Test Particle Method Research Articles

Theoretical calculations of ion acceleration in the vicinity of comet Giacobini‐Zinner

Ionization of cometary neutral molecules produces ions which are picked up by the solar wind. The cometary ion pickup process for comet Giacobini‐Zinner is studied in two ways: (1) with a test particle method in which trajectories are numerically calculated for several thousand ions whose initial locations were chosen randomly with probability proportional to the neutral density and (2) with a quasi‐linear diffusion model. The cometary ion distribution function was calculated with the test particle model at several locations upstream of the bow shock and for several types of magnetic fluctuations (or waves). These waves were allowed to propagate in both directions along the magnetic field at the Alfven speed. Both pitch angle scattering and energy diffusion are evident in the derived ion distributions. The monochromatic waves result in less ion acceleration than turbulent fluctuations with about the same amplitude. The calculated ion distribution functions are in reasonable agreement with the distributions measured in the vicinity of comet Giacobini‐Zinner in 1985 by particle detectors on the ICE spacecraft when the ratio of power in sunward propagating Alfven waves to the power in antisunward propagating waves is assumed to lie between about 20% and 50%. However, the quasi‐linear diffusion model results agree best with the measured distribution functions when the power ratio is only about 3%.

The overlap volume in hard spheres under shear

The Widom test particle method was used to estimate the overlap volume for hard disks under shear flow. The volume of free space which can house an additional particle without overlap with other particles will differ from its equilibrium value because of the distortion of the solvation shell of every particle under the impact of shearing motion. In this way the overlap volume unambiguously characterizes the structure of nonequilibrium systems. The probability of finding voids with necessary sizes decreases with the shear rate as one might expect. Owing to the technical limitation inherent in the method the economically attainable shear rates and densities produced only small effects. Under certain reasonable assumptions the calculated nonequilibrium overlap volumes can be related to a nonequilibrium generalization of the chemical potential. We discuss this possibility.

A computer simulation study of the temperature dependence of the hydrophobic hydration

The test particle method is used to evaluate by molecular dynamics calculations the solubility of rare gases and of methane in water between the freezing point and the critical point. A quantitative agreement is obtained between solubility data and simulation results when the simulated water is modeled by the extended simple point charge model (SPCE). From a thermodynamical point of view, it is shown that the hierarchy of rare gases solubilities in water is governed by the solute–water interaction energy while an entropic term of cavity formation is found to be responsible for the peculiar temperature dependence of the solubility along the coexistence curve, and more precisely, of the solubility minimum exhibited by all the investigated solutes. Near the water critical point, the asymptotic behaviors of the Henry’s constant and of the vapor–liquid partition coefficient, respectively, as deduced from the simulation data follow with a good accuracy the critical laws recently proposed in the literature for these quantities. Moreover, the calculated partial molar volume of the solute shows a steep increase above 473 K and becomes proportional to the isothermal compressibility of the pure solvent in the vicinity of the critical point as it is observed experimentally. From a microscopic point of view, the evaluation of the solute–solvent pair distribution functions permits to establish a relationship between the increase of the solubility with the decrease of the temperature in cold water on the one hand, and the formation of cages of the clathrate-type around the solute on the other hand. Nevertheless, as soon as the boiling point of water is reached the computer simulation shows that the water molecules of the first hydration shell are no longer oriented tangentially to the solute and tend to reorientate towards the bulk. At higher temperatures a deficit of water molecules progressively appears around the solute, a deficit which is directly associated with an increase of the partial molar volume. Although this phenomenon could be related to what is observed in supercritical mixtures it is emphasized that no long range critical fluctuation is present in the simulated sample.

A quark transport theory to describe nucleon-nucleon collisions

On the basis of the Friedberg-Lee model we formulate a semiclassical transport theory to describe the phase-space evolution of nucleon-nucleon collisions on the quark level. The time evolution is given by a Vlasov equation for the quark phase-space distribution and a Klein-Gordon equation for the mean-field describing the nucleon as a soliton bag. The Vlasov equation is solved numerically using an extended test-particle method. We test the confinement mechanism and mean-field effects in (1 + 1)-dimensional simulations.

Recent vapour pressure equations for the Lennard-Jones fluid based on molecular simulations

with 13 = 1 T*/l.316 and the usual reduced quantities p* =po3/e and T* = kT/c This equation is based on vapour pressures obtained from some different simulation methods. Most (65%) of the vapour pressure data used are from Gibbs ensemble simulations (Panagiotopoulos, 1987; Panagiotopoulos et al., 1988; Smit and Frenkel, 1989; Panagiotopoulos, 1991 personal communication with Koutras et al.) and the authors observe a “generally large scatter of the simulation data”. Figure 1 shows the deviation of the Gibbs ensemble vapour pressures from eqn. (1). A more recent method to determine vapour liquid phase equilibria from @rnulations is the NpT + test particle method (?vWer and Fischer, 1990) which has been applied initially to linear molecules and la.@ to linear molecules with quadrupoles modelling real carbon dioxide with good success (Miiller, 1991). In order to facilitate comparison of the NpT + test particle method with other methods the vapour-liquid phase equilibria of the Lennard-Jones fluid have been calculated recently (Lotfi et a1.,1992). It turned out that the data obtained are rather smooth and show excellent thermodynamic consistency. This paper also contains correlation equations for the vapour pressures, the bubble and dew densities, the chemical potentials as well as for the enthalpies of vaporization. The vapour pressure equation is

Semiconductor Deposition Profile Simulation Using Direct Simulation Monte Carlo Method.

A deposition simulator using the DSMC (direct simulation Monte Carlo) method has been developed to investigate deposition profile characteristics on small trenches in semiconductor manufacturing processes from vacuum to atmospheric pressure conditions. This simulator can be applied to several deposition processes such as sputter deposition, plasma chemical vapor deposition, and atomspheric-or low-pressure chemical vapor deposition. In particular, rarefied gas flow fields with low concentrations of reactive gases are calculated using a modified DSMC method (test particle method). In the case of low-pressure processes such as sputter deposition, upstream boundary conditions of the trenches can be calculated by means of flow field analysis in the equipment. The effects of upstream boundary conditions, molecular collisions, sticking coefficients and surface migration on deposition profiles in the trenches were clarified.

A modified real particle method for the calculation of the chemical potentials of molecular systems

We propose a new technique, which is a combination of the test and real particle methods proposed originally by Widom, for the calculation of the chemical potentials of molecular systems from computer simulation. The technique involves the creation of a hole in the fluid by removing a particle from the simulated system, and subsequently reinserting it as a test bead. The equations for the calculation of chemical potentials are derived, and it is shown that the results obtained by this method for Lennard-Jones fluids are accurate over larger ranges in temperature and density than other traditional methods. In spite of these advantages for simple systems, the proposed technique is expected to be of greatest value when dealing with complex systems containing ionic or polymeric molecules.

Monte Carlo calculation of solubilities of high-boiling component in supercritical carbon dioxide

Abstract Eya, H., Iwai, Y., Fukuda, T. and Arai, Y., 1992. Monte Carlo calculation of solubilities of high-boiling component in supercritical carbon dioxide. Fluid Phase Equilibria, 77: 39-51. The test particle method proposed by Widom was applied to calculate the solubilities of naphthalene in supercritical carbon dioxide at 308.15 and 328.15 K. The Lennard-Jones (12-6) potential was used as the intermolecular potential and the Berthelot mixing rule was adopted for unlike molecular pairs. The calculated solubilities are in general higher than the experimental values of solubilities. However, by introducing an intermolecular interaction parameter between carbon dioxide and naphthalene, the calculation results showed good agreement with the experimental values.

Vapour liquid equilibria of the Lennard-Jones fluid from theNpTplus test particle method

Using an improved version of the recently suggested NpT + test particle method, phase equilibria are determined for the Lennard-Jones fluid in the temperature range T* = 0·70 to T* = 1·30 in steps of ΔT* = 0·05. For the final results, gas simulations are necessary only at the two highest temperatures; for T* = 1·20 and downwards the gas phase can be described with sufficient accuracy by the Haar-Shenker-Kohler equation. The resulting vapour pressures, bubble and dew densities can be correlated by the equations , , , with the critical temperature and density being T*c = 1·310 and ρ*c = 0·314, respectively. Then a detailed comparison with other simulation results and perturbation theory results is given. Outstanding findings are that the present data are rather smooth, that they match quite well the early data of Hansen and Verlet (1969, Phys. Rev., 184, 151) and are much closer to perturbation theory than most previous results. Finally, using the vapour pressure equation and directly calculated volume changes and enthalpies of vaporization in combination with the Clausius-Clapeyron equation reveals excellent thermodynamic consistency in the present results.

Re-entry aerodynamics derived from space debris trajectory analysis

This paper considers the technique of orbital analysis as a means of determining the ill-defined gas-surface interaction between spacecraft and atmospheric molecules in low Earth orbit. The interaction is a major uncertainty in trajectory predictions for a body moving within an atmosphere. The rate of change of the orbital period of a debris object, the uncontrolled Salyut 7/ Kosmos 1686 space station, is analysed in order to determine the free molecular drag coefficient. The results are compared with theoretical values for the drag coefficient calculated using a complex representation of the vehicle configuration and motion and applying the Monte Carlo Test Particle method. Results suggest a nature of re-emission very close to the classical diffuse, totally accommodated case was occurring at the surface of the debris object as it approached re-entry. However the determined drag coefficient and therefore the derived interaction are found to be very sensitive to the neutral density and therefore the atmospheric model used in the analysis.

Quantum path integral extension of Widom’s test particle method for chemical potentials with application to isotope effects on hydrogen solubilities in model solids

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Application of the Test Particle Method for the Determination of Single Ion Activity Coefficients in a Real Electrolyte Solution

Article Application of the Test Particle Method for the Determination of Single Ion Activity Coefficients in a Real Electrolyte Solution was published on January 1, 1992 in the journal Zeitschrift für Physikalische Chemie (volume 178, issue 1).

A computer-simulation study of hydrophobic hydration of rare gases and of methane. I. Thermodynamic and structural properties

A theory is proposed to study the hydrophobic hydration of rare gases and methane in water. The Ostwald absorption coefficient γ, the hydration energy ΔE, and entropy ΔS are calculated by combining large-scale molecular-dynamics simulations and test-particle methods. The convergence of calculations is checked with particular care. The structure of the first two hydration shells is analyzed in terms of appropriate pair distribution functions. The picture conveyed by this theory is compared to that provided by the early work.

Pion spectra in a hadronic transport model for relativistic heavy ion collisions.

A set of coupled transport equations for the phase-space distribution functions of nucleons, deltas, and pions is solved with the test particle method to study pion production in relativistic heavy ion collisions. The experimentally observed concave shape of the pion spectra is well reproduced. The mechanism that causes the concave shape of the pion spectra is found to be due to the different contributions of the delta resonance produced during the early and the late stages of the heavy ion collision and due to the energy dependence of the pion and delta absorption cross sections. The dependence of the shape of the pion spectra on beam energy, target and projectile mass, and impact parameter is also studied. An approximate scaling function for the shape parameter of the pion spectra is found.

Determination of the chemical potentials of polymeric systems from Monte Carlo simulations.

We propose a new computer-simulation technique, based on the Widom test-particle method, to calculate the chemical potentials of components in a polymeric system. The technique is based on the insertion of test segments onto a polymer and is applicable for any chain length at gas and liquidlike densities. We perform sample calculations on homopolymers and show that the proposed technique allows for the enumeration of their thermodynamic behavior in the subcritical and supercritical temperature ranges.

A New Version of the Insertion Particle Method for Determining the Chemical Potential by Monte Carlo Simulation

Abstract A new version of the test particle method for determining the chemical potential by Monte Carlo simulations is proposed. The method, applicable to any fluid at any density, combines the Widom's test particle insertion method with the ideas of the scaled particle theory, gradual insertion method and multistage sampling. Its applicability is exemplified by evaluating the chemical potential of the hard sphere fluid at a very high density in semi-grand-canonical and grand-canonical ensembles. A theory estimating the efficiency (i.e. statistical errors) of the method is proposed and the results are compared with the Widom's and gradual insertion methods, and the analytic results.

Effects of Target Erosion on the Growth Rate of Films Fabricated by the Sputtering Method.

The target of a sputtering apparatus usually suffers from nonuniform erosion due to incident ions. The growth rate of deposited films then depends on the distribution of the erosion rate on the target. The test multiparticle method, which is a combination of the Monte Carlo direct simulation method and the test-particle method, is used to calculate atomic motions and depositions in an axisymmetrical sputtering chamber. The effect of the erosion rate on the thickness distribution of the films is clarified in the pressure range of 0.1-1 Pa by having recourse to the obtained density and flow fields of the sputtered atoms.

Dilepton production in heavy-ion collisions

The dynamical evolution of nucleus-nucleus collisions is described by a transport equation of the Uehling-Uhlenbeck type. Our model evolves phase-space distribution functions for nucleons, Δ's, N ∗(1440)-resonances and pions with their isospin degrees of freedom. The equations are solved by the test-particle simulation method. We apply this model to proton-nucleus and nucleus-nucleus collisions from 400 MeV/ A to 2.1 GeV/ A. Our approach is found to correctly describe the spectra of baryons and pions. Furthermore, we calculate the production of dileptons considering proton-neutron and pion bremsstrahlung, Δ and N ∗ decay and π +π − annihilation. The calculations reproduce the data for p+ 9Be and for 40Ca + 40Ca at the bombarding energies of 1 GeV/ A and 2 GeV/ A except for small invariant masses ( M⩽ 200 MeV) where the situation is not fully understood. Above 300 MeV dilepton invariant mass the relevant contributions arise from proton-neutron bremsstrahlung, the Δ Dalitz-decay and π + π − annihilation. At 2 GeV/ A for 40Ca + 40Ca, however, we find the bremsstrahlung contribution to be higher than that from pion annihilation.

Orthobaric Densities from Simulations of the Liquid Vapour Interface

Abstract Molecular dynamics studies of the liquid vapour interface of a Lennard-Jones fluid performed on a CYBER 205 are reported for kT/e = 0.70, 0.85, and 1.10. The main emphasis is on the orthobaric fluid densities: their dependence on different cut-off radii and long range corrections as well as their comparison with the coexisting densities from bulk fluid simulations. As previously reported bubble densities from bulk simulations differ by about 3 per cent at kT/e = 1.10, phase equilibrium was redetermined there with the NpT + test particle method. Concerning the bubble densities from the interface simulations, increase of the cut-off radius and use of long range corrections shift them up rather close to the “bulk” values. The dew densities from the interface simulations which for the usual cut-off radius of 2.5 [sgrave] are mostly too high by a factor of 3 are decreased dramatically by accounting for the long range part of the potential. For a cut-off radius of 5 [sgrave] and long range corrections ...

Vapour liquid equilibrium of a pure fluid from test particle method in combination with NpT molecular dynamics simulations

In order to determine the vapour liquid equilibrium of a pure fluid, the liquid and the vapour branch of the isotherms in the chemical potential μ vs pressure p-diagram, are constructed explicitly. The liquid branch is obtained by molecular dynamics simulations in an NpT-ensemble into which test particles are inserted to calculate the chemical potential. The vapour branch is obtained at lower temperatures by using the second virial coefficient, at higher temperatures it is determined again by simulations. As an example the two-centre Lennard-Jones fluid with elongation L = 0·505 is considered at temperatures ranging from 0·69 to 0·92 of the estimated critical temperature. As expected, the inaccuracies of the liquid chemical potential increase with decreasing temperature as a consequence of the increasing saturated density. The uncertainties in μ/RT range from 0·02 at the highest to 0·10 at the lowest temperature which creates an uncertainty in the reduced vapour pressure Pσ3/ϵ of the order of 0·002. Withi...