A multistage linear array assignment problem

The implementation of certain algorithms on parallel processing computing architectures can involve partitioning contiguous elements into a fixed number of groups, each of which is to be handled by a single processor. It is desired to find an assignment of elements to processors that minimizes the sum of the maximum workloads experienced at each stage. This problem can be viewed as a multi-objective network optimization problem. Polynomially-bounded algorithms are developed for the case of two stages, whereas the associated decision problem (for an arbitrary number of stages) is shown to be NP-complete. Heuristic procedures are therefore proposed and analyzed for the general problem. Computational experience with one of the exact problems, incorporating certain pruning rules, is presented with one of the exact problems. Empirical results also demonstrate that one of the heuristic procedures is especially effective in practice

Aerospace applications on integer and combinatorial optimization

Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem. for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables

Multi-domain active sound control and noise shielding

This paper describes an active sound control methodology based on difference potentials. The main feature of this methodology is its ability to automatically preserve “wanted” sound within a domain while canceling “unwanted” noise from outside the domain. This method of preservation of the wanted sounds by active shielding control is demonstrated with various broadband and realistic sound sources such as human voice and music in multiple domains in a one-dimensional enclosure. Unlike many other conventional active control methods, the proposed approach does not require the explicit characterization of the wanted sound to be preserved. The controls are designed based on the measurements of the total field on the boundaries of the shielded domain only, which is allowed to be multiply connected. The method is tested in a variety of experimental cases. The typical attenuation of the unwanted noise is found to be about 20 dB over a large area of the shielded domain and the original wanted sound field is preserved with errors of around 1 dB and below through a broad frequency range up to 1 kHz. © 2011 Acoustical Society of Americ

Phase transitions in social sciences: two-populations mean field theory

A new mean field statistical mechanics model of two interacting groups of spins is introduced and the phase transition studied in terms of their relative size. A jump of the average magnetization is found for large values of the mutual interaction when the relative percentage of the two populations crosses a critical threshold. It is shown how the critical percentage depends on internal interactions and on the initial magnetizations. The model is interpreted as a prototype of resident-immigrant cultural interaction and conclusions from the social sciences perspectives are drawn

Studies on optimizing potential energy functions for maximal intrinsic hyperpolarizability

We use numerical optimization to study the properties of (1) the class of one-dimensional potential energy functions and (2) systems of point charges in two-dimensions that yield the largest hyperpolarizabilities, which we find to be within 30% of the fundamental limit. We investigate the character of the potential energy functions and resulting wavefunctions and find that a broad range of potentials yield the same intrinsic hyperpolarizability ceiling of 0.709.Comment: 9 pages, 9 figure

Stable Propagation of a Burst Through a One-Dimensional Homogeneous Excitatory Chain Model of Songbird Nucleus HVC

We demonstrate numerically that a brief burst consisting of two to six spikes can propagate in a stable manner through a one-dimensional homogeneous feedforward chain of non-bursting neurons with excitatory synaptic connections. Our results are obtained for two kinds of neuronal models, leaky integrate-and-fire (LIF) neurons and Hodgkin-Huxley (HH) neurons with five conductances. Over a range of parameters such as the maximum synaptic conductance, both kinds of chains are found to have multiple attractors of propagating bursts, with each attractor being distinguished by the number of spikes and total duration of the propagating burst. These results make plausible the hypothesis that sparse precisely-timed sequential bursts observed in projection neurons of nucleus HVC of a singing zebra finch are intrinsic and causally related.Comment: 13 pages, 6 figure

Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly

We investigate the phase behavior of a single-component system in 3 dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an intermediate distance, and a hard-core repulsion at a short distance, similar to potentials used to describe liquid systems such as colloids, protein solutions, or liquid metals. We showed [Nature {\bf 409}, 692 (2001)] that, even with no evidences of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gas--low-density liquid (LDL) critical point, and the other in a gas--high-density liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the 3-parameter space of the soft-core potential and we perform molecular dynamics simulations in the interesting region of parameters. For the equilibrium phase diagram we analyze the structure of the crystal phase and find that, within the considered range of densities, the structure is independent of the density. Then, we analyze in detail the fluid metastable phases and, by explicit thermodynamic calculation in the supercooled phase, we show the absence of the density anomaly. We suggest that this absence is related to the presence of only one stable crystal structure.Comment: 15 pages, 21 figure

Folding transitions of the triangular lattice with defects

A recently introduced model describing the folding of the triangular lattice is generalized allowing for defects in the lattice and written as an Ising model with nearest-neighbor and plaquette interactions on the honeycomb lattice. Its phase diagram is determined in the hexagon approximation of the cluster variation method and the crossover from the pure Ising to the pure folding model is investigated, obtaining a quite rich structure with several multicritical points. Our results are in very good agreement with the available exact ones and extend a previous transfer matrix study.Comment: 16 pages, latex, 5 postscript figure