Completeness of “good” Bethe ansatz solutions of a quantum-group-invariant Heisenberg model

The sl_q(2) quantum-group-invariant Heisenberg model with open boundary conditions is investigated by means of the Bethe ansatz. As is well known, quantum groups for q equal to a root of unity possess a finite number of “good” representations with non-zero q-dimension and “bad” ones with vanishing q-dimension. Correspondingly, the state space of an invariant Heisenberg chain decomposes into “good” and “bad” states. A “good” state may be described by a path of only “good” representations. It is shown that the “good” states are given by all “good” Bethe ansatz solutions with roots restricted to the first periodicity strip, i.e. only positive-parity strings (in the language of Takahashi) are allowed. Applying Bethe's string-counting technique completeness of the “good” Bethe states is proven, i.e. the same number of states is found as the number of all restricted paths on the sl_q(2) Bratteli diagram. It is the first time that a “completeness” proof for an anisotropic quantum-invariant reduced Heisenberg model is performed.     

Mean occurrence frequency and temporal risk analysis of solar particle events

The protection of astronauts from space radiation is required on future exploratory class and long-duration missions. For the accurate projections of radiation doses, a solar cycle statistical model, which quantifies the progression level within the cycle, has been developed. The resultant future cycle projection is then applied to estimate the mean frequency of solar particle events (SPEs) in the near future using a power law function of sunspot number. Detailed temporal behaviors of the recent large event and two historically large events of the August 1972 SPE and the November 1960 SPE are analyzed for dose-rate and cumulative dose equivalent at sensitive organs. Polyethylene shielded “storm shelters” inside spacecraft are studied to limit astronauts’ total exposure at a sensitive site within 10 cSv from a large event as a potential goal that fulfills the ALARA (as low as reasonably achievable) requirement.     

Photon contribution to the “super-hard” pomeron

It is shown that direct photons provide a leading twist mechanism for diffractive jet production in which the jets carry away all of the momentum lost by the proton. Two-photon processes are thus expected to asymptotically dominate “super-hard” pomeron events in ep collisions. We report the expected rates from these events for recent ZEUS and H1 data cuts. We also estimate the direct photon contribution to the “super-hard” pomeron events observed by the CERN UA8 group for collisions. It is again argued that direct photons are the leading mechanism for these events. We find that direct photons are an appreciable fraction of the events seen by UA8.     

Hydrodynamic model for particle size segregation in granular media

We present a hydrodynamic theoretical model for “Brazil nut” size segregation in granular materials. We give analytical solutions for the rise velocity of a large intruder particle immersed in a medium of monodisperse fluidized small particles. We propose a new mechanism for this particle size-segregation due to buoyant forces caused by density variations which come from differences in the local “granular temperature”. The mobility of the particles is modified by the energy dissipation due to inelastic collisions and this leads to a different behavior from what one would expect for an elastic system. Using our model we can explain the size ratio dependence of the upward velocity.     

The ground state of the two-leg Hubbard ladder a density-matrix renormalization group study

We present density-matrix renormalization group results for the ground state properties of two-leg Hubbard ladders. The half-filled Hubbard ladder is an insulating spin-gapped system, exhibiting a crossover from a spin liquid to a band insulator as a function of the interchain hopping matrix element. When the system is doped, there is a parameter range in which the spin gap remains. In this phase, the doped holes from singlet pairs and the pair field and the “4k_F” density correlations associated with pair-density fluctuations decay as power laws, while the “2k_F” charge density wave correlations decay exponentially. We discuss the behavior of the exponents of the pairing and density correlations within this spin-gapped phase. Additional one-band Luttinger liquid phases which occur in the large interband hopping regime are also discussed.     

Divisors on elliptic Calabi-Yau 4-folds and the superpotential in F-theory — I

Each smooth elliptic Calabi-Yau 4-fold determines both a three-dimensional physical theory (a compactification of “M-theory”) and a four-dimensional physical theory (using the “F-theory” construction). A key issue in both theories is the calculation of the “superpotential” of the theory, which by a result of Witten is determined by the divisors D on the 4-fold satisfying X( _D = 1. We propose a systematic approach to identify these divisors, and derive some criteria to determine whether a given divisor indeed contributes. We then apply our techniques in explicit examples, in particular, when the base B of the elliptic fibration is a toric variety or a Fano 3-fold.

When B is Fano, we show how divisors contributing to the superpotential are always “exceptional” (in some sense) for the Calabi-Yau 4-fold X. This naturally leads to certain transitions of X, i.e., birational tranformations to a singular model (where the image of D no longer contributes) as well as certain smoothings of the singular model. The singularities which occur are “canonical”, the same type of singularities of a (singular) Weierstrass model. We work out the transitions. If a smoothing exists, then the Hodge numbers change.

We speculate that divisors contributing to the superpotential are always “exceptional” (in some sense) for X, also in M-theory. In fact we show that this is a consequence of the (log)-minimal model algorithm in dimension 4, which is still conjectural in its generality, but it has been worked out in various cases, among which are toric varieties.     

Discrete gauge symmetry anomalies

It has been recently argued that quantum gravity effects strongly violate all non-gauge symmetries. This would suggest that all low energy discrete symmetries should be gauge symmetries, either continuous or discrete. Acceptable continuous gauge symmetries are constrained by the condition they should be anomaly free. We show here that any discrete gauge symmetry should also obey certain “discrete anomaly cancellation” conditions. These conditions strongly constrains the massles fermion content of the theory and follow from the “parent” cancellation of the usual continuous gauge anomalies. They have interesting applications in model building. As an example we consider the constraints on the Z_N “generalized matter parities” of the supersymmetric standard model. We show that only a few (including the standard R-parity) are “discrete anomaly free” unless the fermion content of the minimal supersymmetric standard model is enlarged.     

On the low-frequency limit of the Schönfeld pulse 1/f law

On the basis of propositions of the common fluctuation theory, peculiarities of small fluctuations in real physical systems with limited sizes are analyzed. It is established that small fluctuations should necessarily be divided into two types of fluctuations: “small” and “very small”. It is shown that the damping process of “small” fluctuations has relaxation character, while the damping process of “very small” fluctuations is of random character, i.e., it represents a random rectangular signal. The probability density of “very small” fluctuations is shown to be Gaussian. The agreement of the obtained results with experimental data acquired from semiconductor-based devices is analyzed. A relation between the generation–recombination noise and phonon number fluctuations in semiconductors is studied. On the basis of this consideration it is shown that the Schönfeld pulse spectrum preserves its well-known 1/f form only in the range of intermediate frequencies; at lower frequencies the spectrum gets saturated. An expression for the low-frequency limit of Schönfeld pulse 1/f law is obtained.     

Chiral symmetry and the A1 contribution to the nucleon-nucleon interaction

The contribution of A₁ exchange to the nucleon-nucleon potential is studied in a broken chiral symmetric model. The A₁ is treated as a finite-width resonance in the πρ s-wave. Connections between pseudoscalar and pseudovector pion-nucleon coupling in the underlying model lagrangian are studied in detail. It is found that large terms in the NN interaction arising from πρ exchange with pseudoscalar coupling are suppressed by interference with a₁ exchange. With pseudovector coupling there is a suppression of the A₁ exchange by the so-called “seagull” terms in πρ exchange which arise from gauge invariance. The suppression becomes an exact cancellation in the limit of infinite ρ and a₁ masses and exact chiral symmetry. We found that inclusion of the a₁ decay into the πρ state strongly modifies the a₁] exchange potential, suppressing the tensor part but leaving the spin-spin part almost unchanged.     

Methane activation over Ag-exchanged ZSM-5 zeolites: A theoretical study

Methane activation catalyzed over Ag-exchanged ZSM-5 zeolites was investigated by using the density functional theory (DFT) with a cluster model. Two different pathways were taken into account in this work: the “alkyl” and the “carbenium” pathways. The activation barriers obtained are 34.09 and 66.63 kcal/mol for the “alkyl” and the “carbenium” pathway, respectively. The calculated results show that the activation barrier of the “alkyl” pathway is smaller than that of “carbenium” pathway. Consequently, the “alkyl” pathway is the preferential reaction pathway. A new mechanism of methane conversion in the presence of ethene was proposed. In the catalytic cycle, the initial step of methane activation proceeds with the “alkyl” pathway and the Ag⁺ cation acts as an acceptor of the methyl group, then ethene reacts with the Ag⁺CH₃⁻ group to form propene. In addition, it is found that the Ag⁺ cations play an important role in the methane activation, compared with the reaction of methane activation over H-ZSM-5.     

Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system’s time evolution. Rather than solving the problem from scratch each time new observations become available, one uses the model to “forecast” the current state, using a prior state estimate (which incorporates information from past data) as the initial condition, then uses current data to correct the prior forecast to a current state estimate. This Bayesian approach is most effective when the uncertainty in both the observations and in the state estimate, as it evolves over time, are accurately quantified. In this article, we describe a practical method for data assimilation in large, spatiotemporally chaotic systems. The method is a type of “ensemble Kalman filter”, in which the state estimate and its approximate uncertainty are represented at any given time by an ensemble of system states. We discuss both the mathematical basis of this approach and its implementation; our primary emphasis is on ease of use and computational speed rather than improving accuracy over previously published approaches to ensemble Kalman filtering. We include some numerical results demonstrating the efficiency and accuracy of our implementation for assimilating real atmospheric data with the global forecast model used by the US National Weather Service.     

Electrical and magnetic properties in Co-P amorphous alloys

Different anomalies in the Hall effect, electrical resistivity, and magnetic susceptibility of simple Co-P amorphous alloys have been observed. We show that the anomalies detected are due to a transition from “para” to “ferromagnetic” order. The transition, which is not well defined, suggests a large compositional inhomogeneity in the samples with high content in P.     

On the reconstruction of the conduction electron spectrum in metal-oxide superconductors owing to the interaction with coherent atomic displacements

A “pseudospin ferromagnet” model is proposed which describes the interaction of conduction electrons with coherent atomic displacements in metal-oxide high-T_c superconductors (HTSC). Non-quasiparticle states (“pseudospinons”) play an important role in this model. They make an appreciable contribution to thermodynamic and transport properties (e.g., to the linear term in specific heat), although not contributing to the density of states at E_F at T=0. In the superconducting phase, the pseudospinons give rise to gapless superconductivity at finite temperatures. For certain model parameter relations, a new energy scale (“Kondo temperature”) may occur in the electron spectrum near E_F. Using the results obtained, experimental data on the thermopower, nuclear spin-lattice relaxation rate and other properties of HTSC are discussed.     

Formation model of bulk etching rate for polymer detectors

Any detector is composed of an enormous number of sensitive microscopic volumes (SMV) mainly in the state “NO” (Katz 1970. Unified Track Theory. In: Seventh International Colloquium on Corpuscular Photography and Visual Solid Detectors. Barcelona, pp. 1–29.). Irradiation evokes some spatial distribution of SMV in the state “Yes”. It can be described by the many-hit model of the SMV response (Ditlov, 1980. Theory of spatial calculation of primary action of d-electrons in track detectors with account of multiple scattering. In: Francois, H., et al. (Eds.), Solid State Nuclear Track Detectors. Pergamon Press, Oxford, pp. 131–141.). It appears that the process of etching can be described by its own many-hit model too, when the etching molecule attacks SMV in the state “Yes”. As a first our step of research, only the bulk rate V_b was considered.     

Evaporation of droplets in the two-dimensional Ginzburg–Landau equation

We consider the problem of coarsening in two dimensions for the real (scalar) Ginzburg–Landau equation. This equation has exactly two stable stationary solutions, the constant functions +1 and −1. We assume most of the initial condition is in the “−1” phase with islands of “+1” phase. We use invariant manifold techniques to prove that the boundary of a circular island moves according to Allen–Cahn curvature motion law. We give a criterion for non-interaction of two arbitrary interfaces and a criterion for merging of two nearby interfaces.     

Magnetic instabilities in the rare earth-3d compounds

Due to the evolution of the band structure through the series, the rare earth R-3d metal compounds form outstanding tools for the study of the 3d and/or 4f magnetic instabilities. Such instabilities are illustrated in this paper for three types of systems: i) the Y-Ni system with a special emphasis on the “thermal spontaneous magnetization” observed in Y₂Ni₇, ii) the R-Co system where “collective electron metamagnetism” and Co antiferromagnetism are observed in the RCo₂ (as in ThCo₅), and in La₂Co_1.7 and La₂Co₃, respectively; iii) the Ce-Ni system where the 4f instability is quite characteristic in the CeNi intermediate valence compound in which large magnetovolume effects were determined.     

Experimental observation of a copious yield of electrons with small transverse momenta in pp collisions at high energies

Inclusive electron and positron emission have been observed for θ_cm = 30° and S = 2800 GeV² at the CERN Intersecting Storage Rings (ISR). Over the transverse momentum interval 0.2 GeV/c < p_T < 1.5 GeV/c, electrons and positrons, which are equal in number within the experimental accuracies, appear to grow with respect to other particles (pions) approximately like 1/p_T. We are unable to explain their number and p_T-dependence in terms of “conventional” mechanisms.     

Methods for evaluating the performance of emitters in plane parallel diodes

The curvature seen in Child's law plots of current-voltage characteristics measured using plane parallel diodes may be analysed in a number of ways to give information about the work function distribution of a cathode. This paper suggests a simple technique for characterising a cathode based on the assumption it has a “top-hat” work function distribution. The technique allows synthetic current/voltage characteristics to be generated which agree well with the practical characteristics from which the parameters of the work function distribution were derived. The parameters of the “top-hat” model may also be used to obtain an equivalent Gaussian work function distribution which gives almost identical synthetic characteristics and Schottky enhancement may be modelled in a rather empirical manner. Since either model gives good predictions, synthetic characteristics may be used to investigate other methods used to characterise cathodes. It is found that there is generally reasonable agreement which could be improved, for most practical work function distributions, by the choice of parameters slightly different from those normally used.     

Flux creep through the surface barrier and columnar defects in HTSC

The rate of flux creep over the surface barrier in clean HTSC samples is found. This rate proves to be significantly different for the cases of vortex entry and escape (relaxation “in” and “out”, respectively). Since a flat surface is topologically similar to the artificial columnar defects, their comparison is useful. The vortex creep over the surface is equivalent to that over the cylinder defect of radius r > λ, whereas the radii of real defects obtained so far are of order . We discuss the effect of the smallness of defect radius on the creep process, which results in very small activation energies U at large critical current J_c. The importance of the increase of the defect radius is predicted.