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Loudspeakers are often modelled as a rigid piston in an infinite baffle. This model is for real loudspeakers somewhat limited in two ways. One issue is that a loudspeaker is not rigid and a second issue is that a loudspeaker is mostly used in a cabinet. Both issues are addressed here by developing the velocity of the radiator in terms oforthogonal polynomials known from optical diffraction theory as Zernike circle polynomials. Using these polynomials we develop semi-analytic expressions for the sound pressure from the radiator in two different cases: as a flexible flat radiator mounted in an infinite baffle, and as the cap of a rigid sphere. In the latter case the comparison is done not only for the pressure but also for other quantitiesviz. the baffle-step response, sound power and directivity, and theacoustic center of the radiator. These quantities are compared withthose from a real loudspeaker.

The theory of orthogonal polynomial (Zernike) expansions of functions on a disk, as used in the diffraction theory of optical aberrations, is applied to obtain (semi-) analytical expressions for the spatial impulse responses arising from a non-uniformly moving, baffled, circular piston. These expressions are in terms of the expansion coefficients of the non-uniformity and the responses of the orthogonal expansion functions. The latter impulse responses have a closed formas finite series involving Legendre functions and the sinc function.The method is compared with a similar method, proposed in P.R. Stepanishen, J. Acoust. Soc. Am. 70, 1176-1181, 1981 where zero-th orderorthogonal Bessel functions, rather than Zernike polynomials, are used as expansion functions. The method is also considered for retrieval of a non-uniform velocity profile from measured spatial impulseresponses on the level of expansion coefficients, which can be applied to acoustic holography for loudspeakers.

It has been suggested by Morse and Ingard that the sound radiation of a loudspeaker in a box is comparable to that of a spherical cap ona rigid sphere. This has been established recently by the present authors, who developed a computation scheme for the forward and inverse calculation of the pressure due to a harmonically excited, flexible cap on a rigid sphere with an axially symmetric velocity distribution. In this paper the comparison is made for other quantities relevant to audio engineers, namely, the baffle-step response, sound power and directivity, and the acoustic center of a radiator.

Multi-access networks may exhibit severe unfairness in throughput,in the sense that some nodes receive structurally higher throughputthan others. Recent studies show that this unfairness is due tolocal differences in the neighborhood structure: Nodes with fewerneighbors receive better access. We study the unfairness in satura-ted linear networks,and adapt the multi-access CSMA protocol toremove the unfairness completely,by choosing the activation ratesof nodes as a specific function of the number of neighbors. We theninvestigate the consequences of this choice of activation rates onthe network-average saturated throughput, and we show that theserates perform well in non-saturated settings.