Role of quark-interchange processes in evolution of mesonic matter

We divide the cross-section for a meson-meson reaction into three parts. The first part is for the quark-interchange process, the second for quark-antiquark annihilation processes and the third for resonant processes. Master rate equations are established to yield time dependence of fugacities of pions, rhos, kaons and vector kaons. The equations include cross-sections for inelastic scattering of pions, rhos, kaons and vector kaons. Cross-sections for quark-interchange-induced reactions, that were obtained in a potential model, are parametrized for convenient use. The number densities of π and ρ (K and K ^* are altered by quark-interchange processes in equal magnitudes but opposite signs. The master rate equations combined with the hydrodynamic equations for longitudinal and transverse expansion are solved with many sets of initial meson fugacities. Quark-interchange processes are shown to be important in the contribution of the inelastic meson-meson scattering to the evolution of mesonic matter.     

Sharp Lower Bounds for the Dimension of the Global Attractor of the Sabra Shell Model of Turbulence

In this work we derive lower bounds for the Hausdorff and fractal dimensions of the global attractor of the Sabra shell model of turbulence in different regimes of parameters. We show that for a particular choice of the forcing term and for sufficiently small viscosity term ν, the Sabra shell model has a global attractor of large Hausdorff and fractal dimensions proportional to log  ν ⁻¹ for all values of the governing parameter ε, except for ε =1. The obtained lower bounds are sharp, matching the upper bounds for the dimension of the global attractor obtained in our previous work. Moreover, the complexity of the dynamics of the shell model increases as the viscosity ν tends to zero, and we describe a precise scenario of successive bifurcations for different parameters regimes. In the “three-dimensional” regime of parameters this scenario changes when the parameter ε becomes sufficiently close to 0 or to 1. We also show that in the “two-dimensional” regime of parameters, for a certain non-zero forcing term, the long-term dynamics of the model becomes trivial for every value of the viscosity. AMS Subject Classifications: 76F20, 76D05, 35Q30     

Basis of irreducible representations of orthogonal groups

A method for constructing a basis of irreducible representations of unitary groupsU _n is generalized to orthogonal groupsO _n. The corresponding algorithm is given for the chain for groupsU _n O _n and also for the chain which is of great relevance in physics.The constructed basis is used for the calculation of the fractional six-particle parentage coefficients for separation of one-, two- and three-particle wave functions. All possible states with excitation quantaN2 are taken into account. The present results, together with previous work, are used for the investigation of the six-quark system, in particular for calculating theD-state probability in the ground state of this system.     

Energy equation of state' of high-density plasmas

The equation of state for fully degenerate high-density plasmas is derived using a modified Thomas-Fermi model. Although the classical TF model is adequate to obtain the energy of an atom at very high densities it fails for low densities. A new version of this model for plasmas is presented which addresses this deficiency by including near-nucleus, exchange and correlation corrections. An analytic formula for the equation of stateE(n _i ) is obtained, valid for all densities (n _i <10²⁶ cm^–3). For low densities, Hartree-Fock results are reproduced with less than 1% error, and the classical result is recovered in the high-density limit.     

Description of α-decay half-lives of heaviest nuclei

The accuracy in describing α-decay half-lives T _α of heavy and superheavy nuclei is studied. A simple five-parameter phenomenological formula, expressing T _α as a function of the α-decay energy Q _α, is considered. It is found that such a formula can describe measured values of T _α within a factor of 1.3 for even-even, 2.1 for odd-even, 3.2 for even-odd, and 4.0 for odd-odd nuclei when measured values of Q _α are taken. This accuracy is decreased by a factor of about 4 when theoretical values of Q _α are used. The latter are obtained within a macroscopic-microscopic approach and reproduce the experimental values of Q _α of the same nuclei with an average accuracy of about 190 keV for even-even, 270 keV for odd-even, 260 keV for even-odd, and 330 keV for odd-odd nuclei. In the analysis, 201 nuclei with proton number Z = 84–111 and neutron number N = 128–161, with measured values of both Q _α and T _α, are taken. The text was submitted by the authors in English.     

Theory of infra-red and optical spectra of antiferromagnets

The contributions of magnons to the optical properties of antiferromagnets having the rutile structure are discussed. The properties considered are electric-dipole active two-magnon absorption in the infra-red, and magnon sidebands on sharp-line exciton transitions in the visible. The discussion is based on a thorough treatment of the properties of excitons and magnons in the antiferromagnetically ordered state. The site-group and space-group symmetries of the magnetic excitations are derived and the selection rules for electric and magnetic dipole transitions are determined. The occurrence of magnetic Davydov splittings of the excitons is investigated, and their symmetry properties throughout the Brillouin zone are derived. The functional dependences of exciton energy on wave vector are calculated. Applications of the theory are made to experimental results on excitons and magnons in MnF₂, FeF₂ and CoF₂.

The possible mechanisms for two-magnon and magnon-sideband absorption are discussed, and the influence of crystal symmetry on these mechanisms is described. The two-magnon state responsible for electric-dipole absorption is identified and selection rules for electric-dipole activity are presented. A spin Hamiltonian for the two-magnon process is set up and used to derive expressions for absorption coefficients for electric vector parallel and perpendicular to the crystal c-axis. Comparison with experiment for MnF₂ yields numerical values for the parameters of the basic coupling mechanism. The exciton-magnon states which give rise to magnon-sideband absorption are explicitly constructed and electric-dipole selection rules are derived for all possible types of sideband. Spin Hamiltonians for the various magnonsideband absorption processes are presented and used to derive expressions for sideband shapes. The results are applied to the experimental spectra for MnF₂ and FeF₂ and the sideband shapes in MnF₂ are calculated numerically. The sideband shapes observable in emission spectra are also briefly discussed.     

Statistical estimates of the influence of the source divergence angle on the characteristics of acoustic radiation transmitted through the atmosphere

The method of statistical simulation (Monte Carlo) is used for the first time to study the influence of the angular source divergence on the characteristics of transmitted acoustic radiation with allowance for the multiple scattering contribution. Results of calculations for a point source of unit power with divergence angles φ = 5, 10, 15, 20, and 25° at frequencies F = 1, 2, 3, and 4 kHz are presented for the outer scale of turbulence L ₀ = 10, 15, 20, 40, 60, and 80 m. It is established that for F = 2 kHz the multiple scattering contribution to the transmitted radiation intensity increases with the outer scale of turbulence from ∼10% (for L ₀ = 10 m) to 90% (for L ₀ = 60 m); for L ₀ = 80 m, the transmitted radiation intensity is virtually completely determined by the contribution of multiple scattering. When the width of the source directivity pattern (2φ) increases from 10 to 50°, the intensity of transmitted acoustic radiation decreases by 96%. Based on the results of statistical simulation, analytical dependences of the transmitted radiation intensity on the sound source divergence angle are suggested for typical sodar frequencies.     

Evaluation of the rate constants of dissociative and ternary recombination reactions of argon ions on the basis of the results of ballistic experiments

AbstractExperimental data on the change in the electron density in the wake of a ballistic object traveling at velocities V _∞=3.4–4.9 km/s in argon at pressures p _∞=30–100 Torr are processed and analyzed. A reaction scheme is proposed which takes into account the recombination of charged particles, processes of ionic conversion, and the excited states of the atom. The solution of the equations of a nonequilibrium boundary layer for flow in the wake is used to formulate the inverse problem of determining the rate constants for dissociative recombination Ar ₂ ⁺ +e→Ar+Ar and ternary recombination Ar⁺+e+Ar→Ar+Ar. The “nearest-neighbor” approximation is used to obtain theoretically an expression for the ternary recombination coefficient as a function of temperature and pressure. Numerous solutions of inverse problems and a comparison with experiments demonstrates the validity of the expression obtained for the ternary recombination coefficient. It is shown that this expression is valid for moderate pressures and complements the Pitaevskii result for low pressures and the Langevin result for high pressures. Zh. Tekh. Fiz. 67, 12–18 (May 1997)     

Molecular dynamics calculations of the hard-sphere equation of state

The equation of state of the hard-sphere fluid is studied by a Monte Carlomolecular dynamics method for volumes ranging from 25V ₀ to 1.6V ₀ , whereV ₀ is the close-packed volume, and for system sizes from 108 to 4000 particles. TheN dependence of the equation of state is compared to the theoretical dependence given by Salsburg for theNPT ensemble, after correction for the ensemble difference, in order to obtain estimates for the thermodynamic limit. The observed values of the pressure are compared with both the [3/2] and the [2/3] Padé approximants to the virial series, using Kratky's value for the fifth virial coefficientB ₅ and choosingB ₆ andB ₇, to obtain a least-squares fit. The resulting values ofB ₆ andB ₇ lie within the uncertainties of the Ree-Hoover-Kratky Monte Carlo estimates for these virial coefficients. The values ofB ₈,B ₉, andB ₁₀ predicted by our optimal [3/2] approximant are also reported. Finally, the Monte Carlo-molecular dynamics equation of state is compared with a number of analytic expressions for the hard-sphere equation of state.Work supported by the Office of Basic Energy Sciences, U.S. Department of Energy.     

高压密封微波消解-ICP-AES法测定五种蒙药中无机元素

采用HNO3-HClO4消解体系分别对额日敦-乌日勒、德都红花七味丸、通拉嘎-5、乌珠目-7、给旺-9等五种蒙药样品进行高压微波消解制样,利用电感耦合等离子体原子发射光谱法(ICP-AES)同时测定了镁、铝、钙、铬、锰、铁、钴、镍、铜、锌、砷、硒、锶、钼、银、镉和铅等17种无机元素的含量。通过添加标准回收实验,回收率均在97.25%~106.35%之间,验证了分析数据的可靠性。所有元素测定结果的相对标准偏差均小于3.3%,具有良好的准确度和精密度。实验结果表明,其中常量元素Ca,Mg和Fe,Mn,Zn,Cu的含量较高,测定结果可为开发研制蒙药新制剂、研制蒙药的质量控制标准和提高蒙药药效提供理论依据。     

Dielectric properties of a mixture of dipolar hard spheres

A theory for the dielectric constant, ε, of a fluid mixture of dipolar hard spheres is formulated by generalizing the methods developed by Ramshaw and Wertheim for the pure fluid case. The resulting expression for ε depends on the pair distribution functions, g _αβ(r ₁, θ₁, r ₂, θ₂) for a dipolar mixture. Due to the unavailability of exact representations for these dipolar pair distribution functions, the results of the mean spherical approximation are employed in the formalism developed. Numerical results are given for ε as calculated from the pair distribution functions for a spherical volume of macroscopic dimensions. The compositional dependence of the ε obtained in this way for a specific mixture is compared with the corresponding properties of the well established theories of Clausius-Mossotti-Debye and Onsager. In addition, the relative importance of the dipole moment and size of the hard sphere parameters in determining ε for a dipolar mixture (the correlative behaviour of which is described by the mean spherical approximation) is evaluated. It is found that the differences in hard core diameters can be largely ignored, in that ε for an ‘effective’ single component fluid can be given to within 2–5 per cent relative error (at worst) of the mean spherical approximation's result. Such an ‘effective pure fluid’ is described as having the same polarization content as the actual mixture being considered. Thereby, the properties of the effective fluid are determined by the quantity y = 4πβ(m ₁ ² ρ₁ + m ₂ ² ρ₂)/9 where m_i and ρ _i are the dipole moment and number density of component i in the binary mixture, with β = (kT)^-1.     

Check of the scaling procedure of track structures of ionizing radiation in nanometric volumes

In nanodosimetry, the track structure of ionizing radiation is characterized by the probability distribution of the number of ionizations produced by an ionizing particle in a target volume. By Monte-Carlo simulations of the track structure, this so called ionization cluster size distribution can be determined for nanometric cylindrical water targets used as substitute for the radiation sensitive biological target, namely a DNA-segment of about 20 base pairs length. Measurements of ionization cluster size distributions are carried out in an ion-counting nanodosimeter filled with an appropriate working gas at low pressure. A scaling procedure was proposed by Grosswendt (2006) to derive an operating pressure depending on the working gas for which the measured ionization cluster size distribution becomes equivalent to the ionization cluster size distribution within a nanometric target of liquid water. This scaling procedure was previously tested by means of Monte-Carlo simulations and is now tested experimentally.Ionization cluster size distributions produced by mono-energetic proton and alpha particle beams in the energy range between 0.1 MeV and 20 MeV were measured at the accelerator facilities of the PTB. The working gases used in this experiment were C₃H₈ and N₂. According to the NIST databases for stopping power and mean ionization energy (NIST, 2009), equivalent cluster size distributions for protons and alpha particles should be obtained for pressures of 0.25 mbar C₃H₈ and 1.2 mbar N₂. Measurements reveal the best agreement with pressures of 0.425 mbar C₃H₈ and 1.2 mbar N₂ for protons and 0.46 mbar C₃H₈ and 1.2 mbar N₂ for alpha particles.     

Broadening of vibrational-rotational lines of the H2S molecule by pressure of monatomic gases

Optimal sets of parameters for a model intermolecular potential that provide the best reproduction of broadening coefficients γ for the absorption lines in the ν₂ band of the H₂S molecule are determined for systems H₂S-A (A = He, Ne, Ar, Kr, and Xe). For H₂S-He, the potential is obtained with the temperature dependence of coefficients γ taken into account for two rotational absorption lines 1₁₀ ← 1₀₁ and 2₁₁ ← 2₀₂. With the potentials obtained, the coefficients γ are calculated for the ν₁ and ν₃ bands and compared with the available experimental data. There are significant discrepancies between the calculated and experimental values of γ.     

Analysis of 2ν1 of HDTe

We have analyzed the 2ν₁ band of HDTe near 4064 cm^?1 for the six stable Te isotopes of mass 130, 128, 126, 125, 124, and 122, fitting them all simultaneously, thereby obtaining values for the ground state molecular constants and upper state constants through fourth power in the angular momenta, including isotopic mass dependencies for A, B, C, and ν₀. More than 700 transitions were assigned and fit with a standard deviation of less than 0.005 cm^?1, both for the Watson reduced Hamiltonian and for a Kivelson-Wilson Hamiltonian reduced by the planarity relationships.     

A numerical study of the likelihood of phase locking

We report the results of numerical computation of the size of the set of ω's for which the hemeomorphism of the circle $\text{f}\text{?}{}_{\mathrm{K}}$,ω(x)=x+ω+K/2π sin (2πx) mod (1) is phased locked, for values of K ranging from 0.1 to 1. The results suggest that for moderate values of K phase locking is unlikely except for small periods, but that for K=1 almost all ω's give phase locking, with large periods accounting for a surprisingly large portion of the total.     

Spectroscopic Parameters of High Overtones of the Vibrations of Molecules

Based on the fundamental equation from the vibration theory of molecules and the operation of direct product of matrices and its properties for eigenvalues and eigenvectors, an equation of overtone vibrations for any high order has been obtained whose solution yields the matrices of vibration modes. Correlations determining changes in the structure parameters, just as expressions for the matrices of the coefficients of kinematic interaction and force constants, and for the parameters of vibrational-rotational interaction have been presented. Using the formulas obtained, the electro-optical parameters of water molecules H₂O and isotopes H₂ ¹⁷O and H₂ ¹⁸O have been calculated for overtones of up to the sixth order within the framework of the semiempirical quantum-chemical CNDO/2 method using the method of numerical differentiation by spline functions.     

Theoretical calculation of turn-on delay time of VCSEL and effect of carriers recombination

It is known that the turn-on delay time, t_d, for semiconductor lasers depends on the functional form of the recombination rate. Previously, an analytic expression for t_d had been obtained, following simple approximations. In this paper, on the basis of the rate equations for quantum well vertical cavity surface emitting lasers (VCSEL), an explicit analytical expression for the turn-on delay of the VCSEL has also been deduced for the general case. The time evolution of the carrier density within the turn-on period of VCSEL has been derived for the case, where the Auger effect is considered as a term proportional to the cube of the carrier density.     

Statistical properties of stock market indices of different economies

Daily changes in the logarithm of stock market index from 1997 to 2004 are analyzed for countries from three subgroups of economies classified by the International Monetary Fund (IMF): developing Asian countries, newly industrialized Asian economies and major advanced economies. For all markets, the daily changes are well fitted by a non-Gaussian stable probability density. The time evolution of the standard deviation of the daily changes for each market obeys a power law. However, the developing Asian countries have the smallest stable density characteristic parameters α and the largest exponents b of the power law, except China's SSEC and India's SENSEX. The values of α and b for these two markets are closer to those of the newly industrialized Asian economies; in particular, those for China's SSEC are close to those for Hong Kong's HSI. The values of α and b for the newly industrialized Asian economies are in between those for the developing Asian countries and major advanced economies, consistent with the results for generalized Hurst exponent [Physica A 324 (2003) 183]. The daily changes for the developing Asian countries and newly industrialized Asian economies have a weak long-range correlation, whereas the daily changes for the major advanced economies have a weak long-range anti-correlation.     

Evaluation of the dosimetric characteristics of a radiophotoluminescent glass dosimeter for high-energy photon and electron beams in the field of radiotherapy

We aimed to evaluate the suitability of a glass dosimeter (GD) for high-energy photon and electron beams in experimental and clinical use, especially for radiation therapy. We examined the expanded dosimetric characteristics of GDs including dose linearity up to 500 Gy, uniformity among GD lots and for individual GDs, the angular dependence, and energy dependence of 4 therapeutic x-ray qualities. In addition, we measured the dosimetric features (dose linearity, uniformity, angular dependence, and energy dependence) of the GD for electron beams of 10 different electron energy qualities. All measurements with the exception of dose linearity for photon beam were performed in a water phantom. For high-energy photon beams, dose linearity has a linear relationship for a dose ranging from 1 to 500 Gy with the coefficient of determination; R² of 0.998. The uniformity of each GD of dose measurements was within ±0.5% for four GD lots and within ±1.2% for 80 GDs. In terms of the effects of photon beam angle, lower absorbed doses of within 1.0% were observed between 60° and 105° than at 90°. The GD energy dependence of 4 photon beam energy qualities was within ±2.0%. On the other hand, the result of the dose linearity for high-energy electron beams showed well fitted regression line with the coefficient of determination; R² of 0.999 between 6 and 20 MeV. The uniformity of GDs exposed to the nominal electron energies 6, 9, 12, 16, and 20 MeV was ±1.2%. In terms of the angular dependence to electron beams, absorbed doses were within 2.0% between 60° and 105° than at 90°. In evaluation of the energy dependence of the GD at nominal electron energies between 5 and 20 MeV, we obtained responses between 1.1% and 3.5% lower than that for a cobalt-60 beam. Our results show that GDs can be used as a detector for determining doses when a high-energy photon beam is used, and that it also has considerable potential for dose measurement of high-energy electron beam.     

Density functional calculation of K-shell spectra of small molecules

Both ΔE_KS and time-dependent density functional theory (TD-DFT) methods, with approximations for the singlet–triplet splitting and for the relativistic corrections, were tested for the calculation of K-shell spectra of Ne, HF, H₂O, NH₃, CH₄, and CO. Results from several exchange-correlation functionals as well as diffuse basis sets were compared with available experimental data. Excellent core excitation and core-electron ionization energies for Ne, HF, H₂O, NH₃, CH₄, and CO can be obtained from ΔE with Perdew–Wang 1986 exchange and Perdew–Wang 1991 correlation functionals; and reasonable intensities for singlet excitations, from TD-DFT with exchange-correlation potential known as statistical average of orbital potentials. The dependence of the quality of ΔE on basis set is as expected: excitations to higher Rydberg levels requiring more diffuse functions. However, the oscillator strength seems to be more sensitive to the quality of the basis set. Suggestions are made for extending the procedure to larger systems.