Nonequilibrium dynamical structure factor of a dilute suspension of active particles in a viscoelastic fluid.

In this work we investigate the dynamics of the number-density fluctuations of a dilute suspension of active particles in a linear viscoelastic fluid. We propose a model for the frequency-dependent diffusion coefficient of the active particles which captures the effect of rotational diffusion on the persistence of their self-propelled motion and the viscoelasticity of the medium. Using fluctuating hydrodynamics, the linearized equations for the active suspension are derived, from which we calculate its dynamic structure factor and the corresponding intermediate scattering function.

Fractional Time Fluctuations in Viscoelasticity: A Comparative Study of Correlations and Elastic Moduli.

We calculate the transverse velocity fluctuations correlation function of a linear and homogeneous viscoelastic liquid by using a generalized Langevin equation () approach. We consider a long-ranged (power-law) viscoelastic memory and a noise with a long-range (power-law) auto-correlation. We first evaluate the transverse velocity fluctuations correlation function for conventional time derivatives C ^ N F ( k → , t ) and then introduce time fractional derivatives in their equations of motion and calculate the corresponding fractional correlation function.