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Twenty-five years of non-equilibrium statistical mechanics: Towards a better understanding of dense fluids

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25 Years of Non-Equilibrium Statistical Mechanics

Part of the book series: Lecture Notes in Physics ((LNP,volume 445))

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Abstract

A survey is given of some of the new insights that have emerged over the last 25 years in the physics of dense non-equilibrium fluids: atomic liquids as well as concentrated colloidal suspensions. First a brief discussion of some previous developments is given: the non-existence of a density expansion of the transport coefficients; the existence of general expressions for the transport coefficients for a fluid in terms of average current time-autocorrelation functions in equilibrium and the slow decay of the latter due to mode-coupling by vortex-diffusion, a new mechanism of diffusion leading to the long time tails. Next, very long range correlations, also due to mode-coupling, in non-equilibrium fluids subject to a temperature gradient and their experimental detection by light or by microwave scattering are discussed. Also, a reinterpretation of the neutron spectra of dense fluids in equilibrium is given in terms of effective fluid eigenmodes and cage-diffusion, the most important diffusion process in dense fluids. Then some recent work on Lattice Gas Cellular Automata and a new connection between transport coefficients and Lyapunov exponents are briefly mentioned. Finally, a far going analogy between the self-diffusion coefficient and the viscosity of atomic liquids and those of concentrated colloidal suspensions is discussed, based on the similarity of Newtonian and Brownian dynamics on long time scales and that of the cage-diffusion processes in both systems. Very similar expressions for the viscosity of these two fluid systems, based on cage-diffusion, are compared with recent experiments.

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References

  1. E. G. D. Cohen, “Fifty Years of Kinetic Theory”, Physica A 194, 229–257 (1994)

    Google Scholar 

  2. J. R. Dorfman and H. van Beijeren, “The Kinetic Theory of Gases”, in: Statistical Mechanics, Part B, B. J. Berne, ed., Plenum Press, New York (1977) Ch.3, 65–179.

    Google Scholar 

  3. S. Chapman and T. G. Cowling, “The Mathematical Theory of Non-uniform Gases”, 3rd ed. Cambridge Mathematical Library Series (Cambridge University Press, Cambridge, 1990).

    Google Scholar 

  4. See, e.g., J. R. Dorfman, “Kinetic and Hydrodynamic Theory of Time Correlation Functions” in: Fundamental Problems in Statistical Mechanics III“, E. G. D. Cohen, ed. (North-Holland, Amsterdam, 1975) p.277–330; E. G. D. Cohen, “The Kinetic Theory of Dense Gases”, in: ibid.II, p.228–275.

    Google Scholar 

  5. R. Zwanzig, “Time-Correlation Functions and Transport Coefficients in Statistical Mechanics”, Ann. Rev. Phys. Chem. 16, 67–102 (1965).

    Google Scholar 

  6. L. Onsager, “Reciprocal Relations in Irreversible Processes. I”, Phys. Rev.37, 405–426 (1931); id., II, Phys. Rev.38, 2265–2279 (1931); S. R. de Groot and P. Mazur, “Nonequilibrium Thermodynamics”, (North-Holland, Amsterdam (1962) p.100.

    Google Scholar 

  7. A current fluctuation is the difference between the actual current and the average current. Since the average currents we consider here all vanish, the current fluctuation equals the actual current.

    Google Scholar 

  8. The decay of < jL(t) >[jL(o)] can be more complicated than the exponential decay given here (cf. the next section).

    Google Scholar 

  9. R. Kubo, M. Yohota and S. Nakajima, “Statistical-Mechanical Theory of Irreversible Processes. II. Response to Thermal Disturbance”, Phys. Soc. Jap. 12, 1203–1211 (1957).

    Google Scholar 

  10. M. S. Green, “Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena. II. Irreversible Processes in Fluids”, J. Chem. Phys. 22, 398–413 (1954).

    Google Scholar 

  11. R. Kubo, “Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems”, J. Phys. Soc. Jap.12, 570–586 (1957).

    Google Scholar 

  12. M. H. Ernst, J. R. Dorfman and E. G. D. Cohen, “Transport Coefficients in Dense Gases I. The Dilute and Moderately Dense Gas”, Physical31, 493–521 (1965).

    Google Scholar 

  13. N. G. van Kampen, “The Case Against Linear Response Theory”, Physica Norvegica 5, 279–284 (1971).

    Google Scholar 

  14. B.J. Alder and T.E. Wainwright, “Velocity Autocorrelations for Hard Spheres”, Phys. Rev. Lett.18, 988–990 (1967); (b) id., “Enhancement of Diffusion by Vortex-like Motion of Classical Hard Particles”, J. Phys. Soc. Jap. Suppl. 26, 267–269 (1969); (c) id., “Decay of Velocity Autocorrelation Function”, Phys. Rev. A1, 18–21 (1970).

    Google Scholar 

  15. Y. Pomeau and P. Résibois, “Time Dependent Correlation Functions and Mode-Mode Coupling Theories”, Phys. Rept. 19, 64–139 (1975).

    Google Scholar 

  16. J. R. Dorfman and E. G. D. Cohen, “Velocity Correlation Functions in Two and Three Dimensions”, Phys. Rev. Lett.25, 1257–1260 (1970); id., “Velocity Correlation Functions in Two and Three Dimensions: Low Density”, Phys. Rev. A6, 776–790 (1972); id., “Velocity Correlation Functions in Two and Three Dimensions: Higher Density”, Phys. Rev. A12, 292–316 (1975); E. G. D. Cohen, “Kinetic Theory of Non-equilibrium Fluids”, Physica A118, 17–42 (1983).

    Google Scholar 

  17. M. H. Ernst, E. H. Hauge and J. M. J. van Leeuwen, “Asymptotic Time Behavior of Correlation Functions”, Phys. Rev. Lett. 25, 1254–1256 (1970); id., “Asymptotic Time Behavior of Correlation Functions. I. Kinetic Terms”, Phys. Rev. A4, 2055–2065 (1971); id., “Asymptotic Time Behavior of Correlation Functions. II. Kinetic and Potential Terms”, J. Stat. Phys.15, 7–22 (1976); id., "Asymptotic Time Behavior of Correlation Functions. III. “Local Equilibrium and Mode-Coupling Theory”, J. Stat. Phys.15, 23–58 (1976).

    Google Scholar 

  18. Y. Pomeau, “A Divergence Free Kinetic Equation for a Dense Boltzmann Gas”, Phys. Lett. A26, 336 (1968); id., “A New Kinetic Theory for a Dense Classical Gas”, id., 27, 601–602 (1968).

    Google Scholar 

  19. L. P. Kadanoff and J. Swift, “Transport Coefficients Near the Liquid Gas Critical Point”, Phys. Rev. 166, 89–101 (1968).

    Google Scholar 

  20. See ref. 1a, fig.1 and p.235.

    Google Scholar 

  21. I. Procaccia, D. Ronis and I. Oppenheim, “Light Scattering from Non-Equilibrium Stationary State: The Implication of Broken Time-Reversal Symmetry”, Phys. Rev. Lett. 42, 287–291 (1979); I. Procaccia, D. Ronis, M. A. Collins, J Ross and I. Oppenheim, “Statistical Mechanics of Stationary States III. Formal Theory”, Phys. Rev. A12, 1290–1306 (1979); D. Ronis, I. Procaccia and I. Oppenheim, “Statistical Mechanics of Stationary States II. Applications to Low Density Systems”, Phys. Rev. A19, 1307–1323 (1979); id., “Statistical Mechanics of Stationary States III. Fluctuations in Dense Fluids with Applications to Light Scattering”, Phys. Rev. A19, 1324–1339 (1979); I. Procaccia, D. Ronis and 1. Oppenheim, “Statistical Mechanics of Stationary States IV. Far From Equilibrium Stationary States and the Regression of Fluctuations”, Phys. Rev. A20, 2533–2546 (1979); D. Ronis, I Procaccia and J. Machta, “Statistical Mechanics of Stationary States VI. Hydrodynamical Fluctuating Theory Far From Equilibrium”, Phys. Rev. A22, 714–724 (1980).

    Google Scholar 

  22. G. Satten and D. Ronis, “Modification of Non-Equilibrium Fluctuations by Interaction with Surfaces”, Phys. Rev. A26, 940–949 (1982).

    Google Scholar 

  23. D. Ronis and I. Procaccia, “Nonlinear Resonant Coupling Between Shear and Heat Fluctuations in Fluids Far From Equilibrium”, Phys. Rev. A26, 1812–1815 (1982).

    Google Scholar 

  24. T. R. Kirkpatrick, E. G. D. Cohen and J. R. Dorfman, “Kinetic Theory of Light Scattering from a Fluid not in Equilibrium”, Phys. Rev. Lett. 42, 862–865 (1979); id., “Hydrodynamic Theory of Light Scattering from a Fluid in a Nonequilibrium Steady State”, Phys. Rev. Lett. 44, 472–475 (1980); id., “Fluctuations in a Nonequilibrium Steady State: Basic Equations”, Phys. Rev. A26, 950–970 (1982); id., “Light Scattering by a Fluid in a Nonequilbrium Steady State I: Small Gradients”, Phys. Rev. A26, 972–994 (1982); id., “Light Scattering by a Fluid in a Nonequilbrium Steady State II: Large Gradients”, Phys. Rev. A26, 995–1014 (1982); R. Schmitz and E. G. D. Cohen, “Fluctuations in a Fluid Under a Stationary Heat Flux I. General Theory“, J. Stat. Phys. 39, 285–316 (1985).

    Google Scholar 

  25. A.-M. S. Tremblay, M. Arai and E. Siggia, “Fluctuations About Hydrodynamic Nonequilibrium Steady States”, Phys. Lett. A76, 57–60 (1980); Phys. Rev. A23, 1451–1480 (1981).

    Google Scholar 

  26. G. van der Zwan, D. Bedeaux and P. Mazur “Light Scattering From a Fluid with a Stationary Temperature Gradient”, Physica A107, 491–508 (1981).

    Google Scholar 

  27. D. Beyssens, Y. Garrabos and G. Zalczer, “Experimental Evidence for Brillouin Aysmmetry Induced by a Temperature Gradient”, Phys. Rev. Lett. 45, 403–406 (1980); (b) H. Kiefte, M. J. Clouter and R. Penney, “Experimental Confirmation of Nonequilibrium Steady-State Theory: Brillouin Scattering in a Temperature Gradient”, Phys. Rev. B30, 4017–4020 (1984); (c) A.-M. S. Tremblay, “Theories of Fluctuations in Nonequilibrium Systems”, in: Recent Developments in Nonequilbrium Thermodynamics, J. Casas-Vazquez, F. Jon and G. Lebon, eds., Lecture Notes in Physics 199, Springer, New York (1984) p. 267–315.

    Google Scholar 

  28. B. M. Law, R. W. Gammon and J.-V. Sengers, “Light Scattering Observations of LongRange Correlations in a Non-Equilibrium Liquid”, Phys. Rev. Lett. 60, 1554–1557 (1988); B. M. Law, P. N. Segrè, R. W. Gammon and J. V. Sengers, “Light-scattering Measurements of Entropy and Viscous Fluctuations in a Liquid Far From Thermal Equilibrium”, Phys. Rev. A 45, 816–824 (1990); P. N. Segrè, R. W. Gammon, J. V. Sengers and B. M. Law, “Rayleigh Scattering in a Liquid Far From Thermal Equilibrium”, Phys. Rev. A45, 714–724 (1992); W. B. Li, P. N. Segrè, R. W. Gammon and J. V. Sengers, “Small-angle Rayleigh Scattering from Nonequilibrium Fluctuations in Liquids and Liquid Mixtures”, Physica A204, 399–436 (1994).

    Google Scholar 

  29. J. R. Dorfman, T. R. Kirkpatrick and J. V. Sengers, “Generic Long-range Correlations in Molecular Fluids”, Ann. Rev. Phys. Chem. 45, (1994).

    Google Scholar 

  30. R. Schmitz and E. G. D. Cohen, “Fluctuations in a Fluid Under a Stationary Heat Flux III. Brillouin Lines”, J. Stat. Phys. 46, 319–348 (1987); id., “Brillouin Scattering From Fluids Subject to Large Thermal Gradients”, Phys. Rev. A35, 2602–2610 (1987).

    Google Scholar 

  31. This is analogous to in quantum mechanics, where for a(n) (allowed) radiative transition of an electron between two energy eigenstates of an atom, i.e., for acoupling to the radiation field, to occur the product of the pair of eigenfunctions corresponding to this pair of states must have a multipole (dipole) character.

    Google Scholar 

  32. R. Schmitz and E. G. D. Cohen, “Fluctuations in a Fluid Under a Stationary Heat Flux II. Slow Part of the Correlation Matrix”, J. Stat. Phys. 40, 431–482 (1985).

    Google Scholar 

  33. R. N. Segrè, R. Schmitz and J. V. Sengers, “Fluctuations in Inhomogeneous and NonEquilibrium Fluids Under the Influence of Gravity”, Physica A195, 31–52 (1993), curve (d) of fig.4.

    Google Scholar 

  34. I. M. de Schepper and E. G. D. Cohen, “Collective Modes in Fluids and Neutron Scattering”, Phys. Rev. A22, 287–289 (1980); id., “Very-Short-Wavelength Collective Modes in Fluids”, J. Stat. Phys. 27, 223–281 (1982).

    Google Scholar 

  35. E. G. D. Cohen and I. M. de Schepper, “Effective Eigenmode Description of Dynamical Processes in Dense Classical Fluids and Fluid Mixtures”, B Nuovo Cimento 12, 521–542 (1990).

    Google Scholar 

  36. See, e.g., S. W. Lovesey, Theory of Neutron Scattering From Condensed Matter, (Clarendon Press, Oxford, 1984) Volume I; J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, (Academic Press, London, 1990).

    Google Scholar 

  37. See, e.g., B. J. Berne and R. Pecora, Dynamic Light Scattering, (Wiley, New York, 1976) ch.X; R. D. Mountain, “Spectral Distribution of Scattered Light in a Simple Fluid”, Rev. Mod. Phys.38, 205–214 (1966).

    Google Scholar 

  38. I. M. de Schepper, E. G. D. Cohen, C. Bruin, J. C. van Rijs, W. Montfrooij and L. A. de Graaf, “Hydrodynamic Time Correlation Functions for a Lennard-Jones Fluid”, Phys. Rev. A38, 271–287 (1988).

    Google Scholar 

  39. U. Bafile, P. Verkerk, F. Barocchi, L. A. de Graaf, Y. B. Suck and H. Mutka, “Onset of Departure From Linearized Hydrodynamic Behavior in Argon Gas Studied With Neutron Brillouin Scattering“, Phys. Rev. Lett. 65, 2394–2397 (1990).

    Google Scholar 

  40. I. M. de Schepper, P. Verkerk, A. A. van Well and L. A. de Graaf, “Short-Wavelength Sound Mode in Liquid Argon”, Phys. Rev. Lett. 50, 974–977 (1983).

    Google Scholar 

  41. B. Kamgar-Parsi, E. G. D. Cohen and I. M. de Schepper, “Dynamcal Processes in Hard-sphere Fluids”, Phys. Rev. A35, 4781–4795 (1987).

    Google Scholar 

  42. A. Campa and E. G. D. Cohen, “Observable Fast Kinetic Eigenmode in Binary Noble-Gas Mixtures”, Phys. Rev. Lett. 61, 853–856 (1988); id., “Kinetic-Sound Propagation in Dilute Gas Mixtures”, Phys. Rev. A39, 4909–4911 (1989); id., “Fast Sound in Binary Fluid Mixtures”, Phys. Rev. A 41, 5451–5463 (1990); id., “Fast and Slow Sound in Binary Fluid Mixtures”, Physica A 174, 214–222 (1991).

    Google Scholar 

  43. W. T. Montfrooij, P. Westerhuijs, V. O. de Haar and I. M. de Schepper, “Fast Sound in a Helium-Neon Mixture Determined by Neutron Scattering”, Phys. Rev. Lett.63, 544–550 (1989); W. T. Montfrooij, “From Visco-Elasticity Towards Thermal Relaxation”, Thesis, Technical University Delft (1990) ch.VI; P. Westerhuijs, “Microscopic Dynamics in Dense Helium Mixtures”, Thesis, Technical University Delft (1991).

    Google Scholar 

  44. G. H. Wegdam, A. Bot, R. P. C. Schram and H. M. de Schaink, “Observation of Fast Sound in Disparate-Mass Gas Mixtures by Light Scattering”, Phys. Rev. Lett. 63, 2697–2700 (1989); M. J. Clouter, H. Luo, H. Kiefte and J. A. Zollweg, “Light Scattering in Gas Mixtures: Evidence of Fast and Slow Sound Modes”, Phys. Rev. A41, 2239–2242 (1990); G. H. Wegdam and 11. M Schaink, “Light Scattering Study of Helium-Xenon Gas Mixtures: Slow Sound”, Phys. Rev. A41, 3419–3420 (1990); R. P. C. Schram, G. H. Wegdam and A. Bot, “Rayleigh Brillouin Light Scattering Study of Both Fast and Slow Sound in Binary Gas Mixtures”, Phys. Rev. A44, 8063–8071 (1991); R. P. C. Schram and G. H. Wegdam, “Fast and Slow Sound in the Two-temperature Model”, Physica A 203, 33–52 (1994).

    Google Scholar 

  45. U. Frisch, B. Hasslacher and Y. Pomeau, “Lattice Gas Automata for the Navier-Stokes Equation”, Phys. Rev. Lett. 56, 1505–1508 (1986); U. Frisch, D. d'Ilumiŕes, B. Hasslacher, P. Lallemand, Y. Pomeau and J. Rivet, “Lattice Gas Hydrodynamics in Two and Three Dimensions”, Complex Systems 1, 649–707 (1987).

    Google Scholar 

  46. S. Wolfram, “Cellular Automata Fluids 1: Basic Theory”, J. Stat. Phys. 45, 471–526 (1986).

    Google Scholar 

  47. S. A. Orszag and V. Yakhot, “Reynolds Number Scaling of Cellular-Automata Hydrodynamics”, Phys. Rev. Lett.56, 1691–1693 (1986); V. Yakhot, B. J. Bayly, and S. A. Orszag, “Analogy Between Hyperscale Transport and Cellular Automata Fluid Dynamics” in: Lattice Gas Methods for Partial Differential Equations, G. D. Doolen, ed., (Addison-Wesley, New York, 1990) p.283–288.

    Google Scholar 

  48. D. H. Rothman and S. Zaleski, “Lattice-gas Models of Phase Separation: Interfaces, Phase Transitions and Multiphase Flow”, Rev. Mod. Phys. (1994).

    Google Scholar 

  49. A. Lawniczak, D. Dab, R. Kapral and J. P. Boon, “Reactive Lattice Gas Automata”, Physica D57, 132–158 (1991); R. Kapral, A. Lawniczak, and P. Masiar, “Reactive Dynamics in a Multispecies Lattice Gas Automata”, J. Chem. Phys. 2762–2776 (1992); D. Dab, J. P. Boon and J. X. Li, “Lattice Gas Automata for Coupled Reaction-Diffusion Equations”, Phys. Rev. Lett. 66, 2535–2538 (1991); R. Kapral, A. Lawniczak and P. Masiar, “Oscillations and Waves in a Reactive Lattice Gas Automaton”, Phys. Rev. Lett. 66, 2539–2542 (1991).

    Google Scholar 

  50. P. M. Binder, “Lattice Models of the Lorentz Gas: Physical and Dynamcal Properties”, Complex Systems 1, 559–574 (1987).

    Google Scholar 

  51. M. H. Ernst and G. A. van Velzen, “Lattice Lorentz Gas”, J. Phys. A 22, 4611–4632 (1989); G. A van Velzen, “Lorentz Lattice Gases”, Thesis, University of Utrecht, Utrecht, The Netherlands (1990).

    Google Scholar 

  52. Th. W. Ruijgrok and E. G. D. Cohen, “Deterministic Lattice Gas Models”, Phys. Lett. A133, 415–418 (1988); E. G. D. Cohen, “New Types of Diffusion in Lattice Gas Cellular Automata” in: Microscopic Simulations of Complex Hydrodynamic Phenomena, M. Maréschal and B. L. Holian, eds., Plenum Press, New York (1992) p.137–152; E. G. D. Cohen and F. Wang, “Diffusion and Propagation in Lorentz Lattice Gases”, in: The Fields Institute Series, Am. Math. Soc. (1994).

    Google Scholar 

  53. A number of previously published results (cf.ref.51) have to be revised, because computer experiments of much longer duration than before have shown a different behavior than previously reported: A. L. Owczarek and T. Prellberg, “Universality of Polymer Collapse in Two Dimensions and Super-Diffusive Behavior in a Lorentz Lattice Gas”, preprint (1994); F. Wang and E. G. D. Cohen, to be published.

    Google Scholar 

  54. L. A. Bunimovich and S. E. Troubetzkoy, “Recurrence Properties of Lorentz Lattice Gas Cellular Automata” J. Stat. Phys.67, 289–302 (1992); id., “Non Gaussian Behavior in Lorentz Lattice Gas Cellular Automata”, in: Proceedings of Dynamics of Complex and Irregular Systems, Ph. Blanchard, ed. (World Scientific, Singapore, 1994); id., “Topological Dynamics of Flipping Lorentz Lattice Gas Models”, J. Stat. Phys. 72, 297–308 (1993); id., “Rotators, Periodicity and Absence of Diffusion in Cyclic Cellular Automata”, J. Stat. Phys. (1994).

    Google Scholar 

  55. H. A. Posch and W. G. Hoover, Lyapunov Instability of Dense Lennard-Jones Fluids”, Phys. Rev. A38, 473–482 (1988); id., “Equilibrium and Nonequilibrium Lyapunov Spectra for Dense Fluids and Solids”, Phys. Rev. A 39, 2175–2188 (1989); H. Posch and W. Hoover, “Nonequilibrium Molecular Dynamics of a Classical Fluid” in: Molecular Liquids: New Perspectives in Physics and Chemistry, J. Texeire-Dial, ed., Kluwer Academic Publishers (1992) p. 527–547.

    Google Scholar 

  56. W. G. Hoover and. W. T. Ashurst, “Non-Equilibrium Molecular Dynamics”, Theor. Chem. Adv. and Persp. 1, 1 (1975); W. G. Hoover, “Molecular Dynamics”, Lecture Notes in Physics 258, (Springer, New York, 1986); id., “Non-Equilibrium Molecular Dynamics: the First 25 Years”, Physica A194, 450–461 (1993); G. Ciccotti and G. Jacucci, “Direct Computation of Dynamcal Response by Molecular Dynamics: The Mobility of a Charged Lennard-Jones Particle”, Phys. Rev. Lett.35, 789–792 (1975).

    Google Scholar 

  57. D. J. Evans and G. P. Morriss, “Non-Newtonian Molecular Dynamics”, Comput. Phys. Rep. 1, 300–343 (1984); id., Statistical Mechanics of Nonequilibrium Liquids, (Academic Press, New York, 1990).

    Google Scholar 

  58. D. J. Evans, E. G. D. Cohen and G. P. Morriss, “The Viscosity of a Simple Fluid From its Maximal Lyapunov Exponents”, Phys. Rev. A42, 5990–5997 (1991).

    Google Scholar 

  59. P. Gaspard and G. Nicolis, “Transport Properties, Lyapunov Exponents and Entropy Per Unit Time”, Phys. Rev. Lett.65, 1693–1696 (1990).

    Google Scholar 

  60. J. R. Dorfman and P. Gaspard, “Chaotic Scattering Theory of Transport and Reaction-Rate Coefficients”, Phys. Rev. E (1995).

    Google Scholar 

  61. E. G. D. Cohen and I. M. de Schepper, “Note on Transport Processes in Dense Colloidal Suspensions”, J. Stat. Phys. 63 241–248 (1991); 65, 419 (1991); (b) id., “The Colloidal Many Body Problem: Colloidal Suspensions as Hard Sphere Fluids”, in: Recent Progress in Many Body Theories, Vol.3, T. L. Ainsworth, C. Campbell, B. Clements and E. Krotcheck, eds., (Plenum Press, New York, 1992) p.387–395; (c) id., “Transport Properties of Concentrated Colloidal Suspensions”, in: Slow Dynamics in Condensed Matter, K. Kawasaki, M. Tokuyama and T. Kawakatsu, eds., Amer. Inst. Phys., New York (1992) p.359–369.

    Google Scholar 

  62. H. Löwen, J.-P. Hansen and J. N. Roux, “Brownian Dynamics and Kinetic Glass Transition in Colloidal Suspensions”, Phys. Rev. A44, 1169–1181 (1991).

    Google Scholar 

  63. I. M. de Schepper, E. G. D. Cohen, H. N. W. Lekkerkerker and P. N. Pusey, “Long Time Diffusion Coefficient in Charged Colloidal Solutions”, J. Phys. Cond. Matt. 1, 6503–6506 (1989); (b) P. N. Pusey, H. N. W. Lekkerkerker, E. G. D. Cohen and I. M. de Schepper, “Analogies Between the Dynamics of Concentrated Charged Colloidal Suspensions and Dense Atomic Liquids”, Physica A164, 12–27 (1990).

    Google Scholar 

  64. See ref. 1,, pp p.251.

    Google Scholar 

  65. I. M. de Schepper, H. E. Smorenburg and E. G. D. Cohen, “Viscoelasticity in Dense Hard Sphere Colloids”, Phys. Rev. Lett. 70, 2178–2181 (1993).

    Google Scholar 

  66. I. M. de Schepper and E. G. D. Cohen, “Rheological Behavior of Concentrated Colloidal Suspensions and Dense Atomic Fluids”, Phys. Lett. A150, 308–310 (1990).

    Google Scholar 

  67. I. M. de Schepper and E. G. D. Cohen, “Viscoelastic and Rheological Behavior of Concentrated Colloidal Suspensions”, Intern. J. of Thermophys. (1995).

    Google Scholar 

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J. J. Brey J. Marro J. M. Rubí M. San Miguel

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Cohen, E.G.D. (1995). Twenty-five years of non-equilibrium statistical mechanics: Towards a better understanding of dense fluids. In: Brey, J.J., Marro, J., Rubí, J.M., San Miguel, M. (eds) 25 Years of Non-Equilibrium Statistical Mechanics. Lecture Notes in Physics, vol 445. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59158-3_32

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