Inertia-preserving secant updates

Corrections to the last two equations of Ref. 1 are given.     

Anharmonic effects in large-amplitude vibrations of metal clusters

Two types of extreme collective motion, large-amplitude many-phonon vibration of the ionic core and rotation of the cluster with high angular momenta, are considered. The interplay between vibration and collective motion towards fission is discussed. A new mechanism of formation and rupture of the neck is proposed which is based on the Franck-Condon principle, and accounts for the interplay between vibration and fission. Under rotation, the change of the shape of the cluster and a phase transition from axially symmetric to triaxial ellipsoid are predicted. For studying the effects, vibrational motion can be induced by laser radiation. Rotational motion may arise in collisions of clusters. Received 26 April 2001 and Received in final form 15 October 2001     

Regions of stability of high-power gyrotron oscillators

The problem of mode competition in a high-power gyrotron oscillator is considered. The regions of parameter space in which a preexisting large-amplitude mode is able to suppress competing satellites are determined for cases in which the coupling coefficients and cavity quality factors for the operating and satellite modes are different. In addition, the effect of beam quality on the regimes of stable single-mode operation is investigated. Generally speaking, the requirement of stable operation favors devices whose interaction length measured by the parameter μ is not too large. It is found that for μ near 10 the operation is relatively stable and μ near 17 is not     

Lattices contained in planar orders are planar

The covering graph of a lattice which is contained in an ordered set with a planar covering graph is itself planar.Presented by R. W. Quackenbush.     

Local solution for the Kadomtsev-Petviashvili equation with periodic conditions

In this article we prove a local existence and uniqueness theorem for the Kadomtsev-Petviashvili Equation (u _t +u _xxx +uu _x ) _x −u _yy =0) in the Sobolev spaces of orders≥3, with initial values in the same spaces, and periodic boundary conditions. This theorem improves previous results based upon the application of singular perturbation techniques.     

The semiclassical limit of a quantum Fermi accelerator

A classical Fermi accelerator model (FAM) is known to show chaotic behavior. The FAM is defined by a free particle bouncing elastically from two rigid walls, one fixed and the other oscillating periodically in time. The central aim of this paper is to connect the quantum and the classical solutions to the FAM in the semiclassical limit. This goal is accomplished using a finite inverted parametric oscillator (FIPO), confined to a box withfixed walls, as an alternative representation of the FAM. In the FIPO representation, an explicit correspondence between classical and quantum limits is accomplished using a Husimi representation of the quasienergy eigenfunctions.     

Sol-Gel Particulate Float Process to Make Vitreous Silica Bodies

Particulate sol-gel technology uses larger particles than that of alkoxide-derived gels and provides larger pore sizes in the gelled object. This allows relatively rapid drying and fabrication of large rods or tubular shapes. However, the formation of more complex or flat shapes, which require extensive surface contact with a mold, is more difficult. The shrinkage during drying, with the significantly greater stress of surface friction due to adhesion, frequently leads to cracking.We have demonstrated a solution to this problem by floating the gel on the surface of a dense liquid. Dry silica panels up to 28 × 40 × 0.7 cm³ were prepared in this way. The use of patterning molds allowed the fabrication of more sophisticated shapes. These bodies were sintered to transparent vitreous silica articles of near net dimensions.     

Point-to-Periodic and Periodic-to-Periodic Connections

In this work we consider computing and continuing connecting orbits in parameter dependent dynamical systems. We give details of algorithms for computing connections between equilibria and periodic orbits, and between periodic orbits. The theoretical foundation for these techniques is given by the seminal work of Beyn in 1994, “On well-posed problems for connecting orbits in dynamical systems”, where a numerical technique is also proposed. Our algorithms consist of splitting the computation of the connection from that of the periodic orbit(s). To set up appropriate boundary conditions, we follow the algorithmic approach used by Demmel, Dieci, and Friedman, for the case of connecting orbits between equilibria, and we construct and exploit the smooth block Schur decomposition of the monodromy matrices associated to the periodic orbits. Numerical examples illustrate the performance of the algorithms. This revised version was published online in July 2006 with corrections to the Cover Date.     

Quantum Nonlocality of Photon Pairs in Interference in a Mach-Zehnder Interferometer

Nonlocal character of entangled photon pairs generated in spontaneous parametric downconversion is demonstrated. One photon from a pair propagates through a Mach-Zehnder interferometer and is detected in coincidence-count measurement with its twin. Width of the coincidence-count interference pattern (measured for various values of path difference in the Mach-Zehnder interferometer) depends on spectral width of the twin as a result of entanglement of photons in a pair. The experimental setup is analyzed for a Gaussian spectral filter and a Fabry-Perot resonator. It is shown that nonlocal interference is much stronger for cw pumping in comparison with femtosecond pulsed pumping for values of parameters commonly used in spontaneous parametric downconversion experiments.     

An Approach to Fuzzy Noncooperative Nash Games

Systems that involve more than one decision maker are often optimized using the theory of games. In the traditional game theory, it is assumed that each player has a well-defined quantitative utility function over a set of the player decision space. Each player attempts to maximize/minimize his/her own expected utility and each is assumed to know the extensive game in full. At present, it cannot be claimed that the first assumption has been shown to be true in a wide variety of situations involving complex problems in economics, engineering, social and political sciences due to the difficulty inherent in defining an adequate utility function for each player in these types of problems. On the other hand, in many of such complex problems, each player has a heuristic knowledge of the desires of the other players and a heuristic knowledge of the control choices that they will make in order to meet their ends.In this paper, we utilize fuzzy set theory in order to incorporate the players' heuristic knowledge of decision making into the framework of conventional game theory or ordinal game theory. We define a new approach to N-person static fuzzy noncooperative games and develop a solution concept such as Nash for these types of games. We show that this general formulation of fuzzy noncooperative games can be applied to solve multidecision-making problems where no objective function is specified. The computational procedure is illustrated via application to a multiagent optimization problem dealing with the design and operation of future military operations.