A relation between moduli space of D-branes on orbifolds and Ising model

We study D-branes transverse to an abelian orbifold C^3/Z_n Z_n. The moduli space of the gauge theory on the D-branes is analyzed by combinatorial calculation based on toric geometry. It is shown that the calculation is related to a problemto count the number of ground states of an antiferromagnetic Ising model. The lattice on which the Ising model is defined is a triangular one defined on the McKay quiver of the orbifold.Comment: 20 pages, 13 figure

Simulation of an 1857-like Mw 7.9 San Andreas Fault Earthquake and the Response of Tall Steel Moment Frame Buildings in Southern California – A Prototype Study

In 1857, an earthquake of magnitude 7.9 occurred on the San Andreas fault, starting at Parkfield and rupturing in a southeasterly direction for more than 360 km. Such a unilateral rupture produces significant directivity toward the San Fernando and Los Angeles basins. The strong shaking in the basins due to this earthquake would have had significant long-period content (2-8 s), and the objective of this study is to quantify the impact of such an earthquake on two 18-story steel moment frame building models, hypothetically located at 636 sites on a 3.5 km grid in southern California. End-to-end simulations include modeling the source and rupture of a fault at one end, numerically propagating the seismic waves through the earth structure, simulating the damage to engineered structures and estimating the economic impact at the other end using high-performance computing. In this prototype study, we use an inferred finite source model of the magnitude 7.9, 2002 Denali fault earthquake in Alaska, and map it onto the San Andreas fault with the rupture originating at Parkfield and propagating southward over a distance of 290 km. Using the spectral element seismic wave propagation code, SPECFEM3D, we simulate an 1857-like earthquake on the San Andreas fault and compute ground motions at the 636 analysis sites. Using the nonlinear structural analysis program, FRAME3D, we subsequently analyze 3-D structural models of an existing tall steel building designed using the 1982 Uniform Building Code (UBC), as well as one designed according to the 1997 UBC, subjected to the computed ground motion at each of these sites. We summarize the performance of these structural models on contour maps of peak interstory drift. We then perform an economic loss analysis for the two buildings at each site, using the Matlab Damage and Loss Analysis (MDLA) toolbox developed to implement the PEER loss-estimation methodology. The toolbox includes damage prediction and repair cost estimation for structural and non-structural components and allows for the computation of the mean and variance of building repair costs conditional on engineering demand parameters (i.e. inter-story drift ratios and peak floor accelerations). Here, we modify it to treat steel-frame high-rises, including aspects such as mechanical, electrical and plumbing systems, traction elevators, and the possibility of irreparable structural damage. We then generate contour plots of conditional mean losses for the San Fernando and the Los Angeles basins for the pre-Northridge and modern code-designed buildings, allowing for comparison of the economic effects of the updated code for the scenario event. In principle, by simulating multiple seismic events, consistent with the probabilistic seismic hazard for a building site, the same basic approach could be used to quantify the uncertain losses from future earthquakes

Stepwise Projection: Toward Brane Setups for Generic Orbifold Singularities

The construction of brane setups for the exceptional series E6,E7,E8 of SU(2) orbifolds remains an ever-haunting conundrum. Motivated by techniques in some works by Muto on non-Abelian SU(3) orbifolds, we here provide an algorithmic outlook, a method which we call stepwise projection, that may shed some light on this puzzle. We exemplify this method, consisting of transformation rules for obtaining complex quivers and brane setups from more elementary ones, to the cases of the D-series and E6 finite subgroups of SU(2). Furthermore, we demonstrate the generality of the stepwise procedure by appealing to Frobenius' theory of Induced Representations. Our algorithm suggests the existence of generalisations of the orientifold plane in string theory.Comment: 22 pages, 3 figure

Weak Interaction Rates Of sd-Shell Nuclei In Stellar Environment Calculated in the Proton-Neutron Quasiparticle Random Phase Approximation

Allowed weak interaction rates for sd-shell nuclei in stellar environment are calculated using a generalized form of proton-neutron quasiparticle RPA model with separable Gamow-Teller forces. Twelve different weak rates are calculated for each nucleus as a function of temperature and density. This project consists of calculation of weak rates for a total of 709 nuclei with masses ranging from A = 18 to 100. This paper contains calculated weak rates for sd-shell nuclei. The calculated capture and decay rates take into consideration the latest experimental energy levels and ft value compilations. The results are also compared with earlier works. Particle emission processes from excited states, previously ignored, are taken into account, and are found to significantly affect some beta decay rates.Comment: 64 pages, 17 figures, rate tables are presented in an abbreviated form to save space. Complete rate tables can be seen in the original pape

Shell Model Study of the Double Beta Decays of 76^{76}Ge, 82^{82}Se and 136^{136}Xe

The lifetimes for the double beta decays of $^{76}$Ge, $^{82}$Se and $^{136}$Xe are calculated using very large shell model spaces. The two neutrino matrix elements obtained are in good agreement with the present experimental data. For $<1$ eV we predict the following upper bounds to the half-lives for the neutrinoless mode: $T^{(0\nu)}_{1/2}(Ge) > 1.85\,10^{25} yr.$, $T^{(0\nu)}_{1/2}(Se) > 2.36\,10^{24} yr.$ and $T^{(0\nu)}_{1/2}(Xe) > 1.21\,10^{25} yr$. These results are the first from a new generation of Shell Model calculations reaching O(10$^{8}$) dimensions

A deformed QRPA formalism for single and two-neutrino double beta decay

We use a deformed QRPA formalism to describe simultaneously the energy distributions of the single beta Gamow-Teller strength and the two-neutrino double beta decay matrix elements. Calculations are performed in a series of double beta decay partners with A = 48, 76, 82, 96, 100, 116, 128, 130, 136 and 150, using deformed Woods-Saxon potentials and deformed Skyrme Hartree-Fock mean fields. The formalism includes a quasiparticle deformed basis and residual spin-isospin forces in the particle-hole and particle-particle channels. We discuss the sensitivity of the parent and daughter Gamow-Teller strength distributions in single beta decay, as well as the sensitivity of the double beta decay matrix elements to the deformed mean field and to the residual interactions. Nuclear deformation is found to be a mechanism of suppression of the two-neutrino double beta decay. The double beta decay matrix elements are found to have maximum values for about equal deformations of parent and daughter nuclei. They decrease rapidly when differences in deformations increase. We remark the importance of a proper simultaneous description of both double beta decay and single Gamow-Teller strength distributions. Finally, we conclude that for further progress in the field it would be useful to improve and complete the experimental information on the studied Gamow-Teller strengths and nuclear deformations.Comment: 33 pages, 19 figures. To be published in Phys. Rev.

Phase transitions in systems with two species of molecular motors

Systems with two species of active molecular motors moving on (cytoskeletal) filaments into opposite directions are studied theoretically using driven lattice gas models. The motors can unbind from and rebind to the filaments. Two motors are more likely to bind on adjacent filament sites if they belong to the same species. These systems exhibit (i) Continuous phase transitions towards states with spontaneously broken symmetry, where one motor species is largely excluded from the filament, (ii) Hysteresis of the total current upon varying the relative concentrations of the two motor species, and (iii) Coexistence of traffic lanes with opposite directionality in multi-filament systems. These theoretical predictions should be experimentally accessible.Comment: 7 pages, 4 figures, epl style (.cls-file included), to appear in Europhys. Lett. (http://www.edpsciences.org/epl

Kaon Condensation in Neutron Star Matter with Hyperons

Based on the Kaplan-Nelson Lagrangian, we investigate kaon condensation in dense neutron star matter allowing for the explicit presence of hyperons. Using various models we find that the condensate threshold is sensitive to the behavior of the scalar density; the more rapidly it increases with baryon density, the lower is the threshold for condensation. The presence of hyperons, particularly the $\Sigma^-$, shifts the threshold for $K^-$ condensation to a higher density. In the mean field approach, with hyperons, the condensate amplitude grows sufficiently rapidly that the nucleon effective mass vanishes at a finite density and a satisfactory treatment of the thermodynamics cannot be achieved. Thus, calculations of kaon-baryon interactions beyond the mean field level appear to be necessary.Comment: 13 pages, latex, 3 figures by fax/mail from [email protected]

Neutrino Opacities in Neutron Stars with Kaon Condensates

The neutrino mean free paths in hot neutron-star matter are obtained in the presence of kaon condensates. The kaon-induced neutrino absorption process, which is allowed only in the presence of kaon condensates, is considered for both nondegenerate and degenerate neutrinos. The neutrino mean free path due to this process is compared with that for the neutrino-nucleon scattering. While the mean free path for the kaon-induced neutrino absorption process is shown to be shorter than the ordinary two-nucleon absorption process by several orders of magnitude when temperature is not very high, the neutrino-nucleon scattering process has still a dominant contribution to the neutrino opacity. Thus, the kaon-induced neutrino absorption process has a minor effect on the thermal and dynamical evolution of protoneutron stars.Comment: 35 pages, 4 figure

Single- and double-beta decay Fermi-transitions in an exactly solvable model

An exactly solvable model suitable for the description of single and double-beta decay processes of the Fermi-type is introduced. The model is equivalent to the exact shell-model treatment of protons and neutrons in a single j-shell. Exact eigenvalues and eigenvectors are compared to those corresponding to the hamiltonian in the quasiparticle basis (qp) and with the results of both the standard quasiparticle random phase approximation (QRPA) and the renormalized one (RQRPA). The role of the scattering term of the quasiparticle hamiltonian is analyzed. The presence of an exact eigenstate with zero energy is shown to be related to the collapse of the QRPA. The RQRPA and the qp solutions do not include this zero-energy eigenvalue in their spectra, probably due to spurious correlations. The meaning of this result in terms of symmetries is presented.Comment: 29 pages, 9 figures included in a Postsript file. Submitted to Physcal Review