The generalized Mittag-Leffler function E-alpha,E-beta (z) has been studied for arbitrary complex argument z is an element of C and parameters alpha is an element of R+ and beta is an element of R. This function plays...
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The generalized Mittag-Leffler function E-alpha,E-beta (z) has been studied for arbitrary complex argument z is an element of C and parameters alpha is an element of R+ and beta is an element of R. This function plays a fundamental role in the theory of fractional differential equations and numerous applications in physics. The Mittag-Leffler function interpolates smoothly between exponential and algebraic functional behaviour. A numerical algorithm for its evaluation has been developed. The algorithm is based on integral representations and exponential asymptotics. Results of extensive numerical calculations for E-alpha,E-beta (z) in the complex z -plane are reported here. We find that all complex zeros emerge from the point z =1 for small alpha. They diverge towards -infinity+(2 k -1)pi i for alpha -> 1(-) and towards -infinity+2 k pi i for alpha -> 1(+) ( k is an element of Z). All the complex zeros collapse pairwise onto the negative real axis for alpha -> 2. We introduce and study also the inverse generalized Mittag-Leffler function L-alpha,L-beta (z) defined as the solution of the equation L-alpha,L-beta (E-alpha,E-beta (z )) = z . We determine its principal branch numerically.
This Note presents a time-integration strategy for computing the evolution of structures embedding shape-memory alloys in a thermomechanical setting. A variational formulation is associated with the scheme proposed, w...
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This Note presents a time-integration strategy for computing the evolution of structures embedding shape-memory alloys in a thermomechanical setting. A variational formulation is associated with the scheme proposed, which allows one to study the existence and unicity of solutions depending on the material model considered. A numerical example is presented to illustrate the method and discuss the influence of the thermomechanical coupling.
The aim of this paper is the analysis of the bias contained in star catalogues, these errors can be obtained by means of kinematics or dynamical methods. In this paper a general method, suitable when the sample is not...
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The aim of this paper is the analysis of the bias contained in star catalogues, these errors can be obtained by means of kinematics or dynamical methods. In this paper a general method, suitable when the sample is not homogeneous is presented.
A new algorithm is proposed for computing the intersection of two plane curves given in rational parametric form. It relies on the Ehrlich-Aberth iteration complemented with some computational tools like the propertie...
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A new algorithm is proposed for computing the intersection of two plane curves given in rational parametric form. It relies on the Ehrlich-Aberth iteration complemented with some computational tools like the properties of Sylvester and Bezout matrices, a stopping criterion based on the concept of pseudo-zero, an inclusion result and the choice of initial approximations based on the Newton polygon. The algorithm is implemented as a Fortran 95 module. From the numerical experiments performed with a wide set of test problems it shows a better robustness and stability with respect to the Manocha-Demmel approach based on eigenvalue computation. In fact, the algorithm provides better approximations in terms of the relative error and performs successfully in many critical cases where the eigenvalue computation fails.
Two algorithms for robust pole assignment by state feedback, proposed by Kautsky, Nichols and Van Dooren (1985) and by Tits and Yang (1996) are briefly reviewed. MATLAB code implementations of these algorithms, place ...
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ISBN:
(纸本)9780780397972
Two algorithms for robust pole assignment by state feedback, proposed by Kautsky, Nichols and Van Dooren (1985) and by Tits and Yang (1996) are briefly reviewed. MATLAB code implementations of these algorithms, place (from the MATLAB Control System Toolbox) and robpole (from SLICOT), are then numerically compared on randomly generated test data sets, as well as on examples from two benchmark collections, in terms of the robustness (insensitivity of poles to variations in plant parameters) of the closed-loop systems they produce. The functions place and robpole are also compared with each other, as well as with the (non robust) pole assignment code pass (from SLICOT) in terms of CPU time and accuracy of the pole assignment.
Different extrapolation strategies are presented for the construction of starting values in implicit Newmark time-stepping schemes used for the solution of the electromagnetic wave equation. The implicit character of ...
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Different extrapolation strategies are presented for the construction of starting values in implicit Newmark time-stepping schemes used for the solution of the electromagnetic wave equation. The implicit character of this schemes implies the solution of a system of linear equations in each time step. The choice of a good start value derived from the extrapolation of the equation system is shown to improve the convergence of the iterative conjugate gradient solver which reduces the total simulation time.
A health monitoring system based on analytical redundancy is developed for satellites on elliptical orbits. Analytical redundancy, which reduces the need for hardware redundancy, uses the modeled dynamic relationship ...
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A health monitoring system based on analytical redundancy is developed for satellites on elliptical orbits. Analytical redundancy, which reduces the need for hardware redundancy, uses the modeled dynamic relationship between system inputs and measured system outputs to form a residual process that is used for detecting and identifying faults. First, the dynamics of the satellite including orbital mechanics and attitude dynamics is modeled as a periodic system. Then, periodic fault detection filters are designed to detect and identify the satellite's actuator and sensor faults. In addition, parity equations are constructed using the algebraic redundant relationship among actuators and sensors. Furthermore, a residual processor is designed to generate the probability of each fault by using a sequential probability test. Finally, the health monitoring system, consisting of periodic fault detection filters, parity equations, and residual processor, is evaluated in the simulation in the presence of disturbances and uncertainty.
In the present study a population balance approach is described to follow the time evolution of molecular polymer properties in free-radical polymerizations. The model formulation is based on the fixed pivot technique...
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In the present study a population balance approach is described to follow the time evolution of molecular polymer properties in free-radical polymerizations. The model formulation is based on the fixed pivot technique (FPT) which was properly adapted to calculate the combined molecular weight - long chain branching distribution. At first the predictive capabilities of the proposed model were tested against experimental measurements and simulation results taken from the open literature, on molecular weight distribution (MWD) of branched polymers. Then the MWD calculated by the FPT was compared with the MWD calculated by the method of classes. However the FPT proved to be a faster method for the calculation of the MWD.
This paper deals with the synthesis of a suboptimal controller based on the solution of the algebraic Riccati equation (ARE). The numerical procedure for obtaining the solution is presented. In applications the contro...
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This paper deals with the synthesis of a suboptimal controller based on the solution of the algebraic Riccati equation (ARE). The numerical procedure for obtaining the solution is presented. In applications the controlled system parameters often differ from the ones used in the ARE. In this case the optimality of the control system and even its stability are questionable. Therefore, it would be very useful to design an adaptive linear suboptimal controller Such a controller should be able to detect changes in the system parameters and adjust its parameters. (C) 2006 Journal of Mechanical Engineering. All rights reserved.
An efficient algorithm for L ∞ -norm calculations, implemented in the SLICOT Library, is described and compared with other available algorithms. The algorithm exploits the Hamiltonian structure of the computational p...
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An efficient algorithm for L ∞ -norm calculations, implemented in the SLICOT Library, is described and compared with other available algorithms. The algorithm exploits the Hamiltonian structure of the computational problem and offers generality and flexibility. Continuous- and discrete-time, standard as well as generalized systems are addressed. Extensive comparisons with other L ∞ -norm solvers show that the generalpurpose SLICOT solver is the most efficient one, especially for standard continuous-time problems.
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