Пучки Гельмгольца--Гаусса с квадратичной радиальной зависимостью

A new class of localized solutions of paraxial parabolic equation is introduced. Each solution is a product of some Gaussian-type localized axisymmetric function (different from the fundamental mode) and an amplitude factor. The latter can be expressed via an arbitrary solution of the Helmholtz equation on an auxiliary two-sheet complex surface. The class under consideration contains well known and novel solutions, including those describing optical vortices of various orders.

Sigmoidal NMFD: Convolutional NMF with Saturating Activations for Drum Mixture Decomposition

In many types of music, percussion plays an essential role to establish the rhythm and the groove of the music. Algorithms that can decompose the percussive signal into its constituent components would therefore be very useful, as they would enable many analytical and creative applications. This paper describes a method for the unsupervised decomposition of percussive recordings, building on the non-negative matrix factor deconvolution (NMFD) algorithm. Given a percussive music recording, NMFD discovers a dictionary of time-varying spectral templates and corresponding activation functions, representing its constituent sounds and their positions in the mix. We observe, however, that the activation functions discovered using NMFD do not show the expected impulse-like behavior for percussive instruments. We therefore enforce this behavior by specifying that the activations should take on binary values: either an instrument is hit, or it is not. To this end, we rewrite the activations as the output of a sigmoidal function, multiplied with a per-component amplitude factor. We furthermore define a regularization term that biases the decomposition to solutions with saturated activations, leading to the desired binary behavior. We evaluate several optimization strategies and techniques that are designed to avoid poor local minima. We show that incentivizing the activations to be binary indeed leads to the desired impulse-like behavior, and that the resulting components are better separated, leading to more interpretable decompositions.

Heat and Moisture Transport Through the Microclimate Air Annulus of the Clothing-Skin System Under Periodic Motion

The study is concerned with the heat and moisture transport in a ventilated fabric-skin system composed of a microclimate air annulus that separates an outer cylindrical fabric boundary and an inner oscillating cylinder representing human skin boundary for open and closed aperture settings at the ends of the cylindrical system. The cylinder ventilation model of Ghaddar et al. (2005, Int. J. Heat Mass Transfer, 48(15), pp. 3151–3166) is modified to incorporate the heat and moisture transport from the skin when contact with fabric occurs at repetitive finite intervals during the motion cycle. During fabric skin contact, the heat and moisture transports are modeled based on the fabric dry and evaporative resistances at the localized touch regions at the top and bottom of points of the cylinder. Experiments were conducted to measure the mass transfer coefficient at the skin to the air annulus under periodic ventilation and to measure the sensible heat loss from the inner cylinder for the two cases of fabric-skin contact and no contact. The model predictions of time-averaged steady-periodic sensible heat loss agreed well with the experimentally measured values at different frequencies. The model results showed that the rate of heat loss increased with increased ventilation frequency at fixed (=amplitude/mean annular spacing). At amplitude factor of 1.4, the latent heat loss in the contact region increased by almost 40% compared to the loss at amplitude factor of 0.8 due to the increase in fabric temperature during contact. The sensible heat loss decreased slightly between 3% at f=60rpm and 5% at f=25rpm in the contact region due to higher air temperature and lack of heat loss by radiation when fabric and skin are in touch. The presence of an open aperture has a limited effect on increasing the total heat loss. For an open aperture system at amplitude factor of 1.4, the increase in heat loss over the closed apertures is 4.4%, 2.8%, and 2.2% at f=25, 40, and 60rpm, respectively.