A C-0 Interior Penalty Method for a Fourth-order Variational Inequality of the Second Kind

In this article, we propose a C-0 interior penalty ((CIP)-I-0) method for the frictional plate contact problem and derive both a priori and a posteriori error estimates. We derive an abstract error estimate in the energy norm without additional regularity assumption on the exact solution. The a priori error estimate is of optimal order whenever the solution is regular. Further, we derive a reliable and efficient a posteriori error estimator. Numerical experiments are presented to illustrate the theoretical results. (c) 2015Wiley Periodicals, Inc.

Cubic Sieve Congruence of the Discrete Logarithm Problem, and fractional part sequences

The Cubic Sieve Method for solving the Discrete Logarithm Problem in prime fields requires a nontrivial solution to the Cubic Sieve Congruence (CSC) x(3) equivalent to y(2)z (mod p), where p is a given prime number. A nontrivial solution must also satisfy x(3) not equal y(2)z and 1 <= x, y, z < p(alpha), where alpha is a given real number such that 1/3 < alpha <= 1/2. The CSC problem is to find an efficient algorithm to obtain a nontrivial solution to CSC. CSC can be parametrized as x equivalent to v(2)z (mod p) and y equivalent to v(3)z (mod p). In this paper, we give a deterministic polynomial-time (O(ln(3) p) bit-operations) algorithm to determine, for a given v, a nontrivial solution to CSC, if one exists. Previously it took (O) over tilde (p(alpha)) time in the worst case to determine this. We relate the CSC problem to the gap problem of fractional part sequences, where we need to determine the non-negative integers N satisfying the fractional part inequality {theta N} < phi (theta and phi are given real numbers). The correspondence between the CSC problem and the gap problem is that determining the parameter z in the former problem corresponds to determining N in the latter problem. We also show in the alpha = 1/2 case of CSC that for a certain class of primes the CSC problem can be solved deterministically in <(O)over tilde>(p(1/3)) time compared to the previous best of (O) over tilde (p(1/2)). It is empirically observed that about one out of three primes is covered by the above class. (C) 2013 Elsevier B.V. All rights reserved.

Variational approach to homogenization of doubly-nonlinear flow in a periodic structure

This work deals with the homogenization of an initial- and boundary-value problem for the doubly-nonlinear system D(t)w - del.(z) over right arrow = g(x, t, x/epsilon) (0.1) w is an element of alpha(u, x/epsilon) (0.2) (z) over right arrow is an element of (gamma) over right arrow (del u, x/epsilon) (0.3) Here epsilon is a positive parameter; alpha and (gamma) over right arrow are maximal monotone with respect to the first variable and periodic with respect to the second one. The inclusions (0.2) and (0.3) are here formulated as null-minimization principles, via the theory of Fitzpatrick MR 1009594]. As epsilon -> 0, a two-scale formulation is derived via Nguetseng's notion of two-scale convergence, and a (single-scale) homogenized problem is then retrieved. (C) 2015 Elsevier Ltd. All rights reserved.

Variational approach to homogenization of doubly-nonlinear flow in a periodic structure

This work deals with the homogenization of an initial- and boundary-value problem for the doubly-nonlinear system D(t)w - del.(z) over right arrow = g(x, t, x/epsilon) (0.1) w is an element of alpha(u, x/epsilon) (0.2) (z) over right arrow is an element of (gamma) over right arrow (del u, x/epsilon) (0.3) Here epsilon is a positive parameter; alpha and (gamma) over right arrow are maximal monotone with respect to the first variable and periodic with respect to the second one. The inclusions (0.2) and (0.3) are here formulated as null-minimization principles, via the theory of Fitzpatrick MR 1009594]. As epsilon -> 0, a two-scale formulation is derived via Nguetseng's notion of two-scale convergence, and a (single-scale) homogenized problem is then retrieved. (C) 2015 Elsevier Ltd. All rights reserved.

Modeling of Piezocomposites using Variational Asymptotic Method

This work presents the development of piezocomposites made up of Macro Fiber Composites (MFCs) for aerospace applications and specifically involves, their computational analysis, material characterization and certain parametric studies. MFC was developed by NASA Langley Research Center in 1996 and currently is being distributed by Smart Material Co. 1] worldwide and finds applications both as an actuator as well as for sensor in various engineering applications. In this work, MFC is being modeled as an actuator and a theoretical formulation based on Variational Asymptotic Method (VAM) 2] is presented to analyse the laminates made up of MFCs. VAM minimizes the total electro-mechanical energy for the MFC laminate and approaches the exact solution asymptotically by making use of certain small parameters inherent to the problem through dimensional reduction. VAM provides closed form solutions for 1D constitutive law, recovery relations of warpings, 3D stress/strain fields and displacements and hence an ideal tool for carrying out parametric and design studies in such applications. VAM is geometrically exact and offers rigorous material characterization through cross-sectional analysis and dimensional reduction.

Analysis of Transverse Shear Strains in Pre-Twisted Thick Beams using Variational Asymptotic Method

The cross-sectional stiffness matrix is derived for a pre-twisted, moderately thick beam made of transversely isotropic materials and having rectangular cross sections. An asymptotically-exact methodology is used to model the anisotropic beam from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy is computed making use of the beam constitutive law and kinematical relations derived with the inclusion of geometrical nonlinearities and an initial twist. The energy functional is minimized making use of the Variational Asymptotic Method (VAM), thereby reducing the cross section to a point on the beam reference line with appropriate properties, forming a 1-D constitutive law. VAM is a mathematical technique employed in the current problem to rigorously split the 3-D analysis of beams into two: a 2-D analysis over the beam cross-sectional domain, which provides a compact semi-analytical form of the properties of the cross sections, and a nonlinear 1-D analysis of the beam reference curve. In this method, as applied herein, the cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged in orders of the small parameters. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that render the 1-D strain measures well-defined. The zeroth-order 3-D warping field thus yielded is then used to integrate the 3-D strain energy density over the cross section, resulting in the 1-D strain energy density, which in turn helps identify the corresponding cross-sectional stiffness matrix. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.

An Approximate Solution Of One-Dimensional Piston Problem

A new theory of shock dynamics has been developed in the form of a finite number of compatibility conditions along shock rays. It has been used to study the growth or decay of shock strength for accelerating or decelerating piston starting with a nonzero piston velocity. The results show good agreement with those obtained by Harten's high resolution TVD scheme.

A Quasi-Newton Adaptive Algorithm for Generalized Symmetric Eigenvalue Problem

In this paper, we first recast the generalized symmetric eigenvalue problem, where the underlying matrix pencil consists of symmetric positive definite matrices, into an unconstrained minimization problem by constructing an appropriate cost function, We then extend it to the case of multiple eigenvectors using an inflation technique, Based on this asymptotic formulation, we derive a quasi-Newton-based adaptive algorithm for estimating the required generalized eigenvectors in the data case. The resulting algorithm is modular and parallel, and it is globally convergent with probability one, We also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices (in the pencil) on the resulting eigenstructure. Simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank-one updating algorithm of Karasalo. Further, the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems.

Integral Formulation of the Problem of Current Distribution in Compulsator Wires of Electromagnetic Launchers and Railguns

Compulsators are power sources of choice for use in electromagnetic launchers and railguns. These devices hold the promise of reducing unit costs of payload to orbit. In an earlier work, the author had calculated the current distribution in compulsator wires by considering the wire to be split into a finite number of separate wires. The present work develops an integral formulation of the problem of current distribution in compulsator wires which leads to an integrodifferential equation. Analytical solutions, including those for the integration constants, are obtained in closed form. The analytical solutions present a much clearer picture of the effect of various input parameters on the cross-sectional current distribution and point to ways in which the desired current density distribution can be achieved. Results are graphically presented and discussed, with particular reference to a 50-kJ compulsator in Bangalore. Finite-element analysis supports the results.

Differential Games of Mixed Type with Control and Stopping Times

We study a zero sum differential game of mixed type where each player uses both control and stopping times. Under certain conditions we show that the value function for this problem exists and is the unique viscosity solution of the corresponding variational inequalities. We also show the existence of saddle point equilibrium for a special case of differential game.

The Implication Problem for Functional and Multivalued Dependencies

Computation of the dependency basis is the fundamental step in solving the implication problem for MVDs in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of an MVD-lattice and develop an algebraic characterization of the inference basis using simple notions from lattice theory. We also establish several properties of MVD-lattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a) computing the inference basis of a given set M of MVDs; (b) computing the dependency basis of a given attribute set w.r.t. M; and (c) solving the implication problem for MVDs. Finally, we show that our results naturally extend to incorporate FDs also in a way that enables the solution of the implication problem for both FDs and MVDs put together.

Quantum first-passage problem

Formulation of quantum first passage problem is attempted in terms of a restricted Feynman path integral that simulates an absorbing barrier as in the corresponding classical case. The positivity of the resulting probability density, however, remains to be demonstrated.

Optimal hydrothermal load flow: Formulation and a successive approximation solution for fixed head systems

This paper deals with the optimal load flow problem in a fixed-head hydrothermal electric power system. Equality constraints on the volume of water available for active power generation at the hydro plants as well as inequality constraints on the reactive power generation at the voltage controlled buses are imposed. Conditions for optimal load flow are derived and a successive approximation algorithm for solving the optimal generation schedule is developed. Computer implementation of the algorithm is discussed, and the results obtained from the computer solution of test systems are presented.

A simplified approach to a three-part Wiener-Hopf problem arising in diffraction theory

A direct and simple approach, utilizing Watson's lemma, is presented for obtaining an approximate solution of a three-part Wiener-Hopf problem associated with the problem of diffraction of a plane wave by a soft strip.