The stochastic motion of ratchets is studied in the context of driven or pumped two-state models. For completely ordered tracks, the ratchets can be characterized both by an effective drift velocity and an effective diffusion coefficient on large scales. These properties are strongly perturbed by the presence of frozen disorder or defects along the tracks. Depending on the defect concentration and on the transition rates between the two states, the ratchets now exhibit several scaling regimes with anomalous transport properties. [S0031-9007 (97)04225-7] PACS numbers: 05.40. + j, 05.70.Ln, 87.10. + e Ratchets are model systems for nonequilibrium transport based on the rectification of thermal fluctuations. This rectification can arise from chemical reactions as envisaged in the classical work on muscle contraction [1] or if different parts of the ratchet are at different (effective) temperatures [2]. Recently, new experimental results on motor proteins [3] have stimulated a lot of theoretical work on such ratchets [4][5][6][7][8][9]. In addition, ratchets have also been discussed theoretically as models for intracellular energy transduction via protrusive forces [10], and artificial ratchets have been constructed experimentally using microstructured electrodes [11] and optical tweezers [12].Most of this work was concerned with single-particle ratchets. Such a ratchet has the following basic features: (i) It consists of a "particle" which can move along a onedimensional "track" where it is subject to a spatially asymmetric potential. The average potential is flat, however, and there is no average force acting on the particle. (ii) The particle can overcome the barriers of the potential via thermally excited fluctuations. (iii) The particle also feels a time-dependent external driving force or pumping mechanism which acts to rectify these thermal fluctuations.In all previous work on single-particle ratchets, the asymmetric potential was taken to be periodic in space corresponding to a completely ordered track. In contrast, we will consider tracks which contain a certain amount of frozen disorder or defects and study the effects of this disorder on the transport properties of the ratchet. In order to illustrate our results, we will explicitly discuss ratchets with sawtooth potentials for which the defects correspond to reversed sawteeth as shown in Fig. 1.It will be shown below that defects act to reduce the efficiency of the ratchets and that this efficiency loss has two general and nontrivial features: (i) The motion of the ratchets is most sensitive to the frozen disorder if it operates in the "resonance regime," i.e., in the regime where it is most effective in the absence of disorder, and (ii) depending on the defect concentration, the ratchets exhibit several scaling regimes with anomalous diffusion and/or anomalous drift. These regimes should be accessible to experiments on natural or artificial ratchets.To proceed, we will consider a particle which moves along a one-dimensional track with coordinate x and whi...

No abstract

SUMMARY With the aim of accurately modelling free‐surface flow of two immiscible fluids, this study presents the development of a new volume‐of‐fluid free‐surface capturing formulation. By building on existing volume‐of‐fluid approaches, the new formulation combines a blended higher resolution scheme with the addition of an artificial compressive term to the volume‐of‐fluid equation. This reduces the numerical smearing of the interface associated with explicit higher resolution schemes while limiting the contribution of the artificial compressive term to ensure the integrity of the interface shape is maintained. Furthermore, the computational efficiency of the the higher resolution scheme is improved through the reformulation of the normalised variable approach and the implementation of a new higher resolution blending function. The volume‐of‐fluid equation is discretised via an unstructured vertex‐centred finite volume method and solved via a Jacobian‐type dual time‐stepping approach. Copyright © 2012 John Wiley & Sons, Ltd.

No abstract

No abstract