Dumbbell diffusion in a spatially periodic potential

Diffusion of active dimers in a Couette flow

We study the 3D dynamics of an elastic dimer consisting of an active swimmer bound to a passive cargo, both suspended in a Couette flow. Using numerical simulations, we determine the diffusivity of such an active dimer in the presence of long-range hydrodynamic interactions for different values of its self-propulsion speed and the Couette flow. We observe that the effect of hydrodynamic interactions is greatly enhanced under the condition that self-propulsion is strong enough to contrast the shear flow. The magnitude of the effect grows with the size of the dimer's constituents relative to their distance, which makes it appreciable under experimental conditions.

Dimer motion on a periodic substrate: spontaneous symmetry breaking and absolute negative mobility

We consider two coupled particles moving along a periodic substrate potential with negligible inertia effects (overdamped limit). Even when the particles are identical and the substrate spatially symmetric, a sinusoidal external driving of appropriate amplitude and frequency may lead to spontaneous symmetry breaking in the form of a permanent directed motion of the dimer. Thermal noise restores ergodicity and thus zero net velocity, but entails arbitrarily fast diffusion of the dimer for sufficiently weak noise. Moreover, upon application of a static bias force, the dimer exhibits a motion opposite to that force (absolute negative mobility). The key requirement for all these effects is a nonconvex interaction potential of the two particles.

Dynamics of two trapped Brownian particles: Shear-induced cross-correlations

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 shear rate and the trap distance. Shear-induced cross-correlations between particle fluctuations along orthogonal directions in the shear plane are found. They are linear in the shear rate, asymmetric in time, and occur for one particle as well as between both particles. Moreover, the shear rate enters as a quadratic correction to the well-known correlations of random displacements along parallel spatial directions. The correlation functions depend on the orientation of the connection vector between the potential minima with respect to the flow direction. As a consequence, the inter-particle cross-correlations between orthogonal fluctuations can have zero, one or two local extrema as a function of time. Possible experiments for detecting these predicted correlations are described.

Diffusion dynamics and first passage time in a two-coupled pendulum system

We present the numerical investigation of diffusion process and features of first passage time (FPT) and mean FPT (MFPT) in a two-coupled damped and periodically driven pendulum system. The effect of amplitude of the external periodic force and phase of the force on diffusion constant, distribution of FPT, P(tFPT), and MFPT is analyzed. Normal diffusion is found. Diffusion constant is found to show power-law variation near intermittency and sudden widening crises while linear variation is observed in the quasiperiodic region. In the intermittency crisis the divergence of diffusion constant is similar to the divergence of mean bursting length. P(tFPT) of critical distances of state variable exhibit periodic multiple peaks with decaying amplitude. MFPT of critical distances also follows power-law variation. Diffusion constant and MFPT are sensitive to the phase factor of the periodic force.

Dynamics of a trapped Brownian particle in shear flows

The Brownian motion of a particle in a harmonic potential, which is simultaneously exposed either to a linear shear flow or to a plane Poiseuille flow is investigated. In the shear plane of both flows the probability distribution of the particle becomes anisotropic and the dynamics is changed in a characteristic manner compared to a trapped particle in a quiescent fluid. The particle distribution takes either an elliptical or a parachute shape or a superposition of both depending on the mean particle position in the shear plane. Simultaneously, shear-induced cross-correlations between particle fluctuations along orthogonal directions in the shear plane are found. They are asymmetric in time. In Poiseuille flow thermal particle fluctuations perpendicular to the flow direction in the shear plane induce a shift of the particle's mean position away from the potential minimum. Two complementary methods are suggested to measure shear-induced cross-correlations between particle fluctuations along orthogonal directions.

Ratcheting of neutral elastic dimers on a charged filament

We consider an elastic neutral dimer formed by two bound equal masses carrying opposite charges and moving along an electrically active filament in one dimension. An ac electrical field drives the two dimer heads, when set free or bound together to form a rigid rod, to opposite directions, thus yielding a zero net dimer current for zero and infinite elastic constants. Under the same driving conditions, an elastically deformable dimer can get rectified and the ensuing net current maximized for an optimal value of dimer elastic constant. The dependence of the dimer current on the periodic charge distribution along the filament is analyzed in terms of global symmetries of the dimer dynamics.

Dumbbell transport and deflection in a spatially periodic potential

We present theoretical results on the deterministic and stochastic motion of a dumbbell carried by a uniform flow through a three-dimensional spatially periodic potential. Depending on parameters like the flow velocity, there are two different kinds of movement: transport along a potential valley and a stair-like motion oblique to the potential trenches. The crossover between these two regimes, as well as the deflection angle, depend on the size of the dumbbell. Moreover, thermal fluctuations cause a resonance-like variation in the deflection angle as a function of the dumbbell extension.