The finite element method has been widely used to discretize the Helmholtz equation with various types of boundary conditions. The strong indefiniteness of the Helmholtz equation makes it difficult to establish stability estimates for the numerical solution. In particular, discontinuous Galerkin methods for Helmholtz equation with a high wave number result in very large matrices since they typi...

A phenomenon which is usually considered as the main disadvantage of photoacoustic Helmholtz cells is photoacoustic background signal resulting from the light absorption by the cell windows. Although there are methods which reduce this background signal, e.g. light wavelength modulation or time domain filtering of the photoacoustic response from the sample, the methods are limited to particular...

In this letter we present a coupled Helmholtz machine for principal component analysis (PCA), where sub-machines are related through sharing some latent variables and associated weights. Then, we present a wake-sleep PCA algorithm for training the coupled Helmholtz machine, showing that the algorithm iteratively determines principal eigenvectors of a data covariance matrix without any rotationa...

The reverse side of Helmholtz paradox is presented here. Helmholtz paradox itself had been formulated as follows: in the ideal (non-viscid) newtonian fluids any vorticity should be stable (constant) during infinite time. It means that if vortex arise in nonviscid newtonian fluid, such a vortex should have the constant strength all the time. In our note to Helmholtz paradox, we proved that Vorte...

Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine or Variational Autoencoder, involves training a top-down directed generative model together with a bottom-up auxiliary model used for approximate inference. Recent results indicate that better generative models can be obtained with better approximat...

This paper presents an approach to the topic extraction from text documents using probabilistic graphical models. Multiple-cause networks with latent variables are used and the Helmholtz machines are utilized to ease the learning and inference. The learning in this model is conducted in a purely data-driven way and does not require prespecified categories of the given documents. Topic words ext...

This paper studies the acoustical properties of hard-backed porous layers with periodically embedded air filled Helmholtz resonators. It is demonstrated that some enhancements in the acoustic absorption coefficient can be achieved in the viscous and inertial regimes at wavelengths much larger than the layer thickness. This enhancement is attributed to the excitation of two specific modes: Helmh...

Modeling of small Helmholtz resonators based on electroacoustical analogies often results in significant disagreement with measurements, as existing models do not take into account some losses that are observed in practical implementations of such acoustical circuits, e.g., in photoacoustic Helmholtz cells. The paper presents a method which introduces loss corrections to the transmission line m...

This paper demonstrates that a hydraulically acting Helmholtz resonator can exist in a piezoelectric–hydraulic pump (PHP) based hybrid actuator, which in turn affects the volumetric efficiency of the PHP. The simulation and experimental results illustrate the effect of Helmholtz resonance on the flow rate performance of the PHP. The study also shows how to shift the Helmholtz resonant frequency...

We demonstrate the existence of vector Helmholtz-Gauss (vHzG) and vector Laplace-Gauss beams that constitute two general families of localized vector beam solutions of the Maxwell equations in the paraxial approximation. The electromagnetic components are determined starting from the scalar solutions of the two-dimensional Helmholtz and Laplace equations, respectively. Special cases of the vHzG...