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.     

In-band M1 and E2 transition rates and collective structures in Ba

Subpicosecond mean lifetimes of eight excited states in ¹²⁸Ba populated via the ⁹⁶Zr(³⁶S,4n) reaction were measured by the Doppler-shift attenuation (DSA) technique using a line-shape analysis. The differential decay-curve method (DDCM) was applied for the lifetime determination. The B(E2) values in the yrast band indicate that the first band-crossing is with a proton S-band. The configuration πh_11/2d_5/2 of the negative-parity semi-decoupled bands is confirmed by the measured B(E2, I → I − 2) and B(M1, I → I − 1) transition strengths. The higher-lying “dipole” band in ¹²⁸Ba can be described as a high-K four-quasiparticle band built on the prolate configuration (πh_11/2d_5/2) (νh_11/2g_7/2).     

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⁺.     

Dynamic contribution to the fishtail effect in a twin-free DyBa2Cu3O7−δ single crystal

Superconducting current densities j_s and dynamic relaxation rates Q d ln j_s/d In(dB_e/dt), where dB_e/dt is the sweep rate of the external magnetic field B_e, were measured as a function of temperature (5 K < T < 65 K) in magnetic fields up to 7 T on a twin-free DyBa₂Cu₃O_7−δ single crystal by means of a high-sensitivity capacitance torque magnetometer. Above 15 K, we observe a “fishtail” effect, i.e. a pronounced minimum in the j_s(B_e) curve at fields around B_e = 1 T. The relaxation rate Q shows an anomalous increase at low fields which is correlated to the minimum in the j_s(B_e) curve. Both the j_s versus B_e and Q versus B_e data are used as input parameters into the generalized inversion scheme developed by Schnack et al. [Phys. Rev. B 48 (1993) 13178] to calculate the true critical current density j_c which is by definition independent of relaxation effects. Interestingly, the j_c(B_e, T) curves derived in this way do not show a minimum. This points clearly to a dynamic contribution to the fishtail effect. The true critical current density j_c(B_e, T) decreases weakly with increasing B_e over the entire measured temperature and field range, as expected for single-vortex pinning. This indicates that the observed fishtail effect is not caused by a crossover from single-vortex pinning to pinning of flux bundles. The temperature dependence of j_c is in good agreement with the predictions of a model based on single-vortex pinning caused by spatial fluctuations in the charge-carrier mean free path.     

An analysis of domain wall ruckling initiated at the points of maximum shear-stress on a braket wall in (110)[001] SiFe

The eddy-current limited ruckling process by which a shaped “ket” domain wall in Goss oriented silicon iron transforms into a “bra” domain wall during magnetization reversal has been calculated from a new initial condition. It is now assumed that the re-oriented segments nucleate at the points of maximum shear stress on the domain wall and not at the surface as in a previous calculation. Both models are compared with experimental data obtained by Morgan and Overshott using Kerr magneto-optic microscopy. This suggests that ruckling is not initiated immediately d B/dT changes sign, but is delayed until the shearing stress is sufficient to nucleate re-oriented segments.     

Binding energy of an exciton bound to ionized donors in quantum dots

Binding energies for an exciton (X) trapped in the two-dimensional quantum dot by a positive ion located on the z axis at a distance d from the dot plane are calculated by using the method of few-body physics. This configuration is called a barrier (D⁺,X) center. The dependence of the binding energy of the ground state of the barrier (D⁺,X) center on the dot radius for a few values of the distance d between the fixed positive ion on the z axis and the dot plane is obtained. We find that when d<0.2nm the barrier (D⁺,X) center does not form a bound state.     

The effects of chain segment motion on ionic diffusion in solid polymer electrolytes

The “vehicular effects” of chain segment motion on ionic diffusion in solid polymer electrolytes have been investigated via numerical simulation on a two-dimensional square lattice where the dynamical variation of chain configuration is presented by translational or rotational bond movement. It is found that (a) both types of bond motion promote continuous diffusion when the fraction (p) of available bonds is below the static percolation threshold of p=0.5 in two dimensions; (b) translational motion of bonds parallel to the direction of diffusion produces larger diffusion coefficients (D) than that by random renewal of the dynamic bond percolation model (DBPM), while the perpendicular motion or rotational motion gives smaller values of D; (c) Smooth lines instead of “stair-case like” curves generated by DBPM are obtained in the mean-squared displacement versus time plot, when bonds are shifting along the diffusion route. The dependence of diffusion coefficients on the variation of motion patterns of bonds is expected to be related to the temperature change under which these patterns are excited accordingly, such that VTF behavior of certain polymer electrolytes may be deduced.     

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.     

Retrieval of cirrus particle sizes using a split-window technique: a sensitivity study

This paper examines the sensitivity of retrieved ice particle sizes using split-window method to the light scattering program for the single scattering calculation. We find that for randomly oriented hexagonal ice particles the retrieval algorithm using the anomalous diffraction theory (ADT) significantly overestimates the mean effective ice particle sizes, D_ge. The retrieved D_ge based on the geometric optics method (GOM) and Mie theory agrees with reference results within 20% when D_ge<30 μm. Based on the speculation that there is no “tunneling” for complex particles, some recent studies suggest that the ADT is an appropriate method to simulate the absorption coefficient for irregularly shaped particles in the infrared. In this study, however, we find that the overestimation of D_ge due to the ADT is largely caused by the neglect of refraction and reflection processes, instead of by the neglect of “tunneling” in the absorption calculations. By considering complex particle shapes such as aggregates with surface roughness, we further find that the retrieved D_ge based on the GOM is not sensitive to the particle shapes. Note that both ADT and GOM do not consider the “tunneling”, but the retrieved D_ge based on the ADT is about two times larger than those based on the GOM. “Tunneling” plays a significant role in the retrieved D_ge only when the D_ge is larger than 30–35 μm. In this study, we also examine the sensitivities of retrieved D_ge to the ice particle size distributions assumed in the retrieval algorithm and to the errors in the emissivities. It is found that when the D_ge is larger than 30–40 μm, the retrieved D_ge becomes very sensitive to the uncertainties related to the ice particle size distributions and to the errors in cirrus emissivities derived from measurements.     

“Missing moment” and perturbative methods for polynomial iterated function systems

An iterated function system (IFS) over a compact metric space X is defined by a set of contractive maps w_i: X → X, i = 1,…,N, with associated nonzero probabilities p_i > 0, p_i = 1. The “parallel” action of the maps defines a unique compact invariant attractor set A X which supports an invariant measure μ and which is balanced with respect to the p_i. For linear , the invariance of μ yields a relation between the moments g_n = ∫ χⁿ dμ which permits their recursive computation from the initial value g₀ = 1. For nonlinear w_i, however, the moment relations are incomplete and do not permit a recursive computation. This paper describes two methods of obtaining accurate estimates of the moments when the IFS maps w_i are polynomials: (i) application of the necessary Hausdorff conditions on the g_i to obtain convergent upper and lower bounds and (ii) a perturbation expansion approach. The methods are applied to some model problems.     

Transformation kinetics in 1-D processes with continuous nucleation: comparison of shielding and phantom effects

A derivation is presented for the fraction of material transformed as a function of time, X(t), for 1-D transformations which occur via continuous nucleation and growth of particles with a distribution of growth velocities. The derivation includes the effects of interparticle shielding as well as shadowed nucleation prevention (“phantoms”). The analytical results are compared with simulations and found to be in close agreement. The shielding effects are more dominant than the phantom effects, though both are important when exact information regarding the extent of transformation is desired.     

Using X(3823)→J/ψπ+π− to identify coupled-channel effects

Very recently, the Belle and BESIII experiments observed a new charmonium-like state X(3823), which is a good candidate for the D-wave charmonium ψ(1³D₂). Because the X(3823) is just near the D ¯D^∗ threshold, the decay X(3823)→ J/ψπ⁺π⁻ can be a golden channel to test the significance of coupled-channel effects. In this work, this decay is considered including both the hidden-charm dipion and the usual quantum chromodynamics multipole expansion (QCDME) contributions. The partial decay width, the dipion invariant mass spectrum distribution dΓ[X(3823) → J/ψπ⁺π⁻]/dm_π⁺_π⁻, and the corresponding dΓ[X(3823) → J/ψπ⁺π⁻]/d cos θ distribution are computed. Many parameters are determined from existing experimental data, so the results depend mainly only on one unknown phase between the QCDME and hidden-charm dipion amplitudes.     

High-resolution gamma-ray spectroscopy of ΛLi

We report on the first observation of hypernuclear γ transitions using germanium detectors. Using a large-acceptance Ge detector system, we observed two γ transitions in _Λ⁷Li, the spin-flip transition at 689±4keV and the transition at 2050±2 keV (preliminary). The strength of the ΛN spin-spin interaction is derived from the energy of the former transition. As for the latter transition, B(E2) was measured to be 3.9±0.6±0.4 e²fm⁴ (preliminary), which indicates a shrinkage of the nuclear size of _Λ⁷Li from ⁶Li and confirms “glue-like role” of Λ.     

Improved constants for the 7820 Å and 7883 Å bands of CO2

High-dispersion spectra of Venus are used to obtain line positions and band constants for the (105)_I and (105)_II bands of CO₂. An improved method of analysis is used to obtain very accurate results. Assuming B″ = 0.390218 and D″ = 13.3 × 10^-8 for the ground state, we find for 7820: ω₀ = 12774.727 cm^-1 ±0.002, B' = 0.374540 ±0.000006, D' = 10.9 × 10^-8 ±0.4, for 7883: ω₀ = 12672.274 cm^-1 ±0.004, B' = 0.375657 ±0.000014, D' = 17.2 × 10^-8 ±1.7,

The values for ω₀ and B' are at least an order of magnitude more accurate than those given by Herzberg and Herzberg in 1953, and the D' values are new.     

Signals of very high energy neutralinos in future cosmic ray detectors

“Top–down” models explain the observation of ultra-high energy cosmic rays (UHECR; E5×10¹⁹ eV) through the decay of very massive, long-lived “X particles”. If superparticles with masses near a TeV exist, X decays also lead to a significant flux of very energetic neutralinos, assumed to be the (stable or long-lived) lightest superparticles. There is a range of energies where neutrinos get absorbed in the Earth, but neutralinos can still traverse it. These neutralinos could in principle be detected. We calculate the detection rate in planned experiments such as OWL and EUSO. For bino-like neutralinos, which have been considered previously, we find detection rates below 1 event per Teraton of target and year in all cases; often the rates are much smaller. In contrast, if the neutralino is higgsino-like, more than ten events per year per Teraton might be observed, if the mass of the X particle is near its lower bound of 10¹² GeV.     

Characterization of nonlinearities in the dose dependence of thermoluminescence

Nonlinearities often occur in the dose dependence of thermoluminescence (TL). These include sublinearity, usually when there is an approach to saturation in the dose dependence, as well as supralinearity, also termed superlinearity in the literature. Different researchers in the field have viewed the effect of supralinearity/superlinearity from two somewhat different points of view. One point of view has to do with the rate of change with dose of the dose dependence function. The other approach is related more to the applications of TL in dosimetry and archaeological and geological dating, and basically has to do with the correction to be made in extrapolation in cases where supra(super) linearity occurs following an initial linear dose range, or prior to such a linear range. In the present work we propose quantitative methods to characterize these nonlinearities. We suggest the use of two different nonlinearity indices, depending upon how one wishes to describe the nonlinearity. We propose use of the term “supra linearity index”, ƒ(D), in cases where the feature of interest is the deviation from linearity, namely, when the correction in extrapolation is the main issue. We propose the term “superlinearity index”, g(D), in dose ranges where the growth is “more than linear” and when extrapolation is not the main issue. We mathematically define each of these indices and give examples of their use for different dose dependencies.     

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.     

Correlations in one-dimensional quantum impurity problems with an external field

We study response functions of integrable quantum impurity problems with an external field at T = 0 using non-perturbative techniques derived from the Bethe ansatz. We develop the first steps of the theory of excitations over the new, field-dependent ground state, leading to renormalized (or “dressed”) form factors. We obtain exactly the low-frequency behaviour of the dynamical susceptibility χ″ (ω) in the double-well problem of dissipative quantum mechanics (or equivalently the anisotropic Kondo problem), and the low-frequency behaviour of the AC noise S_t(ω) for tunnelling between edges in fractional quantum Hall devices. We also obtain exactly the structure of singularities in χ″ (ω) and S_t (ω). Our results differ significantly from previous perturbative approaches.     

Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians

In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of rational curves on complete intersection Calabi-Yau 3-folds in Grassmannians. Using a natural degeneration of Grassmannians G(k, n) to some Gorenstein toric Fano varieties P(k, n) with conifolds singularities which was recently described by Sturmfels, we suggest an explicit mirror construction for Calabi-Yau complete intersections X ⊂ G(k, n) of arbitrary dimension. Our mirror construction is consistent with the formula for the Lax operator conjectured by Eguchi, Hori and Xiong for gravitational quantum cohomology of Grassmannians.