Density profile and flow of miscible fluid with dissimilar constituent masses

A computer simulation model is used to study the density profile and flow of a miscible gaseous fluid mixture consisting of differing constituent masses (m_A=m_B/3) through an open matrix. The density profile is found to decay with the height ∝exp (−m_A(B)h), consistent with the barometric height law. The flux density shows a power-law increase ∝(p_c−p)^μ with μ2.3 at the porosity 1−p above the pore percolation threshold 1−p_c.     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

On the electroweak and gluonic corrections to the hadronic width of the Z boson

The electroweak corrections to the Z-boson hadronic width are presented in a simple analytical form for the width itself, Λ_h, for its ratio to the leptonic width, R_l = Λ_h/Λ_l, for the Λ_b/Λ_h ratio, and for the total width Λ_Z. The rational parametrization, advocated in our recent papers on leptonic decays, simplifies the analysis of the hadronic decays too. There are two main results of this analysis: (1) All electroweak precision measurements agree within 1 σ with the electroweak Born approximation if the gluon coupling constant . Thus the electroweak radiative corrections have not been observed experimentally. The unexpected smallness of electroweak radiative corrections is caused by the mutual cancellation of the large positive contribution of a heavy top quark and the large negative contribution of all other virtual particles. (2) With electroweak radiative corrections being taken into account, the value of extracted from the experimental value of Λ_Z differs by 3σ from that obtained from R_l, if m_t 200 GeV; they agree within 1σ if m_t 150 GeV. Thus a low upper limit on m_t can be obtained from hadronic decays of the Z-boson alone, even without data on its leptonic decays.     

Ionic diffusion and local hopping in copper chalcohalide glasses measured using Cu tracer and I-Mössbauer spectroscopy

For the first time, ⁶⁴Cu tracer measurements of ionic diffusion were performed for several copper-rich glass compositions in the CuI---As₂Se₃, CuI---SbI₃---As₂Se₃, CuI---PbI₂---As₂Se₃, CuI---PbI₂---SbI₃---As₂Se₃ and Cu₂Se---As₂Se₃ systems. In accordance with previous a.c. impedance results and Wagner d.c. polarization measurements, it was found that pure Cu⁺ ion-conducting glasses (50CuI---17PbI₂---33As₂Se₃ and 50CuI---20PbI₂---10SbI₃---20As₂Se₃) exhibit the highest copper tracer diffusion coefficients, D_Cu, and the lowest diffusion activation energies. The values of D_Cu at room temperature are higher by 4.5–5.5 orders of magnitude than those in an As₂Se₃ glass. The Haven ratio, H_R, is found to be 0.52–0.61 (ternary glass) and 0.93–1.00 (quaternary glass). Short-range diffusional displacements of the iodide ions induced by the hopping Cu⁺ ions are also detected in the CuI---PbI₂---SbI₃---As₂Se₃ glassy system using ¹²⁹I-Mössbauer spectroscopy in the temperature range of 4.2 to 305 K. The activation energy of local hopping, E_h ≈ 0.31 eV, is very similar to that of bulk ionic conductivity (0.37 eV) and copper diffusion (≈ 0.33 eV). In contrast to CuI-based vitreous alloys, 50Cu₂Se---50As₂Se₃ glass exhibits D_Cu that are two to five orders of magnitude lower, and the copper ion transport number, t_Cu⁺, is between 10⁻³ and 10⁻⁴ in the temperature range 140–170 °C.     

The algebraic Bethe ansatz for rational braid-monoid lattice models

In this paper we study isotropic integrable systems based on the braid-monoid algebra. These systems constitute a large family of rational multistate vertex models and are realized in terms of the B_n, C_nand D_n Lie algebra and by the superalgebra Osp(n||2m). We present a unified formulation of the quantum inverse scattering method for many of these lattice models. The appropriate fundamental commutation rules are found, allowing us to construct the eigenvectors and the eigenvaluesof the transfer matrix associated to the B_n, C_n, D_n, Osp(2nt-1||2), Osp(2||2nt-2), Osp(2nt-2||2) and Osp(1||2n) models. The corresponding Bethe ansatz equations can be formulated in terms of the root structure of the underlying algebra.     

Relative production of vector and pseudoscalar states for light- and heavy-flavour mesons

The relative fractions of vector, V, and pseudoscalar, P, primary mesons produced in and decays, and primary light-flavour mesons produced in fragmentation processes are explained by the hyperfine mass splitting. The difference in corresponding fractions arises from the difference in the constituent quark masses , m_s, m_c and m_b:

The production ratios for strange, charm and beauty mesons evaluated from the ρ/(3π) ratio, measured at LEP for primary produced ρ and π, agree with the results of LEP and lower energy e⁺e⁻ experiments.     

Commutator representations of differential calculi on the quantum group SUq(2)

Let (Γ, d) be the 3D-calculus or the 4D_±-calculus on the quantum group SU_q (2). We describe all pairs (π, F) of a ^*-representation π of (SU_q(2)) and of a symmetric operator F on the representation space satisfying a technical condition concerning its domain such that there exist a homomorphism of first order differential calculi which maps dx into the commutator [iF, π(x)] for x ε (SU_q (2)). As an application commutator representations of the two-dimensional left-covariant calculus on Podles quantum 2-sphere S_qc² with c = 0 are given.     

Probing the EOS and nn cross section by analyzing the collective flow at high and intermediate energy in the RVUU approach

We have studied the collective flow at high and intermediate energy in a relativistic Vlasov-Uehling-Uhlenbeck (RVUU) approach based on Walecka's QHD-I model, with the aim to probe the nuclear-matter equation of state (EOS) and the in-medium nucleon-nucleon cross section σ. At high energy (1.2 GeV/u), the out-of-plane azimuthal correlation function C(Ψ) is only sensitive to the effective mass m^* and insensitive to the nuclear compressibility K and the effective nucleon-nucleon cross section σ within a reasonable range. We have found that the preferred value of m^* is about 0.85 m. With this value of m^*, from the in-plane mean transverse momentum P_x(Y) which is sensitive to both m^* and σ we have drawn an effective nn cross section σ, namely σ 0.8σ_f where σ_f is the free nucleon-nucleon cross section in Cugnon's parametrization. Taking advantage of the fact that the energy of vanishing flow (EVF) at intermediate energy (around 100 MeV/u) is only sensitive to the nucleon-nucleon cross section σ, we have drawn some information on the nucleon-nucleon cross section σ, namely σ = (1.4±0.2)σ_f.     

The generation problem and the symplectic group

The generation structure of quarks and leptons is studied in a series of extended electroweak models. They are gauge models constructed from subgroups of left-right symmetric SU(4) × S_P^L(6) × S_P^R(6). In particular, SU_C(3) × S_P^L(6) × U_Y(1), as well as SU_C(3) × SU_L(3) × SU_R(3) × U_X(1), are investigated in greater detail. It is shown that models based on such subgroups yield massless first generation fermions at the tree level. They acquire masses from those of the third generation via two-loop radiative corrections. Moreover, since such corrections are induced by charged scalar fields, it is found that there is a natural correlation between the two apparently conflicting inequalities m_u < m_d and m_t > m_b.     

What can we learn from B→DsKπ, Bd→DsKπ and Bd→DsK decays?

We study the nonresonant three-body decays of B⁺→D^(*)−_sK⁺π⁺ and B_d→D_s^(*)−K⁰π⁺. We find that these decays can provide the information on the time-like form factors of D^(*)_sK. We also explicitly investigate B_d→D_s^(*)−K^*+ decays by discriminating the nonresonant contributions with the unknown D^(*)_s wave functions being fixed by the measured mode of B_d→D_s⁻K⁺.     

Understanding DsJ(2317)

We analyze the hadronic and radiative decay modes of the recently observed D_sJ(2317) meson, in the hypothesis that it can be identified with the scalar state of spectrum (D_s0). The method is based on heavy quark symmetries and vector meson dominance ansatz. We find that the hadronic isospin violating mode D_s0→D_sπ⁰ is enhanced with respect to the radiative mode D_s0→D_s^*γ. The estimated width of the meson is Γ(D_s0)7 keV.     

Continuous photoluminescence, time resolved photoluminescence and optically detected magnetic resonance measurements of PbI2 nanometer-sized particles, embedded in SiO2 films

The nanometer sized particles of PbI₂ were embedded in SiO₂ films. X-ray diffraction and the TEM pictures showed the preservation of the bulk layered structure and symmetry. The PL spectrum of the nano-particles exhibited a pronounced blue shift of the exciton band due to quantum size effect. The Lead Iodide represents an exceptionally small exciton Bohr radius (a_B = 19 Å) and a special case in which m_e m_h. The prepared samples contained particles with mean radii, a, in the range a_B < a < 3a_B. Within this limit (with m_e m_h), the experimental results suggest that the electron is localized nearly at the center of the particle, enabling the hole to move around it. Thus, the size confinement permits the creation of an acceptor-like exciton. The PL spectrum revealed additional states, associated with stoichiometric defects either at the interior or surface sites of the nano-particles. These defects act either as donor or acceptor states. The dynamics of the various recombination processes has been investigated by measuring the time resolved PL spectra. The results show a multiexponential behavior of the various recombination emission bands, indicating the occurrence of trapping and detrapping processes. Analysis of these results suggests that the existence of surface states give rise to these complex radiative decay processes. The correlation between donor-acceptor recombination emission bands in the aforementioned samples and lattice imperfections was examined, utilizing optically detected magnetic resonance (ODMR) spectroscopy. The results identified the following imperfection sites: an acceptor site associated with an isotropic Lead vacancy defect, [V⁻]_pb²⁺ and a donor site, associated with an anisotropic Iodine vacancy, [V⁰]_Iodine.     

Remarks on stochastic non-linear birth and death models

The first part of this paper is an attempt to formulate and motivate additional work on the important problem of obtaining global bounds applicable to the controlled truncation of the paper relates specifically to the linear birth, quadratic death model. Asymptotic results are given for the first finite difference ΔT_m where T_m is the exactly known mean time to extinction starting from state m (m= 0,1,…). These results are in terms of the environmental carrying capacity n^* taken to be large. For m near zero ΔT_me^n*/(n^*)²; whereas, for m near n^*ΔT_m ≈ (π/2)^1/2/(n^*)^3/2. This indicates the vastly different time scales in those two regions of state space - with considerably slower action near extinction than near n^*.     

Existence and stability of propagating fronts for an autocatalytic reaction-diffusion system

We study a one-dimensional reaction-diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic (A + B → 2B) and a cubic (A + 2B → 3B) autocatalysis. The parameters of this system are in the ratio D = D_B/D_A of the diffusion constants of the reactant A and the autocatalyst B, and the relative activity k of the cubic reaction. First, for all values of D > 0 and k ≥ 0, we prove the existence of a family of propagating fronts (or travelling waves) describing the advance of the reaction. In particular, in the quadratic case k = 0, we recover the results of Billingham and Needham [Phil. Trans. R. Soc. London A 334 (1991) 1–24]. Then, if D is close to 1 and k is sufficiently small, we prove using energy functionals that these propagating fronts are stable against small perturbations in exponentially weighted Sobolev spaces. This extends part of the results that are known for the scalar equation to which our system reduces when D = 1.     

Oxygen diffusion and surface exchange in La1−xSrxFe0.8Cr0.2O3−δ (x=0.2, 0.4 and 0.6)

Oxygen tracer diffusion (D*) and surface exchange rate constant (k*) have been measured, using isotopic exchange and depth profiling by secondary ion mass spectrometry (SIMS), in La_1−xSr_xFe_0.8Cr_0.2O_3−δ (x=0.2, 0.4 and 0.6). Measurements were made as a function of temperature (700–1000 °C) and oxygen partial pressure (0.21–10⁻²¹ atm) in dry oxygen, water vapour and water vapour/hydrogen/nitrogen mixtures. At high oxygen activity, D* was found to increase with increasing temperature and Sr content. The activation energies for D* in air are 2.13 eV (x=0.2), 1.53 eV (x=0.4) and 1.21 eV (x=0.6). As the oxygen activity decreases, D* increases as expected qualitatively from the increase in oxygen vacancy concentration. Under strongly reducing conditions, the measured values of D* at 1000 °C range from 10⁻⁸ cm² s⁻¹ for x=0.2 to 10⁻⁷ cm² s⁻¹ for x=0.4 and 0.6. The activation energies determined at constant H₂O/H₂ ratio are 1.21 eV (x=0.2), 1.59 eV (x=0.4) and 0.82 eV (x=0.6).

The surface exchange rate constant of oxygen for the H₂O molecule is similar in magnitude to that for the O₂ molecule and both increase with increasing Sr concentration.     

An electrochemical investigation of Li intercalation in the sol-gel LiMn2O4 spinel oxide

An alternative approach for obtaining the LiMn₂O₄ spinel phase is provided by the use of the sol-gel method in aqueous solution. The main electrochemical properties of the sol-gel LiMn₂O₄ phase are reported. In addition to chronopotentiometric and voltammetric experiments, the kinetics of the electrochemical insertion–extraction of lithium in Li_xMn₂O₄ (0.25<x<1) has been investigated using ac impedance spectroscopy. The strong variation of the chemical diffusion coefficient D_Li vs x, in the range 10⁻⁸–10⁻¹¹ cm² s⁻¹ (D_Li is found to be maximum for x=0.55) is critically discussed.     

Neutrino oscillations induced by two-loop radiative mechanism

Two-loop radiative mechanism, when combined with an U(1)_L′ symmetry generated by L_e − L_μ − L_τ (=L′), is shown to provide an estimate of Δm²/Δm²_atm εm_e/m_τ, where ε measures the U(1)_L′-breaking. Since Δm²_atm 3.5×10⁻³ eV², we find that Δm² ε10⁻⁶ eV², which will fall into the allowed region of the LOW solution to the solar neutrino problem for ε 0.1.     

带源项的变系数非线性反应扩散方程的精确解

本文利用广义条件对称方法对带源项的变系数非线性反应扩散方程 f(x)u_t=(g(x)D(u)u_x)_x+h(x)P(u)u_x+q(x)Q(u)进行研究. 当扩散项D(u)取u^m (m≠-1,0,1)和e^u两种重要情形时, 对该方程进行对称约化,得到了具有广义泛函分离变量形式的精确解. 这些精确解包含了该方程对应常系数情况下的解. 关键词： 广义条件对称 精确解 非线性反应扩散方程     

Oxygen tracer diffusion in La1 − xSrxCoO3

Tracer diffusion of ¹⁸O in dense, polycrystalline La_1−xSr_xCoO₃ for x = 0.1 has been measured in the temperature range 400 to 600 °C and at 500 °C for x = 0.2 at an oxygen partial pressure of 1 × 10⁵ Pa. Depth profiles were obtained by secondary ion mass spectrometry. The diffusion coefficient for La_0.9Sr_0.1CoO₃ is given by D = (17–247) exp[(−232 ± 8 kJ/mole)/RT] cm²/s. This value is several orders of magnitude lower than D extrapolated from the results for x = 0.2 measured in the 700–900 °C temperature range. One possible explanation for the discrepancy is that the two measurements reflect different diffusion paths. As expected, La_0.8Sr_0.2CoO₃ exhibits a higher diffusivity at 500 °C than does La_0.9Sr_0.1CoO₃.