed of two naphthalene chromophores connected by an n-methylene bridge. The length of the bridge was varied as a function of the number of methylene units (n = 0, 1, 2, 4, 6), of the general type NnN(i,j), were N denotes naphthalene moiety, n the number of methylene units in the bridge, and (i,j) are the or positions of the bridge at each of the chromophores. We obtained high-quality LIF spectra of these bichromophoric olecules. In the molecules N1N(2,2), N1N(1,2), N2N(2,2), and N2N(1,2), the spectrum is characterized by an intense 0–0 region, with series of low-frequency progressions. These progressions are assigned as vibrational modes of the bridge. The appearance of several series of progressions is explained either by the excitation of different chromophores (in the mixed molecules) or by the excitation of different populated conformers. The spectrum of N4N(1,1) is different in several aspects from these spectra. The origin is shifted farther to the red, to 31,402 cm^–1. Low-frequency progressions or other transitions are not observed near the origin, but typical intrachromophore naphthalene vibrations are intense. The spectra of N6N(1,1) and N6N(2,2) are also characterized by intense intrachromophore vibrations, however, the spectrum of N6N(2,2) is very complicated due to many populated conformations, while that of N6N(1,1) is more simple.     

Quantum shot noise: Expansions in powers of the pulse density

Quantum shot noise consists of individual pulses which contribute time-dependent (operator) potentials toward a total potentialV(t). The averaged quantity T exp _t0 ^t dtV(t) in general can no longer be calculated explicitly, in contrast to the classical case, and expansions are of interest. Noncommutative cumulant expansions are not directly applicable if the correlation functions ofV(t) have singularities, as happens in applications. It is shown here that these expansions, when applied to quantum shot noise, can be partially summed to give expansions in powers of the pulse density. Three types of such expansions are established explicitly, and for two of them the derivation is direct. For one of them the first-order approximation is closely connected to the so-called unified theory of spectral-line broadening.     

A discrete spectrum of solutions of the wave equation with strong cubic nonlinearity

The nonlinear wave equation, _tt –+³=0, has many solutions that are periodic in time and localized in space, all with infinte energies. The search for spherically symmetric solutions that are well represented by the simple approximation, (r, t)A(r) sin t, leads to a discrete spectrum of solutions{ _N (r, t; )}. The solutions are nonlinear wavepackets, and they can be regarded as particles. The asymptotic theory () of the motion of the guiding center of theNth wavepacket, in the presence of a specified potential, is characterized by an infinite mechanical mass and an infinte interaction mass, and they are compatible. The rest mass in the classical relativistic mechanics of guiding centers ism ₀ c ²= _N ; i.e. the spectrum { _N } determines a spectrum of Planck's constants.On leave (1972–73) Université de Paris VI, Département de Mécanique, 75 Paris 5^e, France.