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The resolution of Brownian motion in simulations of micro-particle suspensions can be crucial to reproducing the correct dynamics of individual particles, as well as providing an accurate characterisation of suspension properties. Including…
A microscopic approach is presented for calculating general properties of interacting Brownian particles under steady shearing. We start from exact expressions for shear-dependent steady-state averages, such as correlation and structure…
The nonlinear rheological properties of dense suspensions are discussed within simplified models, suggested by a recent first principles approach to the model of Brownian particles in a constant-velocity-gradient solvent flow. Shear…
Exact and asymptotic formulas relating to dynamical correlations for overdamped Brownian motion are obtained. These formulas include a generalization of the $f$-sum rule from the theory of quantum fluids, a formula relating the static…
The dynamics of two Brownian particles trapped by two neighboring harmonic potentials in a linear shear flow is investigated. The positional correlation functions in this system are calculated analytically and analyzed as a function of the…
Nonreciprocal effective interaction forces can occur between mesoscopic particles in colloidal suspensions that are driven out of equilibrium. These forces violate Newton's third law actio=reactio on coarse-grained length and time scales.…
We propose a reduction scheme for a system constituted by two coupled harmonically-bound Brownian oscillators. We reduce the description by constructing a lower dimensional model which inherits some of the basic features of the original…
Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method [Physica…
We study single-variable approaches for describing stochastic dynamics with small inertia. The basic models we deal with describe passive Brownian particles and phase elements (phase oscillators, rotators, superconducting Josephson…
We propose an alternative theory for the relaxation of density fluctuations in glass-forming fluids. We derive an equation of motion for the density correlation function which is local in time and is similar in spirit to the equation of…
In this work we numerically investigate a new method for the characterization of growing length scales associated with spatially heterogeneous dynamics of glass-forming liquids. This approach, motivated by the formulation of the…
The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently…
We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip…
We present a dynamic density functional theory (dDFT) which takes into accou nt the advection of the particles by a flowing solvent. For potential flows we can use the same closure as in the absence of solvent flow. The structure of the…
A microscopic theory of molecular motion in classical monatomic liquids, proposed by Glass and Rice [Phy. Rev. 176, 239 (1968)], is revisited and extended to incorporate the dynamic friction in the Brownian description of the atomic…
We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of…
Little is known about the coupling of rotation and translation in dense systems. Here, we report results of confocal fluorescence microscopy where simultaneous recording of translational and rotational particle trajectories from a…
As an indicator of cooperative motion in a system of Brownian particles that models two-dimensional colloidal liquids, displacement correlation tensor is calculated analytically and compared with numerical results. The key idea for the…
Concentrated colloidal suspensions are a well-tested model system which has a glass transition. Colloids are suspensions of small solid particles in a liquid, and exhibit glassy behavior when the particle concentration is high; the…
In this expository note we highlight the correlation function method as a unified approach in proving both hydrodynamic limits and fluctuation limits for reaction diffusion particle systems. For simplicity we focus on the case when the…