Locking effects in the finite element approximation of elasticity problems

Summary We consider the finite element approximation of the 2D elasticity problem when the Poisson ratiov is close to 0.5. It is well-known that the performance of certain commonly used finite elements deteriorates asv0, a phenomenon calledlocking. We analyze this phenomenon and characterize the strength of the locking androbustness of varioush-version schemes using triangular and rectangular elements. We prove that thep-andh-p versions are free of locking with respect to the error in the energy norm. A generalization of our theory to the 3D problem is also discussed.The work of this author was supported in part by the Office of Naval Research under Naval Research Grant N00014-90-J-1030The work of this author was supported in part by the Air Force Office of Scientific Research, Air Force Systems Command, U.S. Air Force, under grant AFOSR 89-0252     

Anomalous elastic behaviour of Bi-Pb-Ag composites

Bi-Pb and Bi-Pb-Ag superconducting composites have been prepared by the solid state reaction method. After the usual characterization, ultrasonic longitudinal velocity and attenuation studies have been undertaken over a temperature range 80–300 K by the pulse transmission technique. In contrast to normal solids, the ultrasonic velocities of both the samples in the temperature range 200-100 K are found to decrease with decreasing temperature (softening), followed by a velocity maximum. The samples are also found to exhibit longitudinal attenuation peaks at TEMPERATURES = 260, 160 and 120 K. An attempt has also been made to verify whether the Wachtman's equations can theoretically explain the low-temperature behaviour of the Young's modulus of these materials. A qualitative explanation for both the phenomena of softening of velocity as well as the occurrence of attenuation peaks is given.     

Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems

Summary. A domain with possibly non-Lipschitz boundary is defined as a limit of monotonically expanding or shrinking domains with Lipschitz boundary. A uniquely solvable Dirichlet boundary value problem (DBVP) is defined on each of the Lipschitz domains and the limit of these solutions is investigated. The limit function also solves a DBVP on the limit domain but the problem can depend on the sequences of domains if the limit domain is unstable with respect to the DBVP. The core of the paper consists in estimates of the difference between the respective solutions of the DBVP on two close domains, one of which is Lipschitz and the other can be unstable. Estimates for starshaped as well as rather general domains are derived. Their numerical evaluation is possible and can be done in different ways. Received October 16, 2001 / Revised version received January 16, 2002 / Published online: April 17, 2002 RID="*" ID="*" The research was funded partially by the National Science Foundation under the grants NSF–Czech Rep. INT-9724783 and NSF DMS-9802367 RID="**" ID="**" Support for Jan Chleboun coming from the Grant Agency of the Czech Republic through grant 201/98/0528 is appreciated     

Electrical conductivity and dielectric loss in doped Pb(NO3)2 single crystals

dc ionic conductivity measurements were made on single crystals of Pb(NO₃)₂ doped with monovalent Na⁺ and K⁺ in the temperature range of 100–400°C. In the extrinsic region the conductivity was found to decrease with Na⁺ having a smaller ionic size, and to increase with K⁺ with larger ionic size compared to the host Pb ion. Conductivity is attributed to the mobility of anti-Frenkel defects as in the case of PbF₂. Dielectric loss measurements were made on the Pb(NO₃)₂: K⁺ system in the frequency range of 300 Hz to 20 kHz at different temperatures. Impurity vacancy pairs of the type K⁺-(NO^-₃)_V are found to be responsible for the observed dielectric loss peaks. The maximum peak frequency is found to increase with temperature.     

An Exact Solution for the Optical Absorbance of Thin Films

The electric and magnetic fields within optical thin films are obtained exactly in closed form as solutions of a system of difference equations presented by Berning and utilized by Dill, Neureuther, Tuttle, and Walker in their sample program for modeling optical lithography. The solution allows an explicit closed form expression for the absorbance.     

Aligned magnetic effects through varying permeable bed

The aligned magnetic effects on a steady laminar, viscous, incompressible, conducting fluid down an open inclined channel bounded below by a bed of varying permeability has been studied when the free surface is exposed to atmospheric pressure. Beavers and Joseph slip condition at the interface of the free flow region and the fluid flow in the porous bed and the Darcy’s law in the porous medium have been used. The expressions for velocity, magnetic strength and the mass flow across the cross-section of the channel are obtained.     

Asymptotically exact a posteriori error estimator for biquadratic elements

This paper addresses the finite element method with a posteriori error estimation for elements of degree p = 1 and p = 2. It gives the formulae for the error indicators and error estimators. Basic mathematical characterizations of the estimators are given and it is shown that the estimators for p = 1 and p = 2 have different structures. Numerical examples show the effectivity of the approach and the high quality of the estimator.     

Some optimizations on detecting gravitational wave using convolutional neural network

This work investigates the problem of detecting gravitational wave (GW) events based on simulated damped sinusoid signals contaminated with white Gaussian noise. It is treated as a classification problem with one class for the interesting events. The proposed scheme consists of the following two successive steps: decomposing the data using a wavelet packet, representing the GW signal and noise using the derived decomposition coefficients; and determining the existence of any GW event using a convolutional neural network (CNN) with a logistic regression output layer. The characteristic of this work is its comprehensive investigations on CNN structure, detection window width, data resolution, wavelet packet decomposition and detection window overlap scheme. Extensive simulation experiments show excellent performances for reliable detection of signals with a range of GW model parameters and signal-to-noise ratios. While we use a simple waveform model in this study, we expect the method to be particularly valuable when the potential GW shapes are too complex to be characterized with a template bank.