Optimization of secondary source configuration in enclosure using plane wave decomposition

The optimization of secondary source configuration for an active noise control (ANC) system in its enclosed space generally focuses on noise reduction requirements at discrete points only. This may lead to the poor noise reduction performance in the whole spatial region, and it is necessary to know the information on error sensor positions in advance. To address this problem, a cost function for spatial-region-oriented noise reduction is proposed. The plane wave decomposition of the enclosed sound field is used to obtain the primary field plane waves and the unit secondary field plane wave of each candidate secondary source as the prior knowledge for configuration optimization, so as to formulate a wave-domain ANC cost function. The optimization method adopts the simulated annealing search. Taking a rigid-walled rectangular cavity as an example, the optimization method is firstly compared with two space-domain methods by using analytic values of the wave-domain prior knowledge. The comparison results show that the better reduction of spatial acoustic potential energy can be achieved independent of the error sensor configuration information. Then the estimated values of the wave-domain prior knowledge through measuring randomly distributed microphones are used to optimize the configuration of the ANC system. The optimization results suggest that the noise reduction of spatial acoustic potential energy of the optimized configuration can be better than that of the space-domain method, but the microphone positions have a great influence on the noise reduction performance.

On the Diffusive-Mean Field Limit for Weakly Interacting Diffusions Exhibiting Phase Transitions

The objective of this article is to analyse the statistical behaviour of a large number of weakly interacting diffusion processes evolving under the influence of a periodic interaction potential. We focus our attention on the combined mean field and diffusive (homogenisation) limits. In particular, we show that these two limits do not commute if the mean field system constrained to the torus undergoes a phase transition, that is to say, if it admits more than one steady state. A typical example of such a system on the torus is given by the noisy Kuramoto model of mean field plane rotators. As a by-product of our main results, we also analyse the energetic consequences of the central limit theorem for fluctuations around the mean field limit and derive optimal rates of convergence in relative entropy of the Gibbs measure to the (unique) limit of the mean field energy below the critical temperature.

A thermodynamic approach to rate-type models in deformable ferroelectrics

The purpose of the paper is to establish vector-valued rate-type models for the hysteretic properties in deformable ferroelectrics within the framework of continuum thermodynamics. Unlike electroelasticity and piezoelectricity, in ferroelectricity both the polarization and the electric field are simultaneously independent variables so that the constitutive functions depend on both. This viewpoint is naturally related to the fact that an hysteresis loop is a closed curve in the polarization–electric field plane. For the sake of generality, the deformation of the material and the dependence on the temperature are allowed to occur. The constitutive functions are required to be consistent with the principle of objectivity and the second law of thermodynamics. Objectivity implies that the constitutive equations are form invariant within the set of Euclidean frames. Among other results, the second law requires a general property on the relation between the polarization and the electric field via a differential equation. This equation shows a dependence fully characterized by two quantities: the free energy and a function which is related to the dissipative character of the hysteresis. As a consequence, different hysteresis models may have the same free energy. Models compatible with thermodynamics are then determined by appropriate selections of the free energy and of the dissipative part. Correspondingly, major and minor hysteretic loops are plotted.

Observation of a comb-shaped filamentary plasma array under subcritical condition in 303-GHz millimetre-wave air discharge

Gas breakdown in the millimetre-wave frequency band is an interesting phenomenon in nonlinear dynamics such as self-organized structure formation. We observed the transition between two types of filamentary plasma arrays in air discharge driven by a 303-GHz millimetre wave. Plasma is ignited at a parabolic mirror’s focal point in the overcritical condition. One array parallel to the electric field vector appears with a spacing of λ/4 at the focal point. Filaments then separate into plasma lumps ~10 μs after ignition. At 20 μs, a new comb-shaped array grows in the subcritical condition. Filaments are parallel to the incident beam with spacing of 0.96 λ and elongate towards the incident beam. This comb-shaped array appears only in the electric field plane; bulk plasma with a sharp vertex forms in the magnetic field plane. This array is created by a standing wave structure generated by waves diffracted from the plasma surface. Filamentary plasma array formations can influence the energy absorption by the plasma, which is important for engineering applications such as beamed energy propulsion.

Temperature Variation Effect on a Rectangular Microstrip Patch Antenna

A novel hypothesis is proposed for the radiation pattern of a Rec-tangular Microstrip Patch Antenna sensitive to temperature variations from the ideal room temperature tolerance under which it was manufactured. In order to validate this hypothetical model, equations relating the resonating frequency, patch length and dielectric constant of the antenna to variations from the room temperature were improved. Simulations were carried out to validate the hypoth-esis in the drifts in ambient temperature effects on dimensions of the patch an-tenna and its field radiation patterns; including its directivity, power pattern, max-imum radiation in the electric-field plane.