3,988 research outputs found
Three-frequency resonances in dynamical systems
We investigate numerically and experimentally dynamical systems having three
interacting frequencies: a discrete mapping (a circle map), an exactly solvable
model (a system of coupled ordinary differential equations), and an
experimental device (an electronic oscillator). We compare the hierarchies of
three-frequency resonances we find in each of these systems. All three show
similar qualitative behaviour, suggesting the existence of generic features in
the parameter-space organization of three-frequency resonances.Comment: See home page http://lec.ugr.es/~julya
Global Diffusion in a Realistic Three-Dimensional Time-Dependent Nonturbulent Fluid Flow
We introduce and study the first model of an experimentally realizable
three-dimensional time-dependent nonturbulent fluid flow to display the
phenomenon of global diffusion of passive-scalar particles at arbitrarily small
values of the nonintegrable perturbation. This type of chaotic advection,
termed {\it resonance-induced diffusion\/}, is generic for a large class of
flows.Comment: 4 pages, uuencoded compressed postscript file, to appear in Phys.
Rev. Lett. Also available on the WWW from http://formentor.uib.es/~julyan/,
or on paper by reques
Noise and Inertia-Induced Inhomogeneity in the Distribution of Small Particles in Fluid Flows
The dynamics of small spherical neutrally buoyant particulate impurities
immersed in a two-dimensional fluid flow are known to lead to particle
accumulation in the regions of the flow in which rotation dominates over shear,
provided that the Stokes number of the particles is sufficiently small. If the
flow is viewed as a Hamiltonian dynamical system, it can be seen that the
accumulations occur in the nonchaotic parts of the phase space: the
Kolmogorov--Arnold--Moser tori. This has suggested a generalization of these
dynamics to Hamiltonian maps, dubbed a bailout embedding. In this paper we use
a bailout embedding of the standard map to mimic the dynamics of impurities
subject not only to drag but also to fluctuating forces modelled as white
noise. We find that the generation of inhomogeneities associated with the
separation of particle from fluid trajectories is enhanced by the presence of
noise, so that they appear in much broader ranges of the Stokes number than
those allowing spontaneous separation
Arms and the mollusc: An evolutionary arms race has produced armor based on molluscan biomineralization
A.G.C. acknowledges funding from Project No. PID2020116660GB-I00, funded by Spanish Ministry of Science and Innovation (MCIN/AEI/10.13039/ 501100011033).
Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.More than half a billion years ago in the early Cambrian period, there began an evolutionary arms race between molluscs and their predators, in which molluscs developed armor in the form of a biomineral exoskeletonâa shellâto avoid being eaten by predators that were developing jaws and other novel means of devouring them. The mollusc fabricates multiple layers of shell, each of a particular microstructure of a composite between an inorganic and an organic phase, which are the end result of more than 500 million years of coevolution with increasingly deadly predators. Molluscan biomineralization is an excellent case to study how a biological process produces a complex structure, because the shell is constructed as an extracellular structure in which all construction materials are passed out of the cells to self-assemble outside the cell wall. We consider what is known of the development of multilayer composite armor in the form of nacre (mother of pearl) and the other strong microstructures with which molluscs construct their shells.MCIN/AEI/10.13039/ 501100011033 PID2020116660GB-I00CRUE-CSI
Nonlinear Dynamics of the Perceived Pitch of Complex Sounds
We apply results from nonlinear dynamics to an old problem in acoustical
physics: the mechanism of the perception of the pitch of sounds, especially the
sounds known as complex tones that are important for music and speech
intelligibility
Dynamics of Elastic Excitable Media
The Burridge-Knopoff model of earthquake faults with viscous friction is
equivalent to a van der Pol-FitzHugh-Nagumo model for excitable media with
elastic coupling. The lubricated creep-slip friction law we use in the
Burridge-Knopoff model describes the frictional sliding dynamics of a range of
real materials. Low-dimensional structures including synchronized oscillations
and propagating fronts are dominant, in agreement with the results of
laboratory friction experiments. Here we explore the dynamics of fronts in
elastic excitable media.Comment: Int. J. Bifurcation and Chaos, to appear (1999
Bailout Embeddings and Neutrally Buoyant Particles in Three-Dimensional Flows
We use the bailout embeddings of three-dimensional volume-preserving maps to
study qualitatively the dy- namics of small spherical neutrally buoyant
impurities suspended in a time-periodic incompressible fluid flow. The
accumulation of impurities in tubular vortical structures, the detachment of
particles from fluid trajectories near hyperbolic invariant lines, and the
formation of nontrivial three-dimensional structures in the distribution of
particles are predicted.Comment: 4 pages, 3 figure
Linear resolutions of powers and products
The goal of this paper is to present examples of families of homogeneous
ideals in the polynomial ring over a field that satisfy the following
condition: every product of ideals of the family has a linear free resolution.
As we will see, this condition is strongly correlated to good primary
decompositions of the products and good homological and arithmetical properties
of the associated multi-Rees algebras. The following families will be discussed
in detail: polymatroidal ideals, ideals generated by linear forms and Borel
fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi
deformation
Quantum and classical descriptions of a measuring apparatus
A measuring apparatus is described by quantum mechanics while it interacts
with the quantum system under observation, and then it must be given a
classical description so that the result of the measurement appears as
objective reality. Alternatively, the apparatus may always be treated by
quantum mechanics, and be measured by a second apparatus which has such a dual
description. This article examines whether these two different descriptions are
mutually consistent. It is shown that if the dynamical variable used in the
first apparatus is represented by an operator of the Weyl-Wigner type (for
example, if it is a linear coordinate), then the conversion from quantum to
classical terminology does not affect the final result. However, if the first
apparatus encodes the measurement in a different type of operator (e.g., the
phase operator), the two methods of calculation may give different results.Comment: 18 pages LaTeX (including one encapsulated PostScript figure
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