Diffusion of a Brownian ellipsoid in a force field

Abstract

We calculate the effective long-term convective velocity and dispersive motion of an ellipsoidal Brownian particle in three dimensions when it is subjected to a constant external force. This long-term motion results as a "net" average behavior from the particle rotation and translation on short time scales. Accordingly, we apply a systematic multi-scale technique to derive the effective equations of motion valid on long times. We verify our theoretical results by comparing them to numerical simulations.

Steady diffusion in a drift field: A comparison of large-deviation techniques and multiple-scale analysis

“…The cumulant technique also gives access to higher moments of the displacement. We will also show that a similar behavior as (1), which we recently found for the case of a rotating Brownian particle with a continuous internal state (the particle's orientation) [20] can also be derived from a large deviation argument and second order time-independent perturbation theory. The second goal of the paper is to bring effects such as (1) anew to the attention of the singlemolecule biophysics community, as a possible means to indirectly measure kinetic rates.…”

“…In two additional Appendices C and D we extend for completeness the large deviation analysis to the case of a continuum of internal states, of which one example is a Brownian particle undergoing translation and rotation. We show that an auxiliary equation which appeared in an earlier multiple-scale analysis [20,25], can also be derived by second-order perturbation theory of generating function of the time spent in different orientations. We further show that the large deviation analysis can also be pushed to the third centered moment which we show to generically increase linearly in time, see Appendix D.…”

“…For the term B (2) we introduce yet another auxiliary quantity When m 0 is the Haar measure the averages in (D10) (D12) can be computed by invariance arguments as in [20] and [25].…”

“…Eqs. (C20), (C22) and (C23) generalize the corresponding expressions from[20] to cases where steady state probability is not necessarily uniform.…”

“…Tr[µ]1 jl and the quantity in the parenthesis on the right-hand side of (C20) is the traceless part of the mobility matrix. In[20] and[25] this quantity was denotedγ −1 . Eqs.…”