Time-harmonic Functions Research Articles

Some martingales associated with multivariate Jacobi processes and Aomoto’s Selberg integral

We study β-Jacobi diffusion processes on alcoves in RN, depending on 3 parameters. Using elementary symmetric functions, we present space–time-harmonic functions and martingales for these processes (Xt)t≥0 which are independent from one parameter. This leads to a formula for E(∏i=1N(y−Xt,i)) in terms of classical Jacobi polynomials. For t→∞ this yields a corresponding formula for Jacobi ensembles and thus Aomoto’s Selberg integral.

Numerical Study of an AC MHD Generation with Double-side Exciting Winding

This paper studies physical phenomena, performance and optimal operating point of an AC MHD generator under the slip value by using a numerical simulation. The double-side exciting winding of the generator is considered. Its structure consists of a channel, an insulator and stators. Channel type is a flat rectangular and the liquid flows along the channel as a conductor. Channel wall acted as an insulator separates metal fluid and stator coils. The top and bottom stator winding of the generator is connected to polyphase system. Under this condition, it can produce a magnetic field by means of time harmonic function in the same direction of the metal fluid. An interaction between traveling wave and metal fluid is explained by finite element method under Maxwell's equation and Ohm law. The distribution of magnetic vector potential and magnetic flux density throughout channel is evidently shown in xy-plane. Power flow in AC MHD generator is evaluated by slip value. The optimal operating point of an AC MHD generator performance is reported by active power 0.99kW, reactive power 50kVAR, mechanical power 1.58kW, power dissipation 0.59kW and electrical efficiency 62.5%.

A new model for the study of rain-wind-induced vibrations of a simple oscillator

In this paper, a model equation is presented for the study of rain-wind-induced vibrations of a simple oscillator. As will be shown the presence of raindrops in the wind-field may have an essential influence on the dynamic stability of the oscillator. In this model equation the influence of the variation of the mass of the oscillator due to an incoming flow of raindrops hitting the oscillator and a mass flow which is blown and shaken off is investigated. The time-varying mass is modeled by a time harmonic function whereas simultaneously also time-varying lift and drag forces are considered.

Iterates of the infinitesimal generator and space–time harmonic polynomials of a Markov process

We relate iterates of the infinitesimal generator of a Markov process to space–time harmonic functions. First, we develop the theory for a general Markov process and create a family a space–time martingales. Next, we investigate the special class of subordinators. Combinatorics results on space–time harmonic polynomials and generalized Stirling numbers are developed and interpreted from a probabilistic point of view. Finally, we introduce the notion of pairs of subordinators in duality, investigate the implications on the associated martingales and consider some explicit examples.

The use of the Pontryagin maximum principle in a furtivity problem in time-dependent acoustic obstacle scattering

In this paper we consider a furtivity problem in the context of time-dependent three-dimensional acoustic obstacle scattering. The scattering problem for a ‘passive’ obstacle is the following: an incoming acoustic wavepacket is scattered by a bounded simply connected obstacle with locally Lipschitz boundary having a known boundary acoustic impedance. The scattered wave is the solution of an exterior problem for the wave equation. To make the obstacle furtive we leave ‘passive’ obstacles and we consider ‘active’ obstacles, that is obstacles that, when hit by the incoming wavepacket, react with a pressure current circulating on their boundary. The furtivity problem consists of making the acoustic field scattered by the obstacle ‘as small as possible’ by choosing a control function, that is a pressure current on the boundary of the obstacle, in the function space of the admissible controls. It consists of finding the control function that minimizes a cost functional that will be made precise later. This furtivity problem is of great relevance in many applications. The mathematical model for this furtivity problem is a control problem for the wave equation. In the boundary condition for the wave equation on the boundary of the obstacle we introduce a control function, the so-called pressure current. The cost functional depends on the control function, and on the scattered acoustic field. Note that the scattered field depends on the control function via the boundary conditions. Using the Pontryagin maximum principle we show that, for a suitable choice of the cost functional, the first-order optimality conditions for the furtivity problem considered can be formulated as an exterior problem defined outside the obstacle for a system of two coupled wave equations. This is the main purpose of the paper. Moreover, to solve this exterior problem numerically we develop a highly parallelizable method based on a ‘perturbative series’ of the type proposed in 1. This method obtains the time-dependent scattered field and the control function as superpositions of time harmonic functions. The space-dependent parts of each time harmonic component of the scattered field and of the control function are obtained by solving an exterior boundary value problem for two coupled Helmholtz equations. The mathematical model and the numerical method proposed are validated by studying some test problems numerically. The results obtained with a parallel implementation of the numerical method proposed on the test problems are shown and discussed from the numerical and the physical point of view. The quantitative character of the results obtained is established. Animations (audio, video) relative to the numerical experiments can be found at stacks.iop.org/WRM/11/549. MThis article features online multimedia enhancements

VIBRATION EIGENFREQUENCY ANALYSIS OF A SINGLE-LINK FLEXIBLE MANIPULATOR

We analyse the vibration eigenfrequencies of a flexible slewing beam with a payload attached at one end. A wave propagation method (WPM) is used. There are four types of waves which propagate along a beam—two dispersive waves travelling in opposite directions, and two evanescent waves near the endpoints. We add a fifth time-harmonic function corresponding to oscillation of the beam at the payload end. We show that the large frequencies are asymptotically identical to those for the clamped–free beam, independent of the payload. For small eigenfrequencies, we incorporate WPM with a perturbation iteration procedure, the results of which agree well with “exact” values which result from solving a transcendental equation cited elsewhere in the literature.