Statistical Mechanics of Hard-Particle Systems

A simple Monte Carlo (MC) method is introduced to treat the quantum-mechanical hard-sphere fluid. It uses the relative two-body Slater sum (instead of the classical Boltzmann factor) as a quantum-mechanical probability in the relative two-body configurational space. The MC calculations have been carried out for the hard-sphere fluid with quantum corrections at various densities and for various thermal wavelengths. The results are consistent with the interpretation that, in the quantum-mechanical picture, hard spheres repel each other at distances slightly greater (by an amount of the order of the thermal wavelength λT) than the contact collision distance of the classical treatment. The radial distribution functions of the classical and quantum-mechanical simulations differ considerably. The relative two-body free energy has been obtained from the relative two-body Slater sum, and the total free energy has been estimated (in preliminary calculations) by using the classical expression but replacing the classical hard-sphere diameter by the effective diameter. A good analytical fit to the MC results has been obtained for the equation of state of the quantum-mechanical hard-sphere fluid; the total free energy has been obtained (in extensive calculations) by integrating over the resulting pressures and densities. The pressure, internal energy, and free energy all increase with an increase in the thermal wavelength, i.e., with increasing quantum effect. From the equation of state, the second virial coefficients at various thermal wavelengths are in good agreement with theoretical values in the literature, and the third and fourth virial coefficients are predicted. Evidence has been found for a momentum condensation; the corresponding relative two-body entropy is negative. The heat capacity due to the relative two-particle kinetic energy has been found to be proportional to T−1/2 (approximately) whereas, classically, it is zero.

The contact pair correlation functions and the equation of state for a binary mixture of additive hard disks is obtained using a procedure similar to that leading to the Boublı́k–Mansoori–Carnahan–Starling–Leland equation of state for mixtures of additive hard spheres. The results from the derived equations are tested against new Monte Carlo data obtained for several diameter ratios and mole fractions. The overall agreement is excellent. The equation of state reproduces exactly the second virial coefficient of the mixture and the third with great accuracy. Predicted values of the fourth and fifth virial coefficients are also in very good agreement with numerical data.

Measurements of the gas compressibility of tetrafluoromethane were made in the region, 0–350°, 15–394 atm. From these results, values of the compressibility factor Z=PV/RT, the second, third, and fourth virial coefficients, and the parameters of the Beattie-Bridgeman and Benedict-Webb-Rubin equations of state were derived. The virial coefficients were correlated by the Lennard-Jones (12, 6), Lennard-Jones (28, 7), Stockmayer, and Kihara intermolecular potential energy functions, and numerical values for the molecular parameters were obtained. One of the first tests of the theoretical fourth virial coefficient of the Lennard-Jones (12, 6) potential was made using the experimental fourth virial coefficients of tetrafluoromethane.

The scaled particle theory of Reiss et al. has been extended to hard non-spherical particles and equations analogous to the Percus-Yevick equation have been obtained for mixtures of particles of the same shape but different sizes. The resulting equation of state produces exact second and third virial coefficients which are functions of the average radius, the surface area and the volume of the particle. The equations of state for several systems of hard non-spherical particles are compared with that for a system of hard spheres.

Digital information stored in rotational media, such as Hard Disk Drives (HDD) needs to be reliable and readily accessible. Various studies have been performed on the modal analysis of HDDs and the noise emitted during operation. Analysis performed by Siemens Corporation, IBM and Tyco Fire Protection Products show that HDDs are sensitive to noise. This report initially focusses on identifying the critical frequency ranges and the levels of noise where the performance of the drives reduces. A series of tests have been performed using pink noise at one-third octave frequency bands at sound pressure levels ranging from 80 dB to 130 dB (re 20 µPa) in an anechoic chamber. A detailed description on the test set-up along with the methodology of testing has been provided. Read/write speeds have been used to measure HDD performance. A completely random read/write workload with varied data packet size has been incorporated through a custom LabVIEW program. Serial Advanced Technology Attachment (SATA) drives have been used for the analysis. General trends in performance curves of Enterprise HDD, Laptop drives, Helium filled HDD and Non-Helium filled HDDs are shown. HDD performance is shown to be sensitive to sound pressure levels as low as 85 dB (re 20 µPa) at some frequencies. Depending on the type of the HDD, noise at a frequency range of 2 kHz – 8 kHz beyond certain SPL affect the HDD’s performance up to the point of temporary and even permanent failure. Speculating the observed frequency content to be the resonant frequencies of the internal parts such as the platter and head gimbal assembly, the modal analysis has been performed. The report later focusses on impact test and measurement of the response using non-contact methods on the HDDs platter and head gimbal assembly. A detailed analysis on the test set-up and measurement parameters has been laid out. The modal parameters obtained, provide an insight to the causal for the HDD’s performance reduction and help establish a relation with the results obtained from acoustic experiments. The modal parameters and the response obtained has been validated using Finite Element Analysis. A comprehensive analysis on the failure of HDDs due to modal parameters has been presented.

In this paper, the perturbed virial equations of state with temperature-dependent virial coefficients are constructed using the Carnahan–Starling (CS) hard sphere equation as reference. Considering the second virial coefficient, some critical properties are interaction-independent and the critical packing factor is in the range of that of real fluids. But the critical compressibility factor and the liquid–vapor equilibrium properties disagree with experiments. When both the second and the third virial coefficient are considered, the critical properties are interaction-dependent but are out of the range of experimental results of real fluids. As a conclusion, the fourth virial coefficients are required for further consideration.

Media composed of colliding hard disks (2D) or hard spheres (3D) serve as good approximations for the collective hydrodynamic description of gases, liquids and granular media. In the present study, the compressible hydrodynamics and shock dynamics are studied for a two-dimensional hard-disk medium at both the continuum and discrete particle level descriptions. For the continuum description, closed form analytical expressions for the inviscid hydrodynamic description, shock Hugoniot, isentropic exponent and shock jump conditions were obtained using the Helfand equation of state. The closed-form analytical solutions permitted us to gain physical insight into the role of the material’s density on its compressibility, i.e. how the medium compresses under mechanical loadings and sustains wave motion. Furthermore, the predictions were found in excellent agreement with calculations using the event driven molecular dynamics method involving 30,000 particles over the entire range of compressibility spanning the dilute ideal gas and liquid phases. In all cases, it was found that the energy imparted by the piston motion to the thermalized medium behind the propagating shock was quasi-independent of the medium’s packing fraction, with a correction vanishing with increasing shock Mach numbers.

In the present paper, expansions are obtained for density-independent pair distribution function and second virial coefficient for D-dimensional molecular fluid mixtures of dipolar hard D-spheres in the semiclassical limit. Numerical results for the second virial coefficient are also estimated for binary mixture of (i) hard spheres and dipolar hard spheres and (ii) hard discs and dipolar hard discs. It is found that the quantum effects increase with increase of dipole moment μ2 as well as the concentration x2. The purpose of the present work is to develop a theory for calculating the low density properties of the polar hard D-sphere fluid mixture in the semiclassical limit. We have also developed the theory for estimating the quantum corrections to the density independent pair distribution function (PDF) and second virial coefficient of the polar D-sphere fluid mixtures.Academic Voices Vol.5 2015: 48-55

The Laplace transform of exp (−βH) is the Green's operator of the negative-energy Schrödinger equation (H + W)−1. Conditions are stated under which a large |W| asymptotic series for the Green's operator can be inverse-Laplace-transformed term-by-term to obtain a small β expansion for exp (−βH). This approach and the Watson transformation are used to calculate the first few terms of high-temperature asymptotic expansions for the exchange second virial coefficient for hard spheres and for the Lennard-Jones potential. The known results for the direct second virial coefficient for hard spheres are extended. The Wigner-Kirkwood expansion is calculated to order ℏ6 and used to calculate the direct second virial coefficient for the Lennard-Jones potential through order ℏ6.

In previous works, we derived stationary density distribution functions (DDF) where the local equilibrium is determined by imposing the maximum entropy (MaxEnt) principle, under the scale invariance restrictions, and the minimum entropy production theorem. In this paper we demonstrate that it is possible to reobtain these DDF solely from the MaxEnt principle subject to suitable scale invariant restrictions in all the variables. For the sake of concreteness, we analyse the example of ohmic, fully ionized, tokamak-plasmas, in the weak-collisional transport regime. In this case we show that it is possible to reinterpret the stationary distribution function in terms of the Prigogine distribution function where the logarithm of the DDF is directly linked to the entropy production of the plasma. This leads to the suggestive idea that also the stationary neoclassical distribution functions, for magnetically confined plasmas in the collisional transport regimes, may be derived solely by the MaxEnt principle.

The NpT-ensemble Monte Carlo method previously described, in which the hard-disk interaction is represented by a soft pseudopotential in a reduced configuration space with a fixed periodic enclosure, is used to calculate the equation of state and radial distribution function in the high-density fluid phase. The equation of state agrees within statistical error with the (3, 3) Padé approximant to the six-term virial expansion and, for large enough systems, with Salsburg's analysis of the N dependence. The results also agree with recent Monte Carlo calculations by Chae, Ree, and Ree using the NVT ensemble. Some qualitative results for systems of 48 and 90 disks which lend further support to the now-accepted presence of a solid–fluid phase transition are also presented.

Apparent molar volumes of aqueous solutions of argon and xenon have been calculated using a previously developed comprehensive equation of state for nonelectrolyte systems. The equation consists of a virial expansion truncated after the fourth virial coefficient and a closed-form term approximating higher coefficients. Mixing rules are based on the composition dependence of virial coefficients, which is known from statistical mechanics. The equation accurately represents vapor-liquid and gas-gas equilibria for the Ar+H2O and Xe+H2O systems over wide ranges of pressure and temperature using two binary parameters. With the binary parameters determined from phase equilibrium data, the equation accurately predicts apparent molar volumes Vϕ in the near-critical and far-from-critical regions. Apart from reproducing experimental Vϕ data, the equation reveals remarkable maxima of Vϕ as a function of pressure and temperature in the near-critical region. The implications of this equation with respect to the Ar−H2O potential are discussed via the second virial coefficient.

The problem of demixing in the Asakura-Oosawa colloid-polymer model is considered. The critical constants are computed using truncated virial expansions up to fifth order. While the exact analytical results for the second and third virial coefficients are known for any size ratio, analytical results for the fourth virial coefficient are provided here, and fifth virial coefficients are obtained numerically for particular size ratios using standard Monte Carlo techniques. We have computed the critical constants by successively considering the truncated virial series up to the second, third, fourth, and fifth virial coefficients. The results for the critical colloid and (reservoir) polymer packing fractions are compared with those that follow from available Monte Carlo simulations in the grand canonical ensemble. Limitations and perspectives of this approach are pointed out.

If you are one of the many people who have purchased an IBM PC or compatible with a hard disk (or added a hard disk to your M300 Workstation), you may find yourself with a bit of a problem. The advantages of hard disks have been well documented (see “Hard Disks for the M300 Workstation,” OCLC Micro, vol. 2, no. 1, pp. 15–17). Besides room for large data files, they provide a place to install software program files, eliminating the need for extensive use of diskettes. Unfortunately, once you have this large group of files (which you should have divided into directories), you are faced with the problem of controlling the hard disk. You could spend $100 or more for a commercial hard disk manager, but a combination of DOS batch files and a BASIC menu program can solve the problem less expensively.

Hard disks contain data - frequently an irreplaceable asset of high monetary and non-monetary value. At the same time, hard disks are mechanical devices that consume power, are noisy, and fragile when their platters are rotating. In this paper we demonstrate that hard disks cause different kinds of problems for different types of computer systems and demystify several common misconceptions. We show that solutions developed to date are incapable of solving the power consumption, noise, and data reliability problems without sacrificing hard disk life-time, data reliability, or user convenience. We considered data reliability, recovery, performance, user convenience, and hard disk-caused problems together at the enterprise scale. We have designed GreenFS: a fan-out stackable file system that offers all-time all-data run-time data protection, improves performance under typical user workloads, and allows hard disks to be kept off most of the time. As a result, GreenFS improves enterprise data protection, minimizes disk drive-related power consumption and noise and increases the chances of disk drive survivability in case of unexpected external impacts.