Pure adaptive search in global optimization

Pure adaptive seach iteratively constructs a sequence of interior points uniformly distributed within the corresponding sequence of nested improving regions of the feasible space. That is, at any iteration, the next point in the sequence is uniformly distributed over the region of feasible space containing all points that are strictly superior in value to the previous points in the sequence. The complexity of this algorithm is measured by the expected number of iterations required to achieve a given accuracy of solution. We show that for global mathematical programs satisfying the Lipschitz condition, its complexity increases at mostlinearly in the dimension of the problem.This work was supported in part by NATO grant 0119/89.     

The electron current to a Langmuir probe in a flowing high-pressureplasma

The electron current to a Langmuir probe in a moving high-pressure plasma has been measured and analyzed. The plasma is an atmospheric-pressure propane flame, and the probe's speed relative to the plasma was varied from 10 ms^-1 to 30 ms^-1. The current is linearly dependent on the speed and appears to be comprised of two components-one driven by diffusion and the other by convection. A model is devised which can be used to measure the electron density. By comparing the density computed from this model to that measured from the ion current, it has been possible to measure the electron mobility in the flame gases. The value obtained by the authors is in good agreement with theoretical calculations found in the literature     

Underbody and ground effects on rotating disc flow: a global scale inviscid study

The flow induced by a finite disc rotating near horizontal ground is considered, including the effects of an underbody. This paper concentrates on determining the shape of the free layer beyond the rim of the disc which is horizontal in the absence of the underbody and ground but forced to deform to ensure that conditions across the layer are satisfied when the underbody or ground is added. The far-field behaviour, the inviscid flow produced by a nominally infinite disc near the ground and the global solution for small ground clearances are considered analytically, and the full problem is posed as an integral problem. This is then solved numerically and analytically. Results are presented for various heights of the disc above the ground and for discs with an axisymmetric underbody present. A universal form is found for the farfield shape (which is controlled by entrainment into the free layer) but both the underbody and the ground effects are found to increase very significantly for reduced clearances.     

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.     

Predicting the onset of DNA supercoiling using a non-linear hemitropic elastic rod

Elastic rod models provide a means to interpret single molecule DNA experiments as well as predict DNA behavior under physiological conditions. Here we use an elastic rod model to predict the stability boundary (critical torque vs. applied tension) for single molecule DNA experiments in which the molecule is subjected to applied tension and twist. We discuss the shortcomings of the usual isotropic rod model. We then derive a consistent non-linear material law from the general representation for a hemitropic (chiral) rod. Finally, we present results of a standard bifurcation analysis predicting the stability boundary. We find results from the non-linear hemitropic rod to match the data closely.     

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.     

On subgroups of finite index in compact Hausdorff groups

Let G be a compact Hausdorff group and n a positive integer. It is proved that all subnormal subgroups of G of index dividing n are open if and only if there are only finitely many such subgroups, and that all subgroups of finite index in G are open if and only if there are only countably many such subgroups.