Approximating the monomer-dimer constants through matrix permanent

The monomer-dimer model is fundamental in statistical mechanics. However, it is #P-complete in computation, even for two dimensional problems. A formulation in matrix permanent for the partition function of the monomer-dimer model is proposed in this paper, by transforming the number of all matchings of a bipartite graph into the number of perfect matchings of an extended bipartite graph, which can be given by a matrix permanent. Sequential importance sampling algorithm is applied to compute the permanents. For two-dimensional lattice with periodic condition, we obtain $0.6627\pm0.0002$, where the exact value is $h_2=0.662798972834$. For three-dimensional lattice with periodic condition, our numerical result is $0.7847\pm0.0014$, {which agrees with the best known bound $0.7653 \leq h_3 \leq 0.7862$.}Comment: 6 pages, 2 figure

The influence of collective neutrino oscillations on a supernova r-process

Recently, it has been demonstrated that neutrinos in a supernova oscillate collectively. This process occurs much deeper than the conventional matter-induced MSW effect and hence may have an impact on nucleosynthesis. In this paper we explore the effects of collective neutrino oscillations on the r-process, using representative late-time neutrino spectra and outflow models. We find that accurate modeling of the collective oscillations is essential for this analysis. As an illustration, the often-used "single-angle" approximation makes grossly inaccurate predictions for the yields in our setup. With the proper multiangle treatment, the effect of the oscillations is found to be less dramatic, but still significant. Since the oscillation patterns are sensitive to the details of the emitted fluxes and the sign of the neutrino mass hierarchy, so are the r-process yields. The magnitude of the effect also depends sensitively on the astrophysical conditions - in particular on the interplay between the time when nuclei begin to exist in significant numbers and the time when the collective oscillation begins. A more definitive understanding of the astrophysical conditions, and accurate modeling of the collective oscillations for those conditions, is necessary.Comment: 27 pages, 10 figure

Collective neutrino flavor transitions in supernovae and the role of trajectory averaging

Non-linear effects on supernova neutrino oscillations, associated with neutrino self-interactions, are known to induce collective flavor transitions near the supernova core for theta_13 \neq 0. In scenarios with very shallow electron density profiles, these transformations have been shown to couple with ordinary matter effects, jointly producing spectral distortions both in normal and inverted hierarchy. In this work we consider a complementary scenario, characterized by higher electron density, as indicated by post-bounce shock-wave simulations. In this case, early collective flavor transitions are decoupled from later, ordinary matter effects. Moreover, such transitions become more amenable to both numerical computations and analytical interpretations in inverted hierarchy, while they basically vanish in normal hierarchy. We numerically evolve the neutrino density matrix in the region relevant for self-interaction effects. In the approximation of averaged intersection angle between neutrino trajectories, our simulations neatly show the collective phenomena of synchronization, bipolar oscillations, and spectral split, recently discussed in the literature. In the more realistic (but computationally demanding) case of non-averaged neutrino trajectories, our simulations do not show new significant features, apart from the smearing of ``fine structures'' such as bipolar nutations. Our results seem to suggest that, at least for non-shallow matter density profiles, averaging over neutrino trajectories plays a minor role in the final outcome. In this case, the swap of nu_e and nu_{\mu,\tau} spectra above a critical energy may represent an unmistakable signature of the inverted hierarchy, especially for theta_{13} small enough to render further matter effects irrelevant.Comment: v2 (27 pages, including 9 eps figures). Typos removed, references updated. Minor comments added. Corrected numerical errors in Eq.(6). Matches the published versio

Nambu-Hamiltonian flows associated with discrete maps

For a differentiable map $(x_1,x_2,..., x_n)\to (X_1,X_2,..., X_n)$ that has an inverse, we show that there exists a Nambu-Hamiltonian flow in which one of the initial value, say $x_n$, of the map plays the role of time variable while the others remain fixed. We present various examples which exhibit the map-flow correspondence.Comment: 19 page

Bounds on the Magnetic Fields in the Radiative Zone of the Sun

We discuss bounds on the strength of the magnetic fields that could be buried in the radiative zone of the Sun. The field profiles and decay times are computed for all axisymmetric toroidal Ohmic decay eigenmodes with lifetimes exceeding the age of the Sun. The measurements of the solar oblateness yield a bound <~ 7 MG on the strength of the field. A comparable bound is expected to come from the analysis of the splitting of the solar oscillation frequencies. The theoretical analysis of the double diffusive instability also yields a similar bound. The oblateness measurements at their present level of sensitivity are therefore not expected to measure a toroidal field contribution.Comment: 15 pages, 6 figure

Microscopic Observation Drug Susceptibility Assay for Rapid Diagnosis of Lymph Node Tuberculosis and Detection of Drug Resistance.

In this study, 132 patients with lymphadenopathy were investigated. Fifty-two (39.4%) were diagnosed with tuberculosis (TB). The microscopic observation drug susceptibility (MODS) assay provided rapid (13 days), accurate diagnosis (sensitivity, 65.4%) and reliable drug susceptibility testing (DST). Despite its lower sensitivity than that of other methods, its faster results and simultaneous DST are advantageous in resource-poor settings, supporting the incorporation of MODS into diagnostic algorithms for extrapulmonary TB

Stimulated Neutrino Transformation with Sinusoidal Density Profiles

Large amplitude oscillations between the states of a quantum system can be stimulated by sinusoidal external potentials with frequencies that are similar to the energy level splitting of the states or a fraction thereof. Situations when the applied frequency is equal to an integer fraction of the energy level splittings are known as parametric resonances. We investigate this effect for neutrinos both analytically and numerically for the case of arbitrary numbers of neutrino flavors. We look for environments where the effect may be observed and find that supernova are the one realistic possibility due to the necessity of both large densities and large amplitude fluctuations. The comparison of numerical and analytic results of neutrino propagation through a model supernova reveals it is possible to predict the locations and strengths of the stimulated transitions that occur.Comment: 14 pages, 6 figure

Influence of the single-particle Zeeman energy on the quantum Hall ferromagnet at high filling factors

In a recent paper [B. A. Piot et al., Phys. Rev. B 72, 245325 (2005)], we have shown that the lifting of the electron spin degeneracy in the integer quantum Hall effect at high filling factors should be interpreted as a magnetic-field-induced Stoner transition. In this work, we extend the analysis to investigate the influence of the single-particle Zeeman energy on the quantum Hall ferromagnet at high filling factors. The single-particle Zeeman energy is tuned through the application of an additional in-plane magnetic field. Both the evolution of the spin polarization of the system and the critical magnetic field for spin splitting are well described as a function of the tilt angle of the sample in the magnetic field.Comment: Published in Phys. Rev.