26 research outputs found
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 steps above the top of the semicircle or the triangle. We
show that , i.e. \left shares the KPZ
statistics for the semicircle, while for the triangle. We propose
heuristic derivations of scaling exponents 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