The hydrodynamics of inelastic granular systems

Schofield, Jeremy; Oppenheim, Irwin

doi:10.1016/0378-4371(93)90601-y

Cited by 18 publications

(29 citation statements)

References 13 publications

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“…In this "diffusive regime", the time dependence of the reduced coordinate space probability density P + b (R,t) = dP W + b (R, P ,t) is governed by the Smoluchowski equation [39,40,47] …”

Section: Discussionmentioning

confidence: 99%

Derivation of a Markov state model of the dynamics of a protein-like chain immersed in an implicit solvent

Schofield

Bayat

2014

The Journal of Chemical Physics

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A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local structure and bonding in a coarse-grained sense. The model is based on the assumption that the implicit solvent interacts on a fast time scale with the monomers of the chain compared to the time scale for structural rearrangements of the chain and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. A microscopic theory for the dynamics of the system is developed that reduces to a Markovian model of the kinetics under well-defined conditions. Microscopic expressions for the rate constants that appear in the Markov state model are analyzed and expressed in terms of a temperature-dependent linear combination of escape rates that themselves are independent of temperature. Excellent agreement is demonstrated between the theoretical predictions of the escape rates and those obtained through simulation of a stochastic model of the dynamics of bond formation. Finally, the Markov model is studied by analyzing the eigenvalues and eigenvectors of the matrix of transition rates, and the equilibration process for a simple helix-forming system from an ensemble of initially extended configurations to mainly folded configurations is investigated as a function of temperature for a number of different chain lengths. For short chains, the relaxation is primarily single-exponential and becomes independent of temperature in the low-temperature regime. The profile is more complicated for longer chains, where multi-exponential relaxation behavior is seen at intermediate temperatures followed by a low temperature regime in which the folding becomes rapid and single exponential. It is demonstrated that the behavior of the equilibration profile as the temperature is lowered can be understood in terms of the number of relaxation modes or "folding pathways" that contribute to the evolution of the state populations.

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“…In this "diffusive regime", the time dependence of the reduced coordinate space probability density P + b (R,t) = dP W + b (R, P ,t) is governed by the Smoluchowski equation [39,40,47] …”

Section: Discussionmentioning

confidence: 99%

Derivation of a Markov state model of the dynamics of a protein-like chain immersed in an implicit solvent

Schofield

Bayat

2014

The Journal of Chemical Physics

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“…We will follow closely the method used by Schofield and Oppenheim [12] and study a system of N spherical, smooth and identical grains of mass m constituted by M atoms, M 1. The grains are large enough making quantum effects irrelevant.…”

Section: Fokker-plank Approachmentioning

confidence: 99%

“…With the goal of obtaining a basic first-principles approach to the problem of an inelastic GG, Schofield and Oppenheim [12] derived a set of Fokker-Planck equations for the distribution of positions and velocities for the grain's centers of mass of a GG at the (not necessarily homogeneous) cooling state (no energy-feeding mechanism) tending to true thermal equilibrium. This is a very general method that depends on a time-scale separation between the internal relaxation processes of a grain (fast variables) and the evolution of the long wavelength phenomena for the GG (slow variables) [14].…”

Section: Introductionmentioning

confidence: 99%

“…The basic steps leading to an equation describing the time-evolution for the distribution include postulating the inelastic Boltzmann-Enskog equation [8,9], adding energy feeding mechanisms such as the "democratic" vibration model [1], and deriving Fokker-Planck equations based on a first-principles expansion around equilibrium [12], kinetic theory methods [18], Monte Carlo methods or molecular dynamics simulations [19]. Most of these are effective approaches that ignore the detailed collisional dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Revisiting the first-principles approach to the granular gas steady state

Proleon¹,

Morgado²

2004

Braz. J. Phys.

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We extend a Fokker-Planck formalism, previously used to describe the behavior of a cooling granular gas, with a Hertzian contact potential and viscoelastic radial friction, giving a velocity dependent coefficient of restitution. In the present work, we study the more general case of a steady-state with finite kinetic energy, far from equilibrium, due to the coupling to an external energy-feeding mechanism. Also from first-principles, we extend the validity of the former results.

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“…netic energy of the bodies being transformed into vibrational kinetic energy of the molecules that constitute the material, or being 'expended' creating new surface area as fractures are created or particles break. Because the time scale of typical molecular motions is so much shorter than the time scale of gross motion of the macroscopic particles, any energy transferred to molecular 'heat' is effectively 'lost' from the system of particles and is irrecoverable as kinetic energy of gross motion of individual grains or particles (3). …”

Section: Introductionmentioning

confidence: 99%

Force Models for Particle-Dynamics Simulations of Granular Materials

Walton

1995

Mobile Particulate Systems

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The hydrodynamics of inelastic granular systems

Cited by 18 publications

References 13 publications

Derivation of a Markov state model of the dynamics of a protein-like chain immersed in an implicit solvent

Derivation of a Markov state model of the dynamics of a protein-like chain immersed in an implicit solvent

Revisiting the first-principles approach to the granular gas steady state

Force Models for Particle-Dynamics Simulations of Granular Materials

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