Author

# Matthieu H. Ernst

Other affiliations: University of Michigan

Bio: Matthieu H. Ernst is an academic researcher from Utrecht University. The author has contributed to research in topics: Lattice gas automaton & Boltzmann equation. The author has an hindex of 34, co-authored 114 publications receiving 4122 citations. Previous affiliations of Matthieu H. Ernst include University of Michigan.

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##### Papers

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TL;DR: Etude de la distribution en dimension des agregats dans un processus d'agregation irreversible sans transition de gel: c k (t)∼s −2 φ(k/s), dont on determine les exposants par l'equation de Smoluchowski pour la dimension moyenne de l'agregat.

Abstract: In irreversible aggregation processes without a gelation transition the cluster size distribution approaches a scaling form, ${c}_{k}(t)\ensuremath{\sim}{s}^{\ensuremath{-}2}\ensuremath{\varphi}(\frac{k}{s})$. Usking Smoluchowski's coagulation equation we determine the exponents in the mean cluster size $s(t)\ensuremath{\sim}{t}^{z}$ ($t\ensuremath{\rightarrow}\ensuremath{\infty}$) and in the small- and large-$x$ behavior of the scaling function $\ensuremath{\varphi}(x)$. Depending on certain characteristics of the coagulation coefficients, $\ensuremath{\varphi}(x)\ensuremath{\sim}{x}^{\ensuremath{-}\ensuremath{\tau}}$ ($x\ensuremath{\rightarrow}0$) or $\ensuremath{\varphi}(x)\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}{x}^{\ensuremath{\mu}})$ ($x\ensuremath{\rightarrow}0$) with $\ensuremath{\mu}$ some negative constant. In aggregation processes with gelation a similar scaling form is obtained as $t$ approaches the gel point.

317 citations

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TL;DR: In this article, the asymptotic time behavior of the velocity autocorrelation function and of the kinetic parts of the correlation functions for the shear viscosity and the heat conductivity is derived.

Abstract: The asymptotic time behavior of the velocity autocorrelation function and of the kinetic parts of the correlation functions for the shear viscosity and the heat conductivity is derived. The results are expressed in terms of the transport coefficients and the specific heats and are valid for all densities.

296 citations

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TL;DR: In this article, a modified version of the Enskog equation is proposed to describe the time dependence of the single-particle distribution function in a dense gas of hard spheres, which is not restricted to small spatial non-uniformities and may be used to derive higher-order hydrodynamic equations.

281 citations

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TL;DR: It is argued that the kernelKij∼ijω with ω≃1−1/d effectively models the sol-gel transformation in polymerizing systems and approximately accounts for the effects of cross-linking and steric hindrance neglected in the classical theory of Flory and Stockmayer.

Abstract: Smoluchowski's equation for rapid coagulation is used to describe the kinetics of gelation, in which the coagulation kernel Kij models the bonding mechanism. For different classes of kernels we derive criteria for the occurrence of gelation, and obtain critical exponents in the pre- and postgelation stage in terms of the model parameters; we calculate bounds on the time of gelation to, and give an exact postgelation solution for the model K,j = (/j)'~ (~0 > 1/2) and Kq = a i+j (a > 1). For the model Kig = i '~ +j~ (w < 1, without gelation) initial solutions are given. It is argued that the kernel Kij~(/j') '~ with ~0~ 1 - l/d (d is dimensionality) effectively models the sol-gel transformation in polymerizing systems and approximately accounts for the effects of cross-linking and steric hindrance neglected in the classical theory of Flory and Stockmayer (o~ = 1). For all ~o the exponents, T = ~0 + 3/2 and o = ~ - 1/2, y = (3/2 - o~)/(o~ - 1/2) and /3 = 1, characterize the size distribution, at and slightly below the gel point, under the assumption that scaling is valid.

197 citations

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TL;DR: In this paper, the binary-collision expansion for potentials consisting of a hard core and a soft tail is discussed and the restrictions to their applicability are determined, and the different expressions so far proposed are critically examined.

155 citations

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TL;DR: Van Kampen as mentioned in this paper provides an extensive graduate-level introduction which is clear, cautious, interesting and readable, and could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes.

Abstract: N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

3,647 citations

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TL;DR: In this article, the authors consider the specific effects of a bias on anomalous diffusion, and discuss the generalizations of Einstein's relation in the presence of disorder, and illustrate the theoretical models by describing many physical situations where anomalous (non-Brownian) diffusion laws have been observed or could be observed.

3,383 citations

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01 Jan 1971

TL;DR: In this paper, Ozaki et al. describe the dynamics of adsorption and Oxidation of organic Molecules on Illuminated Titanium Dioxide Particles Immersed in Water.

Abstract: 1: Magnetic Particles: Preparation, Properties and Applications: M. Ozaki. 2: Maghemite (gamma-Fe2O3): A Versatile Magnetic Colloidal Material C.J. Serna, M.P. Morales. 3: Dynamics of Adsorption and Oxidation of Organic Molecules on Illuminated Titanium Dioxide Particles Immersed in Water M.A. Blesa, R.J. Candal, S.A. Bilmes. 4: Colloidal Aggregation in Two-Dimensions A. Moncho-Jorda, F. Martinez-Lopez, M.A. Cabrerizo-Vilchez, R. Hidalgo Alvarez, M. Quesada-PMerez. 5: Kinetics of Particle and Protein Adsorption Z. Adamczyk.

1,870 citations

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TL;DR: The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail and linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long-wavelength limit (wave vector k=0).

Abstract: The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

1,859 citations

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TL;DR: The basic elements of the theory of the lattice Boltzmann equation, a special lattice gas kinetic model for hydrodynamics, are reviewed in this paper, together with some generalizations which allow one to extend the range of applicability of the method to a number of fluid dynamics related problems.

1,812 citations