Stress correlation function and linear response of Brownian particles

Vogel, Florian; Fuchs, Matthias

doi:10.1140/epje/i2020-11993-4

Cited by 13 publications

(5 citation statements)

References 34 publications

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“…In the derivation of eq. (A.2), we used isotropy and inversion symmetry which imply σ(q, t) * F (F ) (q) = − σ(−q, t) * F (F ) (−q) , valid for the full and the reduced dynamics [36]. The kernel arising in E (2) thus is linear in the wave vector for small q. Additionally we used that detailed balance, valid close to equilibrium, gives…”

Section: Time-and Space-dependent Correlationsmentioning

confidence: 99%

Emergence of Goldstone excitations in stress correlations of glass-forming colloidal dispersions

Vogel¹,

Zippelius²,

Fuchs³

2019

EPL

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We compute the dynamic correlations of the nonlocal shear stress at the liquid to glass transition in colloidal dispersions. Whereas Eshelby's elastic pattern is recovered independently of the dynamics, the Goldstone modes of the colloidal glass are diffusive, ω = −iDq 2 , because the transverse momentum is not conserved -excluding propagating transverse sound. Precursors of both, the Goldstone modes and the long-ranged, anisotropic stress correlations, can be observed in the colloidal fluid. The slow diffusive mode dominates the dynamics in the supercooled liquid for wave numbers qξ 1 with a correlation length ξ ∝ τ 1/2 which grows like the square root of the relaxation time τ . Time-and space-dependent stress correlations are anisotropic, decaying like r −5 . These results are derived within a hydrodynamic theory, generalising Maxwell's model to finite wave numbers, after the dynamics has been decomposed into potentially slow modes, associated with the order parameter, and fast microscopic degrees of freedom. Alternatively, hydrodynamic equations, closed by constitutive laws, can be used to predict the linear response of stress to an applied shear flow.

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Section: Time-and Space-dependent Correlationsmentioning

confidence: 99%

Emergence of Goldstone excitations in stress correlations of glass-forming colloidal dispersions

Vogel¹,

Zippelius²,

Fuchs³

2019

EPL

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“…A goal of future investigations would be to derive the values of these coefficients from first principles. Furthermore, investigating the effects of external driving such as shear, see [97] for a mode-coupling study of glassy states, would be worthwhile, as would be to relate to the stress correlation function [98].…”

Section: Discussionmentioning

confidence: 99%

Dynamic decay and superadiabatic forces in the van Hove dynamics of bulk hard sphere fluids

2022

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We study the dynamical decay of the van Hove function of Brownian hard spheres using event-driven Brownian dynamics simulations and dynamic test particle theory. Relevant decays mechanisms include deconfinement of the self particle, decay of correlation shells, and shell drift. Comparison to results for the Lennard-Jones system indicates the generality of these mechanisms for dense overdamped liquids. We use dynamical density functional theory on the basis of the Rosenfeld functional with self interaction correction. Superadiabatic forces are analysed using a recent power functional approximation. The power functional yields a modified Einstein long-time self diffusion coefficient in good agreement with simulation data.

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“…The nonlocal stress correlations can equivalently be computed from purely hydrodynamic considerations, 6,7,9,15 decomposing the flow field into the externally imposed flow and a fluctuating part. The response function to the externally imposed flow is related via the fluctuation-dissipation theorem to the correlation function, discussed here.…”

Section: Discussionmentioning

confidence: 99%