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Using molecular dynamics simulations, we study field free relaxation from a non-uniform initial density, monitored using both density distributions and the dissipation function. When this density gradient is applied to colour labelled particles, the density distribution decays to a sine curve of fundamental wavelength, which then decays conformally towards a uniform distribution. For conformal relaxation, the dissipation function is found to decay towards equilibrium monotonically, consistent with the predictions of the relaxation theorem. When the system is initiated with a more dramatic density gradient, applied to all particles, non-conformal relaxation is seen in both the dissipation function and the Fourier components of the density distribution. At times, the system appears to be moving away from a uniform density distribution. In both cases, the dissipation function satisfies the modified second law inequality, and the dissipation theorem is demonstrated. [ABSTRACT FROM AUTHOR]

As the glass transition is approached from the high temperature side, viewed as a liquid, the properties of the ever more viscous supercooled liquid are continuous functions of temperature and pressure. The point at which we decide to classify the fluid as a solid is therefore subjective. This subjective decision does, however, have discontinuous consequences for how we determine the rheological properties of the glass. We apply the recently discovered relaxation theorem to the time independent, nondissipative, nonergodic glassy state to derive an expression for the phase space distribution of an ensemble of glass samples. This distribution is then used to construct a time dependent linear response theory for aged glassy solids. The theory is verified using molecular dynamics simulations of oscillatory shear for a realistic model glass former with excellent agreement being obtained between the response theory calculations and direct nonequilibrium molecular dynamics calculations. Our numerical results confirm that unlike all the fluid states, including supercooled liquids, a solid glass (in common with crystalline states) has a nonzero value for the zero frequency shear modulus. Of all the states of matter, a supercooled fluid approaching the glass transition has the highest value for the limiting zero frequency shear viscosity. Finally, solid glasses like dilute gases and crystals have a positive temperature coefficient for the shear viscosity whereas supercooled and normal liquids have a negative temperature coefficient. [ABSTRACT FROM AUTHOR]

We study the statistical mechanics of thermal conduction in a classical many-body system that is in contact with two thermal reservoirs maintained at different temperatures. The ratio of the probabilities, that when observed for a finite time, the time averaged heat flux flows in and against the direction required by Fourier’s Law for heat flow, is derived from first principles. This result is obtained using the transient fluctuation theorem. We show that the argument of that theorem, namely, the dissipation function is, close to equilibrium, equal to a microscopic expression for the entropy production. We also prove that if transient time correlation functions of smooth zero mean variables decay to zero at long times, the system will relax to a unique nonequilibrium steady state, and for this state, the thermal conductivity must be positive. Our expressions are tested using nonequilibrium molecular dynamics simulations of heat flow between thermostated walls. [ABSTRACT FROM AUTHOR]

Deterministic thermostats are frequently employed in nonequilibrium molecular dynamics simulations in order to remove the heat produced irreversibly over the course of such simulations. The simplest thermostat is the Gaussian thermostat, which satisfies Gauss’s principle of least constraint and fixes the peculiar kinetic energy. There are of course infinitely many ways to thermostat systems, e.g., by fixing ∑i|pi|μ+1. In the present paper we provide, for the first time, convincing arguments as to why the conventional Gaussian isokinetic thermostat (μ=1) is unique in this class. We show that this thermostat minimizes the phase space compression and is the only thermostat for which the conjugate pairing rule holds. Moreover, it is shown that for finite sized systems in the absence of an applied dissipative field, all other thermostats (μ≠1) perform work on the system in the same manner as a dissipative field while simultaneously removing the dissipative heat so generated. All other thermostats (μ≠1) are thus autodissipative. Among all μ thermostats, only the μ=1 Gaussian thermostat permits an equilibrium state. [ABSTRACT FROM AUTHOR]

Molecular fluids undergoing shear flow are often modeled using a homogeneous nonequilibrium molecular dynamics algorithm. To reach a steady state, this method must be used in conjunction with a thermostating mechanism which duplicates the heat dissipation in the experimental setup (e.g., by conduction to the shearing boundaries). The most commonly used type of thermostat involves fixing the center of mass kinetic (c.m.) temperature. Though perfectly valid, this approach does not seem to be the most realistic for a molecular fluid since heat is removed only through the 3 degrees of freedom of the center of mass for each molecule. The second type of thermostat involves fixing the "atomic" kinetic temperature and therefore takes into account all degrees of freedom. However, since the streaming velocity of atoms within their constituent molecules is unknown, the implementation of such a thermostat is problematic and relies on incorrect assumptions on the streaming velocity of atoms. The recently developed configurational temperature thermostat requires no assumption on the streaming velocity of atoms and takes into account all degrees of freedom. Using a configurational temperature thermostat to thermostat homogeneous shear flow thus seems to be a more realistic approach than the c.m. kinetic thermostat. In this work, we apply this configurational temperature thermostat to the study of linear alkanes (C[sub 10] and C[sub 20]) undergoing shear flow. The results so obtained are compared with those obtained using a c.m. kinetic thermostat. Our aims are (1) to test the influence of the total number of degrees of freedom of the system, (2) to make a connection between the results obtained with the two types of thermostats. By carefully examining the energies of the internal modes, we have been able to characterize the loss of accuracy of a c.m. kinetic thermostat at high shear rates and for high molecular weight compounds. Finally, we establish a correspondence between... [ABSTRACT FROM AUTHOR]

The fluctuation theorem gives an analytic expression for the probability, in a nonequilibrium system of finite size observed for a finite time, that the dissipative flux will flow in the reverse direction to that required by the second law of thermodynamics. In the present paper a local version of the fluctuation theorem (LFT) is derived heuristically. We find that in the case of planar Poiseuille flow of a Newtonian fluid between thermostated walls, nonequilibrium molecular dynamics simulation results support our proposed LFT. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Studies the kinetic energy conserving integrators for Gaussian thermostatted SLLOD. Demonstration of the utility of this scheme using the SLLOD algorithm which is the standard nonequilibrium molecular dynamics algorithm for studying shear flow; Operator-splitting integrators.

In this paper we present the results of nonequilibrium molecular dynamics simulations of an atomic fluid undergoing planar Poiseuille flow through a narrow slit pore. In particular we examine the heat flux vector for such a fluid and find that it displays weak oscillations with wavelengths that are characteristic of the van der Waals particle diameter. Furthermore, we examine the possibility of a coupling of the heat flux vector with the gradient of the square of the strain rate tensor and find that if such a coupling exists it would be undetectable by an examination of the heat flux vector alone. Its existence only manifests itself in the temperature profile, where a quadratic term would appear in addition to the usual quartic profile predicted by classical Navier–Stokes hydrodynamics. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present very precise results for the linear viscosity, thermal conductivity, and self-diffusion coefficient of the Ryckaert–Bellemans model of liquid butane near the boiling point, calculated from their respective Green–Kubo formulas using equilibrium molecular dynamics simulations. These results are used as a basis for the appraisal of previous calculations of these transport coefficients, which vary considerably. We find excellent agreement between our results and the results of the most precise nonequilibrium molecular dynamics simulations. We directly examine the system-size dependence of these transport coefficients for system sizes between 64 and 864 molecules and find that it is negligible, within experimental errors, for the viscosity and the thermal conductivity. The self-diffusion coefficient increases with increasing system size. The long-time decay of the shear stress, heat flux, and velocity autocorrelation function is also discussed quantitatively. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present the results of nonequilibrium molecular dynamics simulations of a model decane fluid performed at constant pressure and compare them with results previously obtained from simulations performed at constant volume. The strain rate dependence of the viscosity at constant pressure is found to differ from that obtained previously at constant volume. The shear thickening at high strain rates observed in constant volume simulations vanishes when the simulations are performed at constant pressure. We also investigate the question of how our low strain rate data for decane can be accurately extrapolated to zero strain rate. We find a well defined first Newtonian region in which the viscosity is independent of strain rate to within errors. The value of the viscosity that we obtain in this region agrees well with the zero strain rate viscosity calculated from the Green–Kubo formula at equilibrium. [ABSTRACT FROM AUTHOR]

We use nonequilibrium molecular dynamics simulations to investigate the rheology of branched and linear alkanes in the dense fluid state. A simplified model alkane [J.-P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comput. Phys. 23, 327 (1977); J.-P. Ryckaert and A. Bellemans, Discuss. Faraday Soc. 66, 95 (1978); G. Ciccotti and J.-P. Ryckaert, Comp. Phys. Rep. 4, 345 (1986); R. Edberg, D. J. Evans, and G. P. Morriss, J. Chem. Phys. 84, 6933 (1986)] composed of sites representing CH2 and CH3 groups with fixed bond lengths and bond angles between sites is used. The model also includes dihedral potential interactions between sites separated by three carbon bonds, and truncated and shifted Lennard-Jones potential interactions between sites on different molecules as well as those separated by more than three bonds on the same molecule. The Edberg–Evans–Morriss nonequilibrium molecular dynamics algorithm [R. Edberg, D. J. Evans, and G. P. Morriss, J. Chem. Phys. 84, 6933 (1986); R. Edberg, G. P. Morriss, and D. J. Evans, J. Chem. Phys. 86, 4555 (1987)] with periodic boundary conditions was used to simulate a system of 108 13-carbon n-alkane (tridecane) molecules and the corresponding 3-armed star branched alkane (5-butyl nonane). Equilibrium and steady state Couette flow simulations were performed. Properties calculated included the viscosity, normal stress differences, radius of gyration, alignment angles, shear induced order, angular velocity and a variety of other properties related to the conformation and dynamics of the molecules. The general features of the results were in agreement with recent simulations of n-decane and n-eicosane [G. P. Morriss, P. J. Daivis, and D. J. Evans, J. Chem. Phys. 94, 7420 (1991)], but the details of the results differed for branched and linear molecules. For example, the general trend of decreasing viscosity at low shear rates followed by an increase in the viscosity at higher strain rates was once again... [ABSTRACT FROM AUTHOR]

A new nonequilibrium molecular dynamics (NEMD) algorithm is used to calculate rate constants for trans–gauche isomerization in pure liquid butane. The new NEMD algorithm is based on macroscopic kinetic relaxation to equilibrium. The kinetic rate constant at T=292 K and ρ=0.583 g/ml is k=kF+kR =4.8×1010 s-1. The transition state theory rate constant is kTST =2.8×1011 s-1. The transmission coefficient is κ=0.17. Transition state theory overestimates the rate constant by a factor of 5. [ABSTRACT FROM AUTHOR]

We present a new algorithm for molecular dynamics simulation involving holonomic constraints. Constrained equations of motion are derived using Gauss’ principle of least constraint. The algorithm uses a fast, exact solution for constraint forces and a new procedure to correct for accumulating numerical errors. We report several simulations of liquid n-butane and n-decane performed with the new algorithm. We obtain an average trans population of 60.6±1.5% in liquid butane at T=291 K and ρ=0.583 g/ml. This result essentially agrees with that from an earlier simulation by Ryckaert and Bellemans [Discuss. Faraday Soc. 66, 95 (1978)]. However, our simulations are substantially more precise; our run lengths are typically ∼20 times longer than those of Ryckaert and Bellemans. Our result also agrees with that from a recent simulation by Wielopolski and Smith (following paper). Thermodynamic and structural data from our simulations also agree well with results from the simulations discussed in the above articles. [ABSTRACT FROM AUTHOR]

In this article we show that atomic thermostats which have been used in the past for nonequilibrium molecular dynamics (NEMD) simulations of molecular fluids were incorrectly formulated. The error stems from an incorrect assumption made about the form of the streaming angular velocity. This assumption is incorrect even in the linear regime. One spurious effect of this atomic thermostat is the generation of a nonsymmetric pressure tensor. We outline a general method, based on a variational principle, for calculating the position and orientation dependent streaming velocity. Using this streaming velocity we develop an atomic thermostat for molecular fluids which does not bias the positional or orientational distribution functions for the fluid. The new atomic thermostat is validated in NEMD simulations of liquid chlorine undergoing planar Couette flow. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Results from extensive nonequilibrium molecular dynamics (NEMD) simulations are presented for liquid chlorine subject to planar Couette flow. Comparisons are made between the so-called atomic and molecular SLLOD algorithms [R. Edberg, G. P. Morriss, and D. J. Evans, J. Chem. Phys. 86, 4555 (1987)] with atomic and molecular thermostats, respectively. These two thermostats differ in the assumptions that are made regarding the streaming velocity. Both thermostats are responsible for the production of string phases characterized by a translational ordering at very high strain rates. In addition, the atomic thermostat is responsible for the existence of a nonvanishing antisymmetric stress and enhanced orientational ordering. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We have simulated sheared liquid n-butane and n-decane by isothermal nonequilibrium molecular dynamics. Both alkanes exhibit nonlinear rheological behavior. Shear thinning at small shear rates, second Newtonian viscosities at moderate shear rates, normal stresses, dilatancy, and birefringence are observed for both fluids. Zero shear rate viscosities were calculated for both fluids: η(γ=0)=0.24 cp for butane at T=292 K, η(γ=0)=0.159 cp for decane at 481 K. These viscosities agree with experimental data for both fluids. The zero shear rate butane viscosity agrees with the Green–Kubo result of Marechal and Ryckaert, Chem. Phys. Lett. 101, 548 (1983). Shear induced molecular rotation, deformation, and alignment are quantitatively described to give a complete picture of molecular behavior in a sheared fluid. Equilibrium and shear simulations of butane with modified dihedral potentials were performed to investigate the effect of molecular conformation on the rheological properties of butane. [ABSTRACT FROM AUTHOR]

We consider two different methods of calculating the relevant average for the non-equilibrium partition identity (NPI), i.e., which result in two different values. At best only one of these will accurately correspond to what is observed. In order to better understand the two outcomes we carry out a detailed error analysis. This analysis is difficult due to the importance of extremely rare events in forming the average, resulting in the necessity to go beyond linear approximations for the error estimates. We begin by analysing the error in the fluctuation relation, and build upon this to estimate the errors in the NPI average. At short durations the full ensemble average always gives the observed average (i.e. the NPI holds). However, at very long durations, given a fixed amount of sampling, the observed average is predicted by treating the probability distribution as a Dirac-delta function. At intermediate times, neither corresponds to the observed average. This has profound implications for non-equilibrium work relations, as first introduced by Jarzynski. [ABSTRACT FROM AUTHOR]

The non-equilibrium free energy theorems show how distributions of work along non-equilibrium paths are related to free energy differences between the equilibrium states at the end points of these paths. In this paper we develop a natural way of barostatting a system and give the first deterministic derivation of the Crooks and Jarzynski relations for these isothermal isobaric systems. We illustrate these relations by applying them to molecular dynamics simulations of a model polymer undergoing stretching. [ABSTRACT FROM AUTHOR]

We use non-equilibrium molecular dynamics simulations to study the flow of a micropolar fluid and to test an extended Navier–Stokes theory (ENS) for such fluids. The angular streaming velocity (which is of course missing in the classical Navier–Stokes theory) and the translational streaming velocity are found to be in good agreement with the predictions of ENS theory. Besides, owing to molecular rotation, the translational streaming velocity profile is shown to deviate from the classical parabolic profile. Finally, temperature profiles calculated using three different expressions (a kinetic translational, a kinetic rotational and a recently derived configurational expression) are found to be in excellent agreement, demonstrating that the equipartition principle still holds in this non-equilibrium system. No deviation from the classical quartic temperature profile is observed. [ABSTRACT FROM AUTHOR]

Non-equilibrium molecular dynamics (NEMD) simulations employing the sinusoidal transverse force (STF) method are used to calculate the wavevector and strain rate dependent shear viscosity of a WCA fluid at a zero wavevector number density of 0.8442 and zero wavevector temperature of 0.722. The functional form of the dependence of shear viscosity on the strain rate and wavevector are examined, in the zero field limit. The ramifications of these results for the possible existence of the Burnett coefficients are discussed. The shear rate dependent viscosity for a range of wavevectors can be fitted to both a Cross analytical form and a formula derived from Quentrec's local order theory. Also it can be fitted to two square-root regimes. The extrapolated zero strain rate viscosities are consistent with a Lorentzian functional form, a Taylor series expansion in q2 and also to a q3/2 variation at low wavevector. This study reveals that with current computational resources it is still not possible to establish the validity of the Burnett coefficients. [ABSTRACT FROM AUTHOR]

Comments on the article, entitled `Molecular simulation and continuum mechanics study of simple fluids in nonisothermal planar Couette flows,' by Khare, de Pablo and Yethiraj, published in the 1997 edition of the `Journal of Chemical Physics'. Comparing results of simulations of planar Couette flow of simpled fluids with and without a thermostat acting on the fluid.

We have solved the convective diffusion equation for a non-Newtonian fluid subject to a large Couette strain field. In this case the self-diffusion tensor is nonsymmetric. We show that the macroscopic mean square displacements that can be derived from the solution of this equation are consistent with the microscopic mean square displacements of Cummings et al.1 obtained by statistical mechanical methods. We also show that the solution of the convective diffusion equation only involves the symmetric part of the diffusion tensor. This implies that it is impossible to evaluate the antisymmetric part of the diffusion tensor with concentration measurements. [ABSTRACT FROM AUTHOR]

Comments on the modified nonequilibrium molecular dynamics for fluid flows. Smooth characteristics of thermostatted nonequilibrium steady state distribution functions; Failure of the chain thermostats to control precise temperature; Consistency of the Lees-Edwards boundary conditions with leapfrog integrator.

Two configurational expressions for the temperature are applied to the calculation of temperature profiles within a confined atomic fluid in a narrow slit pore. The configurational temperatures profiles so obtained are compared to the kinetic temperature, calculated from the equipartition principle, in equilibrium (EMD), and nonequilibrium molecular dynamics (NEMD) simulations of planar Poiseuille flow. We show that one of the configurational expressions exhibits a system-size dependence which prevents its application to the determination of high-resolution temperature profiles. The other expression yields good agreement with the kinetic temperature profile in both equilibrium and nonequilibrium systems. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Green-Kubo and Einstein expressions for the transport coefficients of a fluid in a nonequilibrium steady state can be derived using the fluctuation theorem and by assuming the probability distribution of the time-averaged dissipative flux is Gaussian. These expressions are consistent with those obtained using linear response theory and are valid in the linear regime. It is shown that these expressions are, however, not valid in the nonlinear regime where the fluid is driven far from equilibrium. We advance an argument for why these expressions are only valid in the linear response, zero field limit. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The color-diffusion algorithm is applied to ab initio molecular dynamics simulation of hexagonal LiBH4 to determine the lithium diffusion coefficient and diffusion mechanisms. Even in the best solid lithium ion conductors, the time scale of ion diffusion is too long to be readily accessible by ab initio molecular dynamics at a reasonable computational cost. In our nonequilibrium method, rare events are accelerated by the application of an artificial external field acting on the mobile species; the system response to this perturbation is accurately described in the framework of linear response theory and is directly related to the diffusion coefficient, thus resulting in a controllable approximation. The calculated lithium ionic conductivity of LiBH4 closely matches published measurements, and the diffusion mechanism can be elucidated directly from the generated trajectory [ABSTRACT FROM AUTHOR]