Begell House
International Journal for Multiscale Computational Engineering
International Journal for Multiscale Computational Engineering
1543-1649
2
2
2004
Preface: Multiscale Methods for Emerging Technologies
Narayana R.
Aluru
Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Avenue, Urbana, IL 61801, USA
3
Multiscale Simulation of Electroosmotic Transport Using Embedding Techniques
An embedding multiscale simulation approach and its application to the electroosmotic transport in micro- and nanochannels is presented. The central idea in our multiscale simulation approach is that to analyze a coarse-scale problem, in which atomistic details are important in certain critical regions, one first performs atomistic simulation of a fine-scale system to obtain quantitative information of the system behavior in those critical regions, and then incorporates the quantitative information into continuum simulation of the coarse-scale system. To study the electroosmotic transport, two methods, namely, the modified Poisson-Boltzmann equation and velocity-embedding technique, are developed based on the embedding multiscale simulation approach. Comparison of the ion distribution and velocity profiles obtained from the multiscale simulation with the direct MD results shows very good agreement. Finally, the electroosmotic transport in a 30.0 μm wide slit channel is studied using the proposed methods, and the simulation results indicated that the classical continuum theory is not accurate at high-bulk concentrations.
R.
Qiao
Department of Mechanical and Industrial Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N.Matthews, Urbana, IL 61801
Narayana R.
Aluru
Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Avenue, Urbana, IL 61801, USA
16
Discussion of Hybrid Atomistic-Continuum Methods for Multiscale Hydrodynamics
We discuss hybrid atomistic-continuum methods for multiscale hydrodynamic applications. Both dense-fluid and dilute-gas formulations are considered. The choice of coupling method and its relation to the fluid physics as well as the need for timescale decoupling is highlighted. In particular, by relating the molecular integration timestep to the CFL timestep, we show that compressibility is important in determining the choice of a coupling method. Appropriate coupling techniques for various flow regimes are discussed and proposed. We also discuss recently developed incompressible and compressible hybrid methods for dilute gases. The incompressible framework is based on the Schwarz alternating method, which provides timescale decoupling; the compressible method is a multispecies, fully adaptive mesh and algorithm refinement approach that introduces the direct-simulation Monte Carlo at the finest level of mesh refinement.
Hettithanthrige S.
Wijesinghe
Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, MA 02139
Nicolas G.
Hadjiconstantinou
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
15
Coarse-Grained Molecular Dynamics for Computer Modeling of Nanomechanical Systems
Unique challenges for computer modeling and simulation arise in the course of the development and design of nanoscale mechanical systems. Materials often exhibit unconventional behavior at the nanoscale that can affect device operation and failure. This uncertainty poses a problem because of the limited experimental characterization at these ultrasmall length scales. In this paper, we give an overview of how we have used concurrent multiscale modeling techniques to address some of these issues. Of particular interest are the dynamic and temperature-dependent processes found in nanomechanical systems. We focus on the behavior of submicron mechanical components of Micro-Electro-Mechanical Systems (MEMS) and Nano-Electro-Mechanical Systems (NEMS), especially flexural-mode resonators. The concurrent multiscale methodology we have developed for NEMS employs an atomistic description of millions of atoms in relatively small but key regions of the system, coupled to, and run concurrently with, a generalized finite element model of the periphery. We describe two such techniques. The more precise model, Coarse-Grained Molecular Dynamics (CGMD), describes the dynamics on a mesh of elements, but the equations of motion are built up from the underlying atomistic physics to ensure a smooth coupling between regions governed by different length scales. In many cases the degrees of smoothness of the coupling provided by CGMD is not necessary. The hybrid Coupling of Length Scales methodology, combining molecular dynamics with conventional finite element modeling, provides a suitable technique for these cases at a greatly reduced computation expense. We review these models and some of the results we have obtained regarding size effects in the elasticity and dissipation of nanomechanical systems.
Robert E.
Rudd
Lawrence Livermore National Laboratory, Condensed Matter Physics Div., L-045, Livermore, CA 94551
19
From Density Functional Theory to Microchemical Device Homogenization: Model Prediction of Hydrogen Production For Portable Fuel Cells
Microchemical devices exhibit a wide spectrum of length and time scales. In this paper, we discuss hierarchical multiscale simulation of structured microreactors with square posts. Semiempirical models are used in conjunction with density functional theory to develop quantitative microkinetic models. Sensitivity Analysis (SA) and a posteriori zero-order asymptotics are employed to derive a one-step reaction rate expression that enables efficient computational fluid dynamics (CFD) simulations. The effects of catalyst surface area and dimensionality on microreactor performance are discussed. It is shown that the post microreactor exhibits nearly perfect mixing in the transverse direction, but significant back mixing in the longitudinal direction, especially at low Peclet numbers. A 1D diffusion-convection-reaction (DCR) model, with an effective diffusivity computed using homogenization theory, is employed and found to adequately describe the CFD simulations. This 1D DCR reactor model with one-step reaction model could be an efficient means for reactor optimization while retaining features from diverse scales ranging from quantum mechanics to device structural characteristics.
S. R.
Deshmukh
Department of Chemical Engineering Center for Catalytic Science and Technology (CCST), University of Delaware, Newark, DE 19716-3110
A. B.
Mhadeshwar
Department of Chemical Engineering Center for Catalytic Science and Technology (CCST), University of Delaware, Newark, DE 19716-3110
M. I.
Lebedeva
Department of Chemical Engineering Center for Catalytic Science and Technology (CCST), University of Delaware, Newark, DE 19716-3110
Dionisios G.
Vlachos
Department of Chemical Engineering Center for Catalytic Science and Technology (CCST), University of Delaware, Newark, DE 19716-3110
19
Genetic Programming for Multiscale Modeling
We propose the use of genetic programming (GP)—a genetic algorithm that evolves computer programs—for bridging simulation methods across multiple scales of time and/or length. The effectiveness of genetic programming in multiscale simulation is demonstrated using two illustrative, non-trivial case studies in science and engineering. The first case is multi-timescale materials kinetics modeling, where genetic programming is used to symbolically regress a mapping of all diffusion barriers from only a few calculated ones, thereby avoiding explicit calculation of all the barriers. The GP-regressed barrier function enables use of kinetic Monte Carlo for realistic potentials and simulation of realistic experimental times (seconds). Specifically, a GP regression is applied to vacancy-assisted migration on a surface of a binary alloy and predict the diffusion barriers within 0.1-1% error using 3% (or less) of the barriers. The second case is the development of constitutive relation between macroscopic variables using measured data, where GP is used to evolve both the function form of the constitutive equation as well as the coefficient values. Specifically, GP regression is used for developing a constitutive relation between flow stress and temperature-compensated strain rate based on microstructural characterization for an aluminum alloy AA7055. We not only reproduce a constitutive relation proposed in literature, but also develop a new constitutive equation that fits both low-strain-rate and high-strain-rate data. We hope these disparate example applications exemplify the power of GP for multiscaling at the price, of course, of not knowing physical details at the intermediate scales.
Kumara
Sastry
Department of Material Science & Engineering, Fredrick Seitz Materials Research Laboratory, University of Illinois at Urbana Champaign, Urbana IL 61801
D. D.
Johnson
Department of Material Science & Engineering, Fredrick Seitz Materials Research Laboratory, University of Illinois at Urbana Champaign, Urbana IL 61801
David E.
Goldberg
Department of General Engineering, University of Illinois at Urbana Champaign, Urbana IL 61801
Pascal
Bellon
Department of Material Science & Engineering, Fredrick Seitz Materials Research Laboratory, University of Illinois at Urbana Champaign, Urbana IL 61801
19
Toward Multiscale Modeling of Carbon Nanotube Transistors
Multiscale simulation approaches are needed in order to address scientific and technological questions in the rapidly developing field of carbon nanotube electronics. In this paper, we describe an effort underway to develop a comprehensive capability for multiscale simulation of carbon nanotube electronics. We focus in this paper on one element of that hierarchy, the simulation of ballistic CNTFETs by self-consistently solving the Poisson and Schrödinger equations using the nonequilibrium Green's function (NEGF) formalism. The NEGF transport equation is solved at two levels: i) a semiempirical atomistic level using the pz orbitals of carbon atoms as the basis, and ii) an atomistic mode space approach, which only treats a few subbands in the tube's circumferential direction while retaining an atomistic grid along the carrier transport direction. Simulation examples show that these approaches describe quantum transport effects in nanotube transistors. The paper concludes with a brief discussion of how these semiempirical device-level simulations can be connected to ab initio, continuum, and circuit level simulations in the multiscale hierarchy.
Jing
Guo
School of Electrical and Computer Engineering Purdue University, West Lafayette, IN 47907
Supriyo
Datta
School of Electrical and Computer Engineering Purdue University, West Lafayette, IN 47907
Mark
Lundstrom
School of Electrical and Computer Engineering Purdue University, West Lafayette, IN 47907
M. P.
Anantam
NASA Ames Research Center, Moffett Field, CA 94035
21
A Virtual Atom Cluster Approach to the Mechanics of Nanostructures
A virtual atom cluster (VAC) model that represents the effect of interatomic bonding is developed as the constitutive model for crystal systems. In contrast with the crystal elasticity model, the proposed VAC model is distinguished by the following features: i) It does not build any constitutive relations that involve any stress concept, and ii) it does not use the homogeneous deformation assumption, or equivalently, the Born hypothesis. As a consequence of these attributes, the energy density of the system is embedded in the VAC model and directly related to the deformation mapping. The deformation mapping is constructed through the use of meshfree or finite element shape functions. The high-order continuity property of the meshfree shape functions guarantees the accuracy in describing the geometry and thus the energy of the atomic bond. The resulting formulation computationally more efficient than the continuum-based approach. Finally, the robustness of the method is illustrated through example problems involving various nanostructures.
Dong
Qian
Department of Mechanical, Industrial and Nuclear Engineering University of Cincinnati, Cincinnati, OH 45221-0072
Rohit H.
Gondhalekar
Department of Mechanical, Industrial and Nuclear Engineering University of Cincinnati, Cincinnati, OH 45221-0072
15
Simulation of Biomolecular Systems at Multiple Length and Time Scales
A novel multiscale simulation methodology is presented that is capable of modeling complex biomolecular systems across disparate time and length-scales. The methodology presented here employs novel mesoscopic simulation methods combined with nonequilibrium molecular dynamics at the atomistic level. The resulting disparate length and time scales associated with biological assemblies are thus effectively bridged. As an example, results for the multiscale simulation of Large Unilamellar Vesicles (LUVs) immersed in solvent are presented. It is found that in all cases the LUVs slightly contract to a smaller radius, as compared to the initial perfectly round state, to one where thermal undulations persist. In cases where the effective osmotic stress is altered, the LUVs are observed to expand or contract mesoscopically.
Gary S.
Ayton
Department of Chemistry and Henry Eyring Center for Theoretical Chemistry University of Utah, 315 S. 1400 E. Rm 2020 Salt Lake City, Utah 84112-0850
Gregory A.
Voth
Department of Chemistry and Henry Eyring Center for Theoretical Chemistry University of Utah, 315 S. 1400 E. Rm 2020 Salt Lake City, Utah 84112-0850
23
Coarse-Grained Kinetic Monte Carlo Simulation of Copper Electrodeposition with Additives
A (2+1)D kinetic Monte Carlo (KMC) code was developed for coarse-grained as well as atomic-scale simulations that require detailed consideration of complex surface-reaction mechanisms associated with electrodeposition of copper in the presence of additives. The physical system chosen for simulation is similar to that used by the microelectronics industry to fabricate on-chip interconnects, where additives are used to tailor shape evolution. Although economically significant, such systems are often designed in an empirical manner that would be greatly enhanced by improved understanding of the additive mechanism gained through simulations. By comparing simulated results at atomic as well as coarse-grained scales with theoretical results obtained analytically for various limiting cases of behavior, the validity of the KMC code was tested. It was found that the surface roughness at a specified length scale can be accurately simulated by using a coarse-grained KMC code with lattice spacing of 1/10 or smaller than that of the specified length scale—a result that is particularly useful for comparing experimental data on surface roughness with numerical simulations. For second-order homogeneous surface reactions, it is shown that the KMC-simulated surface coverage approaches the analytical surface coverage as surface mixing is increased by increasing the surface diffusion rate. The results verified the numerical accuracy and the reduced computational cost of the coarse-grained KMC approach for simulating complex chemical and electrochemical mechanisms.
Timothy O.
Drews
Department of Chemical and Biomolecular Engineering University of Illinois at Urbana-Champaign, Urbana, IL 61801
Richard D.
Braatz
Department of Chemical and Biomolecular Engineering University of Illinois at Urbana-Champaign, Urbana, IL 61801
Richard C.
Alkire
Department of Chemical and Biomolecular Engineering University of Illinois at Urbana-Champaign, Urbana, IL 61801
15