Hyperbolic-like estimates for higher order equations

The main goal of this paper is to derive long time estimates of the energy for the higher order hyperbolic equations with time-dependent coefficients. in particular, we estimate the energy in the hyperbolic zone of the extended phase space by means of a function f (t) which depends on the principal part and on the coefficients of the terms of order m - 1. Then we look for sufficient conditions that guarantee the same energy estimate from above in all the extended phase space. We call this class of estimates hyperbolic-like since the energy behavior is deeply depending on the hyperbolic structure of the equation. In some cases, these estimates produce a dissipative effect on the energy. (C) 2012 Elsevier Inc. All rights reserved.

The nuclear electric quadrupole moment of hafnium from the molecular method

The molecular method is used to obtain nuclear electric quadrupole moment (NQM) values for hafnium through electric field gradients (EFGs) at this nucleus in HfO and HfS. Dirac-Coulomb calculations with the Coupled Cluster approach, DC-CCSD (T) and DC-CCSD-T, were carried out to achieve the most accurate estimates of these EFGs. Higher order corrections are also added. Hence, the most reliable values for 177Hf and 179Hf determined here are 3319(33) and 3750(37) mbarn, respectively, in nice accordance with the best currently accepted NQMs for this element. (C) 2012 Elsevier B.V. All rights reserved.

Optimal reactive power flow via the modified barrier Lagrangian function approach

A new approach called the Modified Barrier Lagrangian Function (MBLF) to solve the Optimal Reactive Power Flow problem is presented. In this approach, the inequality constraints are treated by the Modified Barrier Function (MBF) method, which has a finite convergence property: i.e. the optimal solution in the MBF method can actually be in the bound of the feasible set. Hence, the inequality constraints can be precisely equal to zero. Another property of the MBF method is that the barrier parameter does not need to be driven to zero to attain the solution. Therefore, the conditioning of the involved Hessian matrix is greatly enhanced. In order to show this, a comparative analysis of the numeric conditioning of the Hessian matrix of the MBLF approach, by the decomposition in singular values, is carried out. The feasibility of the proposed approach is also demonstrated with comparative tests to Interior Point Method (IPM) using various IEEE test systems and two networks derived from Brazilian generation/transmission system. The results show that the MBLF method is computationally more attractive than the IPM in terms of speed, number of iterations and numerical conditioning. (C) 2011 Elsevier B.V. All rights reserved.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

Parametric resonances in a base-excited double pendulum

Two parametrically-induced phenomena are addressed in the context of a double pendulum subject to a vertical base excitation. First, the parametric resonances that cause the stable downward vertical equilibrium to bifurcate into large-amplitude periodic solutions are investigated extensively. Then the stabilization of the unstable upward equilibrium states through the parametric action of the high-frequency base motion is documented in the experiments and in the simulations. It is shown that there is a region in the plane of the excitation frequency and amplitude where all four unstable equilibrium states can be stabilized simultaneously in the double pendulum. The parametric resonances of the two modes of the base-excited double pendulum are studied both theoretically and experimentally. The transition curves (i.e., boundaries of the dynamic instability regions) are constructed asymptotically via the method of multiple scales including higher-order effects. The bifurcations characterizing the transitions from the trivial equilibrium to the periodic solutions are computed by either continuation methods and or by time integration and compared with the theoretical and experimental results.

Influence of Goertler vortices spanwise wavelength on heat transfer rates

The boundary layer over concave surfaces can be unstable due to centrifugal forces, giving rise to Goertler vortices. These vortices create two regions in the spanwise direction—the upwash and downwash regions. The downwash region is responsible for compressing the boundary layer toward the wall, increasing the heat transfer rate. The upwash region does the opposite. In the nonlinear development of the Goertler vortices, it can be observed that the upwash region becomes narrow and the spanwise–average heat transfer rate is higher than that for a Blasius boundary layer. This paper analyzes the influence of the spanwise wavelength of the Goertler the heat transfer. The equation is written in vorticity-velocity formulation. The time integration is done via a classical fourth-order Runge-Kutta method. The spatial derivatives are calculated using high-order compact finite difference and spectral methods. Three different wavelengths are analyzed. The results show that steady Goertler flow can increase the heat transfer rates to values close to the values of turbulence, without the existence of a secondary instability. The geometry (and computation domain) are presented

Design methodology of piezoelectric energy-harvesting skin using topology optimization

Abstract This paper describes a design methodology for piezoelectric energy harvester s that thinly encapsulate the mechanical devices and expl oit resonances from higher- order vibrational modes. The direction of polarization determines the sign of the pi ezoelectric tensor to avoid cancellations of electric fields from opposite polarizations in the same circuit. The resultant modified equations of state are solved by finite element method (FEM). Com- bining this method with the solid isotropic material with penalization (SIMP) method for piezoelectric material, we have developed an optimization methodology that optimizes the piezoelectric material layout and polarization direc- tion. Updating the density function of the SIMP method is performed based on sensitivity analysis, the sequen- tial linear programming on the early stage of the opti- mization, and the phase field method on the latter stage