14,457 research outputs found
Quasiperiodic graphs at the onset of chaos
We examine the connectivity fluctuations across networks obtained when the
horizontal visibility (HV) algorithm is used on trajectories generated by
nonlinear circle maps at the quasiperiodic transition to chaos. The resultant
HV graph is highly anomalous as the degrees fluctuate at all scales with
amplitude that increases with the size of the network. We determine families of
Pesin-like identities between entropy growth rates and generalized
graph-theoretical Lyapunov exponents. An irrational winding number with pure
periodic continued fraction characterizes each family. We illustrate our
results for the so-called golden, silver and bronze numbers.Comment: arXiv admin note: text overlap with arXiv:1205.190
Incidence of nonextensive thermodynamics in temporal scaling at Feigenbaum points
Recently, in Phys. Rev. Lett. 95, 140601 (2005), P. Grassberger addresses the
interesting issue of the applicability of q-statistics to the renowned
Feigenbaum attractor. He concludes there is no genuine connection between the
dynamics at the critical attractor and the generalized statistics and argues
against its usefulness and correctness. Yet, several points are not in line
with our current knowledge, nor are his interpretations. We refer here only to
the dynamics on the attractor to point out that a correct reading of recent
developments invalidates his basic claim.Comment: To be published in Physica
Holography in the Large J Limit of AdS/CFT Correspondence and Its Applications
We give a brief expository discussion on the holographic correspondence of
correlation functions in the large J limit of AdS/CFT conjecture. We first
review our proposals on the interpretation of the so-called GKPW relation in
the large J limit or BMN limit, which are based upon a tunneling picture in
relating the AdS bulk to its boundary. Some concrete results, explicitly
confirming our picture, are summarized. We then proceed to comment on various
issues related to this subject, such as extension of the present picture to
nonconformal Dp-brane backgrounds, the correlators of deformed Wilson loops,
spinning-string/spin-chain correspondence, and the inclusion of higher
string-loop effects. In particular, as for the deformation of Wilson loops, we
present a typical tunneling world-sheet solution which can be used for direct
derivation of the expectation values of deformed Wilson loops following our
picture.Comment: 21 pages, written version of a talk given at the symposium "Frontiers
of Quantum Science", YITP, Kyoto, Feb. 2005, corrected typos and some minor
revisions of tex
Left atrial trajectory impairment in hypertrophic cardiomyopathy disclosed by geometric morphometrics and parallel transport
The analysis of full Left Atrium (LA) deformation and whole LA deformational trajectory in time has been poorly investigated and, to the best of our knowledge, seldom discussed in patients with Hypertrophic Cardiomyopathy. Therefore, we considered 22 patients with Hypertrophic Cardiomyopathy (HCM) and 46 healthy subjects, investigated them by three-dimensional Speckle Tracking Echocardiography, and studied the derived landmark clouds via Geometric Morphometrics with Parallel Transport. Trajectory shape and trajectory size were different in Controls versus HCM and their classification powers had high AUC (Area Under the Receiving Operator Characteristic Curve) and accuracy. The two trajectories were much different at the transition between LA conduit and booster pump functions. Full shape and deformation analyses with trajectory analysis enabled a straightforward perception of pathophysiological consequences of HCM condition on LA functioning. It might be worthwhile to apply these techniques to look for novel pathophysiological approaches that may better define atrio-ventricular interaction
Dynamical system analysis and forecasting of deformation produced by an earthquake fault
We present a method of constructing low-dimensional nonlinear models
describing the main dynamical features of a discrete 2D cellular fault zone,
with many degrees of freedom, embedded in a 3D elastic solid. A given fault
system is characterized by a set of parameters that describe the dynamics,
rheology, property disorder, and fault geometry. Depending on the location in
the system parameter space we show that the coarse dynamics of the fault can be
confined to an attractor whose dimension is significantly smaller than the
space in which the dynamics takes place. Our strategy of system reduction is to
search for a few coherent structures that dominate the dynamics and to capture
the interaction between these coherent structures. The identification of the
basic interacting structures is obtained by applying the Proper Orthogonal
Decomposition (POD) to the surface deformations fields that accompany
strike-slip faulting accumulated over equal time intervals. We use a
feed-forward artificial neural network (ANN) architecture for the
identification of the system dynamics projected onto the subspace (model space)
spanned by the most energetic coherent structures. The ANN is trained using a
standard back-propagation algorithm to predict (map) the values of the observed
model state at a future time given the observed model state at the present
time. This ANN provides an approximate, large scale, dynamical model for the
fault.Comment: 30 pages, 12 figure
Entropies for severely contracted configuration space
We demonstrate that dual entropy expressions of the Tsallis type apply
naturally to statistical-mechanical systems that experience an exceptional
contraction of their configuration space. The entropic index
describes the contraction process, while the dual index defines the contraction dimension at which extensivity is
restored. We study this circumstance along the three routes to chaos in
low-dimensional nonlinear maps where the attractors at the transitions, between
regular and chaotic behavior, drive phase-space contraction for ensembles of
trajectories. We illustrate this circumstance for properties of systems that
find descriptions in terms of nonlinear maps. These are size-rank functions,
urbanization and similar processes, and settings where frequency locking takes
place
Capturing of a Magnetic Skyrmion with a Hole
Magnetic whirls in chiral magnets, so-called skyrmions, can be manipulated by
ultrasmall current densities. Here we study both analytically and numerically
the interactions of a single skyrmion in two dimensions with a small hole in
the magnetic layer. Results from micromagnetic simulations are in good
agreement with effective equations of motion obtained from a generalization of
the Thiele approach. Skyrmion-defect interactions are described by an effective
potential with both repulsive and attractive components. For small current
densities a previously pinned skyrmion stays pinned whereas an unpinned
skyrmion moves around the impurities and never gets captured. For higher
current densities, j_c1 < j < j_c2, however, single holes are able to capture
moving skyrmions. The maximal cross section is proportional to the skyrmion
radius and to Sqrt(alpha), where alpha is the Gilbert damping. For j > j_c2 all
skyrmions are depinned. Small changes of the magnetic field strongly change the
pinning properties, one can even reach a regime without pinning, j_c2=0. We
also show that a small density of holes can effectively accelerate the motion
of the skyrmion and introduce a Hall effect for the skyrmion.Comment: 11 page
Flexible Weinstein manifolds
This survey on flexible Weinstein manifolds is, essentially, an extract from
our recent joint book.Comment: 41 pages, 8 figure
- …