Diagnostic evaluation of the mean meridional circulation

Summary We evaluate the mean meridional circulation for the Northern and Southern Hemispheres, working with the angular momentum and the mass conservation equations. We derive and equation for the mass stream function on the lines at constant angular momentum and we numerically integrate this equation using the annual mean data related to the periods 1958 through 1963, and 1963 through 1973, as published by Oort and Rasmusson (Atmospheric Circulation Statistics, NOAA Prof. Pap. No., 5 (Rockville, MD, 1971)) and Oort (Global Atmospheric Circulation Statistics, 1958–1973,NOAA Prof. Pap. No. 14 (Rockville, MD, 1983)), respectively. In both hemispheres we find a weak polar cell, a rather intense Ferrel cell and a strong Hadley cell. The values of the intensity of the polar and Ferrel cells are accurately computed, while we are not confident on the numerical values of the intensity of the Hadley cell. because its rising branch is confined in a narrow region close to the Equator where our results are sensible to small variations in the data. Comparison with previous calculations are discussed.     

Analytic Results in the Position-Dependent Mass Schrödinger Problem

We investigate the Schrödinger equation for a particle with a nonuniform solitonic mass density. First, we discuss in extent the (nontrivial) position-dependent mass V(x)=0 case whose solutions are hypergeometric functions in tanh²x. Then, we consider an external hyperbolic-tangent potential. We show that the effective quantum mechanical problem is given by a Heun class equation and find analytically an eigenbasis for the space of solutions. We also compute the eigenstates for a potential of the form V(x)=V₀ sinh²x.     

Scalar particles mass spectrum and localization on FRW branes embedded in a 5D de Sitter bulk

In this paper, we study the scalar fields evolving on a FRW brane embedded in a five-dimensional de Sitter bulk. The scale function and the warp factor, solutions of the Einstein equations, are employed in the five-dimensional Gordon equation describing the massive scalar field, whose wave function depends on the cosmic time and on the extra-dimension. We point out the existence of bounded states and find a minimum value of the effective four-dimensional mass. For the test (scalar) field envelope along the extra-dimension, we derive the corresponding Schrödinger-like equation which is formally that for the Pöschl-Teller potential. Accordingly, we have obtained the quantization law for the mass parameter of the tested scalar field.     

Study of mass transport in rotating couple stress liquid under concentration modulation

A weakly non-linear stability analysis has been performed to examine the effect of time-periodic concentration modulation on the mass transport. We consider an infinite horizontal fluid layer is rotating with angular velocity Ω₁ about Z-axis subjected to an imposed time-periodic boundary concentration (ITBC). The concentration gradient between the plates of the fluid layer consists of a steady part and a time-dependent oscillatory part. The concentration of both walls is modulated in this case. We have expanded the infinitesimal disturbances in terms of power series of amplitude of modulation, which is assumed to be small. Ginzburg–Landau equation is obtained to find the rate of mass transfer. It is found that, the effect of Taylor number is to stabilize the system. Effect of Schmidt number and Couple stress parameter on mass transfer are also discussed. Further, it is found that the mass transport can be controlled by suitably adjusting the frequency and amplitude of modulation .     

Solutions to the nonlinear Schrödinger equation with sequences of initial data converging to a Dirac mass

We study the nonlinear Schrödinger equation with sequences of initial data that converge to a Dirac mass, and study the asymptotic behaviour of solutions. In doing so we find a connection to previously known long time asymptotics. We demonstrate a type of universality in the behaviour of solutions for real initial data, and we also show how this universality breaks down for examples of initial data that are not purely real.     

Hölder-Banach space analysis of the Bethe-Salpeter equation

We find a Hölder Banach space in which the Bethe-Salpeter equation is a compact integral equation as it stands. We study the properties of the solution in preparation for an analysis of linear field theory models of 3-body amplitudes. In particular we study the properties of the Regge poles of the solution and prove the existence and uniqueness of on mass shell scattering amplitudes.     

Heavy quarkonium in vector and scalar channels

We study quarkonium in hot QCD, emphasizing its nature as a short-lived transient with an exponentially decaying wave function. The heavy quark mass allows for a nonrelativistic expansion around the two-quark threshold, and the static potential is then seen to contain a temperature-dependent imaginary part, which leads to an unstable quark-antiquark state. We solve the corresponding Schrödinger equation and estimate the spectral functions in different channels. In particular, through careful evaluation we find a peak also in the scalar channel, although it is strongly suppressed with respect to the vector channel peak. We also plot the dilepton production rate, which shows a peak-like structure even at temperatures so high that the peak in the spectral function has disappeared.     

A Fokker–Planck approach to a moment closure for mixing in variable-density turbulence

ABSTRACT

We develop a theory for the cascade mixing terms in a moment closure approach to binary active scalar mixing in variable-density turbulence. To address the variable-density complications we apply, as a principle and constraint, the conservation of the probability density function (PDF) through a Fokker–Planck equation with bounded sample space whose attractor is the beta PDF with skewness. Mixing is related to a single-point PDF as a realisability principle to provide mathematically rigorous expressions for the small scale statistics in terms of largescale moments. The problem of the unknown small-scale mixing is replaced with the determination of the drift and diffusion terms of a Fokker–Planck equation in a beta-PDF-convergent stochastic process. We find that realisability of a beta-convergent process requires the mixing time-scale ratio, taken as a constant in passive scalar mixing, to be a function of the mean mass fraction, mean fluid density, the Atwood number, the density-volume correlation and moments of the density field. We develop and compare the new model with direct numerical simulations data of non-stationary homogeneous variable-density turbulence.     

5D Dirac Equation in Induced-Matter Theory

According to an induced-matter approach, Liu and Wesson obtained the rest mass of a typical particle from the reduction of a 5D Klein–Gordon equation to a 4D one. Introducing an extra-dimension momentum operator identified with the rest mass eigenvalue operator, we consider a way to generalize the 4D Dirac equation to 5D. An analogous normal Dirac equation is gained when the generalization reduces to 4D. We find the rest mass of a particle in curved space varies with spacetime coordinates and check this for the case of exact solitonic and cosmological solution of the 5D vacuum gravitational field equations.     

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations. Received: 27 April 1998 / Revised: 2 September 1998 / Accepted: 10 September 1998     

The dirac equation in 5-dimensional Wesson gravity

Using the Ma interpretation of 5D Wesson gravity, we construct the corresponding Weyl equation in a quasistatic spherically symmetric gravitational background in order to look at the mass term predicted by the theory. We find that the value of this mass depends strongly on the boundary conditions selected for theg55. As an example we calculate its value at the surface of the earth.     

The Nonsymmetric Kaluza–Klein Theory and Modern Physics A Novel Approach

We consider in the paper the Nonsymmetric Kaluza–Klein Theory finding a condition for a color confinement in the theory. We consider also a Kerner–Wong–Kopczyński equation in this theory. The Nonsymmetric Kaluza–Klein Theory with a spontaneous symmetry breaking and Higgs' mechanism is examined. We find a mass spectrum for a broken gauge bosons and Higgs' particles. We derive a generalization of Kerner–Wong–Kopczyński equation in the presence of Higgs' field. A new term in the equation is a generalization of a Lorentz force term for a Higgs' field. We consider also a bosonic part of GSW (Glashow–Salam–Weinberg) model in our theory, getting masses for W, Z bosons and for a Higgs' boson agreed with an experiment. We consider Kerner–Wong–Kopczyński equation in GSW model obtaining some additional charges coupled to Higgs' field.     

A numerical study of an expanding plasma of quarks in a chiral model

We numerically solve the transport equations for a quark gas described by the the Nambu-Jona-Lasinio model. The mean field equations of motion, which consist of the Vlasov equation for the density and the gap equation for the mean field, are discussed, and energy and momentum conservation are proven. Numerical solutions of the partial differential equations are obtained by applying finite difference methods. For an expanding fireball the light quark mass evolves from small values initially to the value of 350 MeV. This leads to a depletion of the high energy part of the quark spectrum and an enhancement at low momenta. When collisions are included one obtains an equation of the Boltzmann type, where the transition amplitudes depend on the properties of the medium. These equations are given for flavor SU(3), i.e. including strangeness. They are solved numerically in the relaxation time approximation and the time evolution of various observables is given. Medium effects in the relaxation times do not significantly influence the shape of the spectra. The mass of the strange quark changes little during the expansion. The strangeness yield and the slope temperatures of the final spectra are studied as a function of the size of the initial fireball.     

A particle across a medium: How decoherence relates to the index of refraction

We deduce from a microscopic point of view the equation that describes how the state of a particle crossing a medium decoheres. We find out that the part of the density matrix that evolves preserving coherence, is fully described with the index of refraction. Its imaginary part has the origin in the Lindblad operators, which are the responsible of decoherence. We apply our results to the example of a particle crossing a gas: we find a master equation of the Lindblad type, and compute explicitly the Lindblad operators in terms of the interaction potential between the particle and a target of the medium. Two limit situations are treated: when the particle is much heavier than the targets of the medium and vice versa.     

The Mean First Rotation Time of a Planar Polymer

We estimate the mean first time, called the mean rotation time (MRT), for a planar random polymer to wind around a point. This polymer is modeled as a collection of n rods, each of them being parameterized by a Brownian angle. We are led to study the sum of i.i.d. imaginary exponentials with one dimensional Brownian motions as arguments. We find that the free end of the polymer satisfies a novel stochastic equation with a nonlinear time function. Finally, we obtain an asymptotic formula for the MRT, whose leading order term depends on \(\sqrt{n}\) and, interestingly, depends weakly on the mean initial configuration. Our analytical results are confirmed by Brownian simulations.     

Temperature dependence of OH uptake by carbonaceous surfaces of atmospheric importance

Although OH uptake by carbonaceous surfaces is very efficient, it is thought to be negligible to affect the OH and O₃ balance in the lower troposphere. To estimate its contribution in the upper troposphere, we have studied the temperature dependence of OH uptake by carbonaceous surfaces of atmospheric importance over the temperature range from 218 to 298 K. We found that the OH uptake coefficient is weakly dependent of temperature, ranging from 0.1 to 1, as was measured under flow conditions using chemical ionization mass spectrometry. This finding was further used to estimate OH loss on carbonaceous aerosol under upper tropospheric conditions. Our calculations suggested that OH heterogeneous loss may represent a notable sink for OH in the upper troposphere, which is due to both the significantly lower diffusion limitation and weakly temperature-dependent OH uptake. The obtained results may be thus important for aerosol chemistry of the upper troposphere.     

Effective classical stochastic theory for quantum tunneling

The ensemble mean equations for a classical particle moving stochastically obtain the form of fluid equations. When applying the Madelung transformation to write the Schrödinger equation in a fluid-like form we find that the equations are equivalent to the classical ensemble mean equations if an additional force is added to the equations. The latter can be expressed as a pressure gradient force of a fluctuating pressure with zero mean. Here we analyze the mechanism of quantum tunneling through a rectangular potential barrier from this perspective. We find that despite of the vanishing of the mean of the pressure fluctuations their local non zero gradients enable the tunneling by balancing the counter external potential gradients at the two sides of the potential barrier. Consequently, for stationary solutions, the ensemble mean kinetic energy remains unchanged across the boundaries of the barrier.     

The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations

Abstract

We obtain isomonodromic transformations for Heun’s equation by generalizing the Darboux transformation, and we find pairs and triplets of Heun’s equation which have the same monodromy structure. By composing generalized Darboux transformations, we establish a new construction of the commuting operator which ensures that the finite-gap property is satisfied. As an application, we prove some previous conjectures in part III.     

Quasi-particle model for lattice QCD: quark–gluon plasma in?heavy ion collisions

We propose a quasi-particle model to describe the lattice QCD equation of state for pure SU(3) gauge theory in its deconfined state, for T≥1.5T _c. The method involves mapping the interaction part of the equation of state to an effective fugacity of otherwise non-interacting quasi-gluons. We find that this mapping is exact. Using the quasi-gluon distribution function, we determine the energy density and the modified dispersion relation for the single particle energy, in which the trace anomaly is manifest. As an application, we first determine the Debye mass, and then the important transport parameters, viz., the shear viscosity, η, and the shear viscosity to entropy density ratio, h/S\eta/{\mathcal{S}}. We find that both η and h/S\eta/{\mathcal{S}} are sensitive to the interactions, and that the interactions significantly lower both η and h/S\eta/\mathcal{S}.     

Symmetry conserving generalisation of Hartree Fock Bogoliubov theory

We derive a generalisation of the HFB equations which conserve particle number. This is achieved in using the equation of motion method or alternatively the Green's function technique. The price we have to pay is that there is not only one mean field for the particle numberN but a set of coupled mean field equations for the whole bandN, N±2,N±4... Nevertheless we think that our theory is a quite interesting variant in comparison with the conventional projection technique. We apply our theory to simple models and find that the results are excellent.