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The Labík and Smith Monte Carlo simulation technique to implement the Widom particle insertion method is applied using Molecular Dynamics (MD) instead to calculate numerically the insertion probability, P0(η, σ0), of tracer hard-sphere (HS) particles of different diameters, σ0, in a host HS fluid of diameter σ and packing fraction, η, up to 0.5. It is shown analytically that the only polynomial representation of - ln P0(η, σ0) consistent with the limits σ0 → 0 and σ0 → ∞ has necessarily a cubic form, c0(η)+c1(η)σ0=σ +c2(η)(σ0=σ)² +c3(η)(σ0=σ)³. Our MD data for - ln P0(η, σ0) are fitted to such a cubic polynomial and the functions c0(η) and c1(η) are found to be statistically indistinguishable from their exact solution forms. Similarly, c2(η) and c3(η) agree very well with the Boublík-Mansoori- Carnahan-Starling-Leland and Boublík-Carnahan-Starling-Kolafa formulas. The cubic polynomial is extrapolated (high density) or interpolated (low density) to obtain the chemical potential of the host fluid, or σ0 → σ, as βαex = c0 + c1 + c2 + c3. Excellent agreement between the Carnahan-Starling and Carnahan-Starling-Kolafa theories with our MD data is evident. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The mutual entropic depletion force felt by two solute "big" hard spheres immersed in a binary mixture solvent of nonadditive "small" hard spheres is calculated as a function of the surface-to-surface distance by means of canonical Monte Carlo simulations and through a recently proposed rational-function approximation [R. Fantoni and A. Santos, Phys. Rev. E 84, 041201 (2011)]. Four representative scenarios are investigated: symmetric solute particles and the limit where one of the two solute spheres becomes a planar hard wall, in both cases with symmetric and asymmetric solvents. In all cases, the influence on the depletion force due to the nonadditivity in the solvent is determined in the mixed state. Comparison between results from the theoretical approximation and from the simulation shows a good agreement for surface-to-surface distances greater than the smallest solvent diameter. [ABSTRACT FROM AUTHOR]

The fourth virial coefficient of asymmetric nonadditive binary mixtures of hard disks is computed with a standard Monte Carlo method. Wide ranges of size ratio (0.05 <= q <= 0.95) and nonadditivity (-0.5 <= Δ <= 0.5) are covered. A comparison is made between the numerical results and those that follow from some theoretical developments. The possible use of these data in the derivation of new equations of state for these mixtures is illustrated by considering a rescaled virial expansion truncated to fourth order. The numerical results obtained using this equation of state are compared with Monte Carlo simulation data in the case of a size ratio q = 0.7 and two nonadditivities Δ = ±0.2. [ABSTRACT FROM AUTHOR]

A possible approximate route to obtain the equation of state of the monodisperse hard-sphere system in the metastable fluid region from the knowledge of the equation of state of a hard-sphere mixture at high densities is discussed. The proposal is illustrated by using recent Monte Carlo simulation data for the pressure of a binary mixture. It is further shown to exhibit high internal consistency. [ABSTRACT FROM AUTHOR]

The one-dimensional penetrable-square-well fluid is studied using both analytical tools and specialized Monte Carlo simulations. The model consists of a penetrable core characterized by a finite repulsive energy combined with a short-range attractive well. This is a many-body one-dimensional problem, lacking an exact analytical solution, for which the usual van Hove theorem on the absence of phase transition does not apply. We determine a high-penetrability approximation complementing a similar low-penetrability approximation presented in previous work. This is shown to be equivalent to the usual Debye–Hückel theory for simple charged fluids for which the virial and energy routes are identical. The internal thermodynamic consistency with the compressibility route and the validity of the approximation in describing the radial distribution function is assessed by a comparison against numerical simulations. The Fisher–Widom line separating the oscillatory and monotonic large-distance behaviors of the radial distribution function is computed within the high-penetrability approximation and compared with the opposite regime, thus providing a strong indication of the location of the line in all possible regimes. The high-penetrability approximation predicts the existence of a critical point and a spinodal line, but this occurs outside the applicability domain of the theory. We investigate the possibility of a fluid-fluid transition by the Gibbs ensemble Monte Carlo techniques, not finding any evidence of such a transition. Additional analytical arguments are given to support this claim. Finally, we find a clustering transition when Ruelle’s stability criterion is not fulfilled. The consequences of these findings on the three-dimensional phase diagrams are also discussed. [ABSTRACT FROM AUTHOR]

Different theoretical approaches for the thermodynamic properties and the equation of state for multicomponent mixtures of nonadditive hard spheres in d dimensions are presented in a unified way. These include the theory by Hamad, our previous formulation, the original MIX1 theory, a recently proposed modified MIX1 theory, as well as a nonlinear extension of the MIX1 theory proposed in this paper. Explicit expressions for the compressibility factor, Helmholtz free energy, and second, third, and fourth virial coefficients are provided. A comparison is carried out with recent Monte Carlo data for the virial coefficients of asymmetric mixtures and with available simulation data for the compressibility factor, the critical consolute point, and the liquid-liquid coexistence curves. The merits and limitations of each theory are pointed out. [ABSTRACT FROM AUTHOR]

We study structural and thermophysical properties of a one-dimensional classical fluid made of penetrable spheres interacting via an attractive square-well potential. Penetrability of the spheres is enforced by reducing from infinite to finite the repulsive energy barrier in the pair potentials As a consequence, an exact analytical solution is lacking even in one dimension. Building upon previous exact analytical work in the low-density limit [A. Santos, R. Fantoni, and A. Giacometti, Phys. Rev. E 77, 051206 (2008)], we propose an approximate theory valid at any density and in the low-penetrable regime. By comparison with specialized Monte Carlo simulations and integral equation theories, we assess the regime of validity of the theory. We investigate the degree of inconsistency among the various routes to thermodynamics and explore the possibility of a fluid-fluid transition. Finally we locate the dependence of the Fisher–Widom line on the degree of penetrability. Our results constitute the first systematic study of penetrable spheres with attractions as a prototype model for soft systems. [ABSTRACT FROM AUTHOR]

Bounded potentials are good models to represent the effective two-body interaction in some colloidal systems, such as the dilute solutions of polymer chains in good solvents. The simplest bounded potential is that of penetrable spheres, which takes a positive finite value if the two spheres are overlapped, being 0 otherwise. Even in the one-dimensional case, the penetrable-rod model is far from trivial, since interactions are not restricted to nearest neighbors and so its exact solution is not known. In this paper the structural properties of one-dimensional penetrable rods are studied. We first derive the exact correlation functions of the penetrable-rod fluids to second order in density at any temperature, as well as in the high-temperature and zero-temperature limits at any density. It is seen that, in contrast to what is generally believed, the Percus-Yevick equation does not yield the exact cavity function in the hard-rod limit. Next, two simple analytic theories are constructed: a high-temperature approximation based on the exact asymptotic behavior in the limit T→∞ and a low-temperature approximation inspired by the exact result in the opposite limit T→0. Finally, we perform Monte Carlo simulations for a wide range of temperatures and densities to assess the validity of both theories. It is found that they complement each other quite well, exhibiting a good agreement with the simulation data within their respective domains of applicability and becoming practically equivalent on the borderline of those domains. A comparison with numerical solutions of the Percus-Yevick and the hypernetted-chain approximations is also carried out. Finally, a perspective on the extension of our two heuristic theories to the more realistic three-dimensional case is provided. [ABSTRACT FROM AUTHOR]

The contact values g(σ,σ′) of the radial distribution functions of a fluid of (additive) hard spheres with a given size distribution f(σ) are considered. A “universality” assumption is introduced, according to which, at a given packing fraction η,g(σ,σ′)=G(z(σ,σ′)), where G is a common function independent of the number of components (either finite or infinite) and z(σ,σ′)=[2σσ′/(σ+σ′)]μ2/μ3 is a dimensionless parameter, μn being the nth moment of the diameter distribution. A cubic form proposal for the z dependence of G is made and known exact consistency conditions for the point particle and equal size limits, as well as between two different routes to compute the pressure of the system in the presence of a hard wall, are used to express G(z) in terms of the radial distribution at contact of the one-component system. For polydisperse systems we compare the contact values of the wall-particle correlation function and the compressibility factor with those obtained from recent Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

In general, the total kinetic energy in a multicomponent granular gas of inelastic and rough hard spheres is unequally partitioned among the different degrees of freedom. On the other hand, partial energy equipartition can be reached, in principle, under appropriate combinations of the mechanical parameters of the system. Assuming common values of the coefficients of restitution, we use kinetic-theory tools to determine the conditions under which the components of a granular mixture in the homogeneous cooling state have the same translational and rotational temperatures as those of a one-component granular gas ("mimicry" effect). Given the values of the concentrations and the size ratios, the mimicry effect requires the mass ratios to take specific values, the smaller spheres having a larger particle mass density than the bigger spheres. The theoretical predictions for the case of an impurity immersed in a host granular gas are compared against both direct simulation Monte Carlo and molecular dynamics simulations with a good agreement. [ABSTRACT FROM AUTHOR]

As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first nearest-neighbor probability distribution function, $$p_1(r)$$ , is enough to determine the structural and thermodynamic properties of the system. On the other hand, if the interaction between second nearest-neighbor particles is turned on, the analytically exact solution is lost. Not only the knowledge of $$p_1(r)$$ is not sufficient anymore, but even its determination becomes a complex many-body problem. In this work we systematically explore different approximate solutions for one-dimensional second nearest-neighbor fluid models. We apply those approximations to the square-well and the attractive two-step pair potentials and compare them with Monte Carlo simulations, finding an excellent agreement. [ABSTRACT FROM AUTHOR]

The article offers information on the equation of hard-sphere (HS) model. Among the key topics that were discussed include computer simulations, presentation of equation of state (EOS) as graph in compressibility factor, and scaling parameters of HS absolute temperatures. Other topics mentioned are the Monte Carlo (MC) method, coexistence pressure, and freezing point determination.

A recently proposed rational-function approximation [Phys. Rev. E 84, 041201 (2011)] for the structural properties of nonadditive hard spheres is applied to evaluate analytically (in Laplace space) the local density profiles of multicomponent nonadditive hard-sphere mixtures near a planar noiiadditive hard wall. The theory is assessed by comparison with NVT Monte Carlo simulations of binary mixtures with a size ratio 1:3 in three possible scenarios: a mixture with either positive or negative nonadditivity near an additive wall, an additive mixture with a nonadditive wall, and a nonadditive mixture with a nonadditive wall. It is observed that, while the theory tends to underestimate the local densities at contact (especially in the case of the big spheres) it captures very well the initial decay of the densities with increasing separation from the wall and the subsequent oscillations. [ABSTRACT FROM AUTHOR]

The temporal evolution of a dilute granular gas, both in a compressible flow (uniform longitudinal flow) and in an incompressible flow (uniform shear flow), is investigated by means of the direct simulation Monte Carlo method to solve the Boltzmann equation. Emphasis is laid on the identification of a first "kinetic" stage (where the physical properties are strongly dependent on the initial state) subsequently followed by an unsteady "hydrodynamic" stage (where the momentum fluxes are well-defined non-Newtonian functions of the rate of strain). The simulation data are seen to support this two-stage scenario. Furthermore, the rheological functions obtained from simulation are well described by an approximate analytical solution of a model kinetic equation. [ABSTRACT FROM AUTHOR]

The phase diagram of the penetrable square-well fluid is investigated through Monte Carlo simulations of various nature. This model was proposed as the simplest possibility of combining bounded repulsions at short scale and short-range attractions. We prove that the model is thermodynamically stable for sufficiently low values of the penetrability parameter, and in this case the system behaves similarly to the square-well model. For larger penetration, there exists an intermediate region where the system is metastable, with well-defined fluid–fluid and fluid–solid transitions, at finite size, but eventually it becomes unstable in the thermodynamic limit. We characterize the unstable non-extensive phase appearing at high penetrability, where the system collapses into an isolated blob of a few clusters of many overlapping particles each. [ABSTRACT FROM AUTHOR]

We construct a nonperturbative fully analytical approximation for the thermodynamics and the structure of nonadditive hard-sphere fluid mixtures. The method essentially lies in a heuristic extension of the Percus-Yevick solution for additive hard spheres. Extensive comparison with Monte Carlo simulation data shows a generally good agreement, especially in the case of like-like radial distribution functions. [ABSTRACT FROM AUTHOR]

Purpose: In the present work, the authors compare geometrical and Monte Carlo projectors in detail. The geometrical projectors considered were the conventional geometrical Siddon ray-tracer (S-RT) and the orthogonal distance-based ray-tracer (OD-RT), based on computing the orthogonal distance from the center of image voxel to the line-of-response. A comparison of these geometrical projectors was performed using different point spread function (PSF) models. The Monte Carlo-based method under consideration involves an extensive model of the system response matrix based on Monte Carlo simulations and is computed off-line and stored on disk. Methods: Comparisons were performed using simulated and experimental data of the commercial small animal PET scanner rPET. Results: The results demonstrate that the orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions yield better images in terms of contrast and spatial resolution than those obtained after using the conventional method and the multiray-based S-RT. Furthermore, the Monte Carlo-based method yields slight improvements in terms of contrast and spatial resolution with respect to these geometrical projectors. Conclusions: The orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions represent satisfactory alternatives to factorizing the system matrix or to the conventional on-the-fly ray-tracing methods for list-mode reconstruction, where an extensive modeling based on Monte Carlo simulations is unfeasible. [ABSTRACT FROM AUTHOR]

Abstract: A method is devised to measure the first-order Chapman–Enskog (CE) velocity distribution function associated with the heat flux in a dilute granular gas. The method is based on the application of a homogeneous, anisotropic velocity-dependent external force which produces heat flux in the absence of gradients. The form of the force is found under the condition that, in the linear response regime, the deviation of the velocity distribution function from that of the homogeneous cooling state obeys the same linear integral equation as the one derived from the conventional CE expansion. The direct simulation Monte Carlo method is used to solve the corresponding Boltzmann equation and measure the dependence of the (modified) thermal conductivity on the coefficient of normal restitution . Comparison with previous simulation data obtained from the Green–Kubo relations [J.J. Brey, M.J. Ruiz-Montero, P. Mayner, M.I. García de Soria, J. Phys.: Condens. Matter 17 (2005) S2489] shows an excellent agreement, both methods consistently showing that the first Sonine approximation dramatically overestimates the thermal conductivity for high inelasticity (). Since our method is tied to the Boltzmann equation, the results indicate that the failure of the first Sonine approximation is not due to velocity correlation effects absent in the Boltzmann framework. This is further confirmed by an analysis of the first-order CE velocity distribution function and its three first Sonine coefficients obtained from the simulations. [Copyright &y& Elsevier]

Recent Monte Carlo simulation results for the contact values of polydisperse hard-sphere mixtures at a hard planar wall are considered in the light of a universality assumption made in approximate theoretical approaches. It is found that the data appear to fulfill the universality ansatz reasonably well, thus opening up the possibility of inferring the properties of complicated systems from the study of simpler ones. [ABSTRACT FROM AUTHOR]

A class of binary mixtures of Janus fluids formed by colloidal spheres with the hydrophobic hemispheres constrained to point either up or down are studied by means of Gibbs ensemble Monte Carlo simulations and simple analytical approximations. These fluids can be experimentally realized by the application of an external static electrical field. The gas-liquid and demixing phase transitions in five specific models with different patch-patch affinities are analyzed. It is found that a gas-liquid transition is present in all the models, even if only one of the four possible patch-patch interactions is attractive. Moreover, provided the attraction between like particles is stronger than between unlike particles, the system demixes into two subsystems with different composition at sufficiently low temperatures and high densities. [ABSTRACT FROM AUTHOR]

New proposals for the equation of state of four- and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact third virial coefficient) extend, on the one hand, recent similar formulations for hard-disk and (three-dimensional) hard-sphere mixtures and, on the other hand, two of our previous proposals also linking the mixture equation of state and the one of the monocomponent fluid but unable to reproduce the exact third virial coefficient. The old and new proposals are tested by comparison with published molecular dynamics and Monte Carlo simulation results and their relative merit is evaluated. [ABSTRACT FROM AUTHOR]

Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1 ≤ d ≤ 3) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015)], a good agreement being observed. [ABSTRACT FROM AUTHOR]

In a recent paper [F. Vega Reyes et at., Phys. Rev. Lett. 104, 028001 (2010).] we presented a preliminary description of a special class of steady Couette flows in dilute granular gases. In all flows of this class the viscous heating is exactly balanced by inelastic cooling. This yields a uniform heat flux and a linear relationship between the local temperature and flow velocity. The class (referred to as the LTu class) includes the Fourier flow of ordinary gases and the simple shear flow of granular gases as special cases. In the present paper we provide further support for this class of Couette flows by following four different routes, two of them being theoretical (Grad's moment method of the Boltzmann equation and exact solution of a kinetic model) and the other two being computational (molecular dynamics and Monte Carlo simulations of the Boltzmann equation). Comparison between theory and simulations shows a very good agreement for the non-Newtonian rheological properties, even for quite strong inelasticity, and a good agreement for the heat flux coefficients in the case of Grad's method, the agreement being only qualitative in the case of the kinetic model. [ABSTRACT FROM AUTHOR]

Abstract: A realistic dynamic positron-emission tomography (PET) thoracic study was generated, using the 4D NURBS-based (non-uniform rational B-splines) cardiac-torso (NCAT) phantom and a sophisticated model of the PET imaging process, simulating two solitary pulmonary nodules. Three data reduction and blind source separation methods were applied to the simulated data: principal component analysis, independent component analysis and similarity mapping. All methods reduced the initial amount of image data to a smaller, comprehensive and easily managed set of parametric images, where structures were separated based on their different kinetic characteristics and the lesions were readily identified. The results indicate that the above-mentioned methods can provide an accurate tool for the support of both visual inspection and subsequent detailed kinetic analysis of the dynamic series via compartmental or non-compartmental models. [Copyright &y& Elsevier]

We report the emergence of a giant Mpemba effect in the uniformly heated gas of inelastic rough hard spheres: The initially hotter sample may cool sooner than the colder one, even when the initial temperatures differ by more than one order of magnitude. In order to understand this behavior, it suffices to consider the simplest Maxwellian approximation for the velocity distribution in a kinetic approach. The largeness of the effect stems from the fact that the rotational and translational temperatures, which obey two coupled evolution equations, are comparable. Our theoretical predictions agree very well with molecular dynamics and direct simulation Monte Carlo data. [ABSTRACT FROM AUTHOR]

The structural properties of the Jagla fluid are studied by Monte Carlo (MC) simulations, numerical solutions of integral equation theories, and the (semi-analytical) rational-function approximation (RFA) method. In the latter case, the results are obtained from the assumption (supported by our MC simulations) that the Jagla potential and a potential with a hard core plus an appropriate piecewise constant function lead to practically the same cavity function. The predictions obtained for the radial distribution function, g(r), from this approach are compared against MC simulations and integral equations for the Jagla model, and also for the limiting cases of the triangle-well potential and the ramp potential, with a general good agreement. The analytical form of the RFA in Laplace space allows us to describe the asymptotic behavior of g(r) in a clean way and compare it with MC simulations for representative states with oscillatory or monotonic decay. The RFA predictions for the Fisher-Widom and Widom lines of the Jagla fluid are obtained. [ABSTRACT FROM AUTHOR]

Under certain conditions, two samples of fluid at different initial temperatures present a counterintuitive behavior known as the Mpemba effect: it is the hotter system that cools sooner. Here, we show that the Mpemba effect is present in granular fluids, both in uniformly heated and in freely cooling systems. In both cases, the system remains homogeneous, and no phase transition is present. Analytical quantitative predictions are given for how differently the system must be initially prepared to observe the Mpemba effect, the theoretical predictions being confirmed by both molecular dynamics and Monte Carlo simulations. Possible implications of our analysis for other systems are also discussed. [ABSTRACT FROM AUTHOR]