Zero Dissipative, Explicit Numerov-Type Methods for Second Order IVPs with Oscillating Solutions

New explicit, zero dissipative, hybrid Numerov type methods are presented in this paper. We derive these methods using an alternative which avoids the use of costly high accuracy interpolatory nodes. We only need the Taylor expansion at some internal points then. The method is of sixth algebraic order at a cost of seven stages per step while their phase lag order is fourteen. The zero dissipation condition is satisfied, so the methods possess an non empty interval of periodicity. Numerical results over some well known problems in physics and mechanics indicate the superiority of the new method.     

Local Feasible QP-Free Algorithms for the Constrained Minimization of SC1 Functions

We consider the problem of minimizing an SC¹ function subject to inequality constraints. We propose a local algorithm whose distinguishing features are that: (a) a fast convergence rate is achieved under reasonable assumptions that do not include strict complementarity at the solution; (b) the solution of only linear systems is required at each iteration; (c) all the points generated are feasible. After analyzing a basic Newton algorithm, we propose some variants aimed at reducing the computational costs and, in particular, we consider a quasi-Newton version of the algorithm.     

Tomographic reconstruction using heuristic Monte Carlo methods

A tomographic reconstruction method based on Monte Carlo random searching guided by the information contained in the projections of radiographed objects is presented. In order to solve the optimization problem, a multiscale algorithm is proposed to reduce computation. The reconstruction is performed in a coarse-to-fine multigrid scale that initializes each resolution level with the reconstruction of the previous coarser level, which substantially improves the performance. The method was applied to a real case reconstructing the internal structure of a small metallic object with internal components, showing excellent results.     

On the Application of the Auxiliary Problem Principle

The auxiliary problem principle (APP) derives from a general theory on decomposition-coordination methods establishing a comprehensive framework for both one-level and two-level methods. In this paper, the results of the two-level methods of APP are specialized for an efficient application to some engineering problems.     

A quantum chemical study on structure of 1,2-bis(diphenylphosphinoyl)ethane and phenol cocrystal

The cocrystal of 1,2-bis(diphenylphosphinoyl)ethane (DPPEO) with phenol (1:1) were studied theoretically with AM1, PM3, MNDO and MINDO/3 semi-empirical methods to elucidate its structure. The bond lengths and angles from theoretical studies of molecule DPPEO/phenol (1:1) were found to be as expected. Theoretical results, concerning with intermolecular van der Waals forces in cocrystal, were compared with the previously obtained experimental data and AM1 results were found to be the best fit for bond lengths and angles of DPPEO/phenol.     

使用非单调技术的不精确预条件牛顿类方法解非线性方程组

本文提供了预条件不精确牛顿型方法结合非单调技术解光滑的非线性方程组．在合理的条件下证明了算法的整体收敛性．进一步，基于预条件收敛的性质，获得了算法的局部收敛速率，并指出如何选择势序列保证预条件不精确牛顿型的算法局部超线性收敛速率．     

Stationary entanglement between macroscopic mechanical oscillators

We show that the optomechanical coupling between an optical cavity mode and two movable cavity mirrors is able to entangle two different macroscopic oscillation modes of the mirrors. This continuous variable entanglement is maintained by the light bouncing between the mirrors and is robust against thermal noise. In fact, it could be experimentally demonstrated using present technology. Received 2 September 2002 / Received in final form 10 October 2002 Published online 7 January 2003     

A test problem for molecular dynamics integrators

We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense.     

Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin method

The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two‐dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each mode. The oscillatory flow regimes corresponding to each of the three modes are approximated asymptotically. No direct time integration is applied. Good agreement with the previously published results obtained by solution of the time‐dependent Boussinesq equations is reported. Copyright © 2004 John Wiley & Sons, Ltd.