Solution of nonlinear algebraic equations characteristic of filter circuits Summary technical report

Digital computer program developed for solving nonlinear algebraic equations characteristic of filter circuit

Optical links in the angle-data assembly of the 70-meter antennas

In the precision-pointing mode the 70 meter antennas utilize an optical link provided by an autocollimator. In an effort to improve reliability and performance, commercial instruments were evaluated as replacement candidates, and upgraded versions of the existing instruments were designed and tested. The latter were selected for the Neptune encounter, but commercial instruments with digital output show promise of significant performance improvement for the post-encounter period

Partially Unbiased Entangled Bases

In this contribution we group the operator basis for d^2 dimensional Hilbert space in a way that enables us to relate bases of entangled states with single particle mutually unbiased state bases (MUB), each in dimensionality d. We utilize these sets of operators to show that an arbitrary density matrix for this d^2 dimensional Hilbert space system is analyzed by via d^2+d+1 measurements, d^2-d of which involve those entangled states that we associate with MUB of the d-dimensional single particle constituents. The number $d^2+d+1$ lies in the middle of the number of measurements needed for bipartite state reconstruction with two-particle MUB (d^2+1) and those needed by single-particle MUB [(d^2+1)^2].Comment: 5 page

A general low frequency acoustic radiation capability for NASTRAN

A new capability called NASHUA is described for calculating the radiated acoustic sound pressure field exterior to a harmonically-excited arbitrary submerged 3-D elastic structure. The surface fluid pressures and velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior fluid. After the fluid impedance is calculated, most of the required matrix operations are performed using the general matrix manipulation package (DMAP) available in NASTRAN. Far field radiated pressures are then calculated from the surface solution using the Helmholtz exterior integral equation. Other output quantities include the maximum sound pressure levels in each of the three coordinate planes, the rms and average surface pressures and normal velocities, the total radiated power and the radiation efficiency. The overall approach is illustrated and validated using known analytic solutions for submerged spherical shells subjected to both uniform and nonuniform applied loads

Noninteracting Fermions in infinite dimensions

Usually, we study the statistical behaviours of noninteracting Fermions in finite (mainly two and three) dimensions. For a fixed number of fermions, the average energy per fermion is calculated in two and in three dimensions and it becomes equal to 50 and 60 per cent of the fermi energy respectively. However, in the higher dimensions this percentage increases as the dimensionality increases and in infinite dimensions it becomes 100 per cent. This is an intersting result, at least pedagogically. Which implies all fermions are moving with Fermi momentum. This result is not yet discussed in standard text books of quantum statistics. In this paper, this fact is discussed and explained. I hope, this article will be helpful for graduate students to study the behaviours of free fermions in generalised dimensionality.Comment: To appear in European Journal of Physics (2010

Some remarks on the visible points of a lattice

We comment on the set of visible points of a lattice and its Fourier transform, thus continuing and generalizing previous work by Schroeder and Mosseri. A closed formula in terms of Dirichlet series is obtained for the Bragg part of the Fourier transform. We compare this calculation with the outcome of an optical Fourier transform of the visible points of the 2D square lattice.Comment: 9 pages, 3 eps-figures, 1 jpeg-figure; updated version; another article (by M. Baake, R. V. Moody and P. A. B. Pleasants) with the complete solution of the spectral problem will follow soon (see math.MG/9906132

Multifractal eigenstates of quantum chaos and the Thue-Morse sequence

We analyze certain eigenstates of the quantum baker's map and demonstrate, using the Walsh-Hadamard transform, the emergence of the ubiquitous Thue-Morse sequence, a simple sequence that is at the border between quasi-periodicity and chaos, and hence is a good paradigm for quantum chaotic states. We show a family of states that are also simply related to Thue-Morse sequence, and are strongly scarred by short periodic orbits and their homoclinic excursions. We give approximate expressions for these states and provide evidence that these and other generic states are multifractal.Comment: Substantially modified from the original, worth a second download. To appear in Phys. Rev. E as a Rapid Communicatio