Extension of the tridiagonal reduction (FEER) method for complex eigenvalue problems in NASTRAN

As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum were extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order was much lower than that of the full size problem. The reduction process was effected automatically, and thus avoided the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admitted mass, damping, and stiffness matrices which were unrestricted in character, i.e., they might be real, symmetric or nonsymmetric, singular or nonsingular

Analysis of planetary evolution with emphasis on differentiation and dynamics

In order to address the early stages of nebula evolution, a three-dimensional collapse code which includes not only hydrodynamics and radiative transfer, but also the effects of ionization and, possibly, magnetic fields is being addressed. As part of the examination of solar system evolution, an N-body code was developed which describes the latter stages of planet formation from the accretion of planetesimals. To test the code for accuracy and run-time efficiency, and to develop a stronger theoretical foundation, problems were studied in orbital dynamics. A regional analysis of the correlation in the gravity and topography fields of Venus was performed in order to determine the small and intermediate scale subsurface structure

Fitness-dependent topological properties of the World Trade Web

Among the proposed network models, the hidden variable (or good get richer) one is particularly interesting, even if an explicit empirical test of its hypotheses has not yet been performed on a real network. Here we provide the first empirical test of this mechanism on the world trade web, the network defined by the trade relationships between world countries. We find that the power-law distributed gross domestic product can be successfully identified with the hidden variable (or fitness) determining the topology of the world trade web: all previously studied properties up to third-order correlation structure (degree distribution, degree correlations and hierarchy) are found to be in excellent agreement with the predictions of the model. The choice of the connection probability is such that all realizations of the network with the same degree sequence are equiprobable.Comment: 4 Pages, 4 Figures. Final version accepted for publication on Physical Review Letter

Anomalous ordering in inhomogeneously strained materials

We study a continuous quasi-two-dimensional order-disorder phase transition that occurs in a simple model of a material that is inhomogeneously strained due to the presence of dislocation lines. Performing Monte Carlo simulations of different system sizes and using finite size scaling, we measure critical exponents describing the transition of beta=0.18\pm0.02, gamma=1.0\pm0.1, and alpha=0.10\pm0.02. Comparable exponents have been reported in a variety of physical systems. These systems undergo a range of different types of phase transitions, including structural transitions, exciton percolation, and magnetic ordering. In particular, similar exponents have been found to describe the development of magnetic order at the onset of the pseudogap transition in high-temperature superconductors. Their common universal critical exponents suggest that the essential physics of the transition in all of these physical systems is the same as in our model. We argue that the nature of the transition in our model is related to surface transitions, although our model has no free surface.Comment: 5 pages, 3 figure

Percolation and epidemics in a two-dimensional small world

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of "shortcuts" in the small-world network. Our results agree with scaling hypotheses and numerical simulations for the same model.Comment: 7 pages, 3 figures, 2 table

Liquid-liquid transition in supercooled silicon determined by first-principles simulation

First principles molecular dynamics simulations reveal a liquid-liquid phase transition in supercooled elemental silicon. Two phases coexist below $T_c\approx 1232K$. The low density phase is nearly tetra-coordinated, with a pseudogap at the Fermi surface, while the high density phase is more highly coordinated and metallic in nature. The transition is observed through the formation of van der Waals loops in pressure-volume isotherms below $T_c$.Comment: 9 pages 4 figure

Stress analysis of a doubly-curved skin with a flared nozzle port, phase v annual summary report

Computer method for stress and deflection calculation of nozzle flow openings in large pressure vessels

Finite-Size Scaling Critical Behavior of Randomly Pinned Spin-Density Waves

We have performed Monte Carlo studies of the 3D $XY$ model with random uniaxial anisotropy, which is a model for randomly pinned spin-density waves. We study $L \times L \times L$ simple cubic lattices, using $L$ values in the range 16 to 64, and with random anisotropy strengths of $D / 2 J$ = 1, 2, 3, 6 and $\infty$. There is a well-defined finite temperature critical point, $T_c$, for each these values of $D / 2 J$. We present results for the angle-averaged magnetic structure factor, $S (k)$ at $T_c$ for $L = 64$. We also use finite-size scaling analysis to study scaling functions for the critical behavior of the specific heat, the magnetization and the longitudinal magnetic susceptibility. Good data collapse of the scaling functions over a wide range of $T$ is seen for $D / 2 J$ = 6 and $\infty$. For our finite values of $D / 2 J$ the scaled magnetization function increases with $L$ below $T_c$, and appears to approach an $L$-independent limit for large $L$. This suggests that the system is ferromagnetic below $T_c$.Comment: 21 pages in single column format, 20 .eps files, revised and expanded, errors corrected, submitted to PR

Twisting Null Geodesic Congruences, Scri, H-Space and Spin-Angular Momentum

The purpose of this work is to return, with a new observation and rather unconventional point of view, to the study of asymptotically flat solutions of Einstein equations. The essential observation is that from a given asymptotically flat space-time with a given Bondi shear, one can find (by integrating a partial differential equation) a class of asymptotically shear-free (but, in general, twistiing) null geodesic congruences. The class is uniquely given up to the arbitrary choice of a complex analytic world-line in a four-parameter complex space. Surprisingly this parameter space turns out to be the H-space that is associated with the real physical space-time under consideration. The main development in this work is the demonstration of how this complex world-line can be made both unique and also given a physical meaning. More specifically by forcing or requiring a certain term in the asymptotic Weyl tensor to vanish, the world-line is uniquely determined and becomes (by several arguments) identified as the `complex center-of-mass'. Roughly, its imaginary part becomes identified with the intrinsic spin-angular momentum while the real part yields the orbital angular momentum.Comment: 26 pages, authors were relisted alphabeticall

A statistical network analysis of the HIV/AIDS epidemics in Cuba

The Cuban contact-tracing detection system set up in 1986 allowed the reconstruction and analysis of the sexual network underlying the epidemic (5,389 vertices and 4,073 edges, giant component of 2,386 nodes and 3,168 edges), shedding light onto the spread of HIV and the role of contact-tracing. Clustering based on modularity optimization provides a better visualization and understanding of the network, in combination with the study of covariates. The graph has a globally low but heterogeneous density, with clusters of high intraconnectivity but low interconnectivity. Though descriptive, our results pave the way for incorporating structure when studying stochastic SIR epidemics spreading on social networks