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Frederic Van Wijland - One of the best experts on this subject based on the ideXlab platform.
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equilibrium dynamics of the dean kawasaki Equation mode Coupling theory and its extension
Physical Review E, 2014Co-Authors: Bongsoo Kim, Hugo Jacquin, Kyozi Kawasaki, Frederic Van WijlandAbstract:We extend a previously proposed field-theoretic self-consistent perturbation approach for the equilibrium dynamics of the Dean-Kawasaki Equation presented in [Kim and Kawasaki, J. Stat. Mech. (2008) P02004]. By taking terms missing in the latter analysis into account we arrive at a set of three new Equations for correlation functions of the system. These correlations involve the density and its logarithm as local observables. Our new one-loop Equations, which must carefully deal with the noninteracting Brownian gas theory, are more general than the historic mode-Coupling one in that a further approximation corresponding to Gaussian density fluctuations leads back to the original mode-Coupling Equation for the density correlations alone. However, without performing any further approximation step, our set of three Equations does not feature any ergodic-nonergodic transition, as opposed to the historical mode-Coupling approach.
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field theoretic formulation of a mode Coupling Equation for colloids
Physical Review Letters, 2011Co-Authors: Hugo Jacquin, Frederic Van WijlandAbstract:The only available quantitative description of the slowing down of the dynamics upon approaching the glass transition has been, so far, the mode-Coupling theory, developed in the 1980s by Gotze and collaborators. The standard derivation of this theory does not result from a systematic expansion. We present a field-theoretic formulation that arrives at very similar mode-Coupling Equation but which is based on a variational principle and on a controlled expansion in a small dimensionless parameter. Our approach applies to such physical systems as colloids interacting via a mildly repulsive potential. It can in principle, with moderate efforts, be extended to higher orders and to multipoint correlation functions. When a suspension of polymer particles is cooled or compressed, a rapid slowing down of the dynamics occurs, and the suspension gradually becomes solid on experimen- tal time scales, without any apparent change in structure (1). This colloidal glass transition is reminiscent of the phenomenology of molecular glasses. However, colloids are conceptually simpler to analyze: the interaction poten- tial often has a simple repulsive character (instead of a Lennard-Jones form) and their effective dynamics is Brownian (instead of Newtonian). They are also experi- mentally simpler to probe, since colloids are much larger than molecules in simple liquids. An important class of colloids is those who interact via a bounded, repulsive potential. These, due to the existence of a finite energy scale in the potential, exhibit a reentrant behavior at high density—the glass melts upon increasing the density—and the noninteracting liquid is recovered in the limit of infinite density (2-4). All particles evolve in a thermal bath (the solution) and thus undergo individual Brownian motions, while also interacting via a given pair potential v. To make our approach explicit, we chose to study the harmonic spheres model, where the pair potential v is taken to be of the form vðr Þ¼ð 1 � r � Þ 2 � ð1 � r � Þ, but most of the rea- soning will be carried out for an arbitrary, sufficiently well- behaved function v. This model was introduced by Durian (5) in the context of foam mechanics, where vðrÞ plays the role of an effective interaction potential that arises from a coarse-graining procedure, but experimental realizations in colloids (6,7) exist, and it became a model system to study glassy structure and dynamics (8). The position ~ riðtÞ of each of the N particles composing the colloidal suspension evolve under Brownian dynamics, encoded in the following Langevin Equations: d~ ri dt ðt Þ¼�
Hugo Jacquin - One of the best experts on this subject based on the ideXlab platform.
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equilibrium dynamics of the dean kawasaki Equation mode Coupling theory and its extension
Physical Review E, 2014Co-Authors: Bongsoo Kim, Hugo Jacquin, Kyozi Kawasaki, Frederic Van WijlandAbstract:We extend a previously proposed field-theoretic self-consistent perturbation approach for the equilibrium dynamics of the Dean-Kawasaki Equation presented in [Kim and Kawasaki, J. Stat. Mech. (2008) P02004]. By taking terms missing in the latter analysis into account we arrive at a set of three new Equations for correlation functions of the system. These correlations involve the density and its logarithm as local observables. Our new one-loop Equations, which must carefully deal with the noninteracting Brownian gas theory, are more general than the historic mode-Coupling one in that a further approximation corresponding to Gaussian density fluctuations leads back to the original mode-Coupling Equation for the density correlations alone. However, without performing any further approximation step, our set of three Equations does not feature any ergodic-nonergodic transition, as opposed to the historical mode-Coupling approach.
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field theoretic formulation of a mode Coupling Equation for colloids
Physical Review Letters, 2011Co-Authors: Hugo Jacquin, Frederic Van WijlandAbstract:The only available quantitative description of the slowing down of the dynamics upon approaching the glass transition has been, so far, the mode-Coupling theory, developed in the 1980s by Gotze and collaborators. The standard derivation of this theory does not result from a systematic expansion. We present a field-theoretic formulation that arrives at very similar mode-Coupling Equation but which is based on a variational principle and on a controlled expansion in a small dimensionless parameter. Our approach applies to such physical systems as colloids interacting via a mildly repulsive potential. It can in principle, with moderate efforts, be extended to higher orders and to multipoint correlation functions. When a suspension of polymer particles is cooled or compressed, a rapid slowing down of the dynamics occurs, and the suspension gradually becomes solid on experimen- tal time scales, without any apparent change in structure (1). This colloidal glass transition is reminiscent of the phenomenology of molecular glasses. However, colloids are conceptually simpler to analyze: the interaction poten- tial often has a simple repulsive character (instead of a Lennard-Jones form) and their effective dynamics is Brownian (instead of Newtonian). They are also experi- mentally simpler to probe, since colloids are much larger than molecules in simple liquids. An important class of colloids is those who interact via a bounded, repulsive potential. These, due to the existence of a finite energy scale in the potential, exhibit a reentrant behavior at high density—the glass melts upon increasing the density—and the noninteracting liquid is recovered in the limit of infinite density (2-4). All particles evolve in a thermal bath (the solution) and thus undergo individual Brownian motions, while also interacting via a given pair potential v. To make our approach explicit, we chose to study the harmonic spheres model, where the pair potential v is taken to be of the form vðr Þ¼ð 1 � r � Þ 2 � ð1 � r � Þ, but most of the rea- soning will be carried out for an arbitrary, sufficiently well- behaved function v. This model was introduced by Durian (5) in the context of foam mechanics, where vðrÞ plays the role of an effective interaction potential that arises from a coarse-graining procedure, but experimental realizations in colloids (6,7) exist, and it became a model system to study glassy structure and dynamics (8). The position ~ riðtÞ of each of the N particles composing the colloidal suspension evolve under Brownian dynamics, encoded in the following Langevin Equations: d~ ri dt ðt Þ¼�
Miao Xiexing - One of the best experts on this subject based on the ideXlab platform.
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reliability analysis of the velocity matching of coal cutting and caving in fully mechanized top coal caving face
煤炭学报(英文版), 2002Co-Authors: Miao XiexingAbstract:The matching relationship between coal cutting and caving in fully mechanized top-coal caving face is analyzed in detail from the angle of reliability. The Coupling Equation of reliability is established correspondingly, and the mathematical Equation of the coefficient of velocity matching of coal cutting and caving is obtained, which meets a certain reliability demand for making the working procedure of coal caving not influence coal cutting of coal-cutter. The results show that the relationship between the coefficient of the velocity matching and the reliability of coal cutting and caving system is linear on the whole when R 0.9. It is pointed out that different numerical value should be selected for different coal face according to different demand for reliability.
Bongsoo Kim - One of the best experts on this subject based on the ideXlab platform.
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equilibrium dynamics of the dean kawasaki Equation mode Coupling theory and its extension
Physical Review E, 2014Co-Authors: Bongsoo Kim, Hugo Jacquin, Kyozi Kawasaki, Frederic Van WijlandAbstract:We extend a previously proposed field-theoretic self-consistent perturbation approach for the equilibrium dynamics of the Dean-Kawasaki Equation presented in [Kim and Kawasaki, J. Stat. Mech. (2008) P02004]. By taking terms missing in the latter analysis into account we arrive at a set of three new Equations for correlation functions of the system. These correlations involve the density and its logarithm as local observables. Our new one-loop Equations, which must carefully deal with the noninteracting Brownian gas theory, are more general than the historic mode-Coupling one in that a further approximation corresponding to Gaussian density fluctuations leads back to the original mode-Coupling Equation for the density correlations alone. However, without performing any further approximation step, our set of three Equations does not feature any ergodic-nonergodic transition, as opposed to the historical mode-Coupling approach.
Luo Shanming - One of the best experts on this subject based on the ideXlab platform.
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the reliability analysis of the velocity ratio of coal cutting to support moving in fully mechanized top coal caving face
Journal of Xiangtan Mining Institute, 2001Co-Authors: Luo ShanmingAbstract:From the angle of reliability, the system of coal cutting and support moving of high productivity and efficiency work face is analyzed in detail by using the interference theory of strength and stress distribution. The Coupling Equation and calculation formulas of the velocity ratio of coal cutting to support moving are established. The characteristic curve of the velocity ratio consists of three different areas, so the ratio of different work face should be selected according to different demand of reliability. The velocity ratio of coal cutting to support moving can be selected from 1.3 to 1.5 in high productivity and efficiency work face, or from 1.5 to 1.8 in super-length fully mechanized top-coal caving face.2figs.,2tabs.,6refs.
