Class Of Particle Systems Research Articles

What Is a Simple Liquid?

Simple liquids are traditionally defined as many-body systems of classical particles interacting via radially symmetric pair potentials. We suggest that a simple liquid should be defined instead by the property of having strong correlation between virial and potential energy equilibrium fluctuations in the NVT ensemble. There is considerable overlap between the two definitions, but also some notable differences. For instance, in the new definition simplicity is not a property of the intermolecular potential only because a liquid is usually only strongly correlating in part of its phase diagram. Moreover, according to the new definition not all simple liquids are atomic (i.e., with radially symmetric pair potentials) and not all atomic liquids are simple. The main part of the paper motivates the new definition of liquid simplicity by presenting evidence that a liquid is strongly correlating if and only if its intermolecular interactions may be ignored beyond the first coordination shell (FCS). This is demonstrated by NVT simulations of structure and dynamics of 15 atomic and molecular model liquids with a shifted-forces cutoff placed at the first minimum of the radial distribution function. No proof is given that the chemical characterization follows from the strong correlation property, but it is shown to be consistent with the existence of isomorphs in strongly correlating liquids' phase diagram. Finally, we note that the FCS characterization of simple liquids calls into question the basis for standard perturbation theory, according to which the repulsive and attractive forces play fundamentally different roles for the physics of liquids.

Fire and Explosion Hazard Prediction Base on Virtual Reality in Tank Farm

Many fires and explosions happen in tank farm. A fire and explosion simulation method based on VR is used. Tank fire and explosion special effect is realized by classical particle system. The real-time fire growth model, fireball growth model, fireball heat radiation model are created. The shock wave model of BLEVE also is created. The models and results of FDS ( Fire Dynamic Simulator) are built in virtual reality system. It can show the process of fire and explosion development and calculate the hazard of fire and explosion. The virtual reality system can predict and provide a method to control the fire and explosion hazard.

Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions

An open issue in classical relativistic mechanics is the consistent treatment of the dynamics of classical N-body systems of mutually interacting particles. This refers, in particular, to charged particles subject to EM interactions, including both binary interactions and self-interactions (EM-interacting N-body systems). The correct solution to the question represents an overriding prerequisite for the consistency between classical and quantum mechanics. In this paper it is shown that such a description can be consistently obtained in the context of classical electrodynamics, for the case of a N-body system of classical finite-size charged particles. A variational formulation of the problem is presented, based on the N -body hybrid synchronous Hamilton variational principle. Covariant Lagrangian and Hamiltonian equations of motion for the dynamics of the interacting N-body system are derived, which are proved to be delay-type ODEs. Then, a representation in both standard Lagrangian and Hamiltonian forms is proved to hold, the latter expressed by means of classical Poisson Brackets. The theory developed retains both the covariance with respect to the Lorentz group and the exact Hamiltonian structure of the problem, which is shown to be intrinsically non-local. Different applications of the theory are investigated. The first one concerns the development of a suitable Hamiltonian approximation of the exact equations that retains finite delay-time effects characteristic of the binary interactions and self-EM-interactions. Second, basic consequences concerning the validity of Dirac generator formalism are pointed out, with particular reference to the instant-form representation of Poincaré generators. Finally, a discussion is presented both on the validity and possible extension of the Dirac generator formalism as well as the failure of the so-called Currie “no-interaction” theorem for the non-local Hamiltonian system considered here.

Zero-Dipole Summation Method for Precisely Estimating Electrostatic Interactions in Molecular Simulation

For computational studies of materials in a realistic manner, appropriate treatment of the Coulombic interaction is critical. Since the potential function is long-range and has both positive and negative signatures, it is not simple to handle the interaction in an effective manner, i.e., with high accuracy, low computational cost, freedom from artifacts, and ease of implementation. We introduce a novel idea, zero-dipole summation, for evaluating the electrostatic energy of classical particle system. The summation prevents the nonzero-charge and nonzero-dipole states artificially generated by simple cutoff truncation, which causes energetic noise and several artifacts. The currently derived energy formula nevertheless takes a simple pairwise form, which utilizes the cutoff procedure but employs a pairwise function changed from the pure Coulomb formula into a new formula taking account of the neutrality of charges and dipoles in the cutoff sphere (Fukuda et al. (2011) J. Chem. Phys. 134, 164107). This simple pairwise form enables us to effectively apply the scheme to high-performance computation. We discuss the theoretical details of our method and investigate the accuracy, stability, and static and dielectric properties of molecular systems via molecular dynamics simulation. We obtained the electrostatic energy error to be 0.01% at practical cutoff distance for an ionic system and a water system. We estimated the radial distribution function and the distant dependent Kirkwood factor for the water system, and confirmed the agreement with those by the Ewald method. Since the Kirkwood factor is very sensitive to the treatment of the electrostatic interaction, the agreement suggests that our method should be distinguishable from many other cutoff-like methods, which often cause the significant disagreement. Accurate electrostatic energies were also calculated with our method for a membrane protein with explicit ions and membrane and water molecules.

Thermodynamic and structural anomalies of the Gaussian-core model in one dimension

We investigated the equilibrium properties of a one-dimensional system of classical particles which interact in pairs through a bounded repulsive potential with a Gaussian shape. Notwithstanding the absence of a proper fluid–solid phase transition, we found that the system exhibits a complex behaviour, with ‘anomalies’ in the density and in the thermodynamic response functions which closely recall those observed in bulk and confined liquid water. We also discuss the emergence in the cold fluid under compression of an unusual structural regime, characterized by density correlations reminiscent of the ordered arrangements found in clustered crystals.

Lawrence–Doniach model in London approximation as a system of 2D Coulomb particles of two kinds

Thermodynamical properties of layered superconductors with Josephson coupling in zero magnetic field are discussed. It is shown that the Lawrence–Doniach model of layered superconductors in the London approximation can be presented as a system of classical Coulomb particles of two kinds. This representation includes both Josephson and 2D vortex subsystems in absolutely symmetrical way. The model was analyzed by means of the real-space renormalization group approach and in the mean field approximation. It is found that there is no a second order phase transition in the system. Instead of this the model demonstrates the qualitative change of the system properties which can look as a phase transition for experimental purposes.

All-loop calculation of the Reggeon field theory amplitudes via stochastic model

The evolution equations for Green functions of the Reggeon Field Theory (RFT) are equivalent to those of the inclusive distributions for the reaction–diffusion system of classical particles. We use this equivalence to obtain numerically Green functions and amplitudes of the RFT with all loop contributions included. The numerical realization of the approach is described and some important applications including total and elastic proton–proton cross sections are studied. It is shown that the loop diagram contribution is essential but can be imitated in the eikonal cross section description by changing the Pomeron intercept. A role of the quartic Pomeron coupling which is an inherent part of the stochastic model is shown to be negligible for available energies.

Dimension reduction method for ODE fluid models

We develop a new dimension reduction method for large size systems of ordinary differential equations (ODEs) obtained from a discretization of partial differential equations of viscous single and multiphase fluid flow. The method is also applicable to other large-size classical particle systems with negligibly small variations of particle concentration. We propose a new computational closure for mesoscale balance equations based on numerical iterative deconvolution. To illustrate the computational advantages of the proposed reduction method, we use it to solve a system of smoothed particle hydrodynamic ODEs describing single-phase and two-phase layered Poiseuille flows driven by uniform and periodic (in space) body forces. For the single-phase Poiseuille flow driven by the uniform force, the coarse solution was obtained with the zero-order deconvolution. For the single-phase flow driven by the periodic body force and for the two-phase flows, the higher-order (the first- and second-order) deconvolutions were necessary to obtain a sufficiently accurate solution.

Renormalized Kinetic Theory of Classical Fluids in and out of Equilibrium

We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the single-particle phase-space distribution function $f$, the correlation function $C=<\delta f\delta f >$, the retarded and advanced density response functions $\chi^{R,A}=\delta f/\delta\phi$ to an external potential $\phi$, and the associated memory functions $\Sigma^{R,A,C}$. The basis of the theory is an effective action functional $\Omega$ of external potentials $\phi$ that contains all information about the dynamical properties of the system. In particular, its functional derivatives generate successively the single-particle phase-space density $f$ and all the correlation and density response functions, which are coupled through an infinite hierarchy of evolution equations. Traditional renormalization techniques are then used to perform the closure of the hierarchy through memory functions. The latter satisfy functional equations that can be used to devise systematic approximations. The present formulation can be equally regarded as (i) a generalization to dynamical problems of the density functional theory of fluids in equilibrium and (ii) as the classical mechanical counterpart of the theory of non-equilibrium Green's functions in quantum field theory. It unifies and encompasses previous results for classical Hamiltonian systems with any initial conditions. For equilibrium states, the theory reduces to the equilibrium memory function approach. For non-equilibrium fluids, popular closures (e.g. Landau, Boltzmann, Lenard-Balescu) are simply recovered and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose.and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose.

Molecular dynamics scheme for precise estimation of electrostatic interaction via zero-dipole summation principle

We propose a novel idea, zero-dipole summation, for evaluating the electrostatic energy of a classical particle system, and have composed an algorithm for effectively utilizing the idea for molecular dynamics. It conceptually prevents the nonzero-charge and nonzero-dipole states artificially generated by a simple cutoff truncation. The resulting energy formula is nevertheless represented by a simple pairwise function sum, which enables facile application to high-performance computation. By following a heuristic approach to derive the current electrostatic energy formula, we developed an axiomatic approach to construct the method consistently. Explorations of the theoretical details of our method revealed the structure of the generated error, and we analyzed it by comparisons with other methods. A numerical simulation using liquid sodium chloride confirmed that the current method with a small damping factor yielded sufficient accuracy with a practical cutoff distance region. The current energy function also conducts stable numerical integration in a liquid MD simulation. Our method is an extension of the charge neutralized summation developed by Wolf et al. [J. Chem. Phys. 110, 8254 (1999)]. Furthermore, we found that the current method becomes a generalization of the preaveraged potential method proposed by Yakub and Ronchi [J. Chem. Phys. 119, 11556 (2003)], which is based on a viewpoint different from the neutrality. The current study presents these relationships and suggests possibilities for their further applications.

Smoluchowski dynamics and the ergodic-nonergodic transition

We use the recently introduced theory for the kinetics of systems of classical particles to investigate systems driven by Smoluchowski dynamics. We investigate the existence of ergodic-nonergodic (ENE) transitions near the liquid-glass transition. We develop a self-consistent perturbation theory in terms of an effective two-body potential and work to second order in this potential. At second order, we have an explicit relationship between the static structure factor and the effective potential and choose the static structure factor in the case of hard spheres to be given by the solution of the Percus-Yevick approximation for hard spheres. Then, using the analytically determined ENE equation for the ergodicity function, we find an ENE transition for packing fraction η greater than a critical value η(*)=0.76, which is physically unaccessible. The existence of a linear fluctuation-dissipation theorem in the problem is shown and used to great advantage.

Microcanonical Entropy and Dynamical Measure of Temperature for Systems with Two First Integrals

We consider a generic classical many particle system described by an autonomous Hamiltonian H(x 1,…,x N+2) which, in addition, has a conserved quantity V(x 1,…,x N+2)=v, so that the Poisson bracket {H,V} vanishes. We derive in detail the microcanonical expressions for entropy and temperature. We show that both of these quantities depend on multidimensional integrals over sub-manifolds given by the intersection of the constant energy hyper-surfaces with those defined by V(x 1,…,x N+2)=v. We show that temperature and higher order derivatives of entropy are microcanonical observable that, under the hypothesis of ergodicity, can be calculated as time averages of suitable functions. We derive the explicit expression of the function that gives the temperature.

Freezing of Lennard-Jones-type fluids

We put forward an approximate method to locate the fluid-solid (freezing) phase transition in systems of classical particles interacting via a wide range of Lennard-Jones-type potentials. This method is based on the constancy of the properly normalized second derivative of the interaction potential (freezing indicator) along the freezing curve. As demonstrated recently it yields remarkably good agreement with previous numerical simulation studies of the conventional 12-6 Lennard-Jones (LJ) fluid [S.A.Khrapak, M.Chaudhuri, G.E.Morfill, Phys. Rev. B 134, 052101 (2010)]. In this paper, we test this approach using a wide range of the LJ-type potentials, including LJ n-6 and exp-6 models, and find that it remains sufficiently accurate and reliable in reproducing the corresponding freezing curves, down to the triple-point temperatures. One of the possible application of the method--estimation of the freezing conditions in complex (dusty) plasmas with "tunable" interactions--is briefly discussed.

Statistics of Distinguishable Particles and Resolution of the Gibbs Paradox of the First Kind

In physics, there are two distinct paradoxes, which are both known as the “Gibbs paradox”. This article is concerned with only one of them: the false increase in entropy, which is calculated from the process of combining two gases of the same kind consisting of distinguishable particles. In the following, this paradox will be referred to as the Gibbs paradox of the first kind (GP1). (Two particles are said to be distinguishable if they are either non-identical, that is, if they have different properties, or if they are identical and there are microstates which change under transposition of the two particles.) The GP1 is demonstrated and subsequently analyzed. The analysis shows that, for (quantum or classical) systems of distinguishable particles, it is generally uncertain of which particles they consist. The neglect of this uncertainty is the root of the GP1. For the statistical description of a system of distinguishable particles, an underlying set of particles, containing all particles that in principle qualify for being part of the system, is assumed to be known. Of which elements of this underlying particle set the system is composed, differs from microstate to microstate. Thus, the system is described by an ensemble of possible particle compositions. The uncertainty about the particle composition contributes to the entropy of the system. Systems for which all possible particle compositions are equiprobable will be called harmonic. Classical systems of distinguishable identical particles are harmonic as a matter of principle; quantum or classical systems of non-identical particles are not necessarily harmonic, since for them the composition probabilities depend individually on the preparation of the system. Harmonic systems with the same underlying particle set are always correlated; hence, for harmonic systems, the entropy is no longer additive and loses its thermodynamic meaning. A quantity derived from entropy is introduced, the reduced entropy, which, for harmonic systems, replaces the entropy as thermodynamic potential. For identical classical particles, the equivalence (in particular with respect to the second law of thermodynamics) between distinguishability and indistinguishability is proved. The resolution of the GP1 is demonstrated applying the previously found results.

Phase Transitions For Dilute Particle Systems with Lennard-Jones Potential

We consider a classical dilute particle system in a large box with pair-interaction given by a Lennard-Jones-type potential. The inverse temperature is picked proportionally to the logarithm of the particle density. We identify the free energy per particle in terms of a variational formula and show that this formula exhibits a cascade of phase transitions as the temperature parameter ranges from zero to infinity. Loosely speaking, the particle system separates into spatially distant components in such a way that within each phase all components are of the same size, which is the larger the lower the temperature. The main tool in our proof is a new large deviation principle for sparse point configurations.

Ab initio molecular dynamics on the electronic Boltzmann equilibrium distribution

We prove that for a combined system of classical and quantum particles, it is possible to describe a dynamics for the classical particles that incorporates in a natural way the Boltzmann equilibrium population for the quantum subsystem. In addition, these molecular dynamics (MD) do not need to assume that the electrons immediately follow the nuclear motion (in contrast to any adiabatic approach) and do not present problems in the presence of crossing points between different potential energy surfaces (conical intersections or spin-crossings). A practical application of this MD to the study of the effect of temperature on molecular systems presenting (nearly) degenerate states—such as the avoided crossing in the ring-closure process of ozone—is presented.

Classical thermodynamics of particles in harmonic traps

I develop simple thermodynamic relations for a system of noninteracting classical particles confined in an isotropic harmonic trap. The volume occupied by the particles in such a trap is not well defined, and the pressure varies with position, indicating that the thermodynamic relations should be expressed in terms of more appropriate variables. I use the effective spring constant of the trap as a state variable and show that the conjugate state variable is proportional to the ensemble average of the mean squared displacement of the particles from the center of the trap. Thermodynamic relations are derived in terms of these variables, including the pressure and thermal equations of state, the entropy, and the heat capacities. I also consider cyclic thermodynamic processes in a harmonically confined gas.

Fundamental theory of statistical particle dynamics

We present a fundamental theory for the kinetics of systems of classical particles. The theory represents a unification of kinetic theory, Brownian motion, and field theory. It is self-consistent and is the dynamic generalization of the functional theory of fluids in equilibrium. This gives one a powerful tool for investigating the existence of ergodic-nonergodic transitions near the liquid-glass transition.

Translation of Walter Noll’s “Derivation of the Fundamental Equations of Continuum Thermodynamics from Statistical Mechanics”

Assuming a classical statistical system of point particles the fundamental equations of continuum thermomechanics (continuity equation, equation of motion, and energy equation) shall be derived exactly. The macroscopic state functions (density, velocity, stress, energy density, heat flux) are interpreted as expected values.

GPU processing of particle system animation

An approach to particle system processing on a GPU is discussed. Balancing of CPU and GPU loads is described in detail. Original approaches aimed at reducing the data flow from the system memory to the video memory are proposed. A comparison between the proposed GPU-based approach and the classical CPU-based particle system animation is given.