4,904 research outputs found
Classification of Possible Finite-Time Singularities by Functional Renormalization
Starting from a representation of the early time evolution of a dynamical
system in terms of the polynomial expression of some observable f (t) as a
function of the time variable in some interval 0 < t < T, we investigate how to
extrapolate/forecast in some optimal stability sense the future evolution of
f(t) for time t>T. Using the functional renormalization of Yukalov and Gluzman,
we offer a general classification of the possible regimes that can be defined
based on the sole knowledge of the coefficients of a second-order polynomial
representation of the dynamics. In particular, we investigate the conditions
for the occurence of finite-time singularities from the structure of the time
series, and quantify the critical time and the functional nature of the
singularity when present. We also describe the regimes when a smooth extremum
replaces the singularity and determine its position and amplitude. This extends
previous works by (1) quantifying the stability of the functional
renormalization method more accurately, (2) introducing new global constraints
in terms of moments and (3) going beyond the ``mean-field'' approximation.Comment: Latex document of 18 pages + 7 ps figure
Ray optics in flux avalanche propagation in superconducting films
Experimental evidence of wave properties of dendritic flux avalanches in
superconducting films is reported. Using magneto-optical imaging the
propagation of dendrites across boundaries between a bare NbN film and areas
coated by a Cu-layer was visualized, and it was found that the propagation is
refracted in full quantitative agreement with Snell's law. For the studied film
of 170 nm thickness and a 0.9 mkm thick metal layer, the refractive index was
close to n=1.4. The origin of the refraction is believed to be caused by the
dendrites propagating as an electromagnetic shock wave, similar to damped modes
considered previously for normal metals. The analogy is justified by the large
dissipation during the avalanches raising the local temperature significantly.
Additional time-resolved measurements of voltage pulses generated by segments
of the dendrites traversing an electrode confirm the consistency of the adapted
physical picture.Comment: 4 pages, 4 figure
Weighted Fixed Points in Self-Similar Analysis of Time Series
The self-similar analysis of time series is generalized by introducing the
notion of scenario probabilities. This makes it possible to give a complete
statistical description for the forecast spectrum by defining the average
forecast as a weighted fixed point and by calculating the corresponding a
priori standard deviation and variance coefficient. Several examples of
stock-market time series illustrate the method.Comment: two additional references are include
Dendritic flux patterns in MgB2 films
Magneto-opitcal studies of a c-oriented epitaxial MgB2 film with critical
current density 10^7 A/cm^2 demonstrate a breakdown of the critical state at
temperatures below 10 K [cond-mat/0104113]. Instead of conventional uniform and
gradual flux penetration in an applied magnetic field, we observe an abrupt
invasion of complex dendritic structures. When the applied field subsequently
decreases, similar dendritic structures of the return flux penetrate the film.
The static and dynamic properties of the dendrites are discussed.Comment: Accepted to Supercond. Sci. Techno
Mechanism for flux guidance by micrometric antidot arrays in superconducting films
A study of magnetic flux penetration in a superconducting film patterned with
arrays of micron sized antidots (microholes) is reported. Magneto-optical
imaging (MOI) of a YBCO film shaped as a long strip with perpendicular antidot
arrays revealed both strong guidance of flux, and at the same time large
perturbations of the overall flux penetration and flow of current. These
results are compared with a numerical flux creep simulation of a thin
superconductor with the same antidot pattern. To perform calculations on such a
complex geometry, an efficient numerical scheme for handling the boundary
conditions of the antidots and the nonlocal electrodynamics was developed. The
simulations reproduce essentially all features of the MOI results. In addition,
the numerical results give insight into all other key quantities, e.g., the
electrical field, which becomes extremely large in the narrow channels
connecting the antidots.Comment: 8 pages, 7 figure
Level Crossing Analysis of the Stock Markets
We investigate the average frequency of positive slope ,
crossing for the returns of market prices.
The method is based on stochastic processes which no scaling feature is
explicitly required. Using this method we define new quantity to quantify stage
of development and activity of stocks exchange. We compare the Tehran and
western stock markets and show that some stocks such as Tehran (TEPIX) and New
Zealand (NZX) stocks exchange are emerge, and also TEPIX is a non-active market
and financially motivated to absorb capital.Comment: 6 pages and 4 figure
Current-induced dendritic magnetic instability in superconducting MgB2 films
Magneto-optical imaging reveals that in superconducting films of MgB2 a
transport current creates avalanche-like flux dynamics where highly branching
dendritic penetration patterns are formed. The instability is triggered when
the current exceeds a threshold value, and the superconductor, shaped as a long
strip, is initially in the critical state. The instability exists up to 19 K,
which is a much wider temperature range than in previous experiments, where
dendrites were formed by applying a magnetic field. The instability is believed
to be of thermo-magnetic origin indicating that thermal stabilization may
become crucial in applications of MgB2.Comment: 3 pages, 3 figures, resubmitted to Appl.Phys.Let
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