A Computationally Efficient Generalized Poisson Solution for Independent Double-Gate Transistors

Previous techniques used for solving the 1-D Poisson equation ( PE) rigorously for long-channel asymmetric and independent double-gate (IDG) transistors result in potential models that involve multiple intercoupled implicit equations. As these equations need to be solved self-consistently, such potential models are clearly inefficient for compact modeling. This paper reports a different rigorous technique for solving the same PE by which one can obtain the potential profile of a generalized IDG transistor that involves a single implicit equation. The proposed Poisson solution is shown to be computationally more efficient for circuit simulation than the previous solutions.

Four-dimensional current algebra from Chern-Simons theory

We study an abelian Chern-Simons theory on a five-dimensional manifold with boundary. We find it to be equivalent to a higher-derivative generalization of the abelian Wess-Zumino-Witten model on the boundary. It contains a U(1) current algebra with an operational extension.

A generalized Linear Programming based approach to optimal divisible load scheduling

In this paper we propose a general Linear Programming (LP) based formulation and solution methodology for obtaining optimal solution to the load distribution problem in divisible load scheduling. We exploit the power of the versatile LP formulation to propose algorithms that yield exact solutions to several very general load distribution problems for which either no solutions or only heuristic solutions were available. We consider both star (single-level tree) networks and linear daisy chain networks, having processors equipped with front-ends, that form the generic models for several important network topologies. We consider arbitrary processing node availability or release times and general models for communication delays and computation time that account for constant overheads such as start up times in communication and computation. The optimality of the LP based algorithms is proved rigorously.

On the generalized continuum model of dipolar solvation dynamics

The continuum model of dipolar solvation dynamics is reviewed. The effects of non-spherical molecular shapes, of non-Debye dielectric relaxation of the polar solvent and of dielectric inhomogeneity of the solvent around the solute dipole are investigated. Several new theoretical results are presented. It is found that our generalized continuum model, which takes into account the dielectric inhomogeneity of the surrounding solvent, provides a description of solvation dynamics consistent with recent experimental results.

Generalized asymptotic expansions for coupled wavenumbers in fluid-filled cylindrical shells

Analytical expressions are found for the coupled wavenumbers in an infinite fluid-filled cylindrical shell using the asymptotic methods. These expressions are valid for any general circumferential order (n).The shallow shell theory (which is more accurate at higher frequencies)is used to model the cylinder. Initially, the in vacua shell is dealt with and asymptotic expressions are derived for the shell wavenumbers in the high-and the low-frequency regimes. Next, the fluid-filled shell is considered. Defining a relevant fluid-loading parameter p, we find solutions for the limiting cases of small and large p. Wherever relevant, a frequency scaling parameter along with some ingenuity is used to arrive at an elegant asymptotic expression. In all cases.Poisson's ratio v is used as an expansion variable. The asymptotic results are compared with numerical solutions of the dispersion equation and the dispersion relation obtained by using the more general Donnell-Mushtari shell theory (in vacuo and fluid-filled). A good match is obtained. Hence, the contribution of this work lies in the extension of the existing literature to include arbitrary circumferential orders(n). (C) 2010 Elsevier Ltd. All rights reserved.

Generalized Burgers equations and Euler–Painlevé transcendents. III

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986); P. L. Sachdev and K. R. C. Nair, ibid. 28, 977 (1987)] that the Euler–Painlevé equations  y(d2y/dη2)+a(dy/dη)2 +f(η)y(dy/dη)+g(η)y2+b(dy/dη) +c=0 represent generalized Burgers equations (GBE’s) in the same way as Painlevé equations represent the Korteweg–de Vries type of equations. The earlier studies were carried out in the context of GBE’s with damping and those with spherical and cylindrical symmetry. In the present paper, GBE’s with variable coefficients of viscosity and those with inhomogeneous terms are considered for their possible connection to Euler–Painlevé equations. It is found that the Euler–Painlevé equation, which represents the GBE ut+uβux=(δ/2)g(t)uxx, g(t)=(1+t)n, β>0, has solutions, which either decay or oscillate at η=±∞, only when −1

Generalized Equation for Compression Ratio

For highly compressible normally consolidated saturated soil the compression index, Cc, is not constant over the entire pressure range. However, the ratio of the compression index and the initial specific volume, generally known as the compression ratio, appears to be constant. Thus settlement seems to depend on Cc/(1 + e) rather than Cc alone. Using the theoretical zero air voids line and the generalized compressibility equation for normally consolidated saturated soils, a generalized and simple equation for compression has been derived in the form: C'c = 0.003wL.

Noise minimization in RC-active filters using generalized impedance converters

A procedure has been given for minimizing the total output noise of a Generalized Impedance Converter (GIC), subject to constraints dictated by signal handling capability of the Operational Amplifiers and ease of microcircuit fabrication. The noise reduction is achieved only by the adjustment of RC elements of the GIC, and the total output noise after optimization in the example cited is close to the theoretical lower limit. The output noise of a higher-order filter can be reduced by RC-optimizing the individual GIC's of the active realization. Experimental results on a 20–24 kHz channel bank band-pass filter demonstrate the effectiveness of the above procedure.

Simultaneous display of image and spectrum in the same plane: a generalized analysis

A generalized analysis, using the Vander Lugt operational notation, of the building block optical system comprising a single holographic optical element (HOE) for achieving simultaneous display of the spectrum and the image of an object in a single plane, has been carried out. The salient features of this analysis are: (1) it allows comprehensive characterization of the HOE, (2) it provides insights into the many possible configurations for the system, and (3) it explains the existing results in a consistent manner.

An integer arithmetic method to compute generalized matrix inverse and solve linear equations exactly

An algorithm that uses integer arithmetic is suggested. It transforms anm ×n matrix to a diagonal form (of the structure of Smith Normal Form). Then it computes a reflexive generalized inverse of the matrix exactly and hence solves a system of linear equations error-free.

Brownian motion of spins; generalized spin Langevin equation

We derive the Langevin equations for a spin interacting with a heat bath, starting from a fully dynamical treatment. The obtained equations are non-Markovian with multiplicative fluctuations and concommitant dissipative terms obeying the fluctuation-dissipation theorem. In the Markovian limit our equations reduce to the phenomenological equations proposed by Kubo and Hashitsume. The perturbative treatment on our equations lead to Landau-Lifshitz equations and to other known results in the literature.

Euclideanization of Majorana and Weyl Fermions

A continuous procedure is presented for euclideanization of Majorana and Weyl fermions without doubling their degrees of freedom. The Euclidean theory so obtained is SO(4) invariant and Osterwalder-Schrader (OS) positive. This enables us to define a one-complex parameter family of the N=1 supersymmetric Yang-Mills (SSYM) theories which interpolate between the Minkowski and a Euclidean SSYM theory. The interpolating action, and hence the Euclidean action, manifests all the continous symmetries of the original Minkowski space theory.

Existence Theorems for Generalized Hammerstein Equations

In this paper we obtain existence theorems for generalized Hammerstein-type equations K(u)Nu + u = 0, where for each u in the dual X* of a real reflexive Banach space X, K(u): X -- X* is a bounded linear map and N: X* - X is any map (possibly nonlinear). The method we adopt is totally different from the methods adopted so far in solving these equations. Our results in the reflexive spacegeneralize corresponding results of Petry and Schillings.

Control of Agent Swarms using Generalized Centroidal Cyclic Pursuit Laws

One of the major tasks in swarm intelligence is to design decentralized but homogenoeus strategies to enable controlling the behaviour of swarms of agents. It has been shown in the literature that the point of convergence and motion of a swarm of autonomous mobile agents can be controlled by using cyclic pursuit laws. In cyclic pursuit, there exists a predefined cyclic connection between agents and each agent pursues the next agent in the cycle. In this paper we generalize this idea to a case where an agent pursues a point which is the weighted average of the positions of the remaining agents. This point correspond to a particular pursuit sequence. Using this concept of centroidal cyclic pursuit, the behavior of the agents is analyzed such that, by suitably selecting the agents' gain, the rendezvous point of the agents can be controlled, directed linear motion of the agents can be achieved, and the trajectories of the agents can be changed by switching between the pursuit sequences keeping some of the behaviors of the agents invariant. Simulation experiments are given to support the analytical proofs.