Maximum Mesh Size Research Articles

An Evaluation of High Acceleration Voltage Electron Beam Writing on X-Ray Masks

High acceleration voltage electron beam (EB) writing on X-ray masks was evaluated. Normalized dose latitudes of 100 keV for the 0.15 µm line and space (L&S), isolated lines and isolated space patterns were 3.5, 2.7 and 7.6 times larger than those of 25 keV, respectively. It was also found that the back-scattered electrons extend over a range of 10 µm in 100 keV writing. The maximum mesh size in the pattern area density method for proximity effect correction was evaluated by Monte Carlo simulation. When a ±10% pattern size error was permitted for a 0.1 µm line pattern, the 0.3 µm mesh size in 50 keV writing was markedly improved to 5 µm at a higher voltage of 100 keV. Reducing the beam size by half from 60 nm (2σ) in 100 keV writing also increases the mesh size from 0.4 to 5 µm. Moreover, the fine W–Ti patterns of 0.06–0.14 µm were formed using 100 keV Gaussian EB writing and electron cyclotron resonance (ECR) etching systems, where good linearity and linewidth deviations within 9 nm (3σ) were obtained.

Mass-Conserving Front Tracking for Miscible Two-Phase Flow

A critical analysis of the mass conservation properties of the jump discontinuity propagating algorithms in the front-tracking method of Glimm et al. is performed in the context of miscible, two-phase, incompressible flow in porous media. These algorithms do not enforce the conservation of mass properties of the hyperbolic system on any grid of finite discretization size. For the curve propagation algorithm, which is the core of the suite of discontinuity movement algorithms, we show that mass conservation errors vanish linearly with maximum mesh size of the moving grids. We present new curve propagation and redistribution algorithms which conserve mass for any grid of finite spacing. Analogously mass-conserving untangling routines have also been developed. We investigate the performance of these new algorithms for diagonal five-spot computations.

Application of FEM Modal Analysis to the Estimation of Sound Radiation Power.

The estimation theory of sound power which has been established based on the analytical modal analysis is extended to application based on FEM modal analysis. We tried to estimate the sound power radiated from a semisphere, which is a simple model of the lid of an automobile transmission case and is difficult to analyze the natural modes by analytical modal analysis. Next, the mesh size of the FEM model, with which the estimation of sound power will converge within the accuracy of ±0.3 dB, was investigated using some FEM models with various mesh sizes. As a result, the estimated sound power coincided with the measured values with an accuracy sufficient for practical usage, and converged within the accuracy stated above when the maximum mesh size was smaller than one-sixth the wavelength of the highest frequency component. These results were confirmed by applying them to similar structures, such as derby hat and silkhat structures.

Age, Growth, and Catch Analysis of the Commercially Exploited Paddlefish Population in Kentucky Lake, Kentucky-Tennessee

Paddlefish Polyodon spathula from the 1985-1986 commercial harvest from Kentucky Lake, Kentucky-Tennessee, were weighed and their lengths from eye to fork of the tail were measured. During 52 observed trips, commercial fishermen harvested 702 paddlefish (4,002 kg) with 788 gill-net-nights of effort. However, the harvest was a disappointment to the fishermen because catch rates were low, and only 15 gravid females were included in the observed catch. The paddlefish that were aged from dentary bones (N = 362) were 2-16 years old. The age-length equation was a log10 transformation of a linear relationship, and the weight-length equation was a log10 transformation of an algebraic relationship. There were no significant differences in backcalculated growth between sexes. Growth was slower than reported for most other populations. The sex ratio was 1:1, and the youngest sexually mature fish were 6 and 8 years old for males and females, respectively. The age of recruitment and annual mortality were 8 years and 61 % for males and 9 years and 60% for females. Overall recruitment age was 9 years, and annual mortality was 69%. The mean length and weight of paddlefish in the commercial catch was 691 mm and 5.7 kg, the mean commercial catch was 57.1 kg and 13.5 fish per night, and mean catch per unit effort (CPUE) was 3.77 kg/91.4-m net per night. Mean size offish, catch rate, and CPUE were highest during the spawning run. A gill-net mesh size of 127 mm was most popular and caught larger fish. The Kentucky Lake paddlefish population shows several signs of overexploitation: high mortality for several years, a comparatively young population, and a low number of spawners. Therefore, we recommend the creation of a spawning refuge, implementation of a maximum gill-net mesh size, and an increase in commercial fishing license fees for paddlefish management.

Adaptivity and Error Estimation for the Finite Element Method Applied to Convection Diffusion Problems

A detailed analysis is performed for a finite element method applied to the general one-dimensional convection diffusion problem. Piecewise polynomials are used for the trial space. The test space is formed by locally projecting L-spline basis functions onto “upwinded” polynomials. The error is measured in the $L_p$ mesh dependent norm. The method is shown to be quasi-optimal, provided that the input data is piecewise smooth—a reasonable assumption in practice. A posteriors error estimates are derived having the property that the effectivity index $\theta = $ (error estimate/true error) converges to one as the maximum mesh size goes to zero. These error estimates are composed of locally computable error indicators, providing for an adaptive mesh refinement strategy. Numerical results show that $\theta $ is nearly one even on coarse meshes, and optimal rates of convergence are attained by the adaptive procedure. The robustness of the algorithm is tested on a nonlinear turning point problem modeling flow through an expanding duct.

Electrification of the powders used to make titanium carbide by self-propagating synthesis under conditions of sieving and pouring

This article examines the effects of the contacting surface material on the electrification of powders on sieving through brass and nickel sieves with a mesh size of 0.3 mm. The dependence of the specific charge on the sieve material, the mesh size, and the mass flow rate was investigated. The dependence of the specific charge on the length of the surface was examined under pouring conditions. The results indicate that the charges acquired by contact with a nickel sieve were larger than those with a brass one, but the powders constituted by fine-grained magnesium-thermal titanium and titanium of grade PTM had different charges with both types of sieves, while coarse powders of magnesium-thermal titanium in a brass sieve were electrified even more than in a nickel one. It is concluded that to reduce the ignition and explosion hazards arising from the electrification, it is necessary to use brass sieves of maximum mesh size (provided that the process will still operate normally), while the layer thickness during sieving and pouring should be maximal, and the length of the pouring troughs should be minimal.

An error estimate for theH −1 Galerkin method for a parabolic problem with non-smooth initial data

A non-smooth data error estimate with respect to theL 2 norm is shown for a semidiscrete Galerkin-Petrov method for a parabolic problem in one space dimension. If the trial and test spaces consist of piecewise polynomials of degreer−1 inC k anr+1 inC k+2 , respectively, with test functions satisfying boundary conditions, then the error norm is bounded byCh r t −r/2 fort positive, whereh is the maximum mesh size.

Convergence of the ACM Finite Element Scheme for Plate Bending Problems

Summary Convergence rates of the ACM non-conforming scheme are evaluated. This scheme is usually employed for two-dimensional bi-harmonic boundary-value and eigenvalue problems arising from plate bending analysis. When the shape of the domain is rectangular and the exact solution is sufficiently smooth, Z,2~error bounds of moments and deflection and error of eigenvalue are all at the order of square of the maximum mesh size. This result is also confirmed by numerical experiments.

Finite difference techniques for ring capacitors

This paper describes finite difference techniques used to calculate the capacitance of a ring capacitor. The determination of capacitance involves the solution of a Dirichlet boundary value problem and the calculation of the gradient of the solution obtained. Circular cylindrical coordinates are used. Nine point difference approximations are used for the Laplacian and the first derivatives of a function. If this function satisfies Laplace's equation and is sufficiently differentiable, the discretization error of each approximation isO(h 4) whereh is the maximum mesh size.

A computer model of disks of stars

A computer model for isolated disks of stars is described. The evolution of disks of stars is investigated by following the self-consistent motion of large numbers of point masses as they move in the plane of the disk. Two methods for obtaining the gravitational potential are used. In one method the gravitational potential is obtained by summing directly the 1 r contribution from groups of stars and in the other method Fourier transform techniques are used. The behavior of the model has been compared for the two methods by studying the results for the particular case of an initially balanced uniformly rotating disk. Such a system is unstable and breaks up into a number of subsystems during the first rotation. The effect of varying the discretization parameters has been studied. The maximum mesh size used was 128 × 128 and the largest number of stars used was 200,000.