This paper gives a systematic introduction to HMM,the heterogeneous multiscale methods,including the fundamental design principles behind the HMM philosophy and the main obstacles that have to be overcome when using H...
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This paper gives a systematic introduction to HMM,the heterogeneous multiscale methods,including the fundamental design principles behind the HMM philosophy and the main obstacles that have to be overcome when using HMM for a particular *** is illustrated by examples from several application areas,including complex fluids,micro-fluidics,solids,interface problems,stochastic problems,and statistically self-similar *** is given to the technical tools,such as the various constrained molecular dynamics,that have been developed,in order to apply HMM to these *** of mathematical results on the error analysis of HMM are *** review ends with a discussion on some of the problems that have to be solved in order to make HMM a more powerful tool.
Substantial R&D activities are presently under way toward the development of advanced pulsed-laser-based production tools and processes that can enable sophisticated yet effective crystallization of Si films for m...
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We describe a computational framework linking uncertainty quantification (UQ) methods for continuum problems depending on random parameters with equation-free (EF) methods for performing continuum deterministic numeri...
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We consider the construction of point processes from tilings, with equal-volume tiles, of d-dimensional Euclidean space Rd. We show that one can generate, with simple algorithms ascribing one or more points to each ti...
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We consider the construction of point processes from tilings, with equal-volume tiles, of d-dimensional Euclidean space Rd. We show that one can generate, with simple algorithms ascribing one or more points to each tile, point processes which are “superhomogeneous” (or “hyperuniform”)—i.e., for which the structure factor S(k) vanishes when the wave vector k tends to zero. The exponent γ characterizing the leading small-k behavior, S(k→0)∝kγ, depends in a simple manner on the nature of the correlation properties of the specific tiling and on the conservation of the mass moments of the tiles. Assigning one point to the center of mass of each tile gives the exponent γ=4 for any tiling in which the shapes and orientations of the tiles are short-range correlated. Smaller exponents in the range 4−d<γ<4 (and thus always superhomogeneous for d≤4) may be obtained in the case that the latter quantities have long-range correlations. Assigning more than one point to each tile in an appropriate way, we show that one can obtain arbitrarily higher exponents in both cases. We illustrate our results with explicit constructions using known deterministic tilings, as well as some simple stochastic tilings for which we can calculate S(k) exactly. Our results provide an explicit analytical construction of point processes with γ>4. Applications to condensed matter physics, and also to cosmology, are briefly discussed.
This paper presents a systematic approach for finding efficient boundary conditions for molecular dynamics simulations of crystalline solids. These boundary conditions effectively eliminate phonon reflection at the bo...
This paper presents a systematic approach for finding efficient boundary conditions for molecular dynamics simulations of crystalline solids. These boundary conditions effectively eliminate phonon reflection at the boundary and at the same time allow the thermal energy from the bath to be introduced to the system. Our starting point is the Mori-Zwanzig formalism [R. Zwanzig, J. Chem. Phys. 32, 1173 (1960); in Systems Far from Equilibrium, edited by L. Garrido (Interscience, New York, 1980); H. Mori, Prog. Theor. Phys. 33, 423 (1965)] for eliminating the thermal bath, but we take the crucial next step that goes beyond this formalism in order to obtain memory kernels that decay faster. An equivalent variational formulation allows us to find the optimal approximate boundary conditions, after specifying the spatial-temporal domain of dependence for the positions of the boundary atoms. Application to a one-dimensional chain, a two-dimensional Lennard-Jones system, and a three-dimensional model of α-iron with embedded atom potential is presented to demonstrate the effectiveness of this approach.
In order to illustrate the application of the biorthogonal eigenfunction system to receptivity problems and to multimode decomposition, a study case is chosen so that all steps of the method are accompanied by analyti...
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ISBN:
(纸本)1563478978
In order to illustrate the application of the biorthogonal eigenfunction system to receptivity problems and to multimode decomposition, a study case is chosen so that all steps of the method are accompanied by analytical solutions. The receptivity of an inviscid supersonic flow past a flat plate to localized periodic-in-time perturbations emanating from the wall is revisited within the scope of the method of the biorthogonal eigenfunction system for linearized Euler's equations. In addition, application of the biorthogonal eigenfunction system to projection of computational results onto modes of continuous spectra is shown.
We use an “equation-free,” coarse-grained computational approach to accelerate molecular dynamics-based computations of demixing (segregation) of dissimilar particles subject to an upward gas flow (gas-fluidized bed...
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We use an “equation-free,” coarse-grained computational approach to accelerate molecular dynamics-based computations of demixing (segregation) of dissimilar particles subject to an upward gas flow (gas-fluidized beds). We explore the coarse-grained dynamics of these phenomena in gently fluidized beds of solid mixtures of different densities, typically a slow process for which reasonable continuum models are currently unavailable.
Bids during an online auction arrive at unequally-spaced discrete time points. Our goal is to capture the entire continuous price-evolution function by representing it as a functional object. Various nonparametric smo...
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ISBN:
(纸本)1595937005
Bids during an online auction arrive at unequally-spaced discrete time points. Our goal is to capture the entire continuous price-evolution function by representing it as a functional object. Various nonparametric smoothing methods exist to recover the functional object from the observed discrete bid data. Previous studies use penalized polynomial and monotone smoothing splines;however, these require the determination and storage of a large number of coefficients and often lengthy computational time. We present a family of parametric growth curves that describe the price-evolution during online auctions. This approach is parsimonious and has an appealing interpretation in the online auction context. We also provide an automated fitting algorithm that is computationally fast. Methods are illustrated using eBay data. Copyright 2007 ACM.
This work utilizes pulsed, melt-mediated laser crystallization techniques to control the spatial distribution of crystalline zones within an as sputter-deposited amorphous matrix. Since shape memory responses stem fro...
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ISBN:
(纸本)9780912035888
This work utilizes pulsed, melt-mediated laser crystallization techniques to control the spatial distribution of crystalline zones within an as sputter-deposited amorphous matrix. Since shape memory responses stem from crystallographic shifts, only the selectively crystallized regions exhibit these properties. This process provides not only spatial control over the shape memory response, but potentially, through proper use of operational parameters, the shape memory response itself, i.e. phase transformation temperature, transformation strain, recovery stress etc. The solidification process is monitored in situ via transient reflectance. Furthermore, the effects of varying energy density within the irradiated region are examined with respect to the resulting micro-structure via atomic force microscopy (AFM), electron backscatter diffraction (EBSD) and x-ray diffraction (XRD).
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