The ability of a mathematical model to accurately describe a phenomenon depends on how well the model incorporates all relevant aspects, how robust the model is with respect to its mathematical form, and with respect to the numerical values of input parameters. Some models are primarily intended to reproduce known data. In other cases the purpose is to make a prediction outside the range of knowledge, or to establish details in a physical mechanism. These aspects of modelling are discussed, with examples mainly taken from the field of materials science.
The conceptualization of a problem (modeling) and the computational solution of this problem (simulation),is the foundation of Computational Science. This coupled endeavor is unique in several respects. It allows practically any complex system to be analyzed with predictive capability by invoking the multiscale paradigm linking unit-process models at lower length (or time) scales where fundamental principles have been established to calculations at the system level. The community of multiscale materials modeling has evolved into a multidisciplinary group with a number of identified problem areas of interest. Sidney Yip and Tomas Diaz De La Rubia, the editors of this volume, have gathered 18 contributions that showcase the conceptual advantages of modeling which, coupled with the unprecedented computing power through simulations, allow scientists to tackle the formibable problems of our society, such as the search forhydrocarbons, understanding the structure of a virus, or the intersection between simulations and real data in extreme environments. Scientific Modeling and Simulations advocates the scientific virtues of modeling and simulation, and also encourages the cross fertilization between communities, exploitations of high-performance computing, and experiment-simulation synergies. The contents of this book were previously published in Scientific Modeling and Simulations, Vol 15, No. 1-3, 2008.
The use of tight-binding formalism to parametrize electronic structures of crystals and molecules has been a subject of continuous interests since the pioneer work of Slater and Koster [1] more than a half of a century ago. Tight-binding method has attracted more and more attention in the last 20years due to the development of tight-binding potential models that can provide interatomic forces for molecular dynamics simulations of materials [2–7]. The simplicity of the tight-binding description of electronic structures makes the method very economical for large-scale electronic calculations and atomistic simulations [5,9]. However, studies of complex systems require that the tight-binding parameters be “transferable”, [4] i.e., to be able to describe accurately the electronic structures and total energies of a material in different bonding environments. Although tight-binding molecular dynamics has been successfully applied to a number of interesting systems such as carbon fullerenes and carbon nanotubes, [10,11] the transferability of tight-binding potentials is still the major obstruction hindering the wide spread application of the method to more materials of current interest. There are two major approximations made in a typical tight-binding representation of effective one-electronHamiltonianmatrix or band structure based on the Slater-Koster theory
In 1993 The Journal of Computer-Aided Materials Design (JCAD) was launched by a small publishing company in the Netherlands, ESCOM. The Publisher, Dr. Elizabeth Schram, had invited four scientists with common interests in computer simulations of materials to serve as editors. The motivation then was that atomistic and molecular simulations were being recognized as emerging computational tools for materials research, so it seemed reasonable to anticipate that they could be integrated into the process of design. “Since in both analysis and design one can intrinsically exploit the remarkable (and ever-increasing) capabilities of computer hardware and software technology, the intersection of computation, in the broad sense, and materials design, with its holistic nature, naturally delineates a range of issues which need to be addressed at the present time.” As for the name of the Journal, the decision was at least partially influenced by the success of another ESCOM journal, the Journal of Computer-Aided Molecular Design (JCAMD). The four editors were Anthony K. Cheetham (University of California Santa Barbara) Ulrich W. Suter (ETH Zurich), Erich Wimmer (then with Biosym in Paris), and me. After about 3years it was decided that it would be more efficient if one person would act as the Principal Editor to oversee all the operational affairs, with the other three assisting primarily in soliciting manuscripts. The understanding was that this arrangement would rotate about every three years. History shows that I was chosen to go first in this capacity, and subsequent handoffs never occurred. How did things work out? If I were asked, my answer would be the journey was up and down. JCADwitnessed the period when multiscale materials modeling and simulation began to flourish from modest topical workshops to sizable international conferences. One of the most satisfying experiences for me is that the Journal has played a sustained role in building this community. In the late 1990s the DOE launched the initiative ASCI (Accelerated Strategic Computing Initiative) as part of its stockpile stewardship program, which provided major impetus for
The tight-binding method attempts to represent the electronic structure of condensed matter using a minimal atomic-orbital like basis set. To compute tight-binding overlap and Hamiltonian matrices directly from first-principles calculations is a subject of continuous interest. Usually, first-principles calculations are done using a large basis set or long-ranged basis set (e.g. muffin-tin orbitals (MTOs)) in order to get convergent results, while tight-binding overlap and Hamiltonian matrices are based on a short-ranged minimal basis representation. In this regard, a transformation that can carry the electronic Hamiltonian matrix from a large or long-ranged basis representation onto a short-ranged minimal basis representation is necessary to obtain an accurate tight-binding Hamiltonian from first principles. The idea of calculating tight-binding matrix elements directly from a first-principles method was proposed by Andersen and Jepsen in 1984 [1]. They developed a scheme which transforms the electronic band structures of a crystal calculated using a long-ranged
Choice of modulation format plays a critical role in the design and performance of fiber optic communication systems. We discuss the basic physics of electro-optic phase and amplitude modulation and derive model transfer functions for ideal and non-ideal Mach-Zehnder modulators. We describe the generation and characteristics of the standard nonreturn-to-zero (NRZ) modulation format, as well as advanced formats such as return-to-zero (RZ), carrier-suppressed RZ (CSRZ), duobinary, modified duobinary, differential phase-shift keyed (DPSK), and return-to-zero DPSK (RZ-DPSK). Finally, we discuss the relative merits of these formats with respect to a variety of system impairments.
Significant achievements have been demonstrated in computational materials design and its broadening application in concurrent engineering. Best practices are assessed and opportunities for improvement identified, with implications for modeling and simulation in science and engineering. Successful examples of integration in undergraduate education await broader dissemination.
We discuss a number of examples that demonstrate the value of computational modeling as a complementary approach in the physics and chemistry of ice I h , where real-life experiments often do not give direct access to the desired information or whose interpretation typically requires uncontrollable assumptions. Specifically, we discuss two cases in which, guided by experimental insight, density-functional-theory-based first-principles methods are applied to study the properties of lattice defects and their relationship to ice I h s macroscopic behavior. First, we address a question involving molecular point defects, examining the energetics of formation of the molecular vacancy and a number of different molecular interstitial configurations. The results indicate that, as suggested by earlier experiments, a configuration involving bonding to the surrounding hydrogen-bond network is the preferred interstitial structure in ice I h . The second example involves the application of modeling to elucidate on the microscopic origin of the experimental observation that a specific type of ice defect is effectively immobile while others are not. Inspired by previous suggestions that this defect type may be held trapped at other defect sites and our finding that the bound configuration is the preferred interstitial configuration in ice I h , we use first-principles modeling to examine the binding energetics of the specific ice defect to the molecular vacancy and interstitial. The results suggest a preferential binding of the immobile defect to the molecular interstitial, possibly explaining its experimentally observed inactivity.
The exploration and production of oil and natural gas facing unprecedented demands for a secure energy supply worldwide is continuing a long trend to develop and adopt new technologies to help meet this challenge. For many oilfield technologies mathematical modeling and simulation have played a truly enabling role throughout their development and eventually their commercial adoption. Looking ahead, the vision of data-driven “intelligent” oilfields designed and operated using simulations to reach higher recovery factors is becoming a reality. Very little of this vision would be possible let alone make sense without the capability to move information across several simulation domains. We will examine several successes of modeling and simulation as well as current limitations which need to be addressed by new developments in theory, modeling, algorithms and computer hardware. Finally, we will mention several fundamental issues affecting oil recovery for which increased understanding is needed from new experimental methods coupled to simulation.
A fundamental understanding of the glass transition is essential for enabling future breakthroughs in glass science and technology. In this paper, we review recent advances in the modeling of glass transition range behavior based on the enthalpy landscape approach. We also give an overview of new simulation techniques for implementation of enthalpy landscape models, including techniques for mapping the landscape and computing the long-time dynamics of the system. When combined with these new computational techniques, the enthalpy landscape approach can provide for the predictive modeling of glass transition and relaxation behavior on a laboratory time scale. We also discuss new insights from the enthalpy landscape approach into the nature of the supercooled liquid and glassy states. In particular, the enthalpy landscape approach provides for natural resolutions of both the Kauzmann paradox and the question of residual entropy of glass at absolute zero. We further show that the glassy state cannot be described in terms of a mixture of equilibrium liquid states, indicating that there is no microscopic basis for the concept of a fictive temperature distribution and that the glass and liquid are two fundamentally different states. We also discuss the connection between supercooled liquid fragility and the ideal glass transition.
Enveloped viruses are viewed as an opportunity to understand how highly organized and functional biosystems can emerge from a collection of millions of chaotically moving atoms. They are an intermediate level of complexity between macromolecules and bacteria. They are a natural system for testing theories of self-assembly and structural transitions, and for demonstrating the derivation of principles of microbiology from laws of molecular physics. As some constitute threats to human health, a computer-aided vaccine and drug design strategy that would follow from a quantitative model would be an important contribution. However, current molecular dynamics simulation approaches are not practical for modeling such systems. Our multiscale approach simultaneously accounts for the outer protein net and inner protein/genomic core, and their less structured membranous material and host fluid. It follows from a rigorous multiscale deductive analysis of laws of molecular physics. Two types of order parameters are introduced: (1) those for structures wherein constituent molecules retain long-lived connectivity (they specify the nanoscale structure as a deformation from a reference configuration) and (2) those for which there is no connectivity but organization is maintained on the average (they are field variables such as mass density or measures of preferred orientation). Rigorous multiscale techniques are used to derive equations for the order parameters dynamics. The equations account for thermal-average forces, diffusion coefficients, and effects of random forces. Statistical properties of the atomic-scale fluctuations and the order parameters are co-evolved. By combining rigorous multiscale techniques and modern supercomputing, systems of extreme complexity can be modeled.
What do nanoscopic biomolecular complexes between the cells that line our blood vessels have in common with the microscopic silicate glass fiber optics that line our communication highways, or with the macroscopic steel rails that line our bridges? To be sure, these are diverse materials which have been developed and studied for years by distinct experimental and computational research communities. However, the macroscopic functional properties of each of these structurally complex materials pivots on a strong yet poorly understood interplay between applied mechanical states and local chemical reaction kinetics. As is the case for many multiscale material phenomena, this chemomechanical coupling can be abstracted through computational modeling and simulation to identify key unit processes of mechanically altered chemical reactions. In the modeling community, challenges in predicting the kinetics of such structurally complex materials are often attributed to the so-called rough energy landscape, though rigorous connection between this simple picture and observable properties is possible for only the simplest of structures and transition states. By recognizing the common effects of mechanical force on rare atomistic events ranging from molecular unbinding to hydrolytic atomic bond rupture, we can develop perspectives and tools to address the challenges of predicting macroscopic kinetic consequences in complex materials characterized by rough energy landscapes. Here, we discuss the effects of mechanical force on chemical reactivity for specific complex materials of interest, and indicate how such validated computational analysis can enable predictive design of complex materials in reactive environments.
In modelling and simulations there is a risk that one extrapolates into a region where the model is not valid. In this context instabilities are of particular interest, since they can arise without any precursors. This paper discusses instabilities encountered in the field of materials science, with emphasis on effects related to the vibrations of atoms. Examples deal with, i.a., common lattice structures being either metastable or mechanically unstable, negative elastic constants that imply an instability, unexpected variations in the composition dependence of elastic constants in alloys, and mechanisms governing the ultimate strength of perfect crystals.
This paper discusses a set of recent experimental results in which the mechanical properties of monolayer graphene molecules were determined. The results included the second-order elastic modulus which determines the linear elastic behavior and an estimate of the third-order elastic modulus which determines the non-linear elastic behavior. In addition, the distribution of the breaking force strongly suggested the graphene to be free of defects, so the measured breaking strength of the films represented the intrinsic breaking strength of the underlying carbon covalent bonds. The results of recent simulation efforts to predict the mechanical properties of graphene are discussed in light of the experiments. Finally, this paper contains a discussion of some of the extra challenges associated with experimental validation of multi-scale models.
Phenomena in the physical sciences are described with quantities that have a numerical value and a dimension, i.e., a physical unit. Dimensional analysis is a powerful aspect of modeling and simulation. Characteristic quantities formed by a combination of model parameters can give new insights without detailed analytic or numerical calculations. Dimensional requirements lead to Buckingham’s Π theorem—a general mathematical structure of all models in physics. These aspects are illustrated with many examples of modeling, e.g., an elastic beam on supports, wave propagation on a liquid surface, the Lennard-Jones potential for the interaction between atoms, the Lindemann melting rule, and saturation phenomena in electrical and thermal conduction.
Multiscale simulations are evolving into a powerful tool for exploring the nature of complex physical phenomena. We discuss two representative examples of such phenomena, stress corrosion cracking and ultrafast DNA sequencing during translocation through nanopores, which are relevant to practical applications. Multiscale methods that are able to exploit the potential of massively parallel computer architectures, will offer unique insight into such complex phenomena. This insight can guide the design of novel devices and processes based on a fundamental understanding of the link between atomistic-scale processes and macroscopic behavior.
In spite of all efforts, patients diagnosed with highly malignant brain tumors (gliomas), continue to face a grim prognosis. Achieving significant therapeutic advances will also require a more detailed quantitative understanding of the dynamic interactions among tumor cells, and between these cells and their biological microenvironment. Data-driven computational brain tumor models have the potential to provide experimental tumor biologists with such quantitative and cost-efficient tools to generate and test hypotheses on tumor progression, and to infer fundamental operating principles governing bidirectional signal propagation in multicellular cancer systems. This review highlights the modeling objectives of and challenges with developing such in silico brain tumor models by outlining two distinct computational approaches: discrete and continuum, each with representative examples. Future directions of this integrative computational neuro-oncology field, such as hybrid multiscale multiresolution modeling are discussed.
Understanding the dynamic lattice response of solids under the extreme conditions of pressure, temperature and strain rate is a scientific quest that spans nearly a century. Critical to developing this understanding is the ability to probe and model the spatial and temporal evolution of the material microstructure and properties at the scale of the relevant physical phenomena-nanometers to micrometers and picoseconds to nanoseconds. While experimental investigations over this range of spatial and temporal scales were unimaginable just a decade ago, new technologies and facilities currently under development and on the horizon have brought these goals within reach for the first time. The equivalent advancements in simulation capabilities now mean that we can conduct simulations and experiments at overlapping temporal and spatial scales. In this article, we describe some of our studies which exploit existing and new generation ultrabright, ultrafast x-ray sources and large scale molecular dynamics simulations to investigate the real-time physical phenomena that control the dynamic response of shocked materials.
Brute force histogram calculation and a recently developed method to efficiently reconstruct the free energy profile of complex systems (the single-sweep method) are combined with ab initio molecular dynamics to study possible local mechanisms for the diffusion of hydrogen in sodium alanates. These compounds may help to understand key properties of solid state hydrogen storage materials. In this work, the identity of a mobile species observed in experiments characterizing the first dissociation reaction of sodium alanates is investigated. The activation barrier of two suggested processes for hydrogen diffusion in Na3AlH6 is evaluated and, by comparing our results with available experimental information, we are able to discriminate among them and to show that one is compatible with the observed signal while the other is not.
