Periodic orbits contribution to the 2-point correlation form factor for pseudo-integrable systems

The 2-point correlation form factor, $K_2(\tau)$, for small values of $\tau$ is computed analytically for typical examples of pseudo-integrable systems. This is done by explicit calculation of periodic orbit contributions in the diagonal approximation. The following cases are considered: (i) plane billiards in the form of right triangles with one angle $\pi/n$ and (ii) rectangular billiards with the Aharonov-Bohm flux line. In the first model, using the properties of the Veech structure, it is shown that $K_2(0)=(n+\epsilon(n))/(3(n-2))$ where $\epsilon(n)=0$ for odd $n$, $\epsilon(n)=2$ for even $n$ not divisible by 3, and $\epsilon(n)=6$ for even $n$ divisible by 3. For completeness we also recall informally the main features of the Veech construction. In the second model the answer depends on arithmetical properties of ratios of flux line coordinates to the corresponding sides of the rectangle. When these ratios are non-commensurable irrational numbers, $K_2(0)=1-3\bar{\alpha}+4\bar{\alpha}^2$ where $\bar{\alpha}$ is the fractional part of the flux through the rectangle when $0\le \bar{\alpha}\le 1/2$ and it is symmetric with respect to the line $\bar{\alpha}=1/2$ when $1/2 \le \bar{\alpha}\le 1$. The comparison of these results with numerical calculations of the form factor is discussed in detail. The above values of $K_2(0)$ differ from all known examples of spectral statistics, thus confirming analytically the peculiarities of statistical properties of the energy levels in pseudo-integrable systems.Comment: 61 pages, 13 figures. Submitted to Communications in Mathematical Physics, 200

Dual methods and approximation concepts in structural synthesis

Approximation concepts and dual method algorithms are combined to create a method for minimum weight design of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of separable form. These problems are solved by constructing explicit dual functions, which are maximized subject to nonnegativity constraints on the dual variables. It is shown that the joining together of approximation concepts and dual methods can be viewed as a generalized optimality criteria approach. The dual method is successfully extended to deal with pure discrete and mixed continuous-discrete design variable problems. The power of the method presented is illustrated with numerical results for example problems, including a metallic swept wing and a thin delta wing with fiber composite skins

ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included

SPECTRAL PROPERTIES OF BILLIARDS AND QUANTUM CHAOS

The first 800 eigenvalues of the stadium billiard have been evaluated numerically. It is shown that the four spectra obtained (corresponding to the four types of symmetry of the wave function) exhibit the fluctuation properties of the Gaussian Orthogonal Ensemble of Random Matrices. This reinforces the belief that these fluctuation properties are characteristic of quantum chaotic systems

Random matrix ensembles associated with Lax matrices

A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an integrable structure permits to calculate the joint distribution of eigenvalues for these matrices analytically. Spectral statistics of these ensembles are quite unusual and in many cases give rigorously new examples of intermediate statistics

Neurospora Bibliography - 1993

Neurospora Bibliography - 1993 - Every attempt has been made to insure that the citations appear exactly as they do in the original publication

1995 Neurospora bibliography

Every attempt has been made to insure that the citations appear exactly as they do in the original publication. Entries for which the original could not be obtained for verification are indicated by (-). Copies of the bibliography are available on computer discs (please indicate format needed) or by E mail. It can also be read/obtained from the FGSC WWW site