Quasimodularity and large genus limits of Siegel-Veech constants

Quasimodular forms were first studied in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms. We apply this to prove conjectures of Eskin and Zorich on the large genus limits of Masur-Veech volumes and of Siegel-Veech constants. In Part I we connect the geometric definition of Siegel-Veech constants both with a combinatorial counting problem and with intersection numbers on Hurwitz spaces. We introduce modified Siegel-Veech weights whose generating functions will later be shown to be quasimodular. Parts II and III are devoted to the study of the quasimodularity of the generating functions arising from weighted counting of torus coverings. The starting point is the theorem of Bloch and Okounkov saying that q-brackets of shifted symmetric functions are quasimodular forms. In Part II we give an expression for their growth polynomials in terms of Gaussian integrals and use this to obtain a closed formula for the generating series of cumulants that is the basis for studying large genus asymptotics. In Part III we show that the even hook-length moments of partitions are shifted symmetric polynomials and prove a formula for the q-bracket of the product of such a hook-length moment with an arbitrary shifted symmetric polynomial. This formula proves quasimodularity also for the (-2)-nd hook-length moments by extrapolation, and implies the quasimodularity of the Siegel-Veech weighted counting functions. Finally, in Part IV these results are used to give explicit generating functions for the volumes and Siegel-Veech constants in the case of the principal stratum of abelian differentials. To apply these exact formulas to the Eskin-Zorich conjectures we provide a general framework for computing the asymptotics of rapidly divergent power series.Comment: 107 pages, final version, to appear in J. of the AM

Optimization of the extraordinary magnetoresistance in semiconductor-metal hybrid structures for magnetic-field sensor applications

Semiconductor-metal hybrid structures can exhibit a very large geometrical magnetoresistance effect, the so-called extraordinary magnetoresistance (EMR) effect. In this paper, we analyze this effect by means of a model based on the finite element method and compare our results with experimental data. In particular, we investigate the important effect of the contact resistance $\rho_c$ between the semiconductor and the metal on the EMR effect. Introducing a realistic $\rho_c=3.5\times 10^{-7} \Omega{\rm cm}^2$ in our model we find that at room temperature this reduces the EMR by 30% if compared to an analysis where $\rho_c$ is not considered.Comment: 4 pages; manuscript for MSS11 conference 2003, Nara, Japa

A p-multigrid method enhanced with an ILUT smoother and its comparison to h-multigrid methods within Isogeometric Analysis

Over the years, Isogeometric Analysis has shown to be a successful alternative to the Finite Element Method (FEM). However, solving the resulting linear systems of equations efficiently remains a challenging task. In this paper, we consider a p-multigrid method, in which coarsening is applied in the approximation order p instead of the mesh width h. Since the use of classical smoothers (e.g. Gauss-Seidel) results in a p-multigrid method with deteriorating performance for higher values of p, the use of an ILUT smoother is investigated. Numerical results and a spectral analysis indicate that the resulting p-multigrid method exhibits convergence rates independent of h and p. In particular, we compare both coarsening strategies (e.g. coarsening in h or p) adopting both smoothers for a variety of two and threedimensional benchmarks

Nuclear Ground-State Masses and Deformations

We tabulate the atomic mass excesses and nuclear ground-state deformations of 8979 nuclei ranging from $^{16}$O to $A=339$. The calculations are based on the finite-range droplet macroscopic model and the folded-Yukawa single-particle microscopic model. Relative to our 1981 mass table the current results are obtained with an improved macroscopic model, an improved pairing model with a new form for the effective-interaction pairing gap, and minimization of the ground-state energy with respect to additional shape degrees of freedom. The values of only 9 constants are determined directly from a least-squares adjustment to the ground-state masses of 1654 nuclei ranging from $^{16}$O to $^{263}$106 and to 28 fission-barrier heights. The error of the mass model is 0.669~MeV for the entire region of nuclei considered, but is only 0.448~MeV for the region above $N=65$.Comment: 50 pages plus 20 PostScript figures and 160-page table obtainable by anonymous ftp from t2.lanl.gov in directory masses, LA-UR-93-308

Modeling and Analysis Generic Interface for eXternal numerical codes (MAGIX)

The modeling and analysis generic interface for external numerical codes (MAGIX) is a model optimizer developed under the framework of the coherent set of astrophysical tools for spectroscopy (CATS) project. The MAGIX package provides a framework of an easy interface between existing codes and an iterating engine that attempts to minimize deviations of the model results from available observational data, constraining the values of the model parameters and providing corresponding error estimates. Many models (and, in principle, not only astrophysical models) can be plugged into MAGIX to explore their parameter space and find the set of parameter values that best fits observational/experimental data. MAGIX complies with the data structures and reduction tools of ALMA (Atacama Large Millimeter Array), but can be used with other astronomical and with non-astronomical data.Comment: 12 pages, 15 figures, 2 tables, paper is also available at http://www.aanda.org/articles/aa/pdf/forth/aa20063-12.pd

EXAFS study of nickel tetracarbonyl and nickel clusters in zeolite Y

Adsorption and thermal decomposition of Ni(CO)4 in the cage system of zeolite Y have been studied with EXAFS, electron microscopy and IR spectroscopy , Ni(CO)4 is adsorbed as an intact molecule in both cation - free zeolite Y and NaY. Symmetry changes of the molecule in NaY are assigned to the formation of Na—OC-IMi bridges. Thermal treatment of the Ni(CO)4/NaY adduct leads to loss of CO concomitant with the formation of a binodal Ni phase. A major part of the forms clusters with diameter between 0.5 and about 1.5 nm, in addition to larger crystallites (5-30 nm), sticking at the outer surface of the zeolite matrix., The Ni-Ni scattering amplitude indicates increasing average particle size with increasing temperature