Enhanced diffusion and the eigenvalue band structure of Brownian motion in tilted periodic potentials

We consider enhanced diffusion for Brownian motion on a tilted periodic potential. Expressing the effective diffusion in terms of the eigenvalue band structure, we establish a connection between band gaps in the eigenspectrum and enhanced diffusion. We explain this connection for a simple cosine potential with a linear force and then generalize to more complicated potentials including one-dimensional potentials with multiple frequency components and nonseparable multidimensional potentials. We find that potentials with multiple band gaps in the eigenspectrum can lead to multiple maxima or broadening of the force-diffusion curve. These features are likely to be observable in experiments.

Thermodynamic uncertainty relations and molecular-scale energy conversion

The thermodynamic uncertainty relation (TUR) is a universal constraint for nonequilibrium steady states that requires the entropy production rate to be greater than the relative magnitude of current fluctuations. It has potentially important implications for the thermodynamic efficiency of molecular-scale energy conversion in both biological and artificial systems. An alternative multidimensional thermodynamic uncertainty relation (MTUR) has also been proposed. In this paper we apply the TUR and the MTUR to a description of molecular-scale energy conversion that explicitly contains the degrees of freedom exchanging energy via a time-independent multidimensional periodic potential. The TUR and the MTUR are found to be universal lower bounds on the entropy generation rate and provide upper bounds on the thermodynamic efficiency. The TUR is found to provide only a weak bound while the MTUR provides a much tighter constraint by taking into account correlations between degrees of freedom. The MTUR is found to provide a tight bound in the near or far from equilibrium regimes but not in the intermediate force regime. Collectively, these results demonstrate that the MTUR is more appropriate than the TUR for energy conversion processes, but that both diverge from the actual entropy generation in certain regimes.

Reconstructing free-energy landscapes for cyclic molecular motors using full multidimensional or partial one-dimensional dynamic information

Diffusion on a free-energy landscape is a fundamental framework for describing molecular motors. In the landscape framework, energy conversion between different forms of energy, e.g., chemical and mechanical, is explicitly described using multidimensional nonseparable potential landscapes. We present a k-space method for reconstructing multidimensional free-energy landscapes from stochastic single-molecule trajectories. For a variety of two-dimensional model potential landscapes, we demonstrate the robustness of the method by reconstructing the landscapes using full dynamic information, i.e., simulated two-dimensional stochastic trajectories. We then consider the case where the stochastic trajectory is known only along one dimension. With this partial dynamic information, the reconstruction of the full two-dimensional landscape is severely limited in the majority of cases. However, we reconstruct effective one-dimensional landscapes for the two-dimensional model potentials. We discuss the interpretation of the one-dimensional landscapes and identify signatures of energy conversion. Finally, we consider the implications of these results for biological molecular motors experiments.

Outcome of secondary intention healing of full thickness lower eyelid defects in dogs

OBJECTIVES

To assess healing of the canine lower eyelid without anatomical reconstruction.

MATERIALS AND METHODS

Retrospective case series of three client-owned dogs with lower eyelid defects. These dogs that underwent debridement of lower eyelid wounds that were left to heal by secondary intention were assessed for anatomical, functional and aesthetic outcomes.

RESULTS

Two of the cases had previously undergone tumour resection with a lip-to-lid reconstruction and, following flap failure, developed a full thickness defect. The third dog presented with a traumatic laceration. Each dog lost approximately 70 to 90% of the lower eyelid margin. Two received topical antimicrobial eye drops after debridement, while the third dog required no further treatment. Follow-up periods of 3 years, 15 months and 4 months were available. All owners were satisfied with the cosmetic outcome and provided pictures. One owner reported epiphora but no other ophthalmic complications occurred.

CLINICAL SIGNIFICANCE

The result of this small case series supports the notion that not all lower eyelid injuries or tumour resections require anatomical reconstruction. Selected cases can be left to heal by secondary intention with minimal post-operative complications.

Self-induced temperature gradients in Brownian dynamics

Brownian systems often surmount energy barriers by absorbing and emitting heat to and from their local environment. Usually, the temperature gradients created by this heat exchange are assumed to dissipate instantaneously. Here we relax this assumption to consider the case where Brownian dynamics on a time-independent potential can lead to self-induced temperature gradients. In the same way that externally imposed temperature gradients can cause directed motion, these self-induced gradients affect the dynamics of the Brownian system. The result is a coupling between the local environment and the Brownian subsystem. We explore the resulting dynamics and thermodynamics of these coupled systems and develop a robust method for numerical simulation. In particular, by focusing on one-dimensional situations, we show that self-induced temperature gradients reduce barrier-crossing rates. We also consider a heat engine and a heat pump based on temperature gradients induced by a Brownian system in a nonequilibrium potential.

Local discretization method for overdamped Brownian motion on a potential with multiple deep wells

We present a general method for transforming the continuous diffusion equation describing overdamped Brownian motion on a time-independent potential with multiple deep wells to a discrete master equation. The method is based on an expansion in localized basis states of local metastable potentials that match the full potential in the region of each potential well. Unlike previous basis methods for discretizing Brownian motion on a potential, this approach is valid for periodic potentials with varying multiple deep wells per period and can also be applied to nonperiodic systems. We apply the method to a range of potentials and find that potential wells that are deep compared to five times the thermal energy can be associated with a discrete localized state while shallower wells are better incorporated into the local metastable potentials of neighboring deep potential wells.

Intrinsic irreversibility limits the efficiency of multidimensional molecular motors

We consider the efficiency limits of Brownian motors able to extract work from the temperature difference between reservoirs or from external thermodynamic forces. These systems can operate in a variety of modes, including as isothermal engines, heat engines, refrigerators, and heat pumps. We derive analytical results showing that certain classes of multidimensional Brownian motor, including the Smoluchowski-Feynman ratchet, are unable to attain perfect efficiency (Carnot efficiency for heat engines). This demonstrates the presence of intrinsic irreversibilities in their operating mechanism. We present numerical simulations showing that in some cases the loss process that limits efficiency is associated with vortices in the probability current.

Tight-binding approach to overdamped Brownian motion on a bichromatic periodic potential

We present a theoretical treatment of overdamped Brownian motion on a time-independent bichromatic periodic potential with spatially fast- and slow-changing components. In our approach, we generalize the Wannier basis commonly used in the analysis of periodic systems to define a basis of S states that are localized at local minima of the potential. We demonstrate that the S states are orthonormal and complete on the length scale of the periodicity of the fast-changing potential, and we use the S-state basis to transform the continuous Smoluchowski equation for the system to a discrete master equation describing hopping between local minima. We identify the parameter regime where the master equation description is valid and show that the interwell hopping rates are well approximated by Kramers' escape rate in the limit of deep potential minima. Finally, we use the master equation to explore the system dynamics and determine the drift and diffusion for the system.

Thermal fluctuation statistics in a molecular motor described by a multidimensional master equation

We present a theoretical investigation of thermal fluctuation statistics in a molecular motor. Energy transfer in the motor is described using a multidimensional discrete master equation with nearest-neighbor hopping. In this theory, energy transfer leads to statistical correlations between thermal fluctuations in different degrees of freedom. For long times, the energy transfer is a multivariate diffusion process with constant drift and diffusion. The fluctuations and drift align in the strong-coupling limit enabling a one-dimensional description along the coupled coordinate. We derive formal expressions for the probability distribution and simulate single trajectories of the system in the near- and far-from-equilibrium limits both for strong and weak coupling. Our results show that the hopping statistics provide an opportunity to distinguish different operating regimes.

Molecular probe of pairing in the BEC-BCS crossover

We have used optical molecular spectroscopy to probe the many-body state of paired 6Li atoms near a broad Feshbach resonance. The optical probe projects pairs of atoms onto a vibrational level of an excited molecule. The rate of excitation enables a precise measurement of the closed-channel contribution to the paired state. This contribution is found to be quite small, supporting the concept of universality for the description of broad Feshbach resonances. The dynamics of the excitation provide clear evidence for pairing across the BEC-BCS crossover and into the weakly interacting BCS regime.