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Traveling-wave solutions to thin-film equations

Physical Review E 1993年第6期48卷 4423-4423页

作者： Stefanella Boatto Leo P. Kadanoff Piero Olla Computational and Applied Mathematics Program Ryerson Laboratory The University of Chicago Chicago Illinois 60637

Thin films can be effectively described by the lubrication approximation, in which the equation of motion is ht+(hnhxxx)x=0. Here h is a necessarily positive quantity which represents the height or thickness of the film. Different values of n, especially 1, 2, and 3 correspond to different physical situations. This equation permits solutions in the form of traveling disturbances with a fixed form. If u is the propagation velocity, the resulting equation for the disturbance is uhx=(hnhxxx)x. Here, quantitative and qualitative solutions to the equation are presented. The study has been limited to the intervals in x where the solutions are positive. It is found that transitions between different qualitative behaviors occur at n=3, 2, 3/2, and 1/2. For example, if u is not zero, solitonlike solutions defined on a finite interval are only possible for n<3. More specific results can be obtained. In the case in which the velocity is zero, solitons occur for n<2. For n=1, the region 3/21/2, single-minimum solutions diverging at ±∞ are possible. The generic solution, present for all positive values of n, is a receding front, which diverges at finite x for n<0.

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A molecular dynamical study of granular fluids I: The unforced granular gas in two dimensions

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Journal of Scientific Computing 1993年第1期8卷 1-40页

作者： Goldhirsch, I. Tan, M.-L. Zanetti, G. Department of Fluid Mechanics and Heat Transfer Faculty of Engineering Tel-Aviv University Ramat Aviv 69978 Tel-Aviv Israel Program in Applied and Computational Mathematics Princeton University Princeton 08544 New Jersey United States

Results of a numerical study of the dynamics of a collection of disks colliding inelastically in a periodic two-dimensional enclosure are presented. The properties of this system, which is perhaps the simplest model for rapidly flowing granular materials, are markedly different from those known for atomic or moleclar gases, in which collisions are of elastic nature. The most prominent feature characterizing granular systems, even in the idealized situation in which no external forcing exists and the initial condition is statistically homogeneous, is their inherent instability to inhomogeneous fluctuations. Granular "gases" are thus generically nonuniform, a fact that suggests extreme caution in pursuing direct analogies with molecular gases. We find that once an inhomogeneous state sets in, the velocity distribution functions differ from the classical Maxwell-Boltzmann distribution. Other characteristics of the system are different from their counterparts in molecular systems as well. For a given value of the coefficient of restitution, e, a granular system forms clusters of typical separation L₀≈l/(1-e²)^1/2, where l is the mean free path in the corresponding homogeneous system. Most of the fluctuating kinetic energy then resides in the relatively dilute regions that surround the clusters. Systems whose linear dimensions are less then L⁰ do not give rise to clusters;still they are inhomogeneous, the scale of the corresponding inhomogeneity being the longest wavelength allowed by the system's size. The present article is devoted to a detailed numerical study of the above-mentioned clustering phenomenon in two dimensions and in the absence of external forcing. A theoretical framework explaining this phenomenon is outlined. Some general implications as well as practical ramifications are discussed. © 1993 Plenum Publishing Corporation.

关键词： Granular flow dynamics molecular dynamics numerical simulation

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A FOCUS VERNIER FOR OPTICAL LITHOGRAPHY 7

A FOCUS VERNIER FOR OPTICAL LITHOGRAPHY

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7TH ANNUAL CONF ON INTEGRATED CIRCUIT METROLOGY, INSPECTION, AND PROCESS CONTROL

作者： ARNOLD, WH BAROUCH, E HOLLERBACH, U ORSZAG, SA Advanced Micro Devices Inc. Integrated Technology Division MS 79 901 Thompson Place Sunnyvale 94088-3453 CA United States Program in Applied and Computational Mathematics Princeton University Princeton 08544-1000 NJ United States

ISBN: (纸本)0819411604

As the depth of focus of optical steppers grows smaller, it becomesmore important to determine the position of best focus accurately andquickly. This paper describes the use of phase-shifted mask technologyto form a focus vernier: a phase pattern on the stepper reticle which,when imaged in resist, cangive both the magnitude and the direction ofthe focus error. In this, the focus vernier structure is analogous to3overlay verniers. Thus the determination of focus error can be treatedas an alignment problem in the z-axis. This technique is an improvementon previous schemes for the determination of best focus from resistimages as it can indicate both the magnitude of the error and itsdirection in a single exposure. © 1993 Proceedings of SPIE - The International Society for Optical Engineering. All rights reserved.

关键词： Errors

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Evaluation of depth‐of‐focus in photolithography at 193 and 248 nm for feature sizes of 0.25 μm and below

Journal of Vacuum Science & Technology B: Microelectronics a...

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Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena 1993年第6期11卷 2720-2724页

作者： M. Rothschild S. P. Doran E. Barouch U. Hollerbach S. A. Orszag Lincoln Laboratory Massachusetts Institute of Technology Lexington Massachusetts 02173‐9108 Program of Applied and Computational Mathematics Princeton University Princeton New Jersey 08544

The aerial image of alternative exposure systems was calculated in order to determine process latitude in photolithography at 0.25 μm and below. A fast software package was used for both simple and complex mask patterns. The depth‐of‐focus (DOF) was obtained with the aid of exposure–defocus plots at 193 and 248 nm. The numerical aperture and degree of spatial coherence were varied over a wide range. The effects of annular illumination were also studied. It was shown that for most geometries the DOF at 193 nm exceeds that of 248‐nm systems. Only for equal lines and spaces does a 248‐nm tool with annular illumination possess a DOF comparable to that of a conventionally illuminated 193‐nm system.

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Modeling of multilayer ion etching processes

Journal of Vacuum Science & Technology B: Microelectronics a...

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Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena 1993年第4期11卷 1310-1313页

作者： S. J. Sherwin E. Barouch G. E. Karniadakis S. A. Orszag Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08540 Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540

Numerical simulation is used to model ion etching in trilayer lithography. The simulations are capable of capturing the evolution of the boundary between two materials as well as the physically observed phonemena reactive ion etching lag and undercutting. Numerical results are compared with experimental data and a good agreement is found except close to the material interface where the slope of the surface is large. This error is attributed to a purely energy dependent yield used in the simulations.

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Benchmark Tests of Principal Fissile Nuclide Data in JENDL-3 with Simple Fast Critical Assemblies

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Journal of Nuclear Science and Technology 1993年第11期30卷 1087页

作者： TIAN, Dongfeng HASEGAWA, Akira NAKAGAWA, Tsuneo KIKUCHI, Yasuyuki Nuclear Data Center Department of PhysicsTokai Research EstablishmentJapan Atomic Energy Research Institute A visiting scientist through STA Scientist Exchange Program from Institute of Applied Physics and Computational Mathematics

A series of benchmark tests was made to check the neutron nuclear data of main fissile nuclides (239Pu, 236U and 233U) of JENDL-3 for fast reactors. A total of nine critical assemblies were analyzed. They are assemblies of single material, high enrichment and simple geometry with small volume and therefore suitable for nuclear data testing. Criticality calculation was made by ANISN with S16P5 using the VITAMIN-J 175-energy-group. Discussions are made on ken, spectral indices at core center and leakage spectra. From the study, a problem was pointed out relating to the interpolation of secondary-neutron energy distributions for threshold reactions near the threshold energy point adopted in the original JENDL-3 and its remedy was proposed. By the benchmark tests of thus revised JENDL-3 (JENDL-3.1), it was shown that integral experiments for 239Pu and 235U cores were reproduced quite satisfactorily. On the contrary, it was revealed that large deviations for 233U cores from the experiment were due to uncertainties of the fission spectrum and the inelastic scattering cross sections, In the present work, sensitivity of "a" parameter (level density parameter) of Madland-Nix's fission spectrum formula to the integral data was extensively studied. Some recommendations are made to improve JENDL-3.1.

关键词： JENDL-3 fast reactors benchmarks neutrons nuclear data cross section plutonium-239 uranium-235 uranium-233 Madland-Nix's fission spectra k eff spectral index leakage spectra accuracy

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FUZZY MOLECULAR-SURFACES

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JOURNAL OF BIOMOLECULAR STRUCTURE & DYNAMICS 1992年第4期9卷 759-768页

作者： AGISHTEIN, ME Program in Applied and Computational Mathematics Fine Hall Princeton University NJ 08544-1000.

Surface area of a macromolecule, accessible to a solvent, is defined and calculated, taking into account the probabilistic character of atomic positions due to the high frequency atomic vibrations. For a given a space point, we consider a probability of the event, that this point is covered by a macromolecule. A volume is defined as a space integral of this probability field. The envelope, accessible to a solvent molecule center, becomes fuzzy, existing only in a probabilistic sense. The accessible area is defined as a derivative of the envelope volume with respect to the probe size. The accessible area thus defined has the advantage of being an analytic function of atomic coordinates and allows for an arbitrary (not necessarily spherical) probe geometry. Space integration is performed on a rectangular grid, using a third order Runge-Kutta integration scheme and the analytical subgrid averaging.

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SIMULATIONS OF 4-DIMENSIONAL SIMPLICIAL QUANTUM-GRAVITY AS DYNAMIC TRIANGULATION

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MODERN PHYSICS LETTERS A 1992年第12期7卷 1039-1061页

作者： AGISHTEIN, ME MIGDAL, AA Program in Applied and Computational Mathematics Fine Hall Princeton University Princeton NJ 08544–1000 USA

Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. We studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a function of the gravitational one, separating the phases of opened and closed Universe. When the bare cosmological constant approaches this line from above, the four-volume grows: we reached about 5 x 10(4) simplexes, which proved to be sufficient for the statistical limit of infinite volume. However, for the genuine continuum theory of gravity, the parameters of the lattice model should be further adjusted to reach the second order phase transition point, where the correlation length grows to infinity. We varied the gravitational constant, and we found the first order phase transition, similar to the one found in three-dimensional model, except in 4D the fluctuations are rather large at the transition point, so that this is close to the second order phase transition. The average curvature in cutoff units is large and positive in one phase (gravity), and small negative in another (antigravity). We studied the fractal geometry of both phases, using the heavy particle propagator to define the geodesic map, as well as with the old approach using the shortest lattice paths. The heavy propagator geodesic appeared to be much smoother, so that the scaling laws were found, corresponding to finite fractal dimensions: D+ approximately 2.3 in the gravity phase and D- approximately 4.6 in the antigravity phase. Similar, but somewhat lower numbers were obtained from the heat kernel singularity. The influence of the alpha-R2 terms in 2, 3 and 4 dimensions is discussed.

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Parallel spectral-element-Fourier simulation of turbulent flow over riblet-mounted surfaces

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Theoretical and computational Fluid Dynamics 1992年第4期3卷 219-229页

作者： Chu, Douglas Henderson, Ron Karniadakis, George Em Department of Mechanical and Aerospace Engineering and Program in Applied and Computational Mathematics Princeton University Princeton 08544 NJ United States

The flow in a channel with its lower wall mounted with streamwise V-shaped riblets is simulated using a highly efficient spectral-element-Fourier method. The range of Reynolds numbers investigated is 500 to 4000, which corresponds to laminar, transitional, and turbulent flow states. Our results suggest that in the laminar regime there is no drag reduction, while in the transitional and turbulent regimes drag reduction up to 10% exists for the riblet-mounted wall in comparison with the smooth wall of the channel. For the first time, we present detailed turbulent statistics in a complex geometry. These results are in good agreement with available experimental data and provide a quantitative picture of the drag-reduction mechanism of the riblets. © 1992 Springer-Verlag.

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Renormalization theory for eddy diffusivity in turbulent transport

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Physical Review Letters 1992年第20期68卷 3028-3028页

作者： Marco Avellaneda Andrew J. Majda Department of Mathematics Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544

We examine the derivation of eddy-diffusivity equations for transport of passive scalars in a turbulent velocity field. Our main contention is that, in the long-time–large-distance limit, the eddy-diffusivity equations can take very different forms according to the statistical properties of the subgrid velocity, and that these equations depend very sensitively on the interplay between spatial and temporal velocity fluctuations. Such crossovers can be represented in a ‘‘phase diagram’’ involving two relevant statistical parameters. Strikingly, the Kolmogorov-Obukhov statistical theory is shown to lie on a phase-transition boundary.

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