Body simulated

Kent PRC, Flood R Q, Williamson A J, Needs R J, Foulkes W M C and Ra]agopal G 1999 Finite-size errors in quantum many-body simulations of extended systems Phys. Rev. B 59 1917-29... 

Andrew. W. Appel. An efficient program for many-body simulation. SIAM J. Sci. Stat. Comput., 6(1) 85-103, January 1985. 

Compsirison of Geometric Integrators for Rigid Body Simulation... 

Geometric Integrators for Rigid Body Simulation 355 where I = diag(/i,/2,/a) is the (diagonalized) inertial tensor,... 

These experiments confirm observations in the recent articles [20] and [11] symplectic methods easily outperform more traditional quaternionic integration methods in long term rigid body simulations. 

We have described our most recent efforts to calculate vibrational line shapes for liquid water and its isotopic variants under ambient conditions, as well as to calculate ultrafast observables capable of shedding light on spectral diffusion dynamics, and we have endeavored to interpret line shapes and spectral diffusion in terms of hydrogen bonding in the liquid. Our approach uses conventional classical effective two-body simulation potentials, coupled with more sophisticated quantum chemistry-based techniques for obtaining transition frequencies, transition dipoles and polarizabilities, and intramolecular and intermolecular couplings. In addition, we have used the recently developed time-averaging approximation to calculate Raman and IR line shapes for H20 (which involves... 

Another theoretical frontier involves the study of the vibrational spectroscopy of water at other conditions, or in other phases. Here it will be crucially important to use more robust water models, since many effective two-body simulation models were parameterized to give agreement with experiment at one state point room temperature and one atmosphere pressure. We have already seen that using these models at higher or lower temperatures even for liquid water leads to discrepancies. We note that a significant amount of important theoretical work on ice has already been published by Buch and others [71, 72, 111, 175, 176]. 

Tables 3 and 4 contain extrapolations to the long chain Hmit of ratios h and g, obtained from rigid-body simulation data, together with similar numerical val-...

A different approach simulates the thermodynamic parameters of a finite spin system by using Monte Carlo statistics. Both classical spin and quantum spin systems of very large dimension can be simulated, and Monte Carlo many-body simulations are especially suited to fit a spin ensemble with defined interaction energies to match experimental data. In the case of classical spins, the simulations involve solving the equations of motion governing the orientations of the individual unit vectors, coupled to a heat reservoir, that take the form of coupled deterministic nonlinear differential equations.23 Quantum Monte Carlo involves the direct representation of many-body effects in a wavefunction. Note that quantum Monte Carlo simulations are inherently limited in that spin-frustrated systems can only be described at high temperatures.24... 

Frenk White 1997) claimed as universal . Actually, the inner DM density profile found in N-body simulations can take slopes in a wider range, r-O 5 — r 1 5, and it can be flattened or steepened by the presence of a baryonic feedback on DM (Gnedin Primack 2003) or a DM-Dark Energy coupling ( Maccio et al. 2003). 

Cosmic rays (electrons and protons) are actually expected to be produced or injected in the cluster atmospheres by different mechanisms. X-ray observations and N-body simulations both indicate the existence of shocks in the... 

One of the greatest puzzles in galaxy formation theory concerns the distribution of the dark matter. The cold dark matter concentration is predicted from N-body simulations to follow a density profile ... 

Here, rs is a scale factor that is incorporated into the concentration parameter, c = rn/rs. where rv is either the virial radius or the radius at an overdensity, spherically-averaged, of 200. The profile slope parameter 7 is measured in high resolution N-body simulations (,) to be 7 1.2 0.3, and the normalisation parameter A reflects the epoch of formation, typically defined to be when half of the present mass was at overdensity of 200. 

Example results are shown in Eigs. 7.10-7.14 (Pratt and Ashbaugh, 2003). The self-consistent molecular field was obtained iteratively, including an update of t>y performing additional few-body simulations to evaluate the work associated with turning on the molecular field using thermodynamic integration ... 

B. Hendrickson and S. J. Plimpton, Technical Report SAND92-2766, Sandia National Laboratories, Albuquerque, NM, 1992. Parallel Many-Body Simulations Without All-to-All Communication. 

M. S. Warren and J. K. Salmon, Bull. Am. Astronom. Soc., 23, 1345 (1991). A Parallel Treecode for Gravitational N-body Simulations with up to 20 Million Particles. 

Alexander S. G. and Agnor C. B. (1998) N-body simulations of late stage planetary formation with a simple fragmentation model. Icarus 132, 113-124. 

Leinhardt Z. M. and Richardson D. C. (2002) A -body simulations of planetesimal evolution effect of varying impactor mass ratio. Icarus 159, 306—313. 

J. Salmon and M. Warren, Parallel Out-of-core Methods for N-body Simulation, in Proceedings of the Eighth SIAM Conference on Parallel Processing for Scientific Computing, March 1997. 

B. Hendrickson and S. Plimpton, Parallel many-body simulations without all-to-all communication, J. Parallel Distrib. Comput., 27 (1995), 15-25. 

The network level is the domain of, for example, circuit and multi-body simulations. On this level, the physics is described by systems of differential algebraic equations. In spite of the higher level of abstraction, the modeled components are close to physical reality, because we can still recognize physical parts such as resistors and transistors or masses and springs (e.g., [10-15]). 

Although the simulation of ensembles of particles constitutes a huge literature, it is only one aspect of the use of Monte Carlo methods in chemical physics. Basically, whenever one has to calculate integrals over a high-dimensionality space, the Monte Carlo method is potentially the algorithm of choice. Thus, for example, in few-body simulations of chemical reactions, one must integrate over the initial conditions of the reactant molecules, and... 

Although CMD is a substantial breakthrough in the approximate computation of quantum time correlation functions, the determination of the centroid force in Eq. (3.59), as defined by Eq. (3.60), represents an algorithmic challenge for realistic many-body simulations. Equation... 

In testing the flight software implementation, Analex-Denver used IMS default values instead of the actual II constants contained on the flight tape. Generic or default II constants were used because they believed the actual II constants could not be adequately validated in their rigid body simulations, that is, the rigid body simulation of the vehicle would not exercise the filters sufficiently. They found out after the mission failure that if they had used the actual II constants in their simulation, they would have found the order of magnitude error. 

A. Sugino, T. Miyazaki, C. Ohtsuki, Apatite-forming ability of polyglutamic add hydrogels in a body-simulating environment, J. Mater. Sci. Mater. Med. 19 (2008) 2269-2274. 

FIGURE 1 Simulation as animation. A pure rigid-body simulation of dice falling through a lattice produces realistic animation without the talents of a skilled animator. SOURCE 1990 David Baraff. 

This high-level description obviously hides many details. For example, the differential equation may involve either explicitly or implicitly various constraints on the system over time. The state of the system may be discontinuous (usually not in space, but velocity discontinuities are often fundamental to treatments of rigid bodies in contact). If the number of variables describing the system state is high, we may have to deal with very large systems of coupled equations. In some cases even the inherent computational complexity of the simulation itself may be questionable for example, some treatments of rigid-body simulation give rise to individual steps for which the solution is NP-... 

One example of a component-based testing method is the Vehicle Related Pedestrian Safety Index (VERPS) [73, 74]. This index utilizes a linear scale for both active and passive safety measures. The pedestrian head impact in frontal passenger vehicle collisions is assessed using the Head Injury Criterion (HIC) as metric. The method delivers specific results for a given vehicle and pedestrian combination. The evaluation process includes accident data analysis for relevant scenarios, kinematic analysis (via multi-body simulation), hardware component testing, and a procedure to obtain the VERPS index [73, 74]. The VERPS index takes only the probability for AIS3+ head injuries due to impact on the vehicle into account, since this probability can be derived from the HIC measurement. 

Multi-body simulation AP 242 makes it possible to describe kinematic structures (links, articulations, pairings, movements, etc.). These are extended by geometric models such as JT, for instance. Links from the kinematic structure to the geometric elements are established via external references. 

The sHde block (Saint-Venant body) simulates ideal plastic behavior with no strain at aU below a critical yield stress 0 (Figure 2.10), although at and above the critical yield stress the strain increases without Hmit This behavior is frequently invoked in problems of slope stabihty for wet fine-grained materials such as silt and clay, as the sHde block wiU not move due to friction until sufficient stress is applied. 

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