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.     

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.     

Quantum bound states with zero binding energy

After reviewing the general properties of zero-energy quantum states, we give the explicit solutions of the Schrödinger equation with E = 0 for the class of potentials V = −|γ|/r^ν, where −∞ < ν < ∞. For ν > 2, these solutions are normalizable and correspond to bound states, if the angular momentum quantum number l > 0. (These states are normalizable, even for l = 0, if we increase the space dimension, D, beyond 4; i.e for D > 4.) For ν < −2 the above solutions, although unbound, are normalizable. This is true even though the corresponding potentials are repulsive for all r. We discuss the physics of these unusual effects.     

Simulations of migration, fragmentation and coalescence of non-wetting fluids in porous media

A model based on invasion percolation was used to simulate the migration on a non-wetting fluid through a porous medium filled with an immiscible wetting fluid under the influence of a gradient such as that provided by gravity. The migrating fluid clusters undergo both fragmentation and coalescence. The fragment size distribution obtained from two-dimensional simulations in which the gradient g is slowly increased from 0 can be represented by the scaling form N_s(g)s^-2ƒ(s|g|^-z where z=1+(D−1)ν(ν+1). Here D is the fractal dimensionality of invasion percolation, with trapping, and ν is the ordinary percolation correlation length exponent.     

Dyonic membranes

We present dyonic multi-membrane solutions of the N = 2 D = 8 supergravity theory that serves as the effective field theory of the T²-compactified type II superstring theory. The ‘electric’ charge is fractional for generic asymptotic values of an axion field, as for D = 4 dyons. These membrane solutions are supersymmetric, saturate a Bogomolnyi bound, fill out orbits of an subgroup of the type II D = 8 T-duality group, and are non-singular when considered as solutions of T³-compactified D = 11 supergravity. On K₃ compactification to D = 4, the conjectured type II/heterotic equivalence allows the group to be reinterpreted as the S-duality group of the toroidally compactified heterotic string and the dyonic membranes wrapped around homology two-cycles of K₃ as S-duals of perturbative heterotic string states.     

Transport in solid oxide porous electrodes: Effect of gas diffusion

We extend our previous treatment of a mixed ionic electronic conductor membrane, consisting of a porous cathode and anode separated by a thin non-porous layer, to the case where mass transport of molecules in the porous electrodes can be the rate-limiting step. The linearized transport equations for the ion-hole pairs in the solid and of the gas molecules in the pores are characterized by the length scales L_P = √L_d(1 − φ)/Sτ_s and L_g = 2L_p√[τ_sφ/τ(1 − φ)][D_gc_g/D_IEc_i] respectively, where L_d = D_IE/K is the length scale that determines the transition from diffusion limited to surface exchange limited transport in the non-porous electrodes, K is the surface exchange coefficient, D_IE and D_g are the diffusion coefficients of the ion-hole pairs and of the molecules, c_i and c_g are the concentrations of the ions and molecules, S is the pore surface area per unit volume, φ the porosity and τ_s and τ the tortuosities of the solid and pore phases respectively. When L_g L_p, which is the case treated previously, the rate-limiting step in the transport is ionic diffusion and surface exchange. Enhancements in oxygen ion current of two orders in magnitude, over non-porous electrodes, are in principle achievable with porous perovskite MIEC having surface area s = 10⁶ cm⁻¹. When L_g L_p the rate-limiting step is mass transport in the pores and the enhancement in ion current is substantially reduced.     

Diffusion of W on A W(211) plane

The diffusion of W on a (211) plane of a W field emitter has been re-examined by means of the fluctuation autocorrelation method. Diffusion along channels yielded E = 16.8 ± 0.5 kcal, D₀ = (3 ± 1) × 10⁻⁵ cm² s⁻¹. For diffusion across channels E =6.6 kcal, D₀ = 4 × 10⁻⁹cm² s⁻¹ at T < 752 K, and E = 24 kcal, D₀ = 5 × 10⁻⁴ cm² s⁻¹ at T > 752 K. The results for diffusion along channels yield E and D₀ values intermediate between recent results by Wang and Ehrlich [Surf. Sci. 206 (1988) 451] using field ion microscopy (E = 19 kcal, D₀ = 7.7 × 10⁻³ cm² s⁻¹) and Tringides and Gomer [J. Chem. Phys. 84 (1986) 4049], using the same method as the present work but a larger slit (E = 13.3 kcal, D₀ = 7 × 10⁻⁷ cm² s⁻¹). The results for cross channel diffus good agreement with those of Tringides and Gomer below 752 K, where these authors stopped. The new high temperature results suggest that the channel wall exchange mechanism postulated by Tringides and Gomer for cross channel diffusion at low T gives way to diffusion by climbing over the channel walls with higher E but also higher D₀ above 752 K. Possible reasons for the discrepancies between these three sets of results and the absence of cross channel diffusion in the work of Wang and Ehrlich are briefly discussed.     

Microwave absorption and paracoherence excess conductivity studies in high-Tc superconductors

Single phase polycrystalline samples of La_1.8Sr_0.2CuO₄, YBa₂Cu₃O_7−δ and Bi_1.6Pb_0.4Sr₂Ca₂Cu₃O_y high-T_c superconductors have been studied using XRD, SEM, EDAX, (T), χ_AC and EPR techniques. Detailed investigations on low-field-dependent microwave absorption have been carried out in order to investigate the effects of field exposure, field cooling, zero field cooling and amplitude of field variation on the samples. The results have been discussed on the basis of granular model via Josephson junctions of high-T_c superconductors. Over and above, paracoherence excess conductivity analysis has been carried out in all the three samples. The critical exponent (γ) estimated for all the three samples in close vicinity to their respective transition temperatures has an excellent agreement with the theoretically predicted value for 3-dimensional XY-ferromagnet (γ = 1.33 for D = 3, N = 2).     

D-branes and T-duality

We show how the T-duality between D-branes is realized (i) on p-brane solutions (p = 0,…,9) of IIA/IIB supergravity and (ii) on the D-brane actions (p = 0,…, 3) that act as source terms for the p-brane solutions. We point out that the presence of a cosmological constant in the IIA theory leads, by the requirement of gauge invariance, to a topological mass term for the worldvolume gauge field in the 2-brane case.     

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.     

Intersecting M-branes

We present the magnetic duals of Güven's electric-type solutions of D = 11 supergravity preserving 1/4 or 1/8 of the D = 11 supersymmetry. We interpret the electric solutions as n orthogonal intersecting membranes and the magnetic solutions as n orthogonal intersecting 5-branes, with n = 2, 3; these cases obey the general rule that p-branes can self-intersect on (p − 2)-branes. On reduction to D = 4 these solutions become electric or magnetic dilaton black holes with dilaton coupling constant a = 1 (for n = 2) or (for n = 3). We also discuss the reduction to D = 10.     

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.     

Lambda-nucleon interaction potentials

Two-body S-wave, spin dependent, central Λ-N interaction potentials of the form first given by Ram and Downs are constructed to fit the zero energy scattering lengths a_s = −2.25 fm, a_t = −2.08 fm of Herndon and Tang. When assumed to be effective in even-parity states with full strength and in odd-parity states with zero strength, these potentials fit the Λ-p scattering cross section data very well. The binding energy D of the Λ-particle in nuclear matter using these potentials is calculated by the method of independent pair approximation. The potentials that best fit the scattering data give values for D which are only 3–4 MeV lower than that obtained previously with a potential of Hemdon and Tang. It is concluded that the three-body ΛNN forces may be quite important in the calculations of D.     

串列对转双圆柱的多块LB模拟

结合格子玻尔兹曼方法(Lattice Boltzmann Method,简称LBM)和多块网格(Multi-Block Grid)技术,数值研究较小雷诺数(Re=100)下均匀来流绕串列对转双圆柱问题,综合分析圆柱中心间距比S/D和圆柱无量纲旋转速度α对流场结构的影响,考察前、后圆柱的涡脱落形态和升阻力特性.结果表明:当间距比为1.2时存在一临界旋转比α_c,转速超过这一值后前圆柱产生负Magnus效应;间距比为2时,流场出现类似单旋转圆柱时的第二不稳定模态;当间距比较大(S/D=4、6)时,前、后柱之间存在涡脱落,后柱尾涡中出现2S、2S^*、2P、P+S等多种形态.     

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.     

Black hole formation in c=1 string field theory

A suggestion on how black holes may appear in Das-Jevicki collective field theory is given. We study the behaviour of a “test” particle when energy is sent into the system. A perturbation moving near the potential barrier can create a large-distance black hole geometry where the seeming curvature singularity is at the position of the barrier. In the simplest “static” case the exact D=2 black hole metric emerges.     

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.     

Universal properties of self-avoiding walks from two-dimensional field theory

We use the recently conjectured exact S-matrix of the massive O(n) model to derive its form factors and ground state energy. This information is then used in the limit n → 0 to obtain quantitative results for various universal properties of self-avoiding chains and loops. In particular, we give the first theoretical prediction of the amplitude ratio C/D which relates the mean square end-to-end distance of chains to the mean square radius of gyration of closed loops. This agrees with the results from lattice enumeration studies to within their errors, and gives strong support for the various assumptions which enter into the field theoretic derivation. In addition, we obtain results for the scaling function of the structure factor of long loops, and for various amplitude ratios measuring the shape of self-avoiding chains. These quantities are all related to moments of correlation functions which are evaluated as a sum over m-particle intermediate states in the corresponding field theory. We show that in almost all cases, the restriction to m 2 gives results which are accurate to at least one part in 10³. This remarkable fact is traced to a softening of the m > 2 branch cuts relative to their behaviour based on phase space arguments alone, a result which follows from the threshold behaviour of the two-body S-matrix, S(O) = −1. Since this is a general property of interacting 2D field theories, it suggests that similar approximation may well hold for other models. However, we also study the moments of the area of self-avoiding loops, and show that, in this case, the two-particle approximation is not valid.     

Investigation on the Cs 6S1/2 to 7D electric quadrupole transition via monochromatic two-photon process at 767 nm

We experimentally demonstrate the cesium electric quadrupole transition from the 6S_1/2 ground state to the 7D_3/2,5/2 excited state through a virtual level by using a single laser at 767 nm. The excited state energy level population is characterized by varying the laser power, the temperature of the vapor, and the polarization combinations of the laser beams. The optimized experimental parameters are obtained for a high resolution transition interval identification. The magnetic dipole coupling constant A and electric quadrupole coupling constant B for the 7D_3/2,5/2 states are precisely determined by using the hyperfine levels intervals. The results, A = 7.39 (0.06) MHz, B = −0.19 (0.18) MHz for the 7D_3/2 state, and A = −1.79 (0.05) MHz, B =1.05 (0.29) MHz for the 7D_5/2 state, are in good agreement with the previous reported results. This work is beneficial for the determination of atomic structure information and parity non-conservation, which paves the way for the field of precision measurements and atomic physics.