Physics Publications of James F. Lutsko
Generated Mon Oct 15 13:53:43 2018
4073 citations, hindex: 34 as of Oct 15, 2018

[86] Mike Sleutel, James Lutsko, and Alexander E. S. Van Driessche. Mineral Growth beyond the Limits of Impurity Poisoning. Crystal Growth and Design, 18:171, 2018. [ bib | DOI | .pdf | http ]
More often than not, minerals formed in natureare grown at low supersaturation and from sources that areimpure with respect to the crystals’ main building blocks.Quite paradoxically, these conditions are in conflict with theestablished crystal growth theories that focus on the interplaybetween the crystal interface and impurities that are present inthe growth medium. These theories predict a kinetic dead zonefor the cases where low purity is combined with weak drivingforces. Hints toward reconciling this apparent disparity havebeen given by the observation that a specific class of steps, socalledmacrosteps, can circumvent the debilitating kineticeffects of impurities in ways that up until now are poorlyunderstood. In this contribution, we examine the mechanism of crystal growth by means of kinetic Monte Carlo simulation atconditions close to impurity-induced kinetic arrest. In agreement with previous reports, we show that as a result of impuritybinding to the crystal surface, steps spontaneously group into bunches and later condense into macrosteps. A kinetic analysisdemonstrates that these macrosteps are able to evade crystal growth cessation under conditions where single steps are firmlypinned. We identify the mechanism of interstep cooperativity which leads to cessation evasion by macrosteps and demonstrate thatit applies to a range of supersaturation and impurity concentration values. On the basis of these findings, we present a model thatexplains how minerals can grow from mother liquor solutions that would otherwise seem to be nonconducive to crystal growth.

[85] Julien Lam and James F. Lutsko. Lattice induced crystallization of nanodroplets: the role of finite-size effects and substrate properties in controlling polymorphism. Nanoscale, 10:4921, 2018. [ bib | DOI | .pdf | http ]
Targeting specific technological applications requires the control of nanoparticle properties, especially the crystalline polymorph. Freezing a nanodroplet deposited on a solid substrate leads to the formation of crystalline structures. We study the inherent mechanisms underlying this general phenomenon by means of molecular dynamics simulations. Our work shows that different crystal structures can be selected by finely tuning the solid substrate lattice parameter. Indeed, while for our system, face-centered cubic is usually the most preponderant structure, the growth of two distinct polymorphs, hexagonal centered packing and body-centered cubic, was also observed even when the solid substrate was face-centered cubic. Finally, we also demonstrated that the growth of hexagonal centered packing is conditioned by the appearance of large enough body-centered cubic clusters thus suggesting the presence of a cross-nucleation pathway. Our results provide insights into the impact of nanoscale effects and solid substrate properties towards the growth of polymorphic nanomaterials.

[84] Miguel A. Duran-Olivencia, Peter Yatsyshin, Serafim Kalliadasis, and Jim Lutsko. General framework for nonclassical nucleation. New Journal of Physics, 20:083019, 2018. [ bib | DOI | .pdf | http ]
A great deal of experimental evidence suggests that a wide spectrum of phase transitions occur in a multistage manner via the appearance and subsequent transformation of intermediate metastable states. Such multistage mechanisms cannot be explained within the realm of the classical nucleation framework. Hence, there is a strong need to develop new theoretical tools to explain the occurrence and nature of these ubiquitous intermediate phases. Here we outline a unified and self-consistent theoretical framework to describe both classical and nonclassical nucleation. Our framework provides a detailed explanation of the whole multistage nucleation pathway showing in particular that the pathway involves a single energy barrier and it passes through a dense phase, starting from a low-density initial phase, before reaching the final stable state. Moreover, we demonstrate that the kinetics of matter inside subcritical clusters favours the formation of nucleation clusters with an intermediate density, i.e. nucleation precursors. Remarkably, these nucleation precursors are not associated with a local minimum of the thermodynamic potential, as commonly assumed in previous phenomenological approaches. On the contrary, we find that they emerge due to the competition between thermodynamics and kinetiá
[83] James F. Lutsko. Classical density functional theory, unconstrained crystallization, and polymorphic behavior. Phys. Rev. E, 98:012604, 2018. [ bib | DOI | .pdf | http ]
While in principle, classical density functional theory (cDFT) should be a powerful tool for the study ofcrystallization, in practice this has not so far been the case. Progress has been hampered by technical problemswhich have plagued the study of the crystalline systems using the most sophisticated fundamental measure theorymodels. In this paper, the reasons for the difficulties are examined and it is proposed that the tensor functionalscurrently favored are in fact numerically unstable. By reverting to an older, more heuristic model it is shown thatall of the technical difficulties are eliminated. Application to a Lennard-Jones fluid results in a demonstrationof power of cDFT to describe crystallization in a highly inhomogeneous system. First, we show that dropletsattached to a slightly hydrophobic wall crystallize spontaneously upon being quenched. The resulting crystallitesare clearly faceted structures and are predominantly HCP structures. In contrast, droplets in a fully periodiccalculational cell remain stable to lower temperatures and eventually show the same spontaneous localization ofthe density into “atoms” but in an amorphous structure having many of the structural characteristics of a glass.A small change of the protocol leads, at the same temperature, to the formation of crystals, this time with thefcc structure typical of bulk Lennard-Jones solids. The fcc crystals have á
[82] James F. Lutsko. Systematically extending classical nucleation theory. New Journal of Physics, 20:103015, 2018. [ bib | DOI | .pdf ]
The foundation for any discussion of first-order phse transitions is Classical Nucleation The-ory(CNT). CNT, developed in the first half of the twentieth century, is based on a number ofheuristically plausible assumtptions and the majority of theoretical work on nucleation is devotedto refining or extending these ideas. Ideally, one would like to derive CNT from a more fundamen-tal description of nucleation so that its extension, development and refinement could be developedsystematically. In this paper, such a development is described based on a previously established(Lutsko, JCP 136:034509, 2012 ) connection between Classical Nucleation Theory and fluctuatinghydrodynamics. Here, this connection is described without the need for artificial assumtions suchas spherical symmetry. The results are illustrated by application to CNT with moving clusters (along-standing problem in the literature) and the constructrion of CNT for ellipsoidal clusters.

[81] Julien Lam and James F. Lutsko. Solvent-mediated interactions between nanostructures: From water to Lennard-Jones liquid. The Journal of Chemical Physics, 149(13):134703, 2018. [ bib | DOI | .pdf ]
Solvent-mediated interactions emerge from complex mechanisms that depend on the solute structure, its wetting properties, and the nature of the liquid. While numerous studies have focused on the first two influences, here, we compare the results from water and Lennard-Jones liquid in order to reveal to what extent solvent-mediated interactions are universal with respect to the nature of the liquid. Besides the influence of the liquid, the results were obtained with classical density functional theory and brute-force molecular dynamics simulations which allow us to contrast these two numerical techniques.

[80] Jean Pierre Boon and James F. Lutsko. Temporal diffusion: From microscopic dynamics to generalised Fokker-Planck and fractional equations. J. Statistical Physics, 166:1441, 2017. [ bib | .pdf | http ]
The temporal Fokker–Planck equation (Boon et al. in J Stat Phys 3/4: 527, 2003) orpropagation–dispersion equation was derived to describe diffusive processes with temporaldispersion rather than spatial dispersion as in classical diffusion. We present two generalizationsof the temporal Fokker–Planck equation for the first passage distribution functionf j(r, t) of a particle moving on a substrate with time delays τ j . Both generalizations followfrom the first visit recurrence relation. In the first case, the time delays depend on the localconcentration, that is the time delay probability Pj is a functional of the particle distributionfunction and we show that when the functional dependence is of the power law type,Pj ∝ f Μ−1j , the generalized Fokker–Planck equation exhibits a structure similar to that ofthe nonlinear spatial diffusion equation where the roles of space and time are reversed. In thesecond case, we consider the situation where the time delays are distributed according to apower law, Pj ∝ τ −1−α j (with 0 <α< 2), in which case we obtain a fractional propagationdispersionequation which is the temporal analog of the fractional spatial diffusion equation(with space and time interchanged). The analysis shows how certain microscopic mechanismscan lead to non-Gaussian distributions and non-classical scaling exponents.

[79] Julien Lam and James F. Lutsko. Solute particle near a nanopore: influence of size and surface properties on the solvent-mediated forces. Nanoscale, 9:17099, 2017. [ bib | DOI | .pdf | http ]
Nanoscopic pores are used in various systems to attract nanoparticles. In general the behaviour is a resultof two types of interactions: the material specific affinity and the solvent-mediated influence also calledthe depletion force. The latter is more universal but also much more complex to understand since itrequires modeling both the nanoparticle and the solvent. Here, we employed classical density functionaltheory to determine the forces acting on a nanoparticle near a nanoscopic pore as a function of its hydrophobicityand its size. A simple capillary model is constructed to predict those depletion forces for varioussurface properties. For a nanoscopic pore, complexity arises from both the specific geometry and the factthat hydrophobic pores are not necessarily filled with liquid. Taking all of these effects into account andincluding electrostatic effects, we establish a phase diagram describing the entrance and the rejection ofthe nanoparticle from the pore.

[78] James F. Lutsko, Alexander E. S. Van Driessche, Miguel A. Durán-Olivencia, Dominique Maes, and Mike Sleutel. Step Crowding Effects Dampen the Stochasticity of Crystal Growth Kinetics. Phys. Rev. Lett., 116:015501, 2016. [ bib | .pdf | http ]
Crystals grow by laying down new layers of material which can either correspond in size to the height of one unit cell (elementary steps) or multiple unit cells (macrosteps). Surprisingly, experiments have shown that macrosteps can grow under conditions of low supersaturation and high impurity density such that elementary step growth is completely arrested. We use atomistic simulations to show that this is due to two effects: the fact that the additional layers bias fluctuations in the position of the bottom layer towards growth and by a transition, as step height increases, from a 2D to a 3D nucleation mechanism.

[77] James F. Lutsko and Grégoire Nicolis. Mechanism for the stabilization of protein clusters above the solubility curve. Soft Matter, 12:93, 2016. [ bib | .pdf | http ]
Pan, Vekilov and Lubchenko [J. Phys. Chem. B, 2010, 114, 7620] have proposed that dense stable protein clusters appearing in weak protein solutions above the solubility curve are composed of protein oligomers. The hypothesis is that a weak solution of oligomer species is unstable with respect to condensation causing the formation of dense, oligomer-rich droplets which are stabilized against growthby the monomer–oligomer reaction. Here, we show that such a combination of processes can be understood using a simple capillary model yielding analytic expressions for the cluster properties which can be model and show that it is consistent with the predictions of the capillary model. The viability of the used to interpret experimental data. We also construct a microscopic Dynamic Density Functional Theorymechanism is thus confirmed and it is shown how the radius of the stable clusters is related to physically quantities such as the monomer–oligomer rate constants.

[76] James F. Lutsko. Mechanism for the stabilization of protein clusters above the solubility curve: The role of non-ideal chemical reactions. Journal of Physics Condensed Matter, 28:244020, 2016. [ bib | http ]
Dense protein clusters are known to play an important role in nucleation of protein crystals from dilute solutions. While these have generally been thought to be formed from a metastable phase, the observation of similar, if not identical, clusters above the critical point for the dilute-solution/strong-solution phase transition has thrown this into doubt. Furthermore, the observed clusters are stable for relatively long times. Because protein aggregation plays a central role in some pathologies, understanding the nature of such clusters is an important problem. One mechanism for the stabilization of such structures was proposed by Pan, Vekilov and Lubchenko and was investigated using a dynamical density functional theory model which confirmed the viability of the model. Here, we revisit that model and incorporate additional physics in the form of state-dependent reaction rates. We show by a combination of numerical results and general arguments that the state-dependent rates disrupt the stability mechanism. Finally, we argue that the state-dependent reactions correct unphysical aspects of the model with ideal (state-independent) reactions and that this necessarily leads to the failure of the proposed mechanism.

[75] James F. Lutsko and Miguel A. Durán-Olivencia. A Two-parameter Extension of Classical Nucleation Theory. J. Phys. Cond. Matt., 27:235101, 2015. [ bib | .pdf | http ]
A two-variable stochastic model for diffusion-limited nucleation is developedusing a formalism derived from fluctuating hydrodynamics. The model is adirect generalization of the standard Classical Nucleation Theory. Thenucleation rate and pathway are calculated in the weak-noise approximation andare shown to be in good agreement with direct numerical simulations for theweak-solution/strong-solution transition in globular proteins. We find thatClassical Nucleation Theory underestimates the time needed for the formationof a critical cluster by two orders of magnitude and that this discrepancy isdue to the more complex dynamics of the two variable model and not, as oftenis assumed, a result of errors in the estimation of the free energy barrier.

[74] Miguel A. Durán-Olivencia and James F. Lutsko. Mesoscopic nucleation theory for confined systems: A one-parameter model. Phys. Rev. E, 91:022402, 2015. [ bib | .pdf | http ]
Classical nucleation theory has been recently reformulated based on fluctuating hydrodynamics [J.F. Lutsko and M.A. Durán-Olivencia, J. Chem. Phys. 138,244908(2013)]. The present work extends this effort to the case of nucleationin confined systems such as small pores and vesicles. The finite available mass imposes a maximal supercritical cluster size and prohibits nucleation altogether if the system is too small. We quantity the effect of system size on the nuceation rate. We also discuss the effect of relaxing the capillary-model assumption of zero interfacial width resulting in significant changes in the nucleation barrier and nucleation rate.

[73] Mike Sleutel, James F. Lutsko, Dominique Maes, and Alexander E. S. Van Driessche. Mesoscopic impurities expose a nucleation-limited regime of crystal growth. Phys. Rev. Lett., 114:245501, 2015. [ bib | .pdf | http ]

[72] Miguel A. Durán-Olivencia and James F. Lutsko. Unification of classical nucleation theories via unified ItĂŽ-Stratonovich stochastic equation. Phys. Rev. E, 92:032407, 2015. [ bib | .pdf | http ]
Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g. Zeldovich-Frenkel or Becker-Döring-Tunitskii equations. Starting from a phenomenological stochastic differential equation a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that form a recent update of CNT [J.F. Lutsko and M.A. Durán-Olivencia, J. Chem. Phys., 2013, 138, 244908] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios. In particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion or interface transfer.

[71] Jean Pierre Boon and James F. Lutsko. Molecular theory of anomalous diffusion - Application to Fluorescence Correlation Spectroscopy. J. Stat. Phys., 160:622--635, 2015. [ bib | .pdf | http ]
The nonlinear theory of anomalous diffusion is based on particle interactions giving an explicit microscopic description of diffusive processes leading to sub-, normal, or super-diffusion as a result competitive effects between attractive and repulsive interactions. We present the explicit analytical solution to the nonlinear diffusion equation which we then use to compute the correlation function which is experimentally measured by correlation spectroscopy. The theoretical results are applicable in particular to the analysis of fluorescence correlation spectroscopy of marked molecules in biological systems. More specifically we consider the case of fluorescently labeled lipids and we find that the nonlinear correlation spectrum reproduces very well the experimental data indicating sub-diffusive molecular motion of lipid molecules in the cell membrane.

[70] James F. Lutsko, Nélido González-Segredo, Miguel A. Durán-Olivencia, Dominique Maes, Alexander E.S. Van Driessche, and Mike Sleutel. Crystal Growth Cessation Revisited -- the physical basis of step pinning. Crystal Growth and Design, 14:6129--6134, 2014. [ bib | .pdf | http ]
The growth of crystals from solution is a fundamental process of relevance to such diverse areas as X-ray-diffraction structural determination and the role of mineralization in living organisms. A key factor determining the dynamics of crystallization is the effect of impurities on step growth. For over fifty years, all discussions of impurity-step interaction have been framed in the context of the Cabrera--Vermilyea (CV) model for step blocking, which has nevertheless proven difficult to validate experimentally. Here we report on extensive computer simulations which clearly falsify the CV model, suggesting a more complex picture. While reducing to the CV result in certain limits, our approach is more widely applicable, encompassing non-trivial impurity-crystal interactions, mobile impurities and negative growth, among others.

[69] Mike Sleutel, Jim Lutsko, Alexander E. S. Van Driessche, Miguel A. Durán-Olivencia, and Dominique Maes. Observing classical nucleation theory at work by monitoring phase transitions with molecular precision. Nature Communications, 5:5598, 2014. [ bib | .pdf | .html ]
It is widely accepted that many phase transitions do not follow nucleation pathways as envisaged by the classical nucleation theory. Many substances can traverse intermediate states before arriving at the stable phase. The apparent ubiquity of multi-step nucleation has made the inverse question relevant: does multistep nucleation always dominate single-step pathways? Here we provide an explicit example of the classical nucleation mechanism for a system known to exhibit the characteristics of multi-step nucleation. Molecular resolution atomic force microscopy imaging of the two-dimensional nucleation of the protein glucose isomerase demonstrates that the interior of subcritical clusters is in the same state as the crystalline bulk phase. Our data show that despite having all the characteristics typically associated with rich phase behaviour, glucose isomerase 2D crystals are formed classically. These observations illustrate the resurfacing importance of the classical nucleation theory by re-validating some of the key assumptions that have been recently questioned.

[68] James F. Lutsko and Jean Pierre Boon. Comment on “Possible divergences in Tsallis’ thermostatistics” by Plastino A. and Rocca M. C. EuroPhys. Lett., 107:10003, 2014. [ bib | .pdf | http ]
Questions concerning Platino and Rocca, EPL 104 6003 (2013).

[67] James F. Lutsko and Miguel A. Durán-Olivencia. Classical nucleation theory from a dynamical approach to nucleation. J. Chem. Phys., 138:244908, 2013. [ bib | DOI | .pdf | http ]
It is shown that diffusion-limited classical nucleation theory (CNT) can berecovered as a simple limit of the recently proposed dynamical theory ofnucleation based on fluctuating hydrodynamics (Lutsko, JCP 136, 034509(2012)). The same framework is also used to construct a more realistic theoryin which clusters have finite interfacial width. When applied to the dilutesolution/dense solution transition in globular proteins, it is found that theextension gives corrections to the the nucleation rate even for the case ofsmall supersaturations due to changes in the monomer distribution function andto the excess free energy. It is also found that the monomerattachement/detachment picture breaks down at high supersaturationscorresponding to clusters smaller than about 100 molecules. The results alsoconfirm the usual assumption that most important corrections to CNT can beacheived by means of improved estimates of the free energy barrier. The theoryalso illustrates two topics that have received considerable attention in therecent literature on nucleation: the importance sub-dominant corrections tothe capillary model for the free energy and of the correct choice of thereaction coordinate.

[66] James F. Lutsko. Direct correlation function from the consistent fundamental-measure free energies for hard-sphere mixtures. Phys. Rev. E, 87:014103, 2013. [ bib | DOI | .pdf | http ]
In a recent paper [ Phys. Rev. E 86 040102(R) (2012)], Santos presented a self-consistency condition that can be used to limit the possible forms of fundamental measure theory. Here, the direct correlation function, resulting from the Santos functional, is derived, and it is found to be very close to the result of the White Bear density functional, except near the origin where it diverges.

[65] James F. Lutsko and Jean Pierre Boon. Microscopic theory of anomalous diffusion based on particle interactions. Phys. Rev. E, 88:022108, 2013. [ bib | DOI | .pdf | http ]
We present a master equation formulation based on a Markovian random walk model that exhibits subdiffusion, classical diffusion, and superdiffusion as a function of a single parameter. The nonclassical diffusive behavior is generated by allowing for interactions between a population of walkers. At the macroscopic level, this gives rise to a nonlinear Fokker-Planck equation. The diffusive behavior is reflected not only in the mean squared displacement [〈r2(t)âŒȘ∌tÎł with 0<γ≀1.5] but also in the existence of self-similar scaling solutions of the Fokker-Planck equation. We give a physical interpretation of sub- and superdiffusion in terms of the attractive and repulsive interactions between the diffusing particles and we discuss analytically the limiting values of the exponent Îł. Simulations based on the master equation are shown to be in agreement with the analytical solutions of the nonlinear Fokker-Planck equation in all three diffusion regimes.

[64] Jean Pierre Boon, James F. Lutsko, and Christopher Lutsko. Microscopic approach to nonlinear reaction-diffusion: The case of morphogen gradient formation. Phys. Rev. E, 85:021126, 2012. [ bib | DOI | .pdf | http ]
We develop a microscopic theory for reaction-difusion (R-D) processes based on a generalization of Einstein's master equation with a reactive term and we show how the mean field formulation leads to a generalized R-D equation with non-classical solutions. For the n-th order annihilation reaction A+A+A+...+A->0, we obtain a nonlinear reaction-diffusion equation for which we discuss scaling and non-scaling formulations. We find steady states with either solutions exhibiting long range power law behavior (for n>α) showing the relative dominance of sub-diffusion over reaction effects in constrained systems, or conversely solutions (for n<α<n+1) with finite support of the concentration distribution describing situations where diffusion is slow and extinction is fast. Theoretical results are compared with experimental data for morphogen gradient formation.

[63] James F. Lutsko. A dynamical theory of nucleation for colloids and macromolecules. J. Chem. Phys., 136:034509, 2012. [ bib | DOI | .pdf | http ]
A general theory of nucleation for colloids and macromolecules in solution is formulated within the context of fluctuating hydrodynamics. A formalism for the determination of nucleation pathways is developed and stochastic differential equations for the evolution of order parameters are given. The conditions under which the elements of Classical Nucleation Theory are recovered are determined. The theory provides a justification and extension of more heuristic equilibrium approaches based solely on the free energy. It is illustrated by application to the low-concentration/high-concentration transition in globular proteins where a novel two-step mechanism is identified where the first step involves the formation of long-wavelength density fluctuations and the second step is the actual nucleation event occuring within the fluctuation.

[62] James F. Lutsko. Nucleation of colloids and macromolecules: Does the nucleation pathway matter? J. Chem. Phys., 136:134402, 2012. [ bib | DOI | .pdf | http ]
A recent description of diffusion-limited nucleation based on fluctuating hydrodynamics that extends classical nucleation theory predicts a very non-classical two-step scenario whereby nucleation is most likely to occur in spatially extended, low-amplitude density fluctuations. In this paper, it is shown how the formalism can be used to determine the maximum probability of observing any proposed nucleation pathway, thus allowing one to address the question as to their relative likelihood, including of the newly proposed pathway compared to classical scenarios. Calculations are presented for the nucleation of high-concentration droplets in a low-concentration solution of globular proteins and it is found that the relative probabilities (new theory compared to classical result) for reaching a critical nucleus containing Nc molecules scales as e−Nc/3 thus indicating that for all but the smallest nuclei, the classical scenario is extremely unlikely.

[61] James F. Lutsko. On the role of metastable intermediate states in the homogeneous nucleation of solids from solution. Adv. Chem. Phys., 151:137--172, 2012. [ bib | .pdf | http ]
The role of metastable liquid phases in vapor-crystal nucleation is studied using Density Functional Theory(DFT). The model gives a semi-quantitatively accurate description of both the vapor-liquid-solid phase diagram for both simple fluids (Lennard-Jones interactions) and of the low-density/high-density/crystal phase diagram for model globular proteins (ten Wolde-Frenkel interaction). The density profile is characterized by two local order parameters, the average density and the crystallinity. The bulk free energy model is supplemented by squared-derivative terms in these order parameters to account for inhomogeneities thus producing a model similar in spirit to phase-field theory. It is shown that for both interaction models, the vapor-crystal part of the phase-diagram can be separated into regions for which metastable liquid phases are more or less stable than the vapor, but always less stable than the solid. The former case allows for the possibility of double nucleation whereby liquid droplets nucleate from the vapor followed by a separate nucleation of the solid phase within the liquid droplets. Whether or not this actually occurs depends on the relative free energy barriers for vapor-solid and vapor-liquid nucleation and it is shown that for simple fluids, double nucleation is indeed favored at sufficiently large supersaturation. Finally, by studying the minimum free energy path from the vapor to the solid, the separate possibility of transient nucleatioá
[60] James F. Lutsko. Nucleation of colloids and macromolecules in a finite volume. J. Chem. Phys., 137:154903, 2012. [ bib | DOI | http ]
A recently formulated description of homogeneous nucleation for Brownianparticles in the over-damped limit based on fluctuating hydrodynamics isused to determine the nucleation pathway, characterized as the most likelypath (MLP), for the nucleation of a dense-concentration droplet of globularprotein from a dilute solution in a small, finite container. Thecalculations are performed by directly discretizing the equations for theMLP and it is found that they confirm previous results obtained for infinitesystems: the process of homogeneous nucleation begins with along-wavelength, spatially-extended concentration fluctuation that itcondenses to form the pre-critical cluster. This is followed by a classicalgrowth processes. The calculations show that the post-critical growthinvolves the formation of a depletion zone around the cluster whereas nosuch depletion is observed in the pre-critical cluster. The approachtherefore captures dynamical effects not found in classical DensityFunctional Theory studies while consistently describing the formation of thepre-critical cluster.

[59] James F. Lutsko. A dynamical theory of homogeneous nucleation for colloids and macromolecules. J. Chem. Phys., 135:161101, 2011. [ bib | DOI | .pdf | http ]
Homogeneous nucleation is formulated within the context of fluctuating hydrodynamics. It is shown that for a colloidal or macromolecular system in the strong damping limit the most likely path for nucleation can be determined by gradient descent in density space governed by a nontrivial metric fixed by the dynamics. The theory provides a justification and extension of more heuristic equilibrium approaches based solely on the free energy. It is illustrated by application to liquid-vapor nucleation where it is shown that, in contrast to most free energy-based studies, the smallest clusters correspond to long wavelength, small amplitude perturbations.

[58] James F. Lutsko. Density functional theory of inhomogeneous liquids. IV. Squared-gradient approximation and classical nucleation theory. J. Chem. Phys., 134:164501, 2011. [ bib | DOI | .pdf | http ]
The squared-gradient approximation to the modified-core Van der Waals density functional theorymodel is developed. A simple, explicit expression for the SGA coefficient involving only the bulkequation of state and the interaction potential is given. The model is solved for planar interfacesand spherical clusters and is shown to be quantitatively accurate in comparison to computer simulations.An approximate technique for solving the SGA based on piecewise-linear density profilesis introduced and is shown to give reasonable zeroth-order approximations to the numerical solutionof the model. The piecewise-linear models of spherical clusters are shown to be a naturalextension of classical nucleation theory and serve to clarify some of the nonclassical effects previouslyobserved in liquid–vapor nucleation. Nucleation pathways are investigated using both constrainedenergy-minimization and steepest-descent techniques.

[57] James F. Lutsko and Jean Pierre Boon. Questioning the validity of non-extensive thermodynamics for classical Hamiltonian systems. EuroPhysics Letters, 95:20006, 2011. [ bib | DOI | .pdf | .pdf ]
We examine the non-extensive approach to the statistical mechanics of Hamiltoniansystems with H = T +V, where T is the classical kinetic energy. Our analysis starts from thebasics of the formalism by applying the standard variational method for maximizing the entropysubject to the average energy and normalization constraints. The analytical results show i) that thenon-extensive thermodynamics formalism should be called into question to explain experimentalresults described by extended exponential distributions exhibiting long tails, i.e. q-exponentialswith q >1, and ii) that in the thermodynamic limit the theory is only consistent in the range0 q  1 where the distribution has finite support, thus implying that configurations with, e.g.,energy above some limit have zero probability, which is at variance with the physics of systemsin contact with a heat reservoir. We also discuss the (q-dependent) thermodynamic temperatureand the generalized specific heat.

[56] Jean Pierre Boon and James F. Lutsko. Nonextensive formalism and continuous Hamiltonian systems. Physics Letters A, 375:329--334, 2011. [ bib | DOI | .pdf | http ]
A recurring question in nonequilibrium statistical mechanics is what deviation from standard statisticalmechanics gives rise to non-Boltzmann behavior and to nonlinear response, which amounts to identifyingthe emergence of “statistics from dynamics” in systems out of equilibrium. Among several possible analyticaldevelopments which have been proposed, the idea of nonextensive statistics introduced by Tsallisabout 20 years ago was to develop a statistical mechanical theory for systems out of equilibrium wherethe Boltzmann distribution no longer holds, and to generalize the Boltzmann entropy by a more generalfunction Sq while maintaining the formalism of thermodynamics. From a phenomenological viewpoint,nonextensive statistics appeared to be of interest because maximization of the generalized entropy Sqyields the q-exponential distribution which has been successfully used to describe distributions observedin a large class of phenomena, in particular power law distributions for q > 1. Here we re-examine thevalidity of the nonextensive formalism for continuous Hamiltonian systems. In particular we consider theq-ideal gas, a model system of quasi-particles where the effect of the interactions are included in theparticle properties. On the basis of exact results for the q-ideal gas, we find that the theory is restrictedto the range q < 1, which raises the question of its formal validá
[55] James F Lutsko, Julien Laidet, and Patrick Grosfils. Phase behavior of a confined nanodroplet in the grand-canonical ensemble: the reverse liquid–vapor transition. J. Phys.: Cond. Matt., 22(3):035101, 2010. [ bib | .pdf | http ]
The equilibrium density distribution and thermodynamic properties of a Lennard-Jones fluid confined to nanosized spherical cavities at a constant chemical potential was determined using Monte Carlo simulations. The results describe both a single cavity with semi-permeable walls as well as a collection of closed cavities formed at the constant chemical potential. The results are compared to calculations using classical density functional theory (DFT). It is found that the DFT calculations give a quantitatively accurate description of the pressure and structure of the fluid. Both theory and simulation show the presence of a 'reverse' liquid–vapor transition whereby the equilibrium state is a liquid at large volumes but becomes a vapor at small volumes.

[54] Patrick Grosfils and James F. Lutsko. Low-Density/High-Density Liquid Phase Transition for Model Globular Proteins. Langmuir, 26(11):8510--8516, 2010. [ bib | .pdf | http ]
[53] James F. Lutsko, Vasileios Basios, Gregoire Nicolis, John J. Kozak, Mike Sleutel, and Dominique Maes. Kinetic rougheninglike transition with finite nucleation barrier. J. Chem. Phys., 132(3):035102, 2010. [ bib | DOI | .pdf | http ]
Recent observations of the growth of protein crystals have identified two different growth regimes. At low supersaturation, the surface of the crystal is smooth and increasing in size due to the nucleation of steps at defects and the subsequent growth of the steps. At high supersaturation, nucleation occurs at many places simultaneously, the crystal surface becomes rough, and the growth velocity increases more rapidly with increasing supersaturation than in the smooth regime. Kinetic roughening transitions are typically assumed to be due to the vanishing of the barrier for two-dimension nucleation on the surface of the crystal. We show here, by means of both analytic mean-field models and kinetic Monte Carlo simulations, that a transition between different growth modes reminiscent of kinetic roughening can also arise as a kinetic effect occurring at finite nucleation barriers.

Keywords: crystal growth; Monte Carlo methods; nucleation; proteins; reaction kinetics
[52] James F. Lutsko. Recent Developments in Classical Density Functional Theory. Adv. Chem. Phys., 144:1, 2010. [ bib ]
The Density Functional approach to equilibrium statistical mechanics isreviewed. Topics covered include the basic theory behind Density FunctionalTheory, exact density functionals in low dimension, and theories based oneffective liquid approximations. Particular attention is given to morerecent developments such as Fundamental Measure Theory for hard-spheres,Dynamical Density Functional Theory and the determination of statetransition pathways.

[51] James F. Lutsko, Vasileios Basios, Grégoire Nicolis, Tom P. Caremans, Alexander Aerts, Johan A. Martens, Christine E. A. Kirschhock, and Titus S. van Erp. Kinetics of intermediate-mediated self-assembly in nanosized materials: A generic model. J. Chem. Phys., 132(16):164701, 2010. [ bib | DOI | .pdf | http ]
We propose in this paper a generic model of a nonstandard aggregation mechanism forself-assembly processes of a class of materials involving the mediation of intermediates consistingof a polydisperse population of nanosized particles. The model accounts for a long induction periodin the process. The proposed mechanism also gives insight on future experiments aiming at a morecomprehensive picture of the role of self-organization in self-assembly processes.

Keywords: nanostructured materials; numerical analysis; self-assembly
[50] Patrick Grosfils and James F. Lutsko. Dependence of the liquid-vapor surface tension on the range of interaction: A test of the law of corresponding states. J. Chem. Phys., 130(5):054703+, 2009. [ bib | .pdf | http ]
The planar surface tension of coexisting liquid and vapor phases of a fluid of Lennard-Jones atoms is studied as a function of the range of the potential using both Monte Carlo simulations and Density Functional Theory. The interaction range is varied from rc* = 2.5 to rc* = 6 and the surface tension is determined for temperatures ranging from T* = 0.7 up to the critical temperature in each case. The results are shown to be consistent with previous studies. The simulation data are well-described by Guggenheim's law of corresponding states but the agreement of the theoretical results depends on the quality of the bulk equation of state.

Keywords: lutsko
[49] J. F. Lutsko, J. P. Boon, and P. Grosfils. Is the Tsallis entropy stable? EPL (Europhysics Letters), 86(4):40005+, 2009. [ bib | DOI | .pdf | http ]
The question of whether the Tsallis entropy is Lesche-stable is revisited. It is argued that when physical averages are computed with the escort probabilities, the correct application of the concept of Lesche-stability requires use of the escort probabilities. As a consequence, as shown here, the Tsallis entropy is unstable but the thermodynamic averages are stable. We further show that Lesche stability as well as thermodynamic stability can be obtained if the homogeneous entropy is used as the basis of the formulation of non-extensive thermodynamics. In this approach, the escort distribution arises naturally as a secondary structure.

Keywords: lutsko
[48] J. F. Lutsko. Reply to the Comment by M. Iwamatsu. EPL (Europhysics Letters), 86(2):26002+, 2009. [ bib | DOI | .pdf | http ]
Keywords: lutsko
[47] Wm. G. Hoover, Carol G. Hoover, and James F. Lutsko. Microscopic and macroscopic stress with gravitational and rotational forces. Phys. Rev. E, 79:036709, Mar 2009. [ bib | DOI | http ]
Many recent papers have questioned Irving and Kirkwood’s atomistic expression for stress. In Irving and Kirkwood’s approach both interatomic forces and atomic velocities contribute to stress. It is the velocity-dependent part that has been disputed. To help clarify this situation we investigate (i) a fluid in a gravitational field and (ii) a steadily rotating solid. For both problems we choose conditions where the two stress contributions, potential and kinetic, are significant. The analytic force-balance solutions of both these problems agree very well with a smooth-particle interpretation of the atomistic Irving-Kirkwood stress tensor.

[46] James F. Lutsko and Jean P. Boon. Generalized diffusion: A microscopic approach. Phys. Rev. E, 77(5), 2008. [ bib | DOI | .pdf | http ]
The Fokker-Planck equation for the probability f(r,t) to find a random walker at position r at time t is derived for the case that the probability to make jumps depends nonlinearly on f(r,t). The result is a generalized form of the classical Fokker-Planck equation where the effects of drift, due to a violation of detailed balance, and of external fields are also considered. It is shown that in the absence of drift and external fields a scaling solution, describing anomalous diffusion, is possible only if the nonlinearity in the jump probability is of the power law type [ f(r,t)], in which case the generalized Fokker-Planck equation reduces to the porous media equation. Monte Carlo simulations are shown to confirm the theoretical results.

Keywords: lutsko
[45] James F. Lutsko. Density functional theory of inhomogeneous liquids. III. Liquid-vapor nucleation. J. Chem. Phys., 129(124):244501+, 2008. [ bib | .pdf | http ]
The process of nucleation of vapor bubbles from a superheated liquid and of liquid droplets from a supersaturated vapor is investigated using the Modified-Core van der Waals model Density Functional Theory (Lutsko, JCP 128, 184711 (2008)). A novel approach is developed whereby nucleation is viewed as a transition from a metastable state to a stable state via the minimum free energy path which is identified using the nudged elastic-band method for exploring free energy surfaces. This allows for the unbiased calculation of the properties of sub- and super-critical clusters, as well as of the critical cluster. For Lennard-Jones fluids, the results compare well to simulation and support the view that even at high supersaturation nucleation proceeds smoothly rather than via spinodal-like instabilities as has been suggested recently.

Keywords: lutsko
[44] James F. Lutsko. Density functional theory of inhomogeneous liquids. II. A fundamental measure approach. J. Chem. Phys., 128(18), 2008. [ bib | .pdf | http ]
Previously, it has been shown that the direct correlation function for a Lennard–Jones fluid could be modeled by a sum of that for hard-spheres, a mean-field tail, and a simple linear correction in the core region constructed so as to reproduce the (known) bulk equation of state of the fluid [Lutsko, J. Chem. Phys. 127, 054701 (2007)]. Here, this model is combined with ideas from the fundamental measure theory to construct a density functional theory for the free energy. The theory is shown to accurately describe a range of inhomogeneous conditions including the liquid vapor interface, the fluid in contact with a hard wall, and a fluid confined in a slit pore. The theory gives quantitatively accurate predictions for the surface tension, including its dependence on the potential cutoff. It also obeys two important exact conditions: That relating the direct correlation function to the functional derivative of the free energy with respect to density and the wall theorem.

Keywords: lutsko
[43] J. F. Lutsko. Theoretical description of the nucleation of vapor bubbles in a superheated fluid. EPL (Europhysics Letters), 83(4):46007+, 2008. [ bib | DOI | .pdf | http ]
The nucleation of vapor bubbles within a superheated fluid is studied using density functional theory. The nudged elastic band technique is used to find the minimum energy pathway from the metastable uniform liquid to the stable uniform gas thus emphasizing the analogy between the the nucleation problem and that of chemical reactions. The result is both an accurate determination of the critical nucleus and an unbiased description of the density profile at various points along the path between the free energy extrema. This calculation is compared to two other methods: the use of parametrized profiles and constrained minimization of the free energy. The results indicate that the recent claim, based on the constraint method, that bubble nucleation and growth involves an activated instability is incorrect.

Keywords: lutsko_epl_2008
[42] James F. Lutsko. Density functional theory of inhomogeneous liquids. I. The liquid-vapor interface in Lennard-Jones fluids. J. Chem. Phys., 127:054701, 2007. [ bib | .pdf ]
A simple model is proposed for the direct correlation function (DCF) for simple fluids consisting of a hard-core contribution, a simple parametrized core correction, and a mean-field tail. The model requires as input only the free energy of the homogeneous fluid, obtained, e.g., from thermodynamic perturbation theory. Comparison to the DCF obtained from simulation of a Lennard-Jones fluid shows this to be a surprisingly good approximation for a wide range of densities. The model is used to construct a density functional theory for inhomogeneous fluids which is applied to the problem of calculating the surface tension of the liquid-vapor interface. The numerical values found are in good agreement with simulation.

[41] Jean Pierre Boon and James F. Lutsko. From Einstein to generalized diffusion. AIP Conference Proceedings, 965(1):157--164, 2007. [ bib | DOI | .pdf | http ]
We show that from a generalization of Einstein's master equation for the random walk one obtains a generalized equation for diffusion processes. The master equation is generalized by making the particle jump probability Pj(r) a functional of the particle distribution function f(r,t). If one demands that the resulting generalized diffusion equation admits of scaling solutions: f(r;t) = t−gamma/2phi(r/tgamma/2), a power law Pj(r)[proportional]f(r)alpha−1 (with alpha>1) follows, and the solutions exhibit q-exponential forms which are found to be in agreement with the results of Monte-Carlo simulations, providing a microscopic basis validating the nonlinear diffusion equation. We also show that the phenomenological porous media equation is an approximation to the generalized advection-diffusion equation.

Keywords: statistical mechanics; Fokker-Planck equation; diffusion; probability; master equation; transport processes
[40] J. P. Boon and J. F. Lutsko. Nonlinear diffusion from Einstein's master equation. EPL (Europhysics Letters), 80(6):60006 (4pp), 2007. [ bib | .pdf | http ]
We generalize Einstein's master equation for random-walk processes by considering that the probability for a particle at position r to make a jump of length j lattice sites, Pj(r), is a functional of the particle distribution function f(r, t). By multiscale expansion, we obtain a generalized advection-diffusion equation. We show that the power law Pj(r)[?]f(r)a-1 (with a>1) follows from the requirement that the generalized equation admits scaling solutions (f(r;t)=t[?]gph(r/tg)). The solutions have a q-exponential form and are found to be in agreement with the results of Monte Carlo simulations, so providing a microscopic basis validating the nonlinear diffusion equation. Although its hydrodynamic limit is equivalent to the phenomenological porous media equation, there are extra terms which, in general, cannot be neglected as evidenced by the Monte Carlo computations.

[39] James F. Lutsko. Chapman-Enskog expansion about nonequilibrium states with application to the sheared granular fluid. Phys. Rev. E, 73:021302, 2006. [ bib | arXiv | eprint | .pdf | http ]
The Chapman-Enskog method of solution of kinetic equations, such as the Boltzmann equation, is based on an expansion in gradients of the deviations of the hydrodynamic fields from a uniform reference state (e.g., local equilibrium). This paper presents an extension of the method so as to allow for expansions about arbitrary, far-from-equilibrium reference states. The primary result is a set of hydrodynamic equations for studying variations from the arbitrary reference state which, unlike the usual Navier-Stokes hydrodynamics, does not restrict the reference state in any way. The method is illustrated by application to a sheared granular gas which cannot be studied using the usual Navier-Stokes hydrodynamics.

[38] James F. Lutsko and Grégoire Nicolis. Theoretical Evidence for a Dense Fluid Precursor to Crystallization. Phys. Rev. Lett., 96:046102, 2006. Also appeared in February 15, 2006 issue of Virtual Journal of Biological Physics Research. [ bib | arXiv | eprint | .pdf | http ]
We present classical density functional theory calculations of the free-energy landscape for fluids below their triple point as a function of density and crystallinity. We find that, both for a model globular protein and for a simple atomic fluid modeled with a Lennard-Jones interaction, it is free-energetically easier to crystallize by passing through a metastable dense fluid in accord with the Ostwald rule of stages but in contrast to the alternative of ordering and densifying at once as assumed in the classical picture of crystallization.

[37] James F. Lutsko. First principles derivation of Ginzburg–Landau free energy models for crystalline systems. Physica A, 366:229--242, 2006. [ bib | .pdf ]
The expression of the free energy density of a classical crystalline system as a gradient expansion in terms of a set of order parameters is developed using classical density functional theory. The goal here is to extend and complete an earlier derivation by Löwen et al. [Europhys. Lett. 9 (1989) 791]. The limitations of the resulting expressions are also discussed including the boundary conditions needed for finite systems and the fact that the results cannot, at present, be used to take into account elastic relaxation.

[36] James F. Lutsko. Hydrodynamics of an endothermic gas with application to bubble cavitation. J. Chem. Phys., 125:164319, 2006. [ bib | .pdf ]
The hydrodynamics for a gas of hard spheres which sometimes experience inelastic collisions resulting in the loss of a fixed, velocity-independent, amount of energy Delta is investigated with the goal of understanding the coupling between hydrodynamics and endothermic chemistry. The homogeneous cooling state of a uniform system and the modified Navier-Stokes equations are discussed and explicit expressions given for the pressure, cooling rates, and all transport coefficients for D dimensions. The Navier-Stokes equations are solved numerically for the case of a two-dimensional gas subject to a circular piston so as to illustrate the effects of the enegy loss on the structure of shocks found in cavitating bubbles. It is found that the maximal temperature achieved is a sensitive function of Delta with a minimum occurring near the physically important value of Delta 12 000 K 1 eV.

[35] James F. Lutsko. Properties of non-fcc hard-sphere solids predicted by density functional theory. Phys. Rev. E, 74:021121, 2006. [ bib | .pdf ]
The free energies of the fcc, bcc, hcp, and simple cubic phases for hard spheres are calculated as a function of density using the fundamental measure theory models of Rosenfeld et al. [Phys. Rev. E 55, 4245 (1997)], Tarazona [Phys. Rev. Lett. 84, 694 (2001)], and Roth et al. [J. Phys.: Condens. Matter 14, 12063 (2002)] in the Gaussian approximation. For the fcc phase, the present work confirms the vanishing of the Lindemann parameter (i.e., vanishing of the width of the Gaussians) near close packing for all three models and the results for the hcp phase are nearly identical. For the bcc phase and for packing fractions above eta 0.56, all three theories show multiple solid structures differing in the widths of the Gaussians. In all three cases, one of these structures shows the expected vanishing of the Lindemann parameter at close packing, but this physical structure is only thermodynamically favored over the unphysical structures in the Tarazona theory and even then, some unphysical behavior persists at lower densities. The simple cubic phase is stabilized in the model of Rosenfeld et al. for a range of densities and in the Tarazona model only very near close packing.

[34] James F. Lutsko. Ginzburg-Landau theory of the liquid-solid interface and nucleation for hard spheres. Phys. Rev. E, 74:021603, 2006. [ bib | .pdf ]
The Ginzburg-Landau free energy functional for hard spheres is constructed using the fundamental measure theory approach to density functional theory as a starting point. The functional is used to study the liquid-fcc solid planer interface and the properties of small solid clusters nucleating within a liquid. The surface tension for planer interfaces agrees well with simulation and it is found that the properties of the solid clusters are consistent with classical nucleation theory.

[33] James F. Lutsko. Transport properties of dense dissipative hard-sphere fluids for arbitrary energy loss models. Phys. Rev. E, 72:021306, 2005. [ bib | eprint | .pdf | http ]
The solution of the Enskog equation for the one-body velocity distribution of a moderately dense arbitrary mixture of inelastic hard spheres undergoing planar shear flow is described. A generalization of the Grad moment method, implemented by means of a novel generating function technique, is used so as to avoid any assumptions concerning the size of the shear rate. The result is illustrated by using it to calculate the pressure, normal stresses, and shear viscosity of a model polydisperse granular fluid in which grain size, mass, and coefficient of restitution vary among the grains. The results are compared to a numerical solution of the Enskog equation as well as molecular-dynamics simulations. Most bulk properties are well described by the Enskog theory and it is shown that the generalized moment method is more accurate than the simple (Grad) moment method. However, the description of the distribution of temperatures in the mixture predicted by Enskog theory does not compare well to simulation, even at relatively modest densities.

[32] James F. Lutsko and Gregoire Nicolis. The effect of the range of interaction on the phase diagram of a globular protein. J. Chem. Phys., 122:244907, 2005. [ bib | eprint | .pdf | http ]
Thermodynamic perturbation theory is applied to the model of globular proteins studied by ten Wolde and Frenkel [P. R. ten Wolde and D. Frenkel Science 77, 1975 (1997)] using computer simulation. It is found that the reported phase diagrams are accurately reproduced. The calculations show how the phase diagram can be tuned as a function of the length scale of the potential.

[31] J. F. Lutsko and J. P. Boon. Non-extensive diffusion as nonlinear response. Euro. Phys. Lett., 71(6):906--911, 2005. [ bib | eprint | .pdf | .html ]
The porous-media equation has been proposed as a phenomenological ”non-extensive” generalization of classical diffusion. Here, we show that a very similar equation can be derived, in a systematic manner, for a classical fluid by assuming nonlinear response, i.e. that the diffusive flux depends on gradients of a power of the concentration. The present equation distinguishes from the porous-media equation in that it describes generalized classical diffusion, i.e. with r/sqrt(Dt scaling, but with a generalized Einstein relation, and with power-law probability distributions typical of non-extensive statistical mechanics.)

[30] James F. Lutsko. Kinetic theory and hydrodynamics of dense, reacting fluids far from equilibrium. J. Chem. Phys., 120:6325, 2004. [ bib | eprint | .pdf | http ]
The kinetic theory for a fluid of hard spheres which undergo endothermic and/or exothermic reactions with mass transfer is developed. The exact balance equations for concentration, density, velocity, and temperature are derived. The Enskog approximation is discussed and used as the basis for the derivation, via the Chapman–Enskog procedure, of the Navier–Stokes reaction equations under various assumptions about the speed of the chemical reactions. It is shown that the phenomenological description consisting of a reaction–diffusion equation with a convective coupling to the Navier–Stokes equations is of limited applicability.

[29] James F. Lutsko. Rheology of dense polydisperse granular fluids under shear. Phys. Rev. E, 70:061101, 2004. [ bib | .pdf | http ]
The solution of the Enskog equation for the one-body velocity distribution of a moderately dense arbitrary mixture of inelastic hard spheres undergoing planar shear flow is described. A generalization of the Grad moment method, implemented by means of a novel generating function technique, is used so as to avoid any assumptions concerning the size of the shear rate. The result is illustrated by using it to calculate the pressure, normal stresses, and shear viscosity of a model polydisperse granular fluid in which grain size, mass, and coefficient of restitution vary among the grains. The results are compared to a numerical solution of the Enskog equation as well as molecular-dynamics simulations. Most bulk properties are well described by the Enskog theory and it is shown that the generalized moment method is more accurate than the simple (Grad) moment method. However, the description of the distribution of temperatures in the mixture predicted by Enskog theory does not compare well to simulation, even at relatively modest densities.

[28] P. Gaspard and J. Lutsko. Imploding shock wave in a fluid of hard-core particles. Phys. Rev. E, 70:026306, 2004. [ bib | .pdf ]
We report the study of a fluid of hard-disk particles in a contracting cavity. Under supersonic contraction speed, a shock wave converges to the center of the cavity where it implodes, creating a central peak in temperature. The dynamics of the fluid is studied by solving the Euler and Navier-Stokes equations, as well as by molecular dynamics simulations and the Enskog direct simulation Monte Carlo method. The value of the maximum temperature reached at the center of the cavity is systematically investigated with the different methods which give consistent results. Moreover, we develop a scaling theory for the maximum temperature based on the self-similar solutions of Euler's equations and mean-free-path considerations. This scaling theory provides a comprehensive scheme for the interpretation of the numerical results. In addition, the effects of the imploding shock wave on an passively driven isomerization reaction A[r harp over l]B are also studied.

[27] Jean Pierre Boon, Patrick Grosfils, and James F. Lutsko. Propagation-Dispersion Equation. J. Stat. Phys., 113(3-4):527 -- 548, 2003. [ bib | eprint | .pdf | http ]
A propagation-dispersion equation is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the hydrodynamic limit of the first visit equation, an exact microscopic finite difference equation describing the motion of a particle on a lattice whose sites operate as time-delayers. The propagation-dispersion equation should be contrasted with the advection-diffusion equation (or the classical Fokker–Planck equation) as it describes a dispersion process in time (instead of diffusion in space) with a drift expressed by a propagation speed with non-zero bounded values. The temporal dispersion coefficient is shown to exhibit a form analogous to Taylor's dispersivity. Physical systems where the propagation-dispersion equation applies are discussed.

[26] J. P. Boon, P. Grosfils, and J. F. Lutsko. Temporal diffusion. Euro. Phys. Lett., 63:186--192, 2003. [ bib | eprint | .html ]
We consider the general problem of the first-passage distribution of particles whose displacements are subject to time delays. We show that this problem gives rise to a propagation-dispersion equation which is obtained as the large-distance (hydrodynamic) limit of the exact microscopic first-visit equation. The propagation-dispersion equation should be contrasted with the advection-diffusion equation as the roles of space and time are reversed, hence the name temporal diffusion, which is a generic behavior encountered in an important class of systems.

[25] J. W. Dufty, J. J. Brey, and J. Lutsko. Diffusion in a granular fluid. I. Theory. Phys. Rev. E, 65:051303, 2002. [ bib | .pdf | http ]
Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic case as well. This is illustrated here for diffusion of an impurity particle in a fluid undergoing homogeneous cooling. An appropriate scaling of the Liouville equation is described such that the homogeneous cooling ensemble and associated time correlation functions map to those of a stationary state. In this form the familiar methods of linear response can be applied, leading to Green-Kubo and Einstein representations of diffusion in terms of the velocity and mean-square displacement correlation functions. These correlation functions are evaluated approximately using a cumulant expansion and from kinetic theory, providing the diffusion coefficient as a function of the density and the restitution coefficients. Comparisons with results from molecular-dynamics simulation are given in the following companion paper.

[24] J. Lutsko, J. J. Brey, and J. W. Dufty. Diffusion in a granular fluid. II. Simulation. Phys. Rev. E, 65:051304, 2002. [ bib | .pdf | http ]
The linear-response description for impurity diffusion in a granular fluid undergoing homogeneous cooling is developed in the preceding paper. The formally exact Einstein and Green-Kubo expressions for the self-diffusion coefficient are evaluated there from an approximation to the velocity autocorrelation function. These results are compared here to those from molecular-dynamics simulations over a wide range of density and inelasticity, for the particular case of self-diffusion. It is found that the approximate theory is in good agreement with simulation data up to moderate densities and degrees of inelasticity. At higher density, the effects of inelasticity are stronger, leading to a significant enhancement of the diffusion coefficient over its value for elastic collisions. Possible explanations associated with an unstable long wavelength shear mode are explored, including the effects of strong fluctuations and mode coupling.

[23] J. F. Lutsko and J. W. Dufty. Long-ranged correlations in sheared fluids. Phys. Rev. E, 66:041206, 2002. [ bib | .pdf | http ]
The presence of long-ranged correlations in a fluid undergoing uniform shear flow is investigated. An exact relation between the density autocorrelation function and the density-mometum correlation function implies that the former must decay more rapidly than 1/r, in contrast to predictions of simple mode-coupling theory. Analytic and numerical evaluation of a nonperturbative mode-coupling model confirms a crossover from 1/r behavior at ”small” r to a stronger asymptotic power-law decay. The characteristic length scale is [script l][approximate]sqrt( lambda[sub 0]/a), where lambda0 is the sound damping constant and a is the shear rate.

[22] J. F. Lutsko. Atomic-scale structure of hard-core fluids under shear flow. Phys. Rev. E, 66:051109, 2002. [ bib ]
[21] James F. Lutsko. Velocity Correlations and the Structure of Nonequilibrium Hard-Core Fluids. Phys. Rev. Lett., 86:3344, 2001. [ bib | .pdf | http ]
A model for the pair-distribution function of nonequilibrium hard-core fluids is proposed based on a model for the effect of velocity correlations on the structure. Good agreement is found with molecular dynamics simulations of granular fluids and of sheared elastic hard spheres. It is argued that the incorporation of velocity correlations are crucial to correctly modeling atomic scale structure in nonequilibrium fluids.

[20] James F. Lutsko. Model for the atomic-scale structure of the homogeneous cooling state of granular fluids. Phys. Rev. E, 63:061211, 2001. [ bib | .pdf | www: ]
The effect of velocity correlations on the equal-time density autocorrelation function, e.g., the pair distribution function (PDF), of a hard-sphere fluid undergoing shear flow is investigated. The PDF at contact is calculated within the Enskog approximation and is shown to be in good agreement with molecular dynamics simulations for shear rates below the shear-induced ordering transition. These calculations are used to construct a nonequilibrium generalized mean-spherical approximation for the PDF at finite separations, which is also found to agree well with the simulation data.

[19] James F. Lutsko. Viscoelastic effects from the Enskog equation for uniform shear flow. Phys. Rev. E, 58:434, 1998. [ bib | .pdf | http ]
The Enskog kinetic equation for hard spheres is the only tractable theory with which the transport properties of a moderately dense gas can be studied. However, relatively little is known about its solutions outside the linear regime. In this paper two approximate nonlinear solutions of the Enskog equation for uniform shear flow are presented: a perturbative solution to second order in the shear rate and to fourth order in velocity moments and a ”nonperturbative” moment solution to all orders in the shear rate and to second order in the velocity moments. A comparison to the results of nonequilibrium molecular-dynamics simulations shows that the perturbative results give good estimates of the quadratic corrections to the pressure tensor while the nonperturbative solution gives a semiquantitative description of viscoelastic effects including shear thinning and the normal stresses over a wide range of shear rates. The relevance of these results to the construction of kinetic models of the Enskog equation is also discussed.

[18] J. M. Montanero, A. Santos, M. Lee, J. W. Dufty, and J. F. Lutsko. Stability of uniform shear flow. Phys. Rev. E, 57:546--556, 1998. [ bib | .pdf | http ]
The stability of idealized computer shear flow at long wavelengths is studied in detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for small shear rates is given to identify the origin and universality of an instability at any finite shear rate for sufficiently long wavelength perturbations. The analysis is extended to larger shear rates using a low density model kinetic equation. Direct Monte Carlo simulation of this equation is compared with a hydrodynamic description including non-Newtonian rheological effects. The hydrodynamic description of the instability is in good agreement with the direct Monte Carlo simulation for t<50t0, where t0 is the mean free time. Longer time simulations up to 2000t0 are used to identify the asymptotic state as a spatially nonuniform quasistationary state. Finally, preliminary results from molecular dynamics simulation showing the instability are presented and discussed.

[17] James F. Lutsko. Approximate Solution of the Enskog Equation Far from Equilibrium. Phys. Rev. Lett., 78:243, 1997. [ bib | .pdf | http ]
A moment method is used to solve the Enskog equation for the steady-state distribution under conditions of uniform shear flow. Comparison to nonequilibrium molecular dynamics demonstrates that the lowest order solution gives a good quantitative description of nonlinear effects such as shear thinning and normal stresses in a moderately dense fluid. The results are used as a basis in the formulation of a simple and quantitatively accurate kinetic model of the Enskog equation.

[16] James F. Lutsko. Molecular Chaos, Pair Correlations, and Shear-Induced Ordering of Hard Spheres. Phys. Rev. Lett., 77:2225, 1996. [ bib | .pdf | http ]
We present results of molecular dynamics simulations that show that the shear-induced ordering of hard spheres is preceded by the apparent decrease to zero (in certain directions) of the anisotropic pair-distribution function (PDF) at contact. This precursor to the ordering is explained on the basis of a careful interpretation of the meaning of ”molecular chaos” in hard-sphere systems. An ansatz is proposed to model the nonequilibrium PDF at finite separations and is shown to compare well with simulations.

[15] M. Lee, J. W. Dufty, J. M. Montanero, A. Santos, and J. F. Lutsko. Long Wavelength Instability for Uniform Shear Flow. Phys. Rev. Lett., 76:2702--2705, 1996. [ bib | .pdf | http ]
Uniform shear flow is a prototype nonequilibrium state admitting detailed study at both the macroscopic and microscopic levels via theory and computer simulation. It is shown that the hydrodynamic equations for this state have a long wavelength instability. This result is obtained first from the Navier-Stokes equations and shown to apply at both low and high densities. Next, higher order rheological effects are included using a model kinetic theory. The results are compared favorably to those from Monte Carlo simulation.

[14] C. F. Tejero, J. F. Lutsko, J. L. Colot, and M. Baus. Thermodynamic properties of the fluid, fcc, and bcc phases of monodisperse charge-stabilized colloidal suspensions within the Yukawa model. Phys. Rev. A, 46:3373--3379, 1992. [ bib | .pdf | http ]
The thermodynamic properties of the Yukawa model for colloidal suspensions are determined theoretically from the Rogers-Young integral equation for the fluid phase and from a recently introduced van der Waals–like theory for the solid phases. Very good agreement with the Monte Carlo simulations of Meijer and Frenkel [J. Chem. Phys. 94, 2269 (1991)] is found for both the fluid and the (fcc-bcc) solid phases. The location of the two-phase coexistences, however, is shown to involve such small free-energy and density changes that no definite statements about the phase diagram are possible within the present accuracy.

[13] E. Aurell, U. Frisch, J. Lutsko, and M. Vergassola. On the multifractal properties of the energy dissipation derived from turbulence data. J. Fluid Mech., 238:467, 1992. [ bib ]
[12] J. F. Lutsko. Reformulation of nonperturbative density-functional theories of classical nonuniform systems. Phys. Rev. A, 43:4124--4130, 1991. [ bib | .pdf | http ]
It is shown that most nonperturbative density-functional theories of classical systems can be reformulated as second-order truncations of exact perturbative expansions, thus eliminating the ad hoc nature of such theories. This reformulation is used as a basis for discussion as to why some theories work better than others when applied to hard spheres, why most theories perform poorly for continuous potentials, and in what direction they might be modified so as to improve their performance

[11] Marc Baus and James F. Lutsko. Statistical mechanical theories of freezing: Where do we stand? Physica A, 176(1):28--36, 1991. [ bib ]
[10] J F Lutsko and M Baus. The freezing of soft spheres from a simple hard-sphere perturbation theory. J. Phys.: Condens. Matter, 3(33):6547--6552, 1991. [ bib ]
It is shown that a simple perturbation expansion around the free energy of a (BCC/FCC) hard-sphere crystal leads to accurate predictions for the (BCC/FCC) freezing of soft spheres interacting via the inverse-power potential, V(r)= epsilon ( sigma /r)n, for all values of n including the extreme case of the one-component plasma (n=1). In particular, the authors find that for 1<or=n<or=6 there is both a fluid-BCC and BCC-FCC transition whereas for n>6 the BCC phase is unstable and only the fluid-FCC transition survives, in agreement with the computer simulations.

[9] J.F. Lutsko, J-P. Boon, and J.A. Somers. Lattice Gas Simulations of Viscous Fingering in a Porous Medium. In Numerical methods for the Simulation of Multiphase and Complex Flows. Springer-Verlag, 1991. [ bib ]
[8] J. F. Lutsko and M. Baus. Nonperturbative density-functional theories of classical nonuniform systems. Phys. Rev. E, 41:6647--6661, 1990. [ bib | .pdf | http ]
We propose an approximation to the density-functional theory of classical nonuniform systems that reproduces all the formal properties of the free energy and requires only the direct correlation function of the uniform system as input. By introducing additional assumptions into this theory a direct relation can be established with most of the existing nonperturbative theories. When the theory is worked out for the case of the hard-sphere solid, very good agreement is found with the computer simulations. The free energies, pressures, and fluid-solid coexistence data are reproduced to within the error bars of the simulations. The theory also predicts stable bcc and sc phases that could play a role in the final nucleation of the equilibrium fcc phase.

[7] J. F. Lutsko and M. Baus. Can the thermodynamic properties of a solid be mapped onto those of a liquid? Phys. Rev. Lett., 64:761--763, 1990. [ bib | .pdf | http ]
A new approximation to the density-functional theory of classical nonuniform systems is proposed and worked out for the case of the hard-sphere solid. The theory satisfies all the formal properties of the free energy and requires only the direct correlation function of the uniform system as input. the agreement with the computer simulations of the fcc hard-sphere solid is excellent: The resulting free energies, pressures, and fluid-solid coexistence data are reproduced to within the error bars of the simulations. The theory also predicts stable bcc and sc phases which could facilitate the final nucleation into the equilibrium fcc phase.

[6] James F. Lutsko, J. W. Dufty, and S. P. Das. Fluctuations and dissipation in a fluid under shear: Linear dynamics. Phys. Rev. A, 39:1311, 1989. [ bib | .pdf | http ]
A set of nonlinear Langevin equations for fluctuations of the local conserved densities in a fluid under shear is proposed. These equations are a model for the extension of hydrodynamics to very short wavelengths at liquid densities. The hydrodynamic modes associated with the linearized equations are studied as a function of wave vector and shear rate. The degeneracy of the viscous shear modes is lifted by the shear, and one of these modes combines with the heat mode to form a propagating pair. As an example of nonequilibrium fluctuations, the dynamic structure factor is calculated for several values of frequency and wave vector. At large shear rates one pair of propagating modes becomes unstable at a wavelength of the order of the particle size. This instability is suggested as a possible explanation for a shear-induced disorder-order transition seen in computer simulations. Nonlinear mode-coupling effects are studied elsewhere.

[5] J. F. Lutsko and J. W. Dufty. Possible Instability for Shear-Induced Order-Disorder Transition. Phys. Rev. Lett., 57:2775--2778, 1986. [ bib | .pdf | http ]
A simple fluid in uniform isothermal shear flow is studied for conditions used in recent nonequilibrium computer simulations. The short-time dynamics for the local conserved densities is found to be unstable at large shear rates for wave vectors near the peak of the structure factor. The critical shear rates obtained are similar to those for an order-disorder transition observed in the computer simulations.

[4] James W. Dufty and James F. Lutsko. Non-linear Transport and Mode Coupling in Fluids Under Shear. In J. Casas-Vazquez, editor, Recent Developments in Nonequilibrium Statistical, pages 47--84, Berlin, 1986. Springer-Verlag. [ bib ]
[3] J. Lutsko and J. W. Dufty. Hydrodynamic fluctuations at large shear rate. Phys. Rev. A, 32:3040, 1985. [ bib | .pdf | http ]
The nonlinear Navier-Stokes-Langevin equations are used to describe fluctuations in a compressible fluid with uniform shear flow. The hydrodynamic modes for small deviations from the macroscopic nonequilibrium state are calculated, including linear mode coupling of the fluctuating variables with the macroscopic velocity field. The associated correlation functions are determined with the full nonlinear dependence on shear rate required for long times and/or large shear rate. The stationary and joint probability densities are also constructed from the associated Fokker-Planck equation. As an application of these results, the lowest-order mode-coupling contributions to the renormalized shear viscosity are evaluated.

[2] J. Lutsko and J. W. Dufty. Mode-coupling contributions to the nonlinear shear viscosity. Phys. Rev. A, 32:1229--1231, 1985. [ bib | .pdf | http ]
Three different results for the nonanalytic dependence of the shear viscosity on shear rate have been given. This discrepancy is resolved by an independent calculation based on the nonlinear Navier-Stokes-Langevin equations. The relationship to previous calculations and reasons for the differences are described.

[1] James W. Dufty and James F. Lutsko. Structure and Stability of Hydrodynamic Modes for Shear Flow. Kinam, 6:169--181, 1985. [ bib ]

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