Calculation of displacement correlation tensor indicating vortical cooperative motion in two-dimensional colloidal liquids.

As an indicator of cooperative motion in a system of Brownian particles that models two-dimensional colloidal liquids, a displacement correlation tensor is calculated analytically and compared with numerical results. The key idea for the analytical calculation is to relate the displacement correlation tensor, which is a kind of four-point space-time correlation, to the Lagrangian two-time correlation of the deformation gradient tensor. Tensorial treatment of the statistical quantities, including the displacement correlation itself, allows capturing the vortical structure of the cooperative motion. The calculated displacement correlation also implies a negative long-time tail in the velocity autocorrelation, which is a manifestation of the cage effect. Both the longitudinal and transverse components of the displacement correlation are found to be expressible in terms of a similarity variable, suggesting that the cages are nested to form a self-similar structure in the space-time.

• Publication year

  2016

• Venue

  Physical Review E

• Publication date

  2016-04-12

• Fields of study

  Medicine, Physics, Chemistry, Mathematics

• Identifiers
  DOI 10.1103/PhysRevE.94.022125arXiv 1604.03467PMID 27627264
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• The longitudinal and transverse components of the displacement correlation can be written in terms of a similarity variable, consistent with a self-similar cage structure.

  Confidence 0.93

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewKiller Whale (322360f1c1) reviewAK (4715169a40) review
• The calculated displacement correlation implies a negative long-time tail in the velocity autocorrelation as a manifestation of the cage effect.

  Confidence 0.96

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewKiller Whale (322360f1c1) reviewAK (4715169a40) review
• The tensor formulation is used to capture the vortical structure of cooperative motion.

  Confidence 0.90

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewKiller Whale (322360f1c1) reviewAK (4715169a40) review
• The displacement correlation tensor is analytically related to the Lagrangian two-time correlation of the deformation gradient tensor.

  Confidence 0.97

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewKiller Whale (322360f1c1) reviewAK (4715169a40) review

• brownian particles

  particle model, system component

  The model particles whose stochastic motion is used to represent the colloidal liquid.

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewKiller Whale (322360f1c1) reviewAK (4715169a40) review
• cage effect

  phenomenon, dynamical effect

  The transient trapping of a particle by its neighbors in a dense liquid environment.

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewKiller Whale (322360f1c1) reviewAK (4715169a40) review
• deformation gradient tensor

  tensor, deformation measure

  A tensor that describes local deformation and is used in its Lagrangian two-time correlation.

  Aliases: deformation gradient

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewKiller Whale (322360f1c1) reviewAK (4715169a40) review
• displacement correlation tensor

  tensor, correlation measure

  A tensor-valued correlation of particle displacements used to characterize cooperative motion in the colloidal liquid.

  Aliases: displacement-correlation tensor

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewKiller Whale (322360f1c1) reviewAK (4715169a40) review
• similarity variable

  variable, scaling concept

  A scaling variable used to express the longitudinal and transverse displacement-correlation components in a common form.

  Aliases: scaling variable

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewKiller Whale (322360f1c1) reviewAK (4715169a40) review
• two-dimensional colloidal liquids

  system, material

  The two-dimensional dense colloidal system studied as the setting for the cooperative dynamics.

  Aliases: 2D colloidal liquids

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewKiller Whale (322360f1c1) reviewAK (4715169a40) review
• velocity autocorrelation

  correlation measure, dynamical quantity

  The time correlation of a particle's velocity, considered here for its long-time behavior.

  Aliases: VACF

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewKiller Whale (322360f1c1) reviewAK (4715169a40) review
• vortical cooperative motion

  phenomenon, motion pattern

  Coordinated particle motion with vortex-like spatial structure in the colloidal liquid.

  Aliases: vortical motion

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewKiller Whale (322360f1c1) reviewAK (4715169a40) review

• Principles Of Condensed Matter Physics

  2016cited by this paper
• From single-file diffusion to two-dimensional cage diffusion and generalization of the totally asymmetric simple exclusion process to higher dimensions.

  2016cited by this paper
• Mathematical Foundations Of Elasticity

  2016cited by this paper
• Cage effect in supercooled molecular liquids: Local anisotropies and collective solid-like response.

  2016cited by this paper
• Insights from Single-File Diffusion into Cooperativity in Higher Dimensions

  2015cited by this paper
• Exact probability distribution for the two-tag displacement in single-file motion

  2015cited by this paper
• Displacement correlation as an indicator of collective motion in one-dimensional and quasi-one-dimensional systems of repulsive Brownian particles

  2015cited by this paper
• Renormalized dynamics of the Dean-Kawasaki model.

  2015cited by this paper
• Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids.

  2015cited by this paper
• Equilibrium dynamics of the Dean-Kawasaki equation: mode-coupling theory and its extension.

  2014cited by this paper
• Long-range spatial correlations of particle displacements and the emergence of elasticity.

  2014cited by this paper
• Nonlinear Fluctuating Hydrodynamics for Anharmonic Chains

  2013cited by this paper
• Statistically interacting vacancy particles.

  2013cited by this paper
• Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.

  2013cited by this paper
• Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: configuration changes and vibration modes.

  2012cited by this paper
• Slow relaxations and stringlike jump motions in fragile glass-forming liquids: breakdown of the Stokes-Einstein relation.

  2012cited by this paper
• Analytical calculation of four-point correlations for a simple model of cages involving numerous particles.

  2012cited by this paper
• Glass elasticity from particle trajectories.

  2011cited by this paper
• Statistical Physics of Liquids at Freezing and Beyond

  2011cited by this paper
• Journal of Statistical Mechanics: Theory and Experiment

  2011cited by this paper
• Continuum Theory of Single-File Diffusion in Terms of Label Variable

  2011cited by this paper
• Effective Edwards-Wilkinson equation for single-file diffusion.

  2010cited by this paper
• Theoretical perspective on the glass transition and amorphous materials

  2010cited by this paper
• Numerical Study of Roton-Like Collective Excitations in Glassy Materials

  2009cited by this paper
• Geometric interpretation of previtrification in hard sphere liquids.

  2009cited by this paper
• Foundation of fractional Langevin equation: harmonization of a many-body problem.

  2009cited by this paper
• A survey of known results and research areas for n-queens

  2009cited by this paper
• Density of states of colloidal glasses.

  2009cited by this paper
• Stochastic Methods: A Handbook for the Natural and Social Sciences

  2009cited by this paper
• Langevin formulation for single-file diffusion.

  2008cited by this paper
• A fluctuation-dissipation relationship-preserving field theory for interacting Brownian particles: one-loop theory and mode coupling theory

  2008cited by this paper
• Continuum theory of memory effect in crack patterns of drying pastes.

  2008cited by this paper
• Compressing nearly hard sphere fluids increases glass fragility

  2008cited by this paper
• Dynamics of interacting Brownian particles: a diagrammatic formulation.

  2007cited by this paper
• FAST TRACK COMMUNICATION: The mode coupling theory in the FDR-preserving field theory of interacting Brownian particles

  2007cited by this paper
• Spontaneous and induced dynamic fluctuations in glass formers. I. General results and dependence on ensemble and dynamics.

  2006cited by this paper
• Velocity autocorrelation functions of hard-sphere fluids: Long-time tails upon undercooling

  2006cited by this paper
• Dynamical susceptibility of glass formers: contrasting the predictions of theoretical scenarios.

  2005cited by this paper
• Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry

  2005cited by this paper
• ERRATUM: On the rigidity of a hard-sphere glass near random close packing

  2005cited by this paper
• LETTER TO THE EDITOR: Mode-coupling theory and the fluctuation dissipation theorem for nonlinear Langevin equations with multiplicative noise

  2004cited by this paper
• Mode-coupling theory and the glass transition in supercooled liquids

  2004cited by this paper
• Extended ensemble Monte Carlo approach to hardly relaxing problems

  2002cited by this paper
• Time-dependent, four-point density correlation function description of dynamical heterogeneity and decoupling in supercooled liquids

  2000cited by this paper
• Collective Motion

  1999cited by this paper
• Cahn-hilliard theory for unstable granular fluids

  1999cited by this paper
• Cooperativity and spatial correlations near the glass transition: computer simulation results for hard spheres and disks.

  1999cited by this paper
• How Does the Relaxation of a Supercooled Liquid Depend on Its Microscopic Dynamics

  1998cited by this paper
• Growing Spatial Correlations of Particle Displacements in a Simulated Liquid on Cooling toward the Glass Transition

  1998cited by this paper
• Vortex dynamics in turbulence

  1998cited by this paper
• Dynamics of highly supercooled liquids: Heterogeneity, rheology, and diffusion

  1998cited by this paper
• Structural heterogeneity in supercooled liquids and glasses

  1998cited by this paper
• Positivity of the self-diffusion matrix of interacting Brownian particles with hard core

  1998cited by this paper
• Microscopic Analyses of the Dynamical Density Functional Equation of Dense Fluids

  1998cited by this paper
• Statistical mechanics of a two-dimensional system with long-range interactions

  1997cited by this paper
• Algebraic Decay of Velocity Fluctuations in a Confined Fluid

  1997cited by this paper
• 日本物理学会講演概要集 = Meeting abstracts of the Physical Society of Japan

  1997cited by this paper
• LETTER TO THE EDITOR: Langevin equation for the density of a system of interacting Langevin processes

  1996cited by this paper
• Turbulence: The Legacy of A. N. Kolmogorov

  1996cited by this paper
• Calculation of velocity structure functions for vortex models of isotropic turbulence

  1996cited by this paper
• Mesoscopic Modeling in the Kinetic Theory of Adsorbates

  1996cited by this paper
• On the foundations of synergetics

  1996cited by this paper
• An introduction to dynamics of colloids

  1996cited by this paper
• beta relaxation in a highly supercooled state via molecular dynamics simulation.

  1995cited by this paper
• Stochastic Processes in Physics and Chemistry

  1995cited by this paper
• Fluid mechanics

  1994cited by this paper
• Stochastic model of slow dynamics in supercooled liquids and dense colloidal suspensions

  1994cited by this paper
• Relaxation and growth of concentration fluctuations in binary fluids and polymer blends

  1993cited by this paper
• Is there a growing correlation length near the glass transition? (Addendum)

  1991cited by this paper
• Two-tag correlation functions in one-dimensional lattice gases

  1991cited by this paper
• Mode-coupling theory of the glass transition in colloidal systems.

  1991cited by this paper
• Mean square displacement of a tracer particle in a hard-core lattice gas.

  1985cited by this paper
• Diffusion in concentrated lattice gases. III. Tracer diffusion on a one-dimensional lattice

  1983cited by this paper
• The surface statistics of a granular aggregate

  1982cited by this paper
• Site Blocking Effect in Tracer Diffusion on a Lattice

  1980cited by this paper
• Kinetic theory of self-motion in monatomic liquids

  1979cited by this paper
• Dynamics of Polymeric Liquids

  1978cited by this paper
• Diffusion of labeled particles on one-dimensional chains

  1978cited by this paper
• Decay of the Velocity Autocorrelation Function

  1970cited by this paper

• Displacement correlations in a two-dimensional colloidal liquid and their relationship with shear strain correlations.

  2024influential citation
• The Dean–Kawasaki equation and stochastic density functional theory

  2024cites this paper
• Kinetic analysis of pore formation in die-cast metals and influence of absolute pressure on porosity

  2019cites this paper
• Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking

  2018cites this paper
• Two-tag correlations and nonequilibrium fluctuation–response relation in ageing single-file diffusion

  2018cites this paper
• Effects of Cage-Breaking Events in Single-File Diffusion on Elongation Correlation

  2017cites this paper
• Thermodynamic scaling of relaxation: insights from anharmonic elasticity

  2017cites this paper
• Thermodynamic scaling of vibrational dynamics and relaxation.

  2016cites this paper
• Insights from Single-File Diffusion into Cooperativity in Higher Dimensions

  2015cites this paper