280 research outputs found
Broadband dielectric spectroscopy on benzophenone: alpha relaxation, beta relaxation, and mode coupling theory
We have performed a detailed dielectric investigation of the relaxational
dynamics of glass-forming benzophenone. Our measurements cover a broad
frequency range of 0.1 Hz to 120 GHz and temperatures from far below the glass
temperature well up into the region of the small-viscosity liquid. With respect
to the alpha relaxation this material can be characterized as a typical
molecular glass former with rather high fragility. A good agreement of the
alpha relaxation behavior with the predictions of the mode coupling theory of
the glass transition is stated. In addition, at temperatures below and in the
vicinity of Tg we detect a well-pronounced beta relaxation of Johari-Goldstein
type, which with increasing temperature develops into an excess wing. We
compare our results to literature data from optical Kerr effect and depolarized
light scattering experiments, where an excess-wing like feature was observed in
the 1 - 100 GHz region. We address the question if the Cole-Cole peak, which
was invoked to describe the optical Kerr effect data within the framework of
the mode coupling theory, has any relation to the canonical beta relaxation
detected by dielectric spectroscopy.Comment: 11 pages, 7 figures; revised version with new Fig. 5 and some smaller
changes according to referees' demand
A non-autonomous flow system with Plykin type attractor
A non-autonomous flow system is introduced with an attractor of Plykin type
that may serve as a base for elaboration of real systems and devices
demonstrating the structurally stable chaotic dynamics. The starting point is a
map on a two-dimensional sphere, consisting of four stages of continuous
geometrically evident transformations. The computations indicate that in a
certain parameter range the map has a uniformly hyperbolic attractor. It may be
represented on a plane by means of a stereographic projection. Accounting
structural stability, a modification of the model is undertaken to obtain a set
of two non-autonomous differential equations of the first order with smooth
coefficients. As follows from computations, it has the Plykin type attractor in
the Poincar\'{e} cross-section.Comment: 9 pages, 4 figure
Desmoplastic myxoid tumor of pineal region, SMARCB1-mutant, in young adult
We present a young adult woman who developed a myxoid tumor of the pineal region having a SMARCB1 mutation, which was phenotypically similar to the recently described desmoplastic myxoid, SMARCB1-mutant tumor of the pineal region (DMT-SMARCB1). The 24-year-old woman presented with headaches, nausea, and emesis. Neuroimaging identified a hypodense lesion in CT scans that was T1-hypointense, hyperintense in both T2-weighted and FLAIR MRI scans, and displayed gadolinium enhancement. The resected tumor had an abundant, Alcian-blue positive myxoid matrix with interspersed, non-neoplastic neuropil-glial-vascular elements. It immunoreacted with CD34 and individual cells for EMA. Immunohistochemistry revealed loss of nuclear INI1 expression by the myxoid component but its retention in the vascular elements. Molecular analyses identified a SMARCB1 deletion and DNA methylation studies showed that this tumor grouped together with the recently described DMT-SMARCB1. A cerebrospinal fluid cytologic preparation had several cells morphologically similar to those in routine and electron microscopy. We briefly discuss the correlation of the pathology with the radiology and how this tumor compares with other SMARCB1-mutant tumors of the nervous system
The boundary of chaos for interval mappings
A goal in the study of dynamics on the interval is to understand the transition to positive topological entropy. There is a conjecture from the 1980s that the only route to positive topological entropy is through a cascade of period doubling bifurcations. We prove this conjecture in natural families of smooth interval maps, and use it to study the structure of the boundary of mappings with positive entropy. In particular, we show that in families of mappings with a fixed number of critical points the boundary is locally connected, and for analytic mappings that it is a cellular set
On the complexity of some birational transformations
Using three different approaches, we analyze the complexity of various
birational maps constructed from simple operations (inversions) on square
matrices of arbitrary size. The first approach consists in the study of the
images of lines, and relies mainly on univariate polynomial algebra, the second
approach is a singularity analysis, and the third method is more numerical,
using integer arithmetics. Each method has its own domain of application, but
they give corroborating results, and lead us to a conjecture on the complexity
of a class of maps constructed from matrix inversions
Structure determination of the (√3×√3)R30° boron phase on the Si(111) surface using photoelectron diffraction
A quantitative structural analysis of the system Si(111)(√3×√3)R30°−B has been performed using photoelectron diffraction in the scanned energy mode. We confirm that the substitutional S5 adsorption site is occupied and show that the interatomic separations to the three nearest-neighbor Si atoms are 1.98(±0.04)Å, 2.14(±0.13)Å, and 2.21(±0.12)Å. These correspond to the silicon atom immediately below the boron atom, the adatom immediately above, and the three atoms to which it is coordinated symmetrically in the first layer
Parabolic maps with spin: Generic spectral statistics with non-mixing classical limit
We investigate quantised maps of the torus whose classical analogues are
ergodic but not mixing. Their quantum spectral statistics shows non-generic
behaviour, i.e.it does not follow random matrix theory (RMT). By coupling the
map to a spin 1/2, which corresponds to changing the quantisation without
altering the classical limit of the dynamics on the torus, we numerically
observe a transition to RMT statistics. The results are interpreted in terms of
semiclassical trace formulae for the maps with and without spin respectively.
We thus have constructed quantum systems with non-mixing classical limit which
show generic (i.e. RMT) spectral statistics. We also discuss the analogous
situation for an almost integrable map, where we compare to Semi-Poissonian
statistics.Comment: 29 pages, 20 figure
Extreme value laws in dynamical systems under physical observables
Extreme value theory for chaotic dynamical systems is a rapidly expanding
area of research. Given a system and a real function (observable) defined on
its phase space, extreme value theory studies the limit probabilistic laws
obeyed by large values attained by the observable along orbits of the system.
Based on this theory, the so-called block maximum method is often used in
applications for statistical prediction of large value occurrences. In this
method, one performs inference for the parameters of the Generalised Extreme
Value (GEV) distribution, using maxima over blocks of regularly sampled
observations along an orbit of the system. The observables studied so far in
the theory are expressed as functions of the distance with respect to a point,
which is assumed to be a density point of the system's invariant measure.
However, this is not the structure of the observables typically encountered in
physical applications, such as windspeed or vorticity in atmospheric models. In
this paper we consider extreme value limit laws for observables which are not
functions of the distance from a density point of the dynamical system. In such
cases, the limit laws are no longer determined by the functional form of the
observable and the dimension of the invariant measure: they also depend on the
specific geometry of the underlying attractor and of the observable's level
sets. We present a collection of analytical and numerical results, starting
with a toral hyperbolic automorphism as a simple template to illustrate the
main ideas. We then formulate our main results for a uniformly hyperbolic
system, the solenoid map. We also discuss non-uniformly hyperbolic examples of
maps (H\'enon and Lozi maps) and of flows (the Lorenz63 and Lorenz84 models).
Our purpose is to outline the main ideas and to highlight several serious
problems found in the numerical estimation of the limit laws
Ruelle-Perron-Frobenius spectrum for Anosov maps
We extend a number of results from one dimensional dynamics based on spectral
properties of the Ruelle-Perron-Frobenius transfer operator to Anosov
diffeomorphisms on compact manifolds. This allows to develop a direct operator
approach to study ergodic properties of these maps. In particular, we show that
it is possible to define Banach spaces on which the transfer operator is
quasicompact. (Information on the existence of an SRB measure, its smoothness
properties and statistical properties readily follow from such a result.) In
dimension we show that the transfer operator associated to smooth random
perturbations of the map is close, in a proper sense, to the unperturbed
transfer operator. This allows to obtain easily very strong spectral stability
results, which in turn imply spectral stability results for smooth
deterministic perturbations as well. Finally, we are able to implement an Ulam
type finite rank approximation scheme thus reducing the study of the spectral
properties of the transfer operator to a finite dimensional problem.Comment: 58 pages, LaTe
Numerical convergence of the block-maxima approach to the Generalized Extreme Value distribution
In this paper we perform an analytical and numerical study of Extreme Value
distributions in discrete dynamical systems. In this setting, recent works have
shown how to get a statistics of extremes in agreement with the classical
Extreme Value Theory. We pursue these investigations by giving analytical
expressions of Extreme Value distribution parameters for maps that have an
absolutely continuous invariant measure. We compare these analytical results
with numerical experiments in which we study the convergence to limiting
distributions using the so called block-maxima approach, pointing out in which
cases we obtain robust estimation of parameters. In regular maps for which
mixing properties do not hold, we show that the fitting procedure to the
classical Extreme Value Distribution fails, as expected. However, we obtain an
empirical distribution that can be explained starting from a different
observable function for which Nicolis et al. [2006] have found analytical
results.Comment: 34 pages, 7 figures; Journal of Statistical Physics 201
- …