{'fraction_non_alphanumeric': 0.02648440837249039, 'fraction_numerical': 0.003844510892780863, 'mean_word_length': 5.262032085561497, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Computation of transport in Brownian ratchets.

In Brownian ratchets the presence of random fluctuations (noise) can lead to directed diffusion in a periodic potential under nonequilibrium conditions, i.e. to a net unidirectional current. Such processes are thought to underlie macromolecular transport in biological cells and muscle contraction, and they provide a possible basis for nanoscale machinery. In flashing ratchets, where the periodic potential changes discontinuously between two different configurations, transport can occur even under white noise because the nonequilibrium conditions are created by the configurational changes, and the net current is then relatively easy to calculate [1]. In correlation ratchets, on the other hand, the potential is fixed and the nonequilibrium conditions are typically created by the presence of non-white (coloured) noise or, as in the case that we will consider, by white noise with an additional periodic force. The caculation of the current then presents a much more challenging problem. In the present paper we describe how methods for controlling the direction and the amplitude of such currents are being investigated via numerical solution of a variational problem and by digital Monte-Carlo simulation. Under these conditions, the physical situation is closely related to resonant activation – a periodic field-induced resonant reduction of the lifetime of a metastable state, originally observed in a currentbiased Josephson junction [2]. The latter observation stimulated a wide-ranging discussion [3, 4, 5, 6] of the old theoretical problem of escape from a potential well in the presence of a nonadiabatic driving field. Surprisingly, measured field-induced corrections to the log of the activation rate, ln W , were found [6] to be ∝ A over a wide range of field amplitude A, in marked contrast with the ∝ A implied by the intuitively appealing physical picture of field-induced heating. The recently introduced logarithmic susceptibility (LS) [7, 8] is in principle capable of accounting for these observations. It also predicts new mechanisms of resonant rectification and the occurrence of a current reversal with changing parameters where the motion occurs in a spatially periodic asymmetric potential, i.e. in a ratchet. To check these ideas, the model we investigate is