2,389 research outputs found
Optimal Phase Description of Chaotic Oscillators
We introduce an optimal phase description of chaotic oscillations by
generalizing the concept of isochrones. On chaotic attractors possessing a
general phase description, we define the optimal isophases as Poincar\'e
surfaces showing return times as constant as possible. The dynamics of the
resultant optimal phase is maximally decoupled of the amplitude dynamics, and
provides a proper description of phase resetting of chaotic oscillations. The
method is illustrated with the R\"ossler and Lorenz systems.Comment: 10 Pages, 14 Figure
Desynchronizing two oscillators while stimulating and observing only one
Synchronization of two or more self-sustained oscillators is a well-known and
studied phenomenon, appearing both in natural and designed systems. In some
cases, the synchronized state is undesired, and the aim is to destroy synchrony
by external intervention. In this paper, we focus on desynchronizing two
self-sustained oscillators by short pulses delivered to the system in a
phase-specific manner. We analyze a non-trivial case when we cannot access both
oscillators but stimulate only one. The following restriction is that we can
monitor only one unit, be it a stimulated or non-stimulated one. First, we use
a system of two coupled Rayleigh oscillators to demonstrate how a loss of
synchrony can be induced by stimulating a unit once per period at a specific
phase and detected by observing consecutive inter-pulse durations. Next, we
exploit the phase approximation to develop a rigorous theory formulating the
problem in terms of a map. We derive exact expressions for the phase --
isostable coordinates of this coupled system and show a relation between the
phase and isostable response curves to the phase response curve of the
uncoupled oscillator. Finally, we demonstrate how to obtain phase response
information from the system using time series and discuss the differences
between observing the stimulated and unstimulated oscillator
Dual -1 Hahn polynomials and perfect state transfer
We find all the spin chains with perfect state transfer (PST) that are
connected with the dual -1 Hahn polynomials . For
odd we recover a model that had already been identified while for even, we
obtain a new system exhibiting PST.Comment: 11 page
High-order phase reduction for coupled 2D oscillators
Phase reduction is a general approach to describe coupled oscillatory units
in terms of their phases, assuming that the amplitudes are enslaved. For such a
reduction, the coupling should be small, but one also expects the reduction to
be valid for finite coupling. This paper presents a general framework allowing
us to obtain coupling terms in higher orders of the coupling parameter for
generic two-dimensional oscillators and arbitrary coupling terms. The theory is
illustrated with an accurate prediction of Arnold's tongue for the van der Pol
oscillator exploiting higher-order phase reduction
A new model for mixing by double-diffusive convection (semi-convection): I. The conditions for layer formation
The process referred to as "semi-convection" in astrophysics and
"double-diffusive convection in the diffusive regime" in Earth and planetary
sciences, occurs in stellar and planetary interiors in regions which are stable
according to the Ledoux criterion but unstable according to the Schwarzschild
criterion. In this series of papers, we analyze the results of an extensive
suite of 3D numerical simulations of the process, and ultimately propose a new
1D prescription for heat and compositional transport in this regime which can
be used in stellar or planetary structure and evolution models.
In a preliminary study of the phenomenon, Rosenblum et al. (2011) showed
that, after saturation of the primary instability, a system can evolve in one
of two possible ways: the induced turbulence either remains homogeneous, with
very weak transport properties, or transitions into a thermo-compositional
staircase where the transport rate is much larger (albeit still smaller than in
standard convection).
In this paper, we show that this dichotomous behavior is a robust property of
semi-convection across a wide region of parameter space. We propose a simple
semi-analytical criterion to determine whether layer formation is expected or
not, and at what rate it proceeds, as a function of the background
stratification and of the diffusion parameters (viscosity, thermal diffusivity
and compositional diffusivity) only. The theoretical criterion matches the
outcome of our numerical simulations very adequately in the numerically
accessible "planetary" parameter regime, and can easily be extrapolated to the
stellar parameter regime.
Subsequent papers will address more specifically the question of quantifying
transport in the layered case and in the non-layered case.Comment: Submitted to Ap
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Molecular and functional basis of phenotypic convergence in white lizards at White Sands
There are many striking examples of phenotypic convergence in nature, in some cases associated with changes in the same genes. But even mutations in the same gene may have different biochemical properties and thus different evolutionary consequences. Here we dissect the molecular mechanism of convergent evolution in three lizard species with blanched coloration on the gypsum dunes of White Sands, New Mexico. These White Sands forms have rapidly evolved cryptic coloration in the last few thousand years, presumably to avoid predation. We use cell-based assays to demonstrate that independent mutations in the same gene underlie the convergent blanched phenotypes in two of the three species. Although the same gene contributes to light phenotypes in these White Sands populations, the specific molecular mechanisms leading to reduced melanin production are different. In one case, mutations affect receptor signaling and in the other, the ability of the receptor to integrate into the melanocyte membrane. These functional differences have important ramifications at the organismal level. Derived alleles in the two species show opposite dominance patterns, which in turn affect their visibility to selection and the spatial distribution of alleles across habitats. Our results demonstrate that even when the same gene is responsible for phenotypic convergence, differences in molecular mechanism can have dramatic consequences on trait expression and ultimately the adaptive trajectory.Organismic and Evolutionary Biolog
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