Effective temperature and jamming transition in dense,  gently
sheared granular assemblies

Potiguar, Fabrício Q.; Makse, Hernán A.

doi:10.1140/epje/e2006-00017-4

Cited by 35 publications

(34 citation statements)

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“…However, supercooled liquids can also exhibit complicated natures, displaying anisotropic mechanical responses, anisotropic fluctuations [47], and negative shear modulus and negative stress correlations. An understanding of the mechanism underlying these complicated phenomena will lead us to a better comprehension of the violations of the FDT [1][2][3][4][5][6] that they involve, as well as certain consequent modifications of the concept of an effective temperature [13][14][15][16][17][18][19][20][21]. Supercooled liquids composed of spherical or low-molecularweight molecules may be excellent materials for investigating non-equilibrium statistical mechanics.…”

Section: Resultsmentioning

confidence: 99%

“…The relationship between the response and correlation functions is of great interest and importance [1][2][3][4][5][6][13][14][15][16][17][18][19][20][21]. If we use the shear moduli G …”

Section: Violation Of Fluctuation-dissipation Theoremmentioning

confidence: 99%

“…Furthermore, in glassy systems, including supercooled liquids, it has been suggested that the equilibrium form of the FDT holds at long times with the temperature T replaced by an effective temperature T eff [13], which indicates that T eff can be used to relate the response and correlation functions. Several numerical and theoretical works have examined the validity and the role of the effective temperature in such situations [14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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Mechanical responses and stress fluctuations of a supercooled liquid in a sheared non-equilibrium state

Mizuno

Yamamoto

2012

Eur. Phys. J. E

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Abstract.A steady shear flow can drive supercooled liquids into a non-equilibrium state. Using molecular dynamics simulations under steady shear flow superimposed with oscillatory shear strain for a probe, non-equilibrium mechanical responses are studied for a model supercooled liquid composed of binary soft spheres. We found that even in the strongly sheared situation, the supercooled liquid exhibits surprisingly isotropic responses to oscillating shear strains applied in three different components of the strain tensor. Based on this isotropic feature, we successfully constructed a simple two-mode Maxwell model that can capture the key features of the storage and loss moduli, even for highly non-equilibrium state. Furthermore, we examined the correlation functions of the shear stress fluctuations, which also exhibit isotropic relaxation behaviors in the sheared non-equilibrium situation. In contrast to the isotropic features, the supercooled liquid additionally demonstrates anisotropies in both its responses and its correlations to the shear stress fluctuations. Using the constitutive equation (a two-mode Maxwell model), we demonstrated that the anisotropic responses are caused by the coupling between the oscillating strain and the driving shear flow. Due to these anisotropic responses and fluctuations, the violation of the fluctuation-dissipation theorem (FDT) is distinct for different components. We measured the magnitude of this violation in terms of the effective temperature. It was demonstrated that the effective temperature is notably different between different components, which indicates that a simple scalar mapping, such as the concept of an effective temperature, oversimplifies the true nature of supercooled liquids under shear flow. An understanding of the mechanism of isotropies and anisotropies in the responses and fluctuations will lead to a better appreciation of these violations of the FDT, as well as certain consequent modifications to the concept of an effective temperature.

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Section: Resultsmentioning

confidence: 99%

“…The relationship between the response and correlation functions is of great interest and importance [1][2][3][4][5][6][13][14][15][16][17][18][19][20][21]. If we use the shear moduli G …”

Section: Violation Of Fluctuation-dissipation Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mechanical responses and stress fluctuations of a supercooled liquid in a sheared non-equilibrium state

Mizuno

Yamamoto

2012

Eur. Phys. J. E

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“…In terms of novel granular literature, this state of yielding sand can be recognized as being near (or at) the state of jamming transition or jamming threshold [34][35][36][37][38], and it represents the onset of slow flow regime [39,40], which seems to be rate-independent.…”

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confidence: 99%

State equation of mineral sands

Ivšić

2011

Granular Matter

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The pressure-volume analogy between compressible fluids and macroscopic sand bodies (Ivsic et al. in Phys A, 277:47-61, 2000) is further extended using quantitative determination of corresponding empirical constants based on adapted van der Waals state equation. The isothermal constants obtained by interpretation of triaxial sand tests at so called "critical state of sand" are clearly related to the universal ideal gas properties and molar properties of mineral sands. The corresponding constants for sand and gases or other volatile liquids have the same order of magnitude. The apparent bulk repulsion/attraction effects in sand bodies are also discussed.

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“…A recent surprising result is that when considering different conjugate pairs of variables, the static effective temperature determined from one pair can agree with the time-dependent effective temperature from a different pair [13]. The conditions for such agreement are not yet understood, but recent simulation work for granular systems suggests interesting directions of study [14].Experiments probing fluctuation-dissipation measures in granular systems have considered both diffusivities (a static measurement) [15] and the time-dependent fluctuation dissipation relationship [16]. The results on diffusivities is consistent with simulations, at least in the sense that effective temperatures from equipartition definitions do not tend to agree with fluctuation-dissipation…”

mentioning

confidence: 99%

Asymmetric Response of a Jammed Plastic Bead Raft

Twardos

Dennin²

2006

Phys. Rev. Lett.

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Fluctuation-dissipation relations have received significant attention as a potential method for defining an effective temperature in nonequilibrium systems. The successful development of an effective temperature would be an important step in the application of statistical mechanics principles to systems driven far from equilibrium. Many of the systems of interest are sufficiently dense that they are close to the jamming transition, a point at which interesting correlations develop. Here we study the response function in a driven system of plastic beads as a function of the density in order to elucidate the impact of the jamming transition on the use of fluctuation-dissipation relations. The focus is on measuring the response function for applied shear stress. We find that even when the amplitude of the applied stress leads to a linear response in the strain, the time scale of the response is dependent on the direction of the applied stress. The identification of an "effective temperature" for systems driven far from equilibrium that is analogous to a true thermodynamic temperature would represent a major step toward developing a general theory of nonequilibrium behavior. One of the reasons that the concept of an "effective temperature" is so attractive is the centrality of real temperature in thermodynamics and statistical physics. At its most basic, temperature defines when two systems are in thermodynamic equilibrium and determines the direction of heat flow, if any, for systems in contact. Equipartition provides a connection between temperature and average quantities. Temperature enters the relation between thermodynamic quantities, such as specific heat and derivatives of free energies. Einsteintype relations relate various transport coefficients, such as diffusion constants and viscosities, through the temperature. Finally, in linear response theory, temperature enters the relationship between time (or frequency) dependent response functions and correlation functions. The challenge for studies of nonequilibrium systems is the determination of which, if any, of the above uses of temperature is meaningful as an effective temperature. To be a useful concept, a minimum expectation is that multiple definitions of effective temperature agree, and that there is an understanding of why some definitions agree and others do not.The use of effective temperatures in driven systems has a relatively diverse history. For example, granular flows are often characterized by a "granular" temperature that is based on the average kinetic energy of the particles. Another approach can be described as a "configurational" temperature. In these studies, (usually with dense granular matter) the "atoms" are grains, and the phase space is the set of static mechanical configurations in which they can be arranged. By considering all possible jammed configurations, entropy as a function of density is calculated and used to define an effective temperature [1,2,3]. Another approach has been to focus on fluctuations in the system as a means ...

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Effective temperature and jamming transition in dense, gently sheared granular assemblies

Cited by 35 publications

References 50 publications

Mechanical responses and stress fluctuations of a supercooled liquid in a sheared non-equilibrium state

Mechanical responses and stress fluctuations of a supercooled liquid in a sheared non-equilibrium state

State equation of mineral sands

Asymmetric Response of a Jammed Plastic Bead Raft

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