A method for visualization of ventricular fibrillation: Design of a cooled fiberoptically coupled image intensified CCD data acquisition system incorporating wavelet shrinkage based adaptive filtering

The measurement of cardiac transmembrane potential changes with voltage sensitive dyes is in increasing use. Detection of these very small fluorescent alterations using large multiplexed arrays, such as charge coupled device (CCD) cameras at high sampling rates, has proven challenging and usually requires significant averaging to improve the signal-to-noise ratio. To minimize the damage of living tissue stained with voltage sensitive dyes, excitation photon exposure must be limited, with the inevitable consequence of diminishing the fluorescence that is generated. State-of-the-art high frame rate CCD cameras have read noise levels in the 5-10 e(-) rms range, which is at least two orders of magnitude above that required to detect voltage sensitive dye alterations at individual pixels corresponding to 1 mm(2) heart regions illuminated with levels of 100 mW/cm(2) at frame rates approaching 1000 frames/sec. Image intensification is thus required prior to photon quantification. We report here the development of such a data acquisition system using commercially available hardware. Additionally, in the past ten years, a mathematical theory of multiresolution has been developed, and new building blocks called wavelets, allow a signal to be observed at different resolutions. Wavelet analysis also makes possible a new method of extricating signals from noise. We have incorporated spatially adaptive filters based on wavelet denoising of individual pixels to significantly reduce the multiple noise sources present in the acquired data. (c) 1998 American Institute of Physics.     

The dynamics of co- and counter rotating coupled spherical pendula

The dynamics of co- and counter-rotating coupled spherical pendula (two lower pendula are mounted at the end of the upper pendulum) is considered. Linear mode analysis shows the existence of three rotating modes. The linear modes allow us to understand the nonlinear normal modes, which are visualized in frequency-energy plots. With the increase of energy in one mode we observe a symmetry breaking pitchfork bifurcation. In the second part of the paper we consider energy transfer between pendula having different energies. The results for co-rotating (all pendula rotate in the same direction) and counter-rotating motion (one of lower pendula rotates in the opposite direction) are presented. In general, the energy fluctuations in counter-rotating pendula are found to be higher than in the co-rotating case.     

Prediction of the thermal properties of CO2, CO, and Xe laser media

Approximation functions describing the experimental data of thermal conductivity and viscosity of chosen gases (CO₂, N₂, He, Xe, CO, O₂, Ar) are given in the paper. Introduced formulas allow to predict thermal conductivity and temperature distribution of typical high-power laser gas mixture. Examples of temperature distribution in RF excited CO₂, CO, and Xe laser media are shown. Knowledge of the temperature distribution in the laser cavity can be useful for predicting the general properties of laser.     

Effect of thermal annealing in air on scintillation properties of LuAG and LuAG:Pr

Pure and Pr-activated Lu₃Al₅O₁₂ (LuAG) crystals have been grown by the Czochralski method. In order to improve the scintillation properties, several samples have been annealed in air. Various annealing temperatures and periods of time have been tested to determine optimal conditions in the way of scintillation yield and energy resolution enhancement. The largest increase of yield of LuAG:Pr (17%), accompanied by a distinct decrease of resolution, has been observed after annealing at 1100°C for 48 h. On the contrary, in case of undoped LuAG no significant changes following thermal annealing have been noticed.     

On shear correction factors in the non-linear theory of elastic shells

Theoretical values of two correction factors α_s = 5/6 and α_t = 7/10 are established for the respective transverse shear stress resultants and stress couples within the general, dynamically and kinematically exact, six-field theory of elastic shells. These values do not depend on the shell material symmetry, geometry of the base surface, the shell thickness, or any kind of kinematic and/or dynamic constraints. The analysis is based on the complementary energy density following from the transverse shear stresses acting only on the shell cross section. The appropriate quadratic and cubic distributions of the stresses across the thickness allow one to derive the consistent constitutive equations for the transverse shear stress resultants and stress couples with α_s and α_t as the respective correction factors. Four numerical examples of highly non-linear shell structures illustrate the influence of different values of α_s and α_t on the results. In particular, some influence of α_t is noticed on the placement of bifurcation points. In dynamic problem of flight of three intersecting plates analysed with Newmark-type temporal algorithm, the value of α_t influences the moment at which the relative error of total energy of the system begins to grow indefinitely leading to the solution failure.     

A multi-mesh finite element method for Lagrange elements of arbitrary degree

We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviors of these variables, the meshes can be independently adapted. The resulting linear systems are usually much smaller, when compared to the usage of a single mesh, and the overall computational runtime can be more than halved in such cases. Our multi-mesh method works for Lagrange finite elements of arbitrary degree and is independent of the spatial dimension. The approach is well defined, and can be implemented in existing adaptive finite element codes with minimal effort. We show computational examples in 2D and 3D ranging from dendritic growth to solid–solid phase-transitions. A further application comes from fluid dynamics where we demonstrate the applicability of the approach for solving the incompressible Navier–Stokes equations with Lagrange finite elements of the same order for velocity and pressure. The approach thus provides an easy way to implement alternative to stabilized finite element schemes, if Lagrange finite elements of the same order are required.     

Tree structured independence for exponential Brownian functionals

The product of GIG and gamma distributions is preserved under the transformation (x,y)?((x+y)⁻¹,x⁻¹−(x+y)⁻¹)$(x,y)?({(x+y)}^{-1},x^{-1}-{(x+y)}^{-1})$. It is also known that this independence property may be reformulated and extended to an analogous property on trees. The purpose of this article is to show the independence property on trees, which was originally derived outside the framework of stochastic processes, in terms of a family of exponential Brownian functionals.