Computer Simulation Using Particles

Hockney, Roger W.; Eastwood, J.W.

doi:10.1887/0852743920

Cited by 4,660 publications

(4,291 citation statements)

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“…61 We chose the velocity Verlet algorithm, because it yields velocities and positions at a specific time t rather than at other times. 59 The velocities are, in turn, needed to compute the kinetic energy (which is necessary to couple the system to the thermal bath) and to compute friction forces, as is done in the accompanying paper. 54 Another advantage of the velocity Verlet algorithm is that it is symplectic (allowing, in particular, for an approximate conservation of the total energy in long-time simulations 62-64 ) and timereversible.…”

Section: Integrating the Equations Of Motionmentioning

confidence: 99%

Molecular Dynamics with the United-Residue Model of Polypeptide Chains. I. Lagrange Equations of Motion and Tests of Numerical Stability in the Microcanonical Mode

et al. 2005

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The Lagrange formalism was implemented to derive the equations of motion for the physics-based united-residue (UNRES) force field developed in our laboratory. The C α… C α and C α… SC (SC denoting a side-chain center) virtual-bond vectors were chosen as variables. The velocity Verlet algorithm was adopted to integrate the equations of motion. Tests on the unblocked Ala 10 polypeptide showed that the algorithm is stable in short periods of time up to the time step of 1.467 fs; however, even with the shorter time step of 0.489 fs, some drift of the total energy occurs because of momentary jumps of the acceleration. These jumps are caused by numerical instability of the forces arising from the U rot component of UNRES that describes the energetics of side-chain-rotameric states. Test runs on the Gly 10 sequence (in which U rot is not present) and on the Ala 10 sequence with U rot replaced by a simple numerically stable harmonic potential confirmed this observation; oscillations of the total energy were observed only up to the time step of 7.335 fs, and some drift in the total energy or instability of the trajectories started to appear in long-time (2 ns and longer) trajectories only for the time step of 9.78 fs. These results demonstrate that the present U rot components (which are statistical potentials derived from the Protein Data Bank) must be replaced with more numerically stable functions; this work is under way in our laboratory. For the purpose of our present work, a nonsymplectic variable-time-step algorithm was introduced to reduce the energy drift for regular polypeptide sequences. The algorithm scales down the time step at a given point of a trajectory if the maximum change of acceleration exceeds a selected cutoff value. With this algorithm, the total energy is reasonably conserved up to a time step of 2.445 fs, as tested on the unblocked Ala 10 polypeptide. We also tried a symplectic multiple-time-step reversible RESPA algorithm and achieved satisfactory energy conservation for time steps up to 7.335 fs. However, at present, it appears that the reversible RESPA algorithm is several times more expensive than the variable-time-step algorithm because of the necessity to perform additional matrix multiplications. We also observed that, because Ala 10 folds and unfolds within picoseconds in the microcanonical mode, this suggests that the effective (event-based) time unit in UNRES dynamics is much larger than that of all-atom dynamics because of averaging over the fast-moving degrees of freedom in deriving the UNRES potential.

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Section: Integrating the Equations Of Motionmentioning

confidence: 99%

Molecular Dynamics with the United-Residue Model of Polypeptide Chains. I. Lagrange Equations of Motion and Tests of Numerical Stability in the Microcanonical Mode

et al. 2005

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“…The particle-in-cell (PIC) algorithm [38][39][40] consists of numerous consecutive time-steps. At each time-step the field is calculated in the whole volume of interest and ion cloud motion in this field is simulated.…”

Section: Particle-in-cell Algorithmmentioning

confidence: 99%

“…1,2,4,34-37 His calculations were initially performed in 2D Cartesian and cylindrical confinement geometries utilizing the Monte Carlo algorithm to treat ion-neutral collisions. 5,[38][39][40] As was shown by Mitchell, at low magnetic field, high number density, or closely spaced cyclotron frequency separation, the ion motion dynamics becomes considerably more complicated than just a frequency shift. Later on 6 he carried out a more realistic 3D many particles simulation of trapped ion clouds incorporating space charge effects (coulombic and image charge interactions) for a sufficiently large ion population.…”

mentioning

confidence: 95%

Realistic modeling of ion cloud motion in a Fourier transform ion cyclotron resonance cell by use of a particle‐in‐cell approach

Nikolaev

Heeren

Popov

et al. 2007

Rapid Comm Mass Spectrometry

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Using a 'Particle-In-Cell' approach taken from plasma physics we have developed a new threedimensional (3D) parallel computer code that today yields the highest possible accuracy of ion trajectory calculations in electromagnetic fields. This approach incorporates coulombic ion-ion and ion-image charge interactions into the calculation. The accuracy is achieved through the implementation of an improved algorithm (the so-called Boris algorithm) that mathematically eliminates cyclotron motion in a magnetic field from digital equations for ion motion dynamics. It facilitates the calculation of the cyclotron motion without numerical errors. At every time-step in the simulation the electric potential inside the cell is calculated by direct solution of Poisson's equation. Calculations are performed on a computational grid with up to 128 T 128 T 128 nodes using a fast Fourier transform algorithm. The ion populations in these simulations ranged from 1000 up to 1 000 000 ions. A maximum of 3 000 000 time-steps were employed in the ion trajectory calculations. This corresponds to an experimental detection time-scale of seconds. In addition to the ion trajectories integral time-domain signals and mass spectra were calculated. The phenomena observed include phase locking of particular m/z ions (high-resolution regime) inside larger ion clouds. A focus was placed on behavior of a cloud of ions of a single m/z value to understand the nature of Fourier transform ion cyclotron resonance (FTICR) resolution and mass accuracy in selected ion mode detection. The behavior of two and three ion clouds of different but close m/z was investigated as well. Peak coalescence effects were observed in both cases. Very complicated ion cloud dynamics in the case of three ion clouds was demonstrated. It was found that magnetic field does not influence phase locking for a cloud of ions of a single m/z. The ion cloud evolution time-scale is inversely proportional to magnetic field. The number of ions needed for peak coalescence depends quadratically on the magnetic field. Copyright # 2007 John Wiley & Sons, Ltd.The leading role Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) plays in biological mass spectrometry is directly related to its unsurpassed resolution and mass accuracy combined with the possibility of utilizing all known ionization and fragmentation methods. Further improvement of mass accuracy will be greatly facilitated by a more detailed understanding of the motion of ions during ion introduction into the FTICR cell, excitation of their cyclotron motion, fragmentation and detection of induced signal. Starting from the early days of FTICR-MS the theory of ion motion in the ICR cell was an important research topic in this field. The dynamics of single particles inside the FTICR trap was analyzed by many groups in both the FTICR and physics communities. [1][2][3][4][5][6][7][8] The FTICR community has been interested mainly in obtaining a calibration formula, which connects measured frequency with ion mass. 9 The e...

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“…We chose the dimensionless LJ unit throughout the article where the distances, energies, time, and temperature are measured in unit of r, e, s 5 f 0 r 2 /e, 5,14 and e/k B , respectively. The neighbor-list method [37][38][39] and leap-frog method 14,15,40,41 were used in conducting CGH-MD simulation so as to achieve computational efficiency. The integration time step dt was set at 0.002-0.005 in unit of s as suggested in the literature.…”

Section: Methodsmentioning

confidence: 99%

Simulation of DNA electrophoresis in systems of large number of solvent particles by coarse‐grained hybrid molecular dynamics approach

Wang

Liu

et al. 2008

J Comput Chem

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Simulation of DNA electrophoresis facilitates the design of DNA separation devices. Various methods have been explored for simulating DNA electrophoresis and other processes using implicit and explicit solvent models. Explicit solvent models are highly desired but their applications may be limited by high computing cost in simulating large number of solvent particles. In this work, a coarse-grained hybrid molecular dynamics (CGH-MD) approach was introduced for simulating DNA electrophoresis in explicit solvent of large number of solvent particles. CGH-MD was tested in the simulation of a polymer solution and computation of nonuniform charge distribution in a cylindrical nanotube, which shows good agreement with observations and those of more rigorous computational methods at a significantly lower computing cost than other explicit-solvent methods. CGH-MD was further applied to the simulation of DNA electrophoresis in a polymer solution and in a well-studied nanofluidic device. Simulation results are consistent with observations and reported simulation results, suggesting that CGH-MD is potentially useful for studying electrophoresis of macromolecules and assemblies in nanofluidic, microfluidic, and microstructure array systems that involve extremely large number of solvent particles, nonuniformly distributed electrostatic interactions, bound and sequestered water molecules.

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Computer Simulation Using Particles

Cited by 4,660 publications

References 0 publications

Molecular Dynamics with the United-Residue Model of Polypeptide Chains. I. Lagrange Equations of Motion and Tests of Numerical Stability in the Microcanonical Mode

Molecular Dynamics with the United-Residue Model of Polypeptide Chains. I. Lagrange Equations of Motion and Tests of Numerical Stability in the Microcanonical Mode

Realistic modeling of ion cloud motion in a Fourier transform ion cyclotron resonance cell by use of a particle‐in‐cell approach

Simulation of DNA electrophoresis in systems of large number of solvent particles by coarse‐grained hybrid molecular dynamics approach

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