Dynamic simulation

Abstract: One fifth (4 of 20) of the research articles published in the Journal of Educational Statistics in 1988 include simulation studies that justify or illustrate the authors' conclusions. A similar fraction (6 of 33) of the articles in the 1988 volume of Psychometrika include simulations; comparable proportions could be expected in other journals at the boundary of theoretical statistics and social/psychological applications. Due in part to the complexity of the problems tackled today and in part to the availability of cheap, powerful computing—by no means independent influences—simulation and Monte Carlo methods have become both necessary and practical tools for statisticians and applied workers in quantitative areas of education and psychology. Simulation has become popular—not only in the quantitative social sciences, but in all of the mathematical sciences from physics to operations research to number theory—because it is almost always easy to do. This ease of use makes the simulation experimenter vulnerable to two common pitfalls. Selection of the basic source of "random numbers" is often passive: Whatever is available in the computer's standard subroutine library is used. However, the fact that a pseudo-random number generator appears in a popular software package or operating system is hardly reason to trust it, as is shown by the infamous RANDU generator, once popular on IBM mainframes and PDP mini-computers, and by the generators burned into RAM on today's PCs. Simulation design and reporting also deserve special care. Some attempt must be made to assess the accuracy of the simulation estimates: One should accurately estimate and report SE (6) as well as 6. In addition, enough detail should be reported that the interested reader can replicate the study and check the results, just as with other experiments. Yet these considerations are also easy to overlook. Brian D. Ripley's Stochastic Simulation is a short, yet ambitious, survey of modern simulation techniques. Three themes run throughout the book. First, one shoud not take basic simulation subroutines for granted, especially on minior microcomputers where they tend to be poor implementations, implementations of poor algorithms, or both. Second, design of experiments, or variance reduction as it is known in this field, deserves greater consideration. Third, modern methods make it possible to simulate and analyze processes that are dependent over time, and using such processes opens the door to new simulation techniques, such as simulated annealing in optimization. Ripley intends this book to be a "comprehensive guide," and it is indeed most accurately described as a researcher's handbook with examples and

Abstract: This paper presents an easy-to-use battery model applied to dynamic simulation software. The simulation model uses only the battery State-Of-Charge (SOC) as a state variable in order to avoid the algebraic loop problem. It is shown that this model, composed of a controlled voltage source in series with a resistance, can accurately represent four types of battery chemistries. The model's parameters can easily be extracted from the manufacturer's discharge curve, which allows for an easy use of the model. A method is described to extract the model's parameters and to approximate the internal resistance. The model is validated by superimposing the results with the manufacturer's discharge curves. Finally, the battery model is included in the SimPowerSystems (SPS) simulation software and is used in the Hybrid Electric Vehicle (HEV) demo. The results for the battery and for the DC-DC converter are analysed and they show that the model can accurately represent the general behaviour of the battery.

Abstract: Dependent Coordinates and Related Constraints Equations- Kinematic Analysis- Dynamic Analysis: Mass Matrices and External Forces-Dynamic Analysis: Equations of Motion- Static Equilibrium Position and Inverse Dynamics- Numerical Integration of the Equations of Motion- Improved Formulations for Real Time Dynamics Linearized Dynamic Analysis- Special Topics-Forward Dynamics of Flexible Systems- Inverse Dynamics of Flexible Multibodies

Abstract: The term molecular mechanics (MM) refers to the use of simple potential-energy functions (e.g., harmonic oscillator or Coulombic potentials) to model molecular systems. Molecular mechanics approaches are widely applied in molecular structure refinement, molecular dynamics (MD) simulations, Monte Carlo (MC) simulations, and ligand-docking simulations. Typically, molecular mechanics models consist of spherical atoms connected by springs which represent bonds. Internal forces experienced in the model structure are described using simple mathematical functions. For example, Hooke’s law is commonly used to describe bonded interactions, and the nonbonded atoms might be treated as inelastic hard spheres or may interact according to a Lennard-Jones potential. Using these simple models, a molecular dynamics simulation numerically solves Newton’s equations of motion, thus allowing structural fluctuations to be observed with respect to time. Dynamic simulation methods are widely used to obtain information on the time evolution of conformations of proteins and other biological macromolecules1–4 and also kinetic and thermodynamic information. Simulations can provide fine detail concerning the motions of individual particles as a function of time. They can be utilized to quantify the properties of a system at a precision and on a time scale that is otherwise inaccessible, and simulation is, therefore, a valuable tool in extending our understanding of model systems. Theoretical consideration of a system additionally allows one to investigate the specific contributions to a property through “computational alchemy”,5 that is, modifying the simulation in a way that is nonphysical but nonetheless allows a model’s characteristics to be probed. One particular example is the artificial conversion of the energy function from that representing one system to that of another during a simulation. This is an important technique in free-energy calculations.6 Thus, molecular dynamics simulations, along with a range of complementary computational approaches, have become valuable tools for investigating the basis of protein structure and function. This review offers an outline of the origin of molecular dynamics simulation for protein systems and how it has developed into a robust and trusted tool. This review then covers more recent advances in theory and an illustrative selection of practical studies in which it played a central role. The range of studies in which MD has played a considerable or pivotal role is immense, and this review cannot do justice to them; MD simulations of biomedical importance were recently reviewed.4 Particular emphasis will be placed on the study of dynamic aspects of protein recognition, an area where molecular dynamics has scope to provide broad and far-ranging insights. This review concludes with a brief discussion of the future potential offered to advancement of the biological and biochemical sciences and the remaining issues that must be overcome to allow the full extent of this potential to be realized. 1.1. Historical Background MD methods were originally conceived within the theoretical physics community during the 1950s. In 1957, Alder and Wainwright7 performed the earliest MD simulation using the so-called hard-sphere model, in which the atoms interacted only through perfect collisions. Rahman8 subsequently applied a smooth, continuous potential to mimic real atomic interactions. During the 1970s, as computers became more widespread, MD simulations were developed for more complex systems, culminating in 1976 with the first simulation of a protein9,10 using an empirical energy function constructed using physics-based first-principles assumptions. MD simulations are now widely and routinely applied and especially popular in the fields of materials science11,12 and biophysics. As will be discussed later in this review, a variety of experimental conditions may be simulated with modern theories and algorithms. The initial simulations only considered single molecules in vacuo. Over time, more realistic or at least biologically relevant simulations could be performed. This trend is continuing today. The initial protein MD simulation, of the small bovine pancreatic trypsin inhibitor (BPTI), covered only 9.2 ps of simulation time. Modern simulations routinely have so-called equilibration periods much longer than that, and production simulations of tens of nanoseconds are routine, with the first microsecond MD simulation being reported in 1998.13 In addition, the original BPTI simulation included only about 500 atoms rather than the 104-106 atoms that are common today. While much of this advancement results from an immense increase in availability of computing power, major theoretical and methodological developments also contribute significantly. The number of publications regarding MD theory and application of MD to biological systems is growing at an extraordinary pace. A single review cannot do justice to the recent applications of MD. Using data from ISI Web of Science, the authors estimate that during 2005 at least 800 articles will be published that discuss molecular dynamics and proteins. The historical counts are shown in Figure 1. Open in a separate window Figure 1 Articles matching ISI Web of Science query “TS=(protein) AND TS=(molecular dynamics)”.