A mixed spectral and finite difference model to study baroclinic annulus waves

A mixed spectral and finite difference model to study finite amplitude baroclinic waves in a differentially heated rotating annulus is presented. The model consists of the full Navier-Stokes equations and the heat equation. The field variables f = f(r, φ z; t) are decomposed into zonally averaged components f_o(r, z; t) and eddy components f(r, φ, z; t), the latter being periodic in f and represented in terms of Fourier series. The unknowns f_o(r, z; t) and f^{c, s}(r, z; t), which are Fourier amplitudes of f′(r, φ, z; t) are governed by two-dimensional primitive equations with the addition of source terms. These equations are solved semi-implicitly by the alternating direction implicit method on variable grids.A simplified model with two Fourier components which permits self-interaction of the chosen wave and the interaction of the wave and the mean fields had been used to repeat a computation done by G. P. Williams, who used a fully three-dimensional finite difference algorithm. We can reproduce almost all of Williams' results in 1/20 of the computing time with the present model. It only requires 1/30 the additional computer storage of Williams' finite difference model over the axisymmetric problem.The potential of the present model for investigation of multiwave interaction as well as the advantages and disadvantages of the two different approaches is discussed.     

Inverse Laplace transforms of osculatory and hyperosculatory interpolation polynomials

In the numerical calculation of f(t), the inverse Laplace transform of F(p), where f(′) = (1/2πi) °_c−i∞^c+i∞ e^pt F(p)dp, sufficient accuracy is usually obtainable when p³F(p), s > 0, is replaced by an interpolating polynomial in 1/p. From the values of F(p) with F′(p), or with F′(p) and F″(p), for p at points equally spaced on the real axis, an osculatory or hyperosculatory interpolation polynomial for p⁸F(p), namely L_2n−1(x) or L_3n−1(x), where x = 1/p, is obtained in barycentric form. Then f(t) is calculated by a Gaussian-type quadrature formula employing complex values of L_2n−1 or L_3n−1 and instead of p^sF(p) which may be unknown or more difficult to compute. For calculating L_2n−1 and L_3n−1, auxiliary coefficients, suitable for economical storage in the program, are given exactly for n = 2(1)11 and n = 2(1)7, furnishing up to 21st and 20th degree accuracy, respectively.     

Spectral changes of vector Gaussian Schell-model beams passing through an aperture lens

On the basis of the polarization matrix and propagation equation of the cross-spectral density matrix, the spectral changes in the focal plane of vector Gaussian Schell-model (GSM) beams focused by an aperture lens are studied, where the influence of correlation and polarizer on the behavior of the spectral switch is stressed. It is found that the critical position u_c, spectral minimum S_min, and transition height Δ of the spectral switch depend on the auto-correlation but do not depend on the cross-correlation of GSM beams if there is no polarizer. However, in the presence of the polarizer u_c, S_min and Δ depend on both auto- and cross-correlations. The polarizer affects the spectral switch of vector GSM beams, whereas it does not affect the spectral switch of scalar GSM beams.     

The hyperfine splittings in heavy-light mesons and quarkonia

Hyperfine splittings (HFS) are calculated within the Field Correlator Method, taking into account relativistic corrections. The HFS in bottomonium and the B _q (q = n, s) mesons are shown to be in full agreement with experiment if a universal coupling α _HF = 0.310 is taken in perturbative spinspin potential. It gives M(B*) −M(B) = 45.7(3) MeV, M(B _s ^* ) − M(B _s ) = 46.7(3) MeV (n _f = 4), while in bottomonium Δ_HF(b $ \bar b $ \bar b ) = M(Υ(9460)) − M(η _b (1S)) = 63.4 MeV for n _f = 4 and 71.1 MeV for n _f = 5 are obtained; just the latter agrees with recent BaBar data. For unobserved excited states we predict M(Υ(2S))−M(η _b (2S)) = 36(2)MeV,M(Υ(3S))−M(η _b (3S)) = 28(2)MeV, and also M(B _c ^*) = 6334(4) MeV, M(B _c (2S)) = 6868(4) MeV, M(B _c ^* (2S)) = 6905(4) MeV. The mass splittings between D(2³ S ₁) − D(2¹ S ₀), D _s (2³ S ₁) − D _s (2¹ S ₀) are predicted to be ∼75 MeV, which are significantly smaller than in several other studies but agree with the mass splitting between recently observed D(2533) and D*(2610).     

Process πp → ππN at high energies and moderate momenta transferred to the nucleon and the determination of parameters of the f0(980) and f0(1300)

We present the results of simultaneous analysis of the S-wave ππ spectra in the reactions π ⁻ p → (ππ)_S n at p _lab=38 GeV/c (GAMS) and π ⁻ p → (ππ)_S n at p _lab=18 GeV/c (E852 Collaboration) at moderate momenta transferred to the nucleon, |t| ≲ 1.5 (GeV/c)². The t distributions are described by the Reggeized π and a ₁ exchanges provided by the leading and daughter trajectories, while the M _ππ spectra are determined by a set of scalar-isoscalar resonances. With M _ππ distributions averaged over different t intervals, we have found several solutions given by different t-channel-exchange mechanisms at |t| ∼ (0.5–1.5) (GeV/c)², with resonance parameters close to each other. We conclude that, despite a poor knowledge of the structure of the t exchange, the characteristics of resonances such as masses and widths can be reliably determined using the processes under discussion. As to pole positions, we have found (1031±10)−i(35±6) MeV for f ₀(980) and (1315±20)−i(150±30) MeV for f ₀(1300). From Yadernaya Fizika, Vol. 66, No. 5, 2003, pp. 960–972. Original English Text Copyright ? 2003 by Anisovich, Sarantsev. This article was submitted by the authors in English.     

System-parameter dependence of the metallic phase of the non-doped 2D Hubbard model

Naito et al. reported that some non-doped T′-214-type compounds drive high-T_c superconductivity. The compounds are considered to be metallic since on-site Coulomb energy U is moderate and the Fermi surface is much deformed in these compounds. In order to confirm this picture and extract electronic structure information, we have examined the phase diagram of the metallic state of the 2D Hubbard model as a function of U and t′ (with t″ we fixed at − t′/2 here; t′ and t″ are the second- and third-neighbor transfer energies, respectively) by means of the variational Monte–Carlo method. We employed a Jastrow-type Gutzwiller trial wave function. In the studied range of U = 2–12, the boundary value for |t′| at which SDW disappears increases almost linearly with U. Jump-wise transition to the Mott insulator state was not observed. Using the boundary curve and experimental band parameter values, we estimate U  5 for T′-214 compounds. Preceding works are discussed in the last part.     

Sufficient condition for the existence of an inertial manifold for a hyperbolic equation with weak and strong dissipation

In the paper, sufficient conditions for the existence of an inertial manifold for the equation u _tt + 2γ _w u _t − 2γ _s Δu _t − Δu = f(u) + g(u _t) are obtained. The nonlinear functions f and g are assumed to have the Lipschitz property.     

predictions of PMNS and CKM angles

Generalizing a previous model to accommodate the third quark family and CP violation, we present a T^′ model which predicts tribimaximal neutrino (PMNS) mixings while the central predictions for quark mixings are |V_td/V_ts|=0.245 and |V_ub/V_cb|=0.237 with a predicted CP violating KM phase δ_KM=65.8°. All these are acceptably close to experiment, including the KM phase for which the allowed values are 63°<δ_KM<72°, and depend only on use of symmetry T^′×Z₂ to define the model and no additional parameters.     

Excitation of doublet <Emphasis Type="Italic">D</Emphasis>-levels of a lutetium atom by electron impact

The electron-impact excitation of doublet D-levels of the lutetium atom is studied by the method of extended crossing beams. At the exciting electron energy of 50 eV, 64 excitation cross sections are measured. In the electron energy range of 0–250 eV, nine excitation optical functions are recorded. The occurrence of perturbations in the spectral series 6s ²(¹ S)6p ² P ₁^2/○ − 6s ²(¹ S)nd ² D _3/2 is discussed.     

Effect of aerosil dispersions on the nematic-to-isotropic interface

The effect of silica aerosils on the kinetics of the first-order nematic-isotropic (NI) phase transition is phenomenologically described in the framework of the time-dependent Landau-Ginzburg equation. A steady-state solution to the equation is presented such that the NI interface may propagate with a solitary-like wave profile under constant quenching. The results provide a plausible basis for the interpretation of the dynamical effects of quenched disorder in the liquid-crystal systems, caused by randomly interconnected porous media, such as aerosils. In the low silica aerosil ρ_s ( ≤0.1 g/cm^3) regime, the calculated values of the interface velocity v(T,ρ_s), the interface thickness κ(T,ρ_s), and the critical radius of a spherical nucleus of new nematic phase in a bulk isotropic environment, composed of polar molecules, such as 4-n-octyl- 4^′- cyanobiphenyl and 4-n-heptyl- 4^′- cyanobiphenyl shows that the effect of silica aerosils on the kinetics is reflected in a shifting of the set of temperature-dependent curves to lower temperature values.-1     

From macroscopic to atomic motions in liquid metals

Summary In the present review of liquid dynamics studies on liquid metals are reported. Particularly the case of liquid lead is reviewed because this case was carefully studied by neutron scattering technique,S(Q,ω) being determined at two widely different temperaturesT=623 K andT=1170 K and therefore different densities. In addition extensive supplementary MD simulations were made using a 16 384-particle system. The simulations ranged from a determination of an effective pair potential for lead to simulation of the density correlation functionsF(Q,t) andF _s(Q,t), as well as the longitudinal and transversal current correlation functionsJ ₁(Q,t) andJ _T(Q,t). The MD simulation ?calibrated? via the experimentalS(Q) andS(Q,ω) was used to prolong the range of neutron data to draw conclusions regarding such quantities as dispersion relations for the current correlationsJ ₁(Q,t) andJ _T(Q,t), the generalized viscosity functions ν₁(Q,t), ν₁(Q) and ν_s(Q). Information regarding bulk viscosity ν_B(Q) is also gained. Conclusions are drawn regarding the relative importance of the derived pair potential form by comparison to corresponding hard-sphere data. The general framework of linearized hydrodynamic equations for the macroscopic situation transforming to visco-elastic equations of motion for finite wave-length and high frequency works well also for the case of a continuous potential. The region of transition from simple visco-elastic to hydrodynamic behaviour is occurring at wavelengths in the range (12÷20) ? for the cases studied. The spatial properties of the viscosity functions ν₁(r), ν_s(r) and ν_B(r) are found to correlate well with the range of the radial distribution function for the liquid. The general results for liquid lead probably have wide range of applicability to other simple liquids with similarS(Q) andg(r) properties. The authors have agreed not to receive proofs for correction.     

Improved three-dimensional control of a single strontium ion in an endcap trap

An endcap ion trap is described for trapping and laser cooling of a single strontium-88 ion. The 422 nm cooling laser is offset locked to the Doppler-free 5s ²S_1/2(F^′′=2)–6p ²P_1/2(F^′=3) transition in ⁸⁵Rb using saturation spectroscopy. The peak fluorescence signal from a single ion is around 6.0×10⁴ counts/s with the cooling laser at saturation intensity. Optical pumping of the ion in zero magnetic field is eliminated by the use of two 1092 nm repumper laser beams incident on the ion to create a time-varying polarisation. The ion’s micromotion can be reduced in all three dimensions, and the motional sidebands on the weak 5s ²S_1/2–4d ²D_5/2 quadrupole transition in ⁸⁸Sr⁺ have been observed. These results show the ion to be confined to less than a wavelength in three dimensions.     

New method to determine the domain wall energy in thin uniaxial films with perpendicular easy axis and large saturation magnetization

The surface energy density, γ, of domain walls in thin uniaxial films with perpendicular easy axis is usually found either by measurements of the domain pattern period of the stripe domain pattern or by determination of the bubble collapse field and diameter. However, when the saturation magnetization is large, the widths of stripe domains and bubbles become smaller than the minimum optical resolution, and optical observation becomes impossible. The method proposed in this paper is based on measurements of the susceptibility S = d (M/M_s)/d(H_a/4πM_s) of the stripe pattern at M = 0. Optical observations are avoided. The only additional important quantities are the saturation magnetization M_s and the film thickness. The method has been successfully applied to MnBi films (M_s = 625 G). The determination of γ in this material yields γ = (15 ± 1) erg/cm².     

Exact stationary probability distribution for a simple model of a nonequilibrium phase transition

We derive the exact stationary probability distribution for the coupled system of Langevin equationsd _t u=u–u s,d _t s=–s+d ²+F(t).     

Coincidence theorem for the direct correlation function of hard-particle fluids

The Mayerf-function for purely hard particles of arbitrary shape satisfiesf ²(1, 2)=–f(1, 2). This relation can be introduced into the graphical expansion of the direct correlation functionc(1, 2) to obtain a graphical expression for the case of exact coincidence, in position and orientation, of two identical hard cores. The resulting expression forc(1, 1)+1 contains only graphsG fromc(1), the sum of irreducible graphs with one labeled point. Relative to its coefficient inc(1),G occurs inc(1, 1) with an additional factorR _c which is 1 for the leading graph in the expansion and of the form 2–2L(G) for all other graphs. HereL(G)=0, 1, 2,..., is a nonnegative integer. Topological analysis is used to derive an expression forL(G) in terms of the connectivity properties ofG.     

A possible assignment for the ground scalar meson nonet

Based on the main assumption that a₀(980) and D ^* _sJ(2317) belong to the 1³P₀ q¯ multiplet, in the framework of Regge phenomenology and meson-meson mixing, it is suggested that a₀(980), K ^* ₀(1052), f₀(1099) and f₀(530) constitute the ground scalar meson nonet, and that the f₀(1099) is composed mostly of s¯, while the f₀(530) is mainly a u¯ + d¯ system. It is supposed that these states would likely correspond to the observed scalar states a₀(980), κ(900), f₀(980) and f₀(600)/σ, respectively. The agreement between the present findings and those given by other different approaches is satisfactory.     

Scaling and long-range dependence in option pricing II: Pricing European option with transaction costs under the mixed Brownian–fractional Brownian model

This paper deals with the problem of discrete-time option pricing by the mixed Brownian–fractional Brownian model with transaction costs. By a mean-self-financing delta hedging argument in a discrete-time setting, a European call option pricing formula is obtained. In particular, the minimal pricing c_min(t,s_t) of an option under transaction costs is obtained, which shows that timestep δt and Hurst exponent H play an important role in option pricing with transaction costs. In addition, we also show that there exists fundamental difference between the continuous-time trade and discrete-time trade and that continuous-time trade assumption will result in underestimating the value of a European call option.     

On the spectroscopy in ee annihilation

The properties of the radial excitations of the , ω and mesons are discussed. In particular it is proposed to identify the recently observed states at √s 1.5, 1.82 and 2.13 GeV in e⁺e⁻ annihilation with the _D ≡ ³D₁(λλ), ″ and ′″ mesons respectively. The ′ meson is suggested to lie in the vicinity of 1.5 GeV and strongly coupled to the _D. The ″(1.6) width is also suggested to be smaller than previously reported.     

Existence of Solutions of a Kinetic Equation Modeling Cometary Flows

A global existence theorem is presented for a kinetic problem of the form _t f+v· _x f=Q(f), f(t=0)=f ₀, where Q(f) is a simplified model wave–particle collision operator extracted from quasilinear plasma physics. Evaluation of Q(f) requires the computation of the mean velocity of the distribution f. Therefore, the assumptions on the data are such that vacuum regions, where the mean velocity is not well defined, are excluded. Also the initial data are assumed to have bounded total energy. As additional results conservation laws for mass, momentum, and energy are derived, as well as an entropy dissipation law and the propagation of higher order moments.