Energy current magnification in coupled oscillator loops

Motivated by studies on current magnification in quantum mesoscopic systems we consider sound and heat transmission in classical models of oscillator chains. A loop of coupled oscillators is connected to two leads through which one can either transmit monochromatic waves or white noise signal from heat baths. We look for the possibility of current magnification in this system due to some asymmetry introduced between the two arms in the loop. We find that current magnification is indeed obtained for particular frequency ranges. However the integrated current shows the effect only in the presence of a pinning potential for the atoms in the leads. We also study the effect of anharmonicity on current magnification.Comment: 5 pages, 5 figure

Spanning trees short or small

We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is the $k$MST problem in which we require a tree of minimum weight spanning at least $k$ nodes in an edge-weighted graph. We show that the $k$MST problem is NP-hard even for points in the Euclidean plane. We provide approximation algorithms with performance ratio $2\sqrt{k}$ for the general edge-weighted case and $O(k^{1/4})$ for the case of points in the plane. Polynomial-time exact solutions are also presented for the class of decomposable graphs which includes trees, series-parallel graphs, and bounded bandwidth graphs, and for points on the boundary of a convex region in the Euclidean plane. We also investigate the problem of finding short trees, and more generally, that of finding networks with minimum diameter. A simple technique is used to provide a polynomial-time solution for finding $k$-trees of minimum diameter. We identify easy and hard problems arising in finding short networks using a framework due to T. C. Hu.Comment: 27 page

Bicriteria Network Design Problems

We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a <subgraph \from a given subgraph-class that minimizes the second objective subject to the budget on the first. We consider three different criteria - the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same %(note that the cost functions continue to be different) we present a ``black box'' parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs we use a cluster-based approach to devise a approximation algorithms --- the solutions output violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. We show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur

DESIGN SIMULATION & IMPLEMENTATION OF FOUR QUADRANT OPERATION OF DC DRIVE

Use of microcontroller based system has given flexibility for implementation of closed loop operation, to get variable speed of DC motor irrespective of supply fluctuation and load variation by incrementing or decrementing firing angle for dual convertor. In dual converters with non circulating current, only one converter operates at a time and another converter is temporarily blocked from conducting by withdrawing firing pulses to the Thyristors. Since only one converter operates at a time no reactors are required between the converters. The paper includes details on design of zero crossing detectors to detect zero crossing instant of A.C. input to converters to determine firing angle, control circuit is designed to read some input parameters like 8-bit digitized set speed and actual speed from taco generator, use of two double pole switch to read direction and acceleration. Current limiting circuit using Hall effect IC to detect threshold voltage level corresponding to desire current limit to provide over load protection. Software development in assembly language for 89s51 microcontroller to provide real time control

Stochastic pump of interacting particles

We consider the overdamped motion of Brownian particles, interacting via particle exclusion, in an external potential that varies with time and space. We show that periodic potentials that maintain specific position-dependent phase relations generate time-averaged directed current of particles. We obtain analytic results for a lattice version of the model using a recently developed perturbative approach. Many interesting features like particle-hole symmetry, current reversal with changing density, and system-size dependence of current are obtained. We propose possible experiments to test our predictions.Comment: 4 pages, 2 figure

Adversarial Scheduling Analysis of Game Theoretic Models of Norm Diffusion

In (Istrate, Marathe, Ravi SODA 2001) we advocated the investigation of robustness of results in the theory of learning in games under adversarial scheduling models. We provide evidence that such an analysis is feasible and can lead to nontrivial results by investigating, in an adversarial scheduling setting, Peyton Young's model of diffusion of norms. In particular, our main result incorporates into Peyton Young's model