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Simulating Normalized Constants: From Importance Sampling to Bridge Sampling to Path Sampling
, 1998
"... Computing (ratios of) normalizing constants of probability models is a fundamental computational problem for many statistical and scientific studies. Monte Carlo simulation is an effective technique, especially with complex and highdimensional models. This paper aims to bring to the attention of ..."
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Cited by 172 (4 self)
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Computing (ratios of) normalizing constants of probability models is a fundamental computational problem for many statistical and scientific studies. Monte Carlo simulation is an effective technique, especially with complex and highdimensional models. This paper aims to bring to the attention of general statistical audiences of some effective methods originating from theoretical physics and at the same time to explore these methods from a more statistical perspective, through establishing theoretical connections and illustrating their uses with statistical problems. We show that the acceptance ratio method and thermodynamic integration are natural generalizations of importance sampling, which is most familiar to statistical audiences. The former generalizes importance sampling through the use of a single “bridge ” density and is thus a case of bridge sampling in the sense of Meng and Wong. Thermodynamic integration, which is also known in the numerical analysis literature as Ogata’s method for highdimensional integration, corresponds to the use of infinitely many and continuously connected bridges (and thus a “path”). Our path sampling formulation offers more flexibility and thus potential efficiency to thermodynamic integration, and the search of optimal paths turns out to have close connections with the Jeffreys prior density and the Rao and Hellinger distances between two densities. We provide an informative theoretical example as well as two empirical examples (involving 17 to 70dimensional integrations) to illustrate the potential and implementation of path sampling. We also discuss some open problems.
MessagePassing MultiCell Molecular Dynamics on the Connection Machine 5
 Parallel Computing
, 1993
"... We present a new scalable algorithm for shortrange molecular dynamics simulations on distributed memory MIMD multicomputer based on a messagepassing multicell approach. We have implemented the algorithm on the Connection Machine 5 (CM5) and demonstrate that mesoscale molecular dynamics with mor ..."
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Cited by 26 (4 self)
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We present a new scalable algorithm for shortrange molecular dynamics simulations on distributed memory MIMD multicomputer based on a messagepassing multicell approach. We have implemented the algorithm on the Connection Machine 5 (CM5) and demonstrate that mesoscale molecular dynamics with more than 10 8 particles is now possible on massively parallel MIMD computers. Typical runs show single particle updatetimes of 0:15¯s in 2 dimensions (2D) and approximately 1¯s in 3 dimensions (3D) on a 1024 node CM5 without vector units, corresponding to more than 1.8 GFlops overall performance. We also present a scaling equation which agrees well with actually observed timings. To appear in Parallel Computing (1993) Present address: Department of Mathematics, University of Oregon, Eugene, OR 97403. y To whom correspondence should be addressed. 1 Introduction The molecular dynamics (MD) method [1, 2, 3] has been known for several decades and has been used successfully in atomistic...
Relation between Spall Strength and Mesoparticle Velocity Dispersion
 International Journal of Impact Engineering
, 1999
"... Summary — From the plate impact experiments there were found out that the maximum spall strength corresponds just to the tests where the mesoparticle velocity dispersion is also maximum. In the paper computer investigation of this phenomenon is presented. Molecular dynamics method is used. It is sho ..."
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Cited by 8 (4 self)
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Summary — From the plate impact experiments there were found out that the maximum spall strength corresponds just to the tests where the mesoparticle velocity dispersion is also maximum. In the paper computer investigation of this phenomenon is presented. Molecular dynamics method is used. It is shown that increase of the initial dispersion from zero to 15–25m/s leads to the essentially increase of the material strength. The further increase of the initial dispersion leads to the slow decrease of the material strength, so the strengthdispersion characteristic has maximum.
Molecular Dynamics Simulations Of Polymer Systems
"... A brief general introduction into Molecular Dynamics methods for polymers is given. For the statics and dynamics of an isolated chain, a simple microcanonical algorithm is severely hampered by ergodicity problems due to mode conservation. Coupling the system to a Langevin heat bath solves this probl ..."
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Cited by 1 (0 self)
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A brief general introduction into Molecular Dynamics methods for polymers is given. For the statics and dynamics of an isolated chain, a simple microcanonical algorithm is severely hampered by ergodicity problems due to mode conservation. Coupling the system to a Langevin heat bath solves this problem, but also screens hydrodynamic interactions for a chain in a bath of solvent molecules. Rouse scaling laws should hold whenever longrange interactions and entanglements are not important; this is important for controlling the relevant time scales as well as for checking the correctness of simulation algorithms. As an application, a single chain in a bath of solvent particles is discussed. In this system, the longrange nature of the hydrodynamic interaction induces pronounced finite size effects, which are analyzed using Ewald summation methods. Furthermore, simulations on the dynamics of entangled melts are considered. Starting from the reptation picture, we discuss the difficulties t...
Journal of Statistical Physics, Vol. 82. Nos. 5/6, 1996 TwoDimensional Gas of Disks: Thermal Conductivity
, 1995
"... The phenomenon of heat conduction in a twodimensional gas of N hard disks is studied in the hydrostatic regime by means of nonequilibrium molecular dynamics (N ranging from 100 to 8000). For systems with N>~I500 the temperature and density profiles observed are in excellent agreement with the co ..."
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The phenomenon of heat conduction in a twodimensional gas of N hard disks is studied in the hydrostatic regime by means of nonequilibrium molecular dynamics (N ranging from 100 to 8000). For systems with N>~I500 the temperature and density profiles observed are in excellent agreement with the continuous theory, but the conductivity k differs from the one derived from Enskog's theory in a systematic way. This difference seems to slowly decrease with increasing density.
Computational Mechanical Modeling of the Behavior of Carbon Nanotubes
"... Abstract: This paper presents a computational method for the mechanical simulation of carbon nanotubes, whose complexity is linear on the number of atoms. The regularity of a graphene lattice at its energy ground permits the definition of a tiling scheme that is applied to the surface of nanometric ..."
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Abstract: This paper presents a computational method for the mechanical simulation of carbon nanotubes, whose complexity is linear on the number of atoms. The regularity of a graphene lattice at its energy ground permits the definition of a tiling scheme that is applied to the surface of nanometric carbon pipes. The scheme employs elementary Yshaped cells and proposes a coherent combination of a discrete approach with a continuous elastic beam reference for the numerical simulation of complex structures. In the molecular region, the employed potential is obtained from the local harmonic approximation and leads to an explicit formulation of the acting forces, therefore permitting the dynamical prediction of large deformations as bending and torsion. The study includes a numerical consistency check based on the conservation of the global energy of the molecular system. As a conclusion, future developments and possible applications of the proposed scheme are presented.
Transport Properties of Anisotropic Polar Fluids: 2. Dipolar Interaction
, 906
"... Number of figures: 12 ..."
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Determination of Proper Time Step for Molecular Dynamics Simulation
, 2000
"... In this study we have investigated the determination of proper time step in molecular dynamics simulation. Since the molecular dynamics is mathematically related to nonlinear dynamics, the analysis of eigenvalues is used to explain the relationship between the time step and dynamics. The tracings of ..."
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In this study we have investigated the determination of proper time step in molecular dynamics simulation. Since the molecular dynamics is mathematically related to nonlinear dynamics, the analysis of eigenvalues is used to explain the relationship between the time step and dynamics. The tracings of H2 and CO2 molecular dynamics simulation agrees very well with the analytical solutions. For H2, the time step less than 1.823 fs provides stable dynamics. For CO2, 3.808 fs might be the maximum time step for proper molecular dynamics. Although this results were derived for most simple cases of hydrogen and carbon dioxide, we could quantitatively explain why improperly large time step destroyed the molecular dynamics. From this study we could set the guide line of the proper time step for stable dynamics simulation in molecular modeling software.
COLLISION FREQUENCY OF LENNARDJONES FLUIDS AT HIGH DENSITIES BY EQUILIBRIUM MOLECULAR DYNAMICS SIMULATION
, 2009
"... 2Permanent address. Arising from the inability of theoretical calculations to give accurate descriptions of (shear) viscosity in rare gases at high densities, we investigated the likely cause of discrepancy between theory and experiments. Molecular Dynamics simulations were performed to calculate tr ..."
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2Permanent address. Arising from the inability of theoretical calculations to give accurate descriptions of (shear) viscosity in rare gases at high densities, we investigated the likely cause of discrepancy between theory and experiments. Molecular Dynamics simulations were performed to calculate transport coefficents and collision frequency of rare gases at high densities and different temperatures using a LennardJones modelled pair potential. The results, when compared with experiments show an underestimation of the viscosity calculated through the GreenKubo formalism, but in agreement with some other calculations performed by other groups. In the present work the origin of the underestimation is considered. Analyses of the transport coefficients show a very high collision frequency which suggests an atom may spend much less time in the neighbourhood of the fields of force of another atom and that the distribution in the systems studied adjusts itself to a nearly Maxwellian type which resulted in a locally and temporarily slowly varying temperature. We show that the time spent in the fields of force is so small compared with relaxation time thereby leading to a possible reduction in local velocity autocorrelation between atoms. 1 I.
unknown title
"... rtm noabling one to go directly from a microscopic Hamiltonian to the macroscopic properties measured in experiments. Because of the power of the methods, they are used in most areas of pure and applied science; an appreciable fraction of total scientific computer usage is taken up by simulations o ..."
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rtm noabling one to go directly from a microscopic Hamiltonian to the macroscopic properties measured in experiments. Because of the power of the methods, they are used in most areas of pure and applied science; an appreciable fraction of total scientific computer usage is taken up by simulations of one sort or another. tered. In the first approach, one assumes the Hamiltonian is given. As Dirac said above, it is just a question of working out the details—a problem for an applied mathematician. This implies that the exactness of simulation is very important. But what properties of a manybody system can we calculate without making any uncontrolled approximations and thereby answer Laplace’s and Dirac’s speculations? Today, we are far from solving typical problems in quantum physics from this view*Electronic address: