Homogeneous Cooling with Repulsive and Attractive Long-range Interactions

Müller, Micha-Klaus; Luding, Stefan

doi:10.1063/1.3180022

Cited by 5 publications

(4 citation statements)

References 63 publications

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“…In the limit of zero density and rather weak long-range forces, a Boltzmann-like correction factor to the energy dissipation rate was determined using kinetic theory arguments for the energy dissipation rate. For repulsive systems [204][205][206][207]:…”

Section: Long-range Forcesmentioning

confidence: 99%

Towards dense, realistic granular media in 2D

Luding¹

2009

Nonlinearity

133

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The development of an applicable theory for granular matter -with both qualitative and quantitative value -is a challenging prospect, given the multitude of states, phases and (industrial) situations it has to cover. Given the general balance equations for mass, momentum, and energy, the limiting case of dilute and almost elastic granular gases, where kinetic theory works perfectly well, is the starting point.In most systems, low density coexists with very high density, where the latter is an open problem for kinetic theory. Furthermore, many additional non-linear phenomena and material properties are important in realistic granular media, involving, e.g.: (i) multi-particle interactions and elasticity (ii) strong dissipation, (iii) friction, (iv) long-range forces and wet contacts (v) wide particle size-distributions, and (vi) various particle shapes. Note that, while some of these issues are more relevant for high density, others are important for both low and high densities; some of them can be dealt with by means of kinetic theory, some can not. This paper is a review of recent progress towards more realistic models for dense granular media in 2D, even though most of the observations, conclusions, and corrections given are qualitatively true also in 3D. Starting from an elastic, frictionless and monodisperse hard sphere gas, the (continuum) balance equations of mass, momentum and energy are given. The equation of state, the (Navier-Stokes level) transport coefficients and the energy-density dissipation rate are considered. Several corrections are applied to those constitutive material laws -one by one -in order to account for the realistic physical effects and properties listed above.

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Section: Long-range Forcesmentioning

confidence: 99%

Towards dense, realistic granular media in 2D

Luding¹

2009

Nonlinearity

133

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“…Haff's law is valid only for particles with hard-core interaction in the homogeneous cooling state (HCS). For long range interaction, Müller and Luding [20,28] predicted, using a modified pseudo-Liouville operator formalism, a reduced cooling rate due to the repulsive forces and an increased rate due to attractive forces (extending the results of [36]). In their theory, the ratio of the potential at contact, φ (see subsection 4.1), to the temperature is the control parameter,…”

Section: Dissipation Rate Modification Due To Attraction and Repulsionmentioning

confidence: 58%

“…magnetic, interactions considered [26,27]). Simulations are compared to the mean-field theory by Müller and Luding [20,28], which only features a modified cooling due to either repulsion or attraction. Our goal is to understand how dissipation and non-contact interactions act together, and what kind of dynamics is caused by the interplay of both mechanisms active at the same time in a free cooling granular system.…”

Section: Introductionmentioning

confidence: 99%

Free cooling phase-diagram of hard-spheres with short- and long-range interactions

González

Thornton

Luding

2014

Eur. Phys. J. Spec. Top.

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We study the stability, the clustering and the phase-diagram of free cooling granular gases. The systems consist of mono-disperse particles with additional non-contact (long-range) interactions, and are simulated here by the event-driven molecular dynamics algorithm with discrete (short-range shoulders or wells) potentials (in both 2D and 3D). Astonishingly good agreement is found with a mean field theory, where only the energy dissipation term is modified to account for both repulsive or attractive non-contact interactions. Attractive potentials enhance cooling and structure formation (clustering), whereas repulsive potentials reduce it, as intuition suggests. The system evolution is controlled by a single parameter: the non-contact potential strength scaled by the fluctuation kinetic energy (granular temperature). When this is small, as expected, the classical homogeneous cooling state is found. However, if the effective dissipation is strong enough, structure formation proceeds, before (in the repulsive case) non-contact forces get strong enough to undo the clustering (due to the ongoing dissipation of granular temperature). For both repulsive and attractive potentials, in the homogeneous regime, the cooling shows a universal behaviour when the (inverse) control parameter is used as evolution variable instead of time. The transition to a non-homogeneous regime, as predicted by stability analysis, is affected by both dissipation and potential strength. This can be cast into a phase diagram where the system changes with time, which leaves open many challenges for future research.

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“…In these systems (and others) the particles (or other entities) can interact via various (and often complicated) means. 11 For example, system components can have attractive and/or repulsive long-range interactions [329], can be cohesive [330], and/or can interact with one another via chemical gradients [331,332], electric charges [333][334][335], or through other molecular or mechanical processes [336]. In each of these cases, interaction strengths can yield edge weights, either as the sole relationship studied between entities in a graph or as one of several inter-entity relationships in a multilayer network.…”

Section: Beyond Granular Materialsmentioning

confidence: 99%

Network Analysis of Particles and Grains

Papadopoulos,

Porter,

Daniels

et al. 2017

Preprint

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The arrangements of particles and forces in granular materials have a complex organization on multiple spatial scales that ranges from local structures to mesoscale and system-wide ones. This multiscale organization can affect how a material responds or reconfigures when exposed to external perturbations or loading. The theoretical study of particle-level, force-chain, domain, and bulk properties requires the development and application of appropriate physical, mathematical, statistical, and computational frameworks. Traditionally, granular materials have been investigated using particulate or continuum models, each of which tends to be implicitly agnostic to multiscale organization. Recently, tools from network science have emerged as powerful approaches for probing and characterizing heterogeneous architectures across different scales in complex systems, and a diverse set of methods have yielded fascinating insights into granular materials. In this paper, we review work on network-based approaches to studying granular matter and explore the potential of such frameworks to provide a useful description of these systems and to enhance understanding of their underlying physics. We also outline a few open questions and highlight particularly promising future directions in the analysis and design of granular matter and other kinds of material networks.

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Homogeneous Cooling with Repulsive and Attractive Long-range Interactions

Cited by 5 publications

References 63 publications

Towards dense, realistic granular media in 2D

Towards dense, realistic granular media in 2D

Free cooling phase-diagram of hard-spheres with short- and long-range interactions

Network Analysis of Particles and Grains

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