The Finite Upper Half Space and Related Hypergraphs

AbstractA space generalizing the finite upper half plane is presented along with a projective action by the finite general linear group. A volume generalizing the pseudo-distance on the finite upper half plane is also given. Then this volume is used to create hypergraphs which are analyzed with respect to the Ramanujan property

Band Crossing and Signature Splitting in Odd Mass fp Shell Nuclei

Structure of two sets of mirror nuclei: 47V - 47Cr and 49Cr - 49Mn, as well as 49V and 51Mn, is studied using the projected shell model. Their yrast spectra are described as an interplay between the angular momentum projected states around the Fermi level which carry different intrinsic K-quantum numbers. The deviations from a regular rotational sequence are attributed to band crossing and signature splitting, which are usually discussed in heavy nuclear systems. Our results agree reasonably with experimental data, and are comparable with those from the full $pf$ shell model calculations.Comment: 3 figures, submitted to Nucl. Phys.

Neutrino absortion cross sections in supernova environment

We study charged-current neutrino cross sections on neutronrich nuclei in the mass $A\sim60$ region. Special attention is paid to environmental effects, i.e. finite temperature and density, on the cross sections. As these effects are largest for small neutrino energies, it is sufficient to study only the Gamow-Teller (GT) contributions to the cross sections. The relevant GT strength distributions are derived from large-scale shell model calculations. We find that the low-energy cross sections are enhanced at finite temperatures. However, for $(\nu_e,e^-)$ reactions Pauli blocking of the electrons in the final state makes the cross sections for low-energy neutrinos much smaller than for the competing inelastic scattering on electrons at moderate and large densities. Absorption cross sections for low-energy antineutrinos are strongly enhanced at finite temperatures.Comment: 11 pages, 4 figure

Neutral-current neutrino reactions in the supernova environment

We study the neutral-current neutrino scattering for four nuclei in the iron region. We evaluate the cross sections for the relevant temperatures during the supernova core collapse and derive Gamow-Teller distributions from large-scale shell-model calculations. We show that the thermal population of the excited states significantly enhances the cross sections at low neutrino energies. Calculations of the outgoing neutrino spectra indicate the prospect of neutrino upscattering at finite temperatures. Both results are particularly notable in even-even nuclei.Comment: 14 pages, 4 figures, accepted in Phys. Lett. B

Adaptive Detection of Instabilities: An Experimental Feasibility Study

We present an example of the practical implementation of a protocol for experimental bifurcation detection based on on-line identification and feedback control ideas. The idea is to couple the experiment with an on-line computer-assisted identification/feedback protocol so that the closed-loop system will converge to the open-loop bifurcation points. We demonstrate the applicability of this instability detection method by real-time, computer-assisted detection of period doubling bifurcations of an electronic circuit; the circuit implements an analog realization of the Roessler system. The method succeeds in locating the bifurcation points even in the presence of modest experimental uncertainties, noise and limited resolution. The results presented here include bifurcation detection experiments that rely on measurements of a single state variable and delay-based phase space reconstruction, as well as an example of tracing entire segments of a codimension-1 bifurcation boundary in two parameter space.Comment: 29 pages, Latex 2.09, 10 figures in encapsulated postscript format (eps), need psfig macro to include them. Submitted to Physica

Study of the stabilization energies of halide-water clusters: An application of first-principles interaction potentials based on a polarizable and flexible model

The aim of this work is to compute the stabilization energy Estab(n) of [ X(H2O)n ]- (X=F, Br, and I for n=1 – 60) clusters from Monte Carlo simulations using first-principles ab initio potentials. Stabilization energy of [ X(H2O)n ]- clusters is defined as the difference between the vertical photodeachment energy of the cluster and the electron affinity of the isolated halide. On one hand, a study about the relation between cluster structure and the Estab(n) value, as well as the dependence of the latter with temperature is performed, on the other hand, a test on the reliability of our recently developed first-principles halide ion-water interaction potentials is carried out. Two different approximations were applied: (1) the Koopmans’ theorem and (2) calculation of the difference between the interaction energy of [ X(H2O)n ]- and [ X(H2O)n ] clusters using the same ab initio interaction potentials. The developed methodology allows for using the same interaction potentials in the case of the ionic and neutral clusters with the proviso that the charge of the halide anion was switched off in the latter. That is, no specific parametrization of the interaction potentials to fit the magnitude under study was done. The good agreement between our predicted Estab(n) and experimental data allows us to validate the first-principles interaction potentials developed elsewhere and used in this study, and supports the fact that this magnitude is mainly determined by electrostatic factors, which can be described by our interaction potentials. No relation between the value of Estab(n) and the structure of clusters has been found. The diversity of Estab(n) values found for different clusters with similar interaction energy indicates the need for statistical information to properly estimate the stabilization energy of the halide anions. The effect of temperature in the prediction of the Estab(n) is not significant as long as it was high enough to avoid cluster trapping into local equilibrium configurations which guarantees an appropriate sampling of the configurational space. Parallel tempering method was applied in particular cases to guarantee satisfactory sampling of clusters at low temperatureDirección General de Investigaciones Científicas y Técnicas BQU2002- 0221

Thermal Bremsstrahlung photons probing the nuclear caloric curve

Hard-photon (E$_{\gamma}>$ 30 MeV) emission from second-chance nucleon-nucleon Bremsstrahlung collisions in intermediate energy heavy-ion reactions is studied employing a realistic thermal model. Photon spectra and yields measured in several nucleus-nucleus reactions are consistent with an emission from hot nuclear systems with temperatures $T\approx$ 4 - 7 MeV. The corresponding caloric curve in the region of excitation energies $\epsilon^\star\approx$ 3{\it A} - 8{\it A} MeV shows lower values of $T$ than those expected for a Fermi fluid.Comment: 13 pages, 3 figures. To appear in Physics Letters

On the halide hydration study: Development of first-principles halide ion-water interaction potential based on a polarizable model

The development of first-principles halide-water interaction potentials for fluoride and iodide anions is presented. The model adopted is the mobile charge densities in harmonic oscillator that allows for a flexible and polarizable character of the interacting particles. The set of points of the quantum mechanical potential energy surfaces are calculated up to the MP2 level. The nonadditive many-body contributions were included explicitly at the three-body terms. Structural and energetic properties of the [ X(H2O)n ]- clusters (n=1 – 6) are studied with the new interaction potentials developed. Halide aqueous solutions are also studied by means of Monte Carlo simulations. The agreement between experimental and our predicted estimations shows the good behavior of the proposed potentials. The developed potentials are able to properly describe both the microsolvation of clusters in gas phase and their hydration in aqueous solutions. The different nature of the interactions among F-, Br-, I- and water appears in the set of studied properties, thus giving a gradual change in the behavior along the group.Dirección General de Investigaciones Científicas y Técnicas BQU2002-0221

"Resonance" phenomena in thermal diffusion processes in two-layer structures

The dependence on chopper frequency of the effective thermal diffusivity and effective thermal conductivity in photoacoustic experiments is discussed. The theoretical model of a two-layer structure at rear-surface illumination in the high frequency limit is considered. It is shown that the effective thermal diffusivity presents ``resonance'' while the effective thermal conductivity sharply changes its magnitude and sign. Such ``resonant'' behavior strongly depends on the surface thermal conductivities associated with the interface thermal contacts.Comment: 13 pages, 3 figure

Coarse Projective kMC Integration: Forward/Reverse Initial and Boundary Value Problems

In "equation-free" multiscale computation a dynamic model is given at a fine, microscopic level; yet we believe that its coarse-grained, macroscopic dynamics can be described by closed equations involving only coarse variables. These variables are typically various low-order moments of the distributions evolved through the microscopic model. We consider the problem of integrating these unavailable equations by acting directly on kinetic Monte Carlo microscopic simulators, thus circumventing their derivation in closed form. In particular, we use projective multi-step integration to solve the coarse initial value problem forward in time as well as backward in time (under certain conditions). Macroscopic trajectories are thus traced back to unstable, source-type, and even sometimes saddle-like stationary points, even though the microscopic simulator only evolves forward in time. We also demonstrate the use of such projective integrators in a shooting boundary value problem formulation for the computation of "coarse limit cycles" of the macroscopic behavior, and the approximation of their stability through estimates of the leading "coarse Floquet multipliers".Comment: Submitted to Journal of Computational Physic