Anomalous 1D fluctuations of a simple 2D random walk in a large deviation regime

The following question is the subject of our work: could a two-dimensional random path pushed by some constraints to an improbable "large deviation regime", possess extreme statistics with one-dimensional Kardar-Parisi-Zhang (KPZ) fluctuations? The answer is positive, though non-universal, since the fluctuations depend on the underlying geometry. We consider in details two examples of 2D systems for which imposed external constraints force the underlying stationary stochastic process to stay in an atypical regime with anomalous statistics. The first example deals with the fluctuations of a stretched 2D random walk above a semicircle or a triangle. In the second example we consider a 2D biased random walk along a channel with forbidden voids of circular and triangular shapes. In both cases we are interested in the dependence of a typical span \left \sim t^{\gamma} of the trajectory of $t$ steps above the top of the semicircle or the triangle. We show that $\gamma = \frac{1}{3}$, i.e. \left shares the KPZ statistics for the semicircle, while $\gamma=0$ for the triangle. We propose heuristic derivations of scaling exponents $\gamma$ for different geometries, justify them by explicit analytic computations and compare with numeric simulations. For practical purposes, our results demonstrate that the geometry of voids in a channel might have a crucial impact on the width of the boundary layer and, thus, on the heat transfer in the channel.Comment: 17 pages, 8 figures, some parts of the paper are rewritte

Eigenvalue detachment, BBP transition and constrained Brownian motion

We discuss the eigenvalue detachment transition in terms of scaling of fluctuations in ensembles of paths located near convex boundaries of various physical nature. We consider numerically the BBP-like (Baik-Ben Arous-P\'ech\'e) transition from the Gaussian to the Tracy-Widom scaling of fluctuations in several statistical systems for both canonical and microcanonical ensembles and identify the corresponding control parameter in each case. In particular, for fixed path length (microcanonical) ensemble of paths located in the vicinity of a partially permeable semicircle, the transition occurs at the critical value of a permeability. The Tracy-Widom regime and the BBP-like transition for fluctuations are discussed in terms of the Jakiw-Teitelbom (JT) gravity with a radial cutoff which, in turn, has an interpretation as a ensemble of fixed length world-line geometrically constrained trajectories of a charged particle in an effective transversal magnetic field.Comment: 24 pages, 6 figure

Spontaneous synchronization of two bistable pyridine-furan nanosprings connected by an oligomeric bridge

The intensive development of nanodevices acting as two-state systems has motivated the search for nanoscale molecular structures whose long-term conformational dynamics are similar to the dynamics of bistable mechanical systems such as Euler arches and Duffing oscillators. Collective synchrony in bistable dynamics of molecular-sized systems has attracted immense attention as a potential pathway to amplify the output signals of molecular nanodevices. Recently, pyridin-furan oligomers of helical shape that are a few nanometers in size and exhibit bistable dynamics similar to a Duffing oscillator have been identified through molecular dynamics simulations. In this article, we present the case of dynamical synchronization of these bistable systems. We show that two pyridine-furan springs connected by a rigid oligomeric bridge spontaneously synchronize vibrations and stochastic resonance enhances the synchronization effect

Spontaneous Vibrations and Stochastic Resonance of Short Oligomeric Springs

There is growing interest in molecular structures that exhibit dynamics similar to bistable mechanical systems. These structures have the potential to be used as nanodevices with two distinct states. Particularly intriguing are structures that display spontaneous vibrations and stochastic resonance. Previously, through molecular dynamics simulations, it was discovered that short pyridine-furan springs, when subjected to force loading, exhibit the bistable dynamics of a Duffing oscillator. In this study, we extend these simulations to include short pyridine-pyrrole and pyridine-furan springs in a hydrophobic solvent. Our findings demonstrate that these systems also display the bistable dynamics of a Duffing oscillator, accompanied by spontaneous vibrations and stochastic resonance activated by thermal noise.Comment: arXiv admin note: substantial text overlap with arXiv:2110.0409

Секреты создания успешных брендов в России и за рубежом

Статья посвящена актуальной на сегодняшний день проблеме создания успешных брендов на российском рынке и за рубежом. В настоящее время развитие у отечественного брендинга продолжается, и многие компании берут за основу иностранный путь создания бренда, поскольку их рынок очень хорошо развит в этом направлении. Значительное внимание уделяется изучению основных положений создания успешного бренда