Oscillations in the Determination of Renyi Dimension

To describe the degree of chaos of a strange attractor created by a nonlinear map, GRASSBERGER [1] revived Renyi Dimension D_q which is a common generalization of both metric capacity D₀ and information dimension D₁. But often, the numerical determination of D_q is complicated by an oscillating effect first investigated by BADII and PUOLITI [5] for a dimension similar to D₀. This effect is studied in the present paper. We consider the conditions for the appearance of oscillations and the dependence on q, and we give some numerical examples.     

Universal Teichmüller Space and DiffS 1/S 1

We point out that the coset space DiffS ¹/S ¹ is a dense complex submanifold of the Universal Teichmüller SpaceS of compact Riemann spaces of genus g1. A holomorphic map ofS into the inifinite dimensional Segal diskD ₁ is constructed. This is the Universal analogue of the map of Teichmüller spaces into the Siegel disk provided by the period matrix. The Kähler potential for the general homogenous metric on DiffS ¹/S ¹ is computed explicitly using the map intoD ₁. Some applications to string theory are discussed.This work was supported in part by the U.S. Department of Energy Contract No. DE-AC02-76ER13065     

f-α Spectrum of circle map

We present an analytic perturbative method for calculatingf(α) and the generalized dimensionD _q of the critical invariant circle of the polynomial circle map. The scaling behaviour is found to depend onz, the exponent defining the map. The asymptotic bounds of the scaling constantsα(z) andδ(z) are verified analytically.     

M2Sn17(M=Ni，Mn)及其阴离子的几何结构、电子结构和磁性的计算研究

采用密度泛函理论(density functional theory, DFT)中的广义梯度近似(generalized gradient approximation, GGA) 对Ni₂Sn₁₇，Mn₂Sn₁₇，［Ni₂Sn₁₇］^4-和［Mn₂Sn₁₇］^2-三种同分异构体的几何结构、电子 关键词： 2Sn₁₇')" href="#">Ni₂Sn₁₇ 2Sn₁₇')" href="#">Mn₂Sn₁₇ 几何结构 电子结构和磁性 密度泛函理论     

Noise map validation by continuous noise monitoring

This paper presents a comparison of two noise assessments in the Gdansk agglomeration in Poland. One is based on the noise map produced by computational method for the city in 2007, the second one is based on real data from continuous measurements acquired by a noise monitoring network operating in the city since 2008. Differences are shown and analyzed. Additionally, seasonal and weekday influence on noise indicators (L_DEN, L_D, L_E and L_N) is analyzed and discussed in this paper.     

Poisson Geometry of Discrete Series Orbits,and Momentum Convexity for Noncompact Group Actions

The main result of this paper is a convexity theorem for momentum mappings of certain Hamiltonian actions of noncompact semisimple Lie groups. The image is required to fall within a certain open subset D of the (dual of the) Lie algebra, and the momentum map itself is required to be proper as a map to D. The set D corresponds roughly, via the orbit method, to the discrete series of representations of the group, Much of the paper is devoted to the study of D itself, which consists of the Lie algebra elements which have compact centralizer. When the group is Sp(2n), these elements are the ones which are called 'strongly stable' in the theory of linear Hamiltonian dynamical systems, and our results may be seen as a generalization of some of that theory to arbitrary semisimple Lie groups. As an application, we prove a new convexity theorem for the frequency sets of sums of positive definite Hamiltonians with prescribed frequencies.     

Relation of Experimental Features of P-Even,T-Odd Asymmetries in Ternary Nuclear Fission Induced by Cold Polarized Neutrons to Triple and Quintuple Scalar Correlations

In employing the concept of the isotropy of space, the coefficients D of P-even, T-odd asymmetry in the angular distributions of prescission alpha particles emitted as third particles in the ternary fission of nonoriented target nuclei that is induced by polarized cold neutrons are expressed in the lowest orders of perturbation theory in the neutron polarization vector in terms of two P-even scalar coefficients D₃ and D₅ associated with, respectively, triple and quintuple correlations depending on the unit vectors k_α, k_LF, and σ_n, which determine the features of the coefficients being studied. On the basis of the above representation, the experimental values of the coefficients D₃ and D₅ are determined by using the experimental values of D and the angular distributions of alpha particles emitted in the analogous reaction induced by unpolarized neutrons. The resulting coefficients D₃ and D₅ are compared with the analogous coefficients found by means of the classical method of trajectory calculations and by means of quantum-mechanical fission theory relying on the concept that it is the rotational mechanism that is responsible for the appearance of the asymmetries being studied. It turns out that the classical method, which disregards the interference between fission amplitudes for different S-wave neutron resonances, leads to an irremovable contradiction between the calculated coefficient D₃ and the analogous experimental coefficient for the ²³³U target nucleus. In the case of employing the quantum-mechanical approach, it is concluded that three-body calculations of the Coriolis interaction—perturbed amplitude of the angular distributions of alpha particles moving in the Coulomb fields of fission fragments are required for the ²³³U target nucleus.

     

[2.2]Paracyclophane: theoretical study of its lower excited states and of the zero-field splitting parameters D

The lower excited singlet and triplet states and the zero-field splitting parameters D of [2.2]paracyclophane are studied within a semiempirical π theory which takes into account overlap effects between the two benzene rings, transanular and through-bond interaction via the methylene bridges. Whereas the singlet energies depend strongly on the through-bond interaction and the mutual polarization of σ core and π system this is not the case for the energies and zero-field splitting parameters D of the two lowest triplet states. The deformations of the benzene rings in [2.2]paracyclophane lead only to a small decrease of the excitation energies of about 0·2 eV. The D parameter can be written as a sum D = D_A + D_B + D_AB with the intrasubunit contributions D_A and D_B of the conjugated subunits A and B of the phane and an intersubunit term D_AB . We demonstrate that the deformations reduce the intrasubunit terms D_A and D_B and that they are crucial for the decrease of the D values of [2.2]paracyclophane with respect to p-xylene. The difference between the D values of the first and second triplet states is governed by the intersubunit term D_AB which has a different sign in the two states. However, this difference does not depend markedly on the transanular interaction. A further reduction of D_A and D_B in the first triplet state only is caused by transanular interaction by means of symmetrical charge-transfer terms in the wavefunction.     

Theory of spin diffusion in liquid-phase polymer systems

A general theory of spin diffusion in condensed media is constructed by the method of Zwanzig-Mori projection operators using the superpositional approximation to decouple the many-particle correlation functions. The spin diffusion coefficient is expressed in the form D _sp=D _tr+D _f , where D _tr is the contribution associated with translational displacements of the molecules and D _f is the contribution caused by intermolecular flip-flop processes. The expression for D _tr differs from the well-known Kubo-Green formula for the self-diffusion coefficient D _sd in that the integrand contains an additional factor P _f (t), which is the probability of the molecular spins not participating in intermolecular flip-flop transitions over the time t. A microscopic expression is obtained for D _f in the form of a time integral of the intermolecular dipole-dipole dynamic correlation functions. For liquid-phase polymer system with fairly high molecular mass the condition D _sp≫D _sd is satisfied. Zh. éksp. Teor. Fiz. 114, 538–554 (August 1998)     

Local state probabilities for solvable restricted solid-on-solid models:A n,D n,D n (1) , andA n (1)

The local state probabilities (LSPs) are exactly computed for four hierarchies of solvable lattice models. They are restricted solid-on-solid (RSOS) models whose local states and their adjacent conditions are specified by Dinkin diagrams of typesA _n,D _n,D _n ⁽¹⁾ andA _n ⁽¹⁾ . The LSPs are expressed in terms of modular functions characterized by branching identities among the theta functions. Their automorphic properties are used to study the critical behaviors. Some fine structures are found in the spectrum of the critical exponents.     

Nonane droplet combustion with and without buoyant convection: Flame structure, burning rate and extinction in air and helium

The burning and extinction characteristics of isolated small nonane droplets are examined in a buoyant convective environment and in an environment with no external axial convection (as created by doing experiments at low gravity) to promote spherical droplet flames. The ambience is air and a mixture of 30%O₂/70%He to assess the influence of soot formation. The initial droplet diameter (D_o) ranges from 0.4 to 0.95 mm. Measurements are reported of the extinction diameter and time to extinction, and of the evolution of droplet diameter, flame diameter, soot shell diameter, burning rate, and broadband radiative emissions.In a buoyancy-free environment for air larger droplets burn slower than smaller droplets for the range of D_o examined, which is attributed to the influence of soot. In the presence of a buoyant flow in air, no influence of D_o is observed on the burning rate while the buoyant flames are still heavily sooting. The effect of D_o is believed to be due to a combination of dominance of the nonluminous, nonsooting, portion of the buoyant flame around the forward half of the droplet on heat transport and the secondary role of the luminous wake portion of the flame. In a non-sooting helium inert at low gravity, no effect of D_o is found on the evolution of droplet diameter.Flame extinction is observed only in the 30%O₂/70%He ambience. For all of the observations, extinction appears to occur before the disappearance of the droplet which is then followed by a period of evaporation. The extinction diameter and time to extinction increases with D_o and an empirical correlation is presented for these two variables.     

First principles calculations of alloying element diffusion coefficients in Ni using the five-frequency model

The diffusion coefficients of several alloying elements(Al,Mo,Co,Ta,Ru,W,Cr,Re) in Ni are directly calculated using the five-frequency model and the first principles density functional theory.The correlation factors provided by the five-frequency model are explicitly calculated.The calculated diffusion coefficients show their excellent agreement with the available experimental data.Both the diffusion pre-factor(D 0) and the activation energy(Q) of impurity diffusion are obtained.The diffusion coefficients above 700 K are sorted in the following order:DAl>DCr>DCo>DTa>DMo>DRu>DW>D Re.It is found that there is a positive correlation between the atomic radius of the solute and the jump energy of Ni that results in the rotation of the solute-vacancy pair(E 1).The value of E 2-E 1(E 2 is the solute diffusion energy) and the correlation factor each also show a positive correlation.The larger atoms in the same series have lower diffusion activation energies and faster diffusion coefficients.     

Quantum Perfect Correlations and Hardy’s Nonlocality Theorem

In this paper the failure of Hardy's nonlocality proof for the class of maximally entangled states is considered. A detailed analysis shows that the incompatibility of the Hardy equations for this class of states physically originates from the fact that the existence of quantum perfect correlations for the three pairs of two-valued observables (D ₁₁, D ₂₁), (D ₁₁, D ₂₂), and (D ₁₂, D ₂₁) [in the sense of having with certainty equal (different) readings for a joint measurement of any one of the pairs (D ₁₁, D ₂₁), (D ₁₁, D ₂₂), and (D ₁₂, D ₂₁)], necessarily entails perfect correlation for the pair of observables (D ₁₂, D ₂₂) [in the sense of having with certainty equal (different) readings for a joint measurement of the pair (D ₁₂, D ₂₂)]. Indeed, the set of these four perfect correlations is found to satisfy the CHSH inequality, and then no violations of local realism will arise for the maximally entangled state as far as the four observables D _ij, i,j = 1 or 2, are concerned. The connection between this fact and the impossibility for the quantum mechanical predictions to give the maximum possible theoretical violation of the CHSH inequality is pointed out. Moreover, it is generally proved that the fulfillment of all the Hardy nonlocality conditions necessarily entails a violation of the resulting CHSH inequality. The largest violation of this latter inequality is determined.     

Rotational structure of the 000, 010, 100, 020, and 001 vibrational states of the D216O molecule: Spectroscopic assignment of rotational levels up to J, Ka = 30 and analysis of published data

The complete spectroscopic assignment of calculated Partridge-Schwenke rotational energy levels up to J, K _a = 30 is presented for the 000, 010, 100, 020, and 001 vibrational states of the D₂ ¹⁶O molecule. The nonpolynomial model of an effective rotational Hamiltonian is used to perform the assignment and to analyze the experimental energy levels available in the literature for these states. The results obtained are compared with the data calculated by other authors. The results of this study can be useful in searching for and identifying new, highly excited rotational levels of D₂ ¹⁶O, as well as in creating the databases of parameters of rovibrational transitions of the water molecule.     

Modeling of Surface Diffusion in hcp Zr and Ti

The statics and dynamics of vacancies and adatoms on different surface orientations in two hcp materials are studied by using static relaxation techniques and many-body potentials. Formation and migration energies and entropies as well as attempt frequencies are evaluated and used in the random walk approach to obtain correlation factors and diffusivities. It is found that the main features of surface diffusion are dominated by jumps on and between a few atomic layers, so that a consistent comparison between the two mechanisms is feasible. The activation energies and the diffusivities for different environments, namely, bulk Q _b, D _b, symmetric grain boundaries Q _gb, D _gb, and surfaces, Q _s, D _s, calculated using the same simulation technique and interatomic potentials, fulfil the expected relationships Q _s < Q _gb < Q _b and D _s > D _gb > D _b. It is also found that generally adatoms are faster surface diffusers than vacancies.     

Implantation doping of germanium with Sb,As, and P

The ions of Sb, As, and P have been implanted into germanium at energies ranging from 200 keV to 700 keV. Annealing was performed at 400°C, 550°C, and 650°C. The doping profile was determined by differentialCV-measurements. Strong outdiffusion (80%) and diffusion into the bulk material was observed after annealing. The remaining doping concentration and the diffusion constants were determined by a computer fit at 650°C. We foundD _Sb=1.8×10⁻¹³ cm²/s,D _As=9×10⁻¹⁴ cm²/s andD _P=4×10⁻¹⁴ cm²/s. Lower values of the diffusion constant were determined when the samples were covered with a SiO₂ layer.     

Symbolic computations for the two-Coulomb-centers problem in the space of arbitrary dimension

The case of small intercenter distances in the D-dimensional two-Coulomb-centers problem (Z ₁ eZ ₂) _D (D ≥ 2) is studied by solving separated wave equations. The usage of the Maple symbolic computation system (Maple Waterloo Software, Inc. See ) for solving the problem is under discussion. The obtained results are compared with the previous asymptotic and numerical treatments. The correspondence between energy terms of the systems (Z ₁ eZ ₂)₃ and (Z ₁ eZ ₂) _D is founded. The text was submitted by the authors in English.     

Implementation Aspects of 3D Lattice-BGK: Boundaries, Accuracy, and a New Fast Relaxation Method

In many realistic fluid-dynamical simulations the specification of the boundary conditions, the error sources, and the number of time steps to reach a steady state are important practical considerations. In this paper we study these issues in the case of the lattice-BGK model. The objective is to present a comprehensive overview of some pitfalls and shortcomings of the lattice-BGK method and to introduce some new ideas useful in practical simulations. We begin with an evaluation of the widely used bounce-back boundary condition in staircase geometries by simulating flow in an inclined tube. It is shown that the bounce-back scheme is first-order accurate in space when the location of the non-slip wall is assumed to be at the boundary nodes. Moreover, for a specific inclination angle of 45 degrees, the scheme is found to be second-order accurate when the location of the non-slip velocity is fitted halfway between the last fluid nodes and the first solid nodes. The error as a function of the relaxation parameter is in that case qualitatively similar to that of flat walls. Next, a comparison of simulations of fluid flow by means of pressure boundaries and by means of body force is presented. A good agreement between these two boundary conditions has been found in the creeping-flow regime. For higher Reynolds numbers differences have been found that are probably caused by problems associated with the pressure boundaries. Furthermore, two widely used 3D models, namelyD₃Q₁₅andD₃Q₁₉, are analysed. It is shown that theD₃Q₁₅model may induce artificial checkerboard invariants due to the connectivity of the lattice. Finally, a new iterative method, which significantly reduces the saturation time, is presented and validated on different benchmark problems.     

Size and interface effects on Curie temperature of perovskite ferroelectric nanosolids

A simple and unified model, without any adjustable parameter, is established for size effect on Curie temperature of low-dimensional ferroelectrics (thin films, nanowires and nanoparticles), T _c(D), where D denotes size of low-dimensional ferroelectrics. T _c(D) function is based on consideration on the size dependence of spontaneous polarization of low-dimensional ferroelectrics P _s(D), which is determined by the misfit strain at the ferroelectrics/substrate interface. It is shown that P _s(D) and T _c(D) functions decrease or increase when the misfit strain is tensile or compressive. The numerically predicted results are in agreement with the available experimental results of BaTiO₃ and PbTiO₃ nanoparticles and thin films.     

Heavy-light mesons and quark constantsf B,f D in the vacuum correlator method

Quark constantsf _M and masses ofB, D, andD _S mesons are calculated using the vacuum correlator method, suggested recently for long-distance nonperturbative QCD. The dynamical input is standard current quark masses, string tension and _s( _QCD). The electronic width of , and calculated with the same parameters agrees with experiment. Hyperfine splitting ofD, D _s mesons is also reproduced. The resulting values off _B,f _D,f _Ds are 0.17, 0.21 and 0.25 GeV, respectively;f _D andf _Ds are within recent experimental bounds. It is shown thatf _M does obey the asymptoticM ^–1/2 law forM>5 GeV.