15,539 research outputs found
Controlling Chimeras
Coupled phase oscillators model a variety of dynamical phenomena in nature
and technological applications. Non-local coupling gives rise to chimera states
which are characterized by a distinct part of phase-synchronized oscillators
while the remaining ones move incoherently. Here, we apply the idea of control
to chimera states: using gradient dynamics to exploit drift of a chimera, it
will attain any desired target position. Through control, chimera states become
functionally relevant; for example, the controlled position of localized
synchrony may encode information and perform computations. Since functional
aspects are crucial in (neuro-)biology and technology, the localized
synchronization of a chimera state becomes accessible to develop novel
applications. Based on gradient dynamics, our control strategy applies to any
suitable observable and can be generalized to arbitrary dimensions. Thus, the
applicability of chimera control goes beyond chimera states in non-locally
coupled systems
Rare behaviour of a catalyst pellet catalyst dynamics
Temperature overshoots and undershoots were found for a Pd on alumina catalyst pellet in its course towards a new steady state after a change in concentration of one of the reactants ethylene or hydrogen. When cooling the pellet, after heat-up by reaction, with pure hydrogen a sudden temperature peak appears after a short time.\ud
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A mathematical model is introduced, which can explain the over- and undershoots by slow ad- or desorption on the active sites of the catalyst of one of the reactants
On the graphical extraction of multipole mixing ratios of nuclear transitions
We propose a novel graphical method for determining the mixing ratios
{\delta} and their associated uncertainties for mixed nuclear transitions. It
incorporates the uncertainties both on both the measured and the theoretical
conversion coefficients. The accuracy of the method has been studied by
deriving the corresponding probability density function. The domains of
applicability of the method are carefully defined
Neural Sensor Fusion for Spatial Visualization on a Mobile Robot
An ARTMAP neural network is used to integrate visual information and ultrasonic sensory information on a B 14 mobile robot. Training samples for the neural network are acquired without human intervention. Sensory snapshots are retrospectively associated with the distance to the wall, provided by on~ board odomctry as the robot travels in a straight line. The goal is to produce a more accurate measure of distance than is provided by the raw sensors. The neural network effectively combines sensory sources both within and between modalities. The improved distance percept is used to produce occupancy grid visualizations of the robot's environment. The maps produced point to specific problems of raw sensory information processing and demonstrate the benefits of using a neural network system for sensor fusion.Office of Naval Research and Naval Research Laboratory (00014-96-1-0772, 00014-95-1-0409, 00014-95-0657
Renormalization in the Henon family, I: universality but non-rigidity
In this paper geometric properties of infinitely renormalizable real
H\'enon-like maps in are studied. It is shown that the appropriately
defined renormalizations converge exponentially to the one-dimensional
renormalization fixed point. The convergence to one-dimensional systems is at a
super-exponential rate controlled by the average Jacobian and a universal
function . It is also shown that the attracting Cantor set of such a map
has Hausdorff dimension less than 1, but contrary to the one-dimensional
intuition, it is not rigid, does not lie on a smooth curve, and generically has
unbounded geometry.Comment: 42 pages, 5 picture
Stably non-synchronizable maps of the plane
Pecora and Carroll presented a notion of synchronization where an
(n-1)-dimensional nonautonomous system is constructed from a given
-dimensional dynamical system by imposing the evolution of one coordinate.
They noticed that the resulting dynamics may be contracting even if the
original dynamics are not. It is easy to construct flows or maps such that no
coordinate has synchronizing properties, but this cannot be done in an open set
of linear maps or flows in , . In this paper we give examples of
real analytic homeomorphisms of such that the non-synchronizability is
stable in the sense that in a full neighborhood of the given map, no
homeomorphism is synchronizable
The genotype-phenotype relationship in multicellular pattern-generating models - the neglected role of pattern descriptors
Background: A deep understanding of what causes the phenotypic variation arising from biological patterning
processes, cannot be claimed before we are able to recreate this variation by mathematical models capable of
generating genotype-phenotype maps in a causally cohesive way. However, the concept of pattern in a
multicellular context implies that what matters is not the state of every single cell, but certain emergent qualities
of the total cell aggregate. Thus, in order to set up a genotype-phenotype map in such a spatiotemporal pattern
setting one is actually forced to establish new pattern descriptors and derive their relations to parameters of the
original model. A pattern descriptor is a variable that describes and quantifies a certain qualitative feature of the
pattern, for example the degree to which certain macroscopic structures are present. There is today no general
procedure for how to relate a set of patterns and their characteristic features to the functional relationships,
parameter values and initial values of an original pattern-generating model. Here we present a new, generic
approach for explorative analysis of complex patterning models which focuses on the essential pattern features
and their relations to the model parameters. The approach is illustrated on an existing model for Delta-Notch
lateral inhibition over a two-dimensional lattice.
Results: By combining computer simulations according to a succession of statistical experimental designs,
computer graphics, automatic image analysis, human sensory descriptive analysis and multivariate data modelling,
we derive a pattern descriptor model of those macroscopic, emergent aspects of the patterns that we consider
of interest. The pattern descriptor model relates the values of the new, dedicated pattern descriptors to the
parameter values of the original model, for example by predicting the parameter values leading to particular
patterns, and provides insights that would have been hard to obtain by traditional methods.
Conclusion: The results suggest that our approach may qualify as a general procedure for how to discover and
relate relevant features and characteristics of emergent patterns to the functional relationships, parameter values
and initial values of an underlying pattern-generating mathematical model
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