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Адрес: Московская область, г. Черноголовка, просп. академика Семенова, д. 1-A
Адрес: Москва, ул. Ст. Басманная, д. 21/4, стр. 5
Persistent motion of passive asymmetric bodies in non-equilibrium media has been experimentally observed in a variety of settings. However, fundamental constraints on the efficiency of such motion are not fully explored. Understanding such limits, and ways to circumvent them, is important for efficient utilization of energy stored in agitated surroundings for purposes of taxis and transport. Here, we examine such issues in the context of erratic movements of a passive asymmetric dumbbell driven by non-equilibrium noise. For uncorrelated (white) noise, we find a (non-Boltzmann) joint probability distribution for the velocity and orientation, which indicates that the dumbbell preferentially moves along its symmetry axis. The dumbbell thus behaves as an Ornstein–Uhlenbeck walker, a prototype of active matter. Exploring the efficiency of this active motion, we show that in the over-damped limit, the persistence length l of the dumbbell is bound from above by half its mean size, while the propulsion speed v∥ is proportional to its inverse size. The persistence length can be increased by exploiting inertial effects beyond the over-damped regime, but this improvement always comes at the price of smaller propulsion speeds. This limitation is explained by noting that the diffusivity of a dumbbell, related to the product v∥ l, is always less than that of its components, thus severely constraining the usefulness of passive dumbbells as active particles.
We demonstrate that two surface waves propagating at a small angle 2θ to each other generate large-scale (compared to the wavelength) vertical vorticity owing to hydrodynamic nonlinearity in a viscous fluid. The horizontal geometric structure of the induced flow coincides with the structure of the Stokes drift in an ideal fluid, but its steady-state amplitude is larger and it penetrates deeper into the fluid volume as compared to the Stokes drift. In an unbounded fluid, the steady-state amplitude and penetration depth are increased by the factor of 1/sinθ and the evolution time of the induced flow can be estimated as 1/(4νk^2 sin^2 θ), where ν is the fluid kinematic viscosity and k is the wave number. Also, we study how the finite depth of the fluid and a thin insoluble liquid film that possibly covers the fluid surface due to contamination effect the generation of large-scale vorticity and discuss the physical consequences of this phenomenon in the context of recent experiments.
Restart—interrupting a stochastic process followed by a new start—is known to improve the mean time to its completion, and the general conditions under which such an improvement is achieved are now well understood. Here, we explore how restart affects other important metrics of first-passage phenomena, namely, the median and the mode of the first-passage time distribution. Our analysis provides a general criterion for when restart lowers the median time and demonstrates that restarting is always helpful in reducing the mode. Additionally, we show that simple nonuniform restart strategies allow to optimize the mean and the median first-passage times, regardless of the characteristic timescales of the underlying process. These findings are illustrated with the canonical example of a diffusive search with resetting.
The effective lifetime of a quantum state can increase (the quantum Zeno effect) or decrease (the quantum anti-Zeno effect) in the response to increasing frequency of the repeated measurements and the multiple transitions between these two regimes are potentially possible within the same system. An interesting question arising in this regards is how to choose the optimal schedule of repeated measurements to achieve the maximal possible decay rate of a given quantum state. Addressing the issue of optimality in the quantum Zeno dynamics, we derive a range of rigorous results, which are, due to generality of the theoretical framework adopted here, applicable to the majority of models appeared in the quantum Zeno literature. In particular, we prove the universal dominance of the regular stroboscopic sampling in the sense that it always provides the shortest expected decay time among all possible measurement procedures. However, the implementation of the stroboscopic protocol requires the knowledge of the optimal sampling period which may depend on the fine details of the quantum problem. We demonstrate that this difficulty can be overcome with the tricky non-regular measurement schedule inspired by the scale-free restart strategy used to speed up the completion of the probabilistic algorithms and Internet tasks in computer science as it allows to achieve a near-optimal decay rate in the absence of detailed knowledge of the underlying quantum statistics. Besides, our general approach reveals unexpected universality displayed by the quantum systems subject to the optimally tuned rate of Poissonian measurements and the simple statistical criteria to discriminate between Zeno and anti-Zeno regimes following from this universality. We illustrate our findings with an example of Zeno dynamics in the system of optically-trapped ultra-cold atoms and discuss the implications arising from them.