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

Galactic civilizations: Population dynamics and interstellar diffusion

The interstellar diffusion of galactic civilizations is reexamined by potential theory; both numerical and analytical solutions are derived for the nonlinear partial differential equations which specify a range of relevant models, drawn from blast wave physics, soil science, and, especially, population biology. An essential feature of these models is that, for all civilizations, population growth must be limited by the carrying capacity of the environment. Dispersal is fundamentally a diffusion process; a density-dependent diffusivity describes interstellar emigration. Two models are considered: the first describing zero population growth (ZPG), and the second which also includes local growth and saturation of a planetary population, and for which an asymptotic traveling wave solution is found

Limb-darkening and the structure of the Jovian atmosphere

By observing the transit of various cloud features across the Jovian disk, limb-darkening curves were constructed for three regions in the 4.6 to 5.1 mu cm band. Several models currently employed in describing the radiative or dynamical properties of planetary atmospheres are here examined to understand their implications for limb-darkening. The statistical problem of fitting these models to the observed data is reviewed and methods for applying multiple regression analysis are discussed. Analysis of variance techniques are introduced to test the viability of a given physical process as a cause of the observed limb-darkening

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

Quantum Property Testing

A language L has a property tester if there exists a probabilistic algorithm that given an input x only asks a small number of bits of x and distinguishes the cases as to whether x is in L and x has large Hamming distance from all y in L. We define a similar notion of quantum property testing and show that there exist languages with quantum property testers but no good classical testers. We also show there exist languages which require a large number of queries even for quantumly testing

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

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

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