Nonequilibrium fluctuation-dissipation relations of interacting Brownian particles driven by shear

Krüger, Matthias; Fuchs, Matthias

doi:10.1103/physreve.81.011408

Cited by 15 publications

(36 citation statements)

References 75 publications

(218 reference statements)

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“…This lends further support to the earlier discussion of nonequilibrium fluctuationdissipation ratios and Einstein relations within MCT and its schematic models, as the equivalent approximations have been used there [11,15,32].…”

Section: Discussionsupporting

confidence: 80%

From equilibrium to steady-state dynamics after switch-on of shear

2010

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A relation between equilibrium, steady-state, and waiting-time dependent dynamical two-time correlation functions in dense glass-forming liquids subject to homogeneous steady shear flow is discussed. The systems under study show pronounced shear thinning, i.e., a significant speedup in their steady-state slow relaxation as compared to equilibrium. An approximate relation that recovers the exact limit for small waiting times is derived following the integration through transients (ITT) approach for the nonequilibrium Smoluchowski dynamics, and is exemplified within a schematic model in the framework of the mode-coupling theory of the glass transition (MCT).Computer simulation results for the tagged-particle density correlation functions corresponding to wave vectors in the shear-gradient directions from both event-driven stochastic dynamics of a twodimensional hard-disk system and from previously published Newtonian-dynamics simulations of a three-dimensional soft-sphere mixture are analyzed and compared with the predictions of the ITTbased approximation. Good qualitative and semi-quantitative agreement is found. Furthermore, for short waiting times, the theoretical description of the waiting time dependence shows excellent quantitative agreement to the simulations. This confirms the accuracy of the central approximation used earlier to derive fluctuation dissipation ratios (Phys. Rev. Lett. 102, 135701). For intermediate waiting times, the correlation functions decay faster at long times than the stationary ones. This behavior is predicted by our theory and observed in simulations.

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Section: Discussionsupporting

confidence: 80%

From equilibrium to steady-state dynamics after switch-on of shear

2010

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“…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%

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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“…There has been a lot of interest in recent years in the dynamics of interacting Brownian particles [9][10][11][12][13][14]. The reason for this interest is twofold [15].…”

mentioning

confidence: 99%

“…Second, interacting Brownian particles constitute the simplest model system, on which one can test techniques and approximations of nonequilibrium statistical mechanics. Many-particle systems may exhibit some features not found in the single-particle counterparts, such as phase transitions, spontaneous ratchet effects, and negative mobility [9][10][11][12][13][14]. The interacting Brownian ratchets been proposed for a variety of applications, including molecular motors [2], friction [16], diffusion of dimers on surfaces [17], diffusion of colloidal particles [18], DNA translocation through a nanopore [19], charge density waves [20], and arrays of Josephson junctions [21].…”

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confidence: 99%

Particle diode: Rectification of interacting Brownian ratchets

Zhong

2011

Phys. Rev. E

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Transport of Brownian particles interacting with each other via the Morse potential is investigated in the presence of an ac driving force applied locally at one end of the chain. By using numerical simulations, we find that the system can behave as a particle diode for both overdamped and underdamped cases. For low frequencies, the transport from the free end to the ac acting end is prohibited, while the transport from the ac acting end to the free end is permitted. However, the polarity of the particle diode will reverse for medium frequencies. There exists an optimal value of the well depth of the interaction potential at which the average velocity takes its maximum. The average velocity υ decreases monotonically with the system size N by a power law υ ∝ N −1 .

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Nonequilibrium fluctuation-dissipation relations of interacting Brownian particles driven by shear

Cited by 15 publications

References 75 publications

From equilibrium to steady-state dynamics after switch-on of shear

From equilibrium to steady-state dynamics after switch-on of shear

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

Particle diode: Rectification of interacting Brownian ratchets

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