Cycle and circle tests of balance in gain graphs: Forbidden minors and their groups

We examine two criteria for balance of a gain graph, one based on binary cycles and one on circles. The graphs for which each criterion is valid depend on the set of allowed gain groups. The binary cycle test is invalid, except for forests, if any possible gain group has an element of odd order. Assuming all groups are allowed, or all abelian groups, or merely the cyclic group of order 3, we characterize, both constructively and by forbidden minors, the graphs for which the circle test is valid. It turns out that these three classes of groups have the same set of forbidden minors. The exact reason for the importance of the ternary cyclic group is not clear. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Method of lines with boundary elements for 1‐D transient diffusion‐reaction problems

Time‐dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi‐implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

Acoustic reflection from a baffled elastic/piezoelectric plate

A finite difference/boundary integral procedure to determine the acoustic reflected pressure from a fluid-loaded bi-laminated plate is described. The bi-laminate is composed of a piezoelectric layer and an elastic layer in contact with the fluid, and is held by an acoustically hard baffle. In the numerical model, the fluid pressure at fluid/solid interface is replaced by a continuum of point sources weighted by the normal acceleration of the elastic plate, and the governing equation system is solved in the solid domain. With the normal acceleration found, the reflected pressure in the fluid is determined by an integral expression involving the Green's function. It is demonstrated that an appropriate applied voltage potential across the piezoelectric layer has the effect of cancelling either the reflected or scattered pressure of the plate at any chosen field points in the fluid. Project supported by the National Natural Science Foundation of China (No. 10172039).     

Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040     

Fractional Derivatives Applied to Phase-Space Reconstructions

The concept and application of phase-space reconstructions are reviewed. Fractional derivatives are then proposed for the purpose of reconstructing dynamics from a single observed time history. A procedure is presented in which the fractional derivatives of time series data are obtained in the frequency domain. The method is applied to the Lorenz system. The ability of the method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and correlation dimensions. The reconstruction is compared to the commonly used method of delays in order to assess the choice of reconstruction parameters, and also the quality of results.     

Robust Speed Control of a Low Damped Electromechanical System Based on CRONE Control: Application to a Four Mass Experimental Test Bench

Robust speed control of a low damped electromechanical system with backlash is studied, controlled load angular speed being not measured. The proposed control strategy combines a Luenberger observer (load angular speed and load torque disturbance estimations) and a robust CRONE controller. The observer provides estimation of the load angular speed and of the disturbance torque applied on the load. Through the computation of only three independent parameters (as many as a PID controller), the CRONE controller permits to ensure the robust speed control of the load in spite of plant parametric variations and speed observation errors. The proposed control strategy is applied to a four mass experimental test bench.     

A complete boundary integral formulation for compressible Navier–Stokes equations

A complete boundary integral formulation for compressible Navier–Stokes equations with time discretization by operator splitting is developed using the fundamental solutions of the Helmholtz operator equation with different order. The numerical results for wall pressure and wall skin friction of two‐dimensional compressible laminar viscous flow around airfoils are in good agreement with field numerical methods. Copyright © 2004 John Wiley & Sons, Ltd.     

Order conditions for linearly implicit fractional step Runge Kutta methods

^{In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of ‘simpler’ linear differentialoperators and a nonlinear term.}     

Trefftz,collocation, and other boundary methods—A comparison

In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Motion Control by ZV Shaper Synthesis Extended for Fractional Systems and Its Application to CRONE Control

Shaping command input or preshaping is used for reducing system oscillation in motion control. Desired systems inputs are altered so that the system finishes the requested move without residual oscillation. This technique, developed by N.C. Singer and W.P. Seering, is used for example in the aerospace field, in particular in flexible structure control. This paper presents the study of ZV shaper for explicit fractional derivative systems (generalized derivative systems). A robustness study of ZV shaper is then presented and applied to improve second generation CRONE control response time. Results from simulation and from a DC motor bench are also given.