1,289 research outputs found
Inverse Statistics in the Foreign Exchange Market
We investigate intra-day foreign exchange (FX) time series using the inverse
statistic analysis developed in [1,2]. Specifically, we study the time-averaged
distributions of waiting times needed to obtain a certain increase (decrease)
in the price of an investment. The analysis is performed for the Deutsch
mark (DM) against the US. With high statistical
significance, the presence of "resonance peaks" in the waiting time
distributions is established. Such peaks are a consequence of the trading
habits of the markets participants as they are not present in the corresponding
tick (business) waiting time distributions. Furthermore, a new {\em stylized
fact}, is observed for the waiting time distribution in the form of a power law
Pdf. This result is achieved by rescaling of the physical waiting time by the
corresponding tick time thereby partially removing scale dependent features of
the market activity.Comment: 8 pages. Accepted Physica
Optimal Investment Horizons for Stocks and Markets
The inverse statistics is the distribution of waiting times needed to achieve
a predefined level of return obtained from (detrended) historic asset prices
\cite{optihori,gainloss}. Such a distribution typically goes through a maximum
at a time coined the {\em optimal investment horizon}, , which
defines the most likely waiting time for obtaining a given return . By
considering equal positive and negative levels of return, we reported in
\cite{gainloss} on a quantitative gain/loss asymmetry most pronounced for short
horizons. In the present paper, the inverse statistics for 2/3 of the
individual stocks presently in the DJIA is investigated. We show that this
gain/loss asymmetry established for the DJIA surprisingly is {\em not} present
in the time series of the individual stocks nor their average. This observation
points towards some kind of collective movement of the stocks of the index
(synchronization).Comment: Subm. to Physica A as Conference Proceedings of Econophysics
Colloquium, ANU Canberra, 13-17 Nov. 2005. 6 pages including figure
Scaling and the prediction of energy spectra in decaying hydrodynamic turbulence
Few rigorous results are derived for fully developed turbulence. By applying
the scaling properties of the Navier-Stokes equation we have derived a relation
for the energy spectrum valid for unforced or decaying isotropic turbulence. We
find the existence of a scaling function . The energy spectrum can at any
time by a suitable rescaling be mapped onto this function. This indicates that
the initial (primordial) energy spectrum is in principle retained in the energy
spectrum observed at any later time, and the principle of permanence of large
eddies is derived. The result can be seen as a restoration of the determinism
of the Navier-Stokes equation in the mean. We compare our results with a
windtunnel experiment and find good agreement.Comment: 4 pages, 1 figur
New Algorithm for Parallel Laplacian Growth by Iterated Conformal Maps
We report a new algorithm to generate Laplacian Growth Patterns using
iterated conformal maps. The difficulty of growing a complete layer with local
width proportional to the gradient of the Laplacian field is overcome. The
resulting growth patterns are compared to those obtained by the best algorithms
of direct numerical solutions. The fractal dimension of the patterns is
discussed.Comment: Sumitted to Phys. Rev. Lett. Further details at
http://www.pik-potsdam.de/~ander
Pulses in the Zero-Spacing Limit of the GOY Model
We study the propagation of localised disturbances in a turbulent, but
momentarily quiescent and unforced shell model (an approximation of the
Navier-Stokes equations on a set of exponentially spaced momentum shells).
These disturbances represent bursts of turbulence travelling down the inertial
range, which is thought to be responsible for the intermittency observed in
turbulence. Starting from the GOY shell model, we go to the limit where the
distance between succeeding shells approaches zero (``the zero spacing limit'')
and helicity conservation is retained. We obtain a discrete field theory which
is numerically shown to have pulse solutions travelling with constant speed and
with unchanged form. We give numerical evidence that the model might even be
exactly integrable, although the continuum limit seems to be singular and the
pulses show an unusual super exponential decay to zero as when , where is the {\em
golden mean}. For finite momentum shell spacing, we argue that the pulses
should accelerate, moving to infinity in a finite time. Finally we show that
the maximal Lyapunov exponent of the GOY model approaches zero in this limit.Comment: 27 pages, submitted for publicatio
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Mode-locking and the transition to chaos in dissipative systems
Dissipative systems with two competing frequencies exhibit transitions to chaos. We have investigated the transition through a study of discrete maps of the circle onto itself, and by constructing and analyzing return maps of differential equations representing some physical systems. The transition is caused by interaction and overlap of mode-locked resonances and takes place at a critical line where the map losses invertibility. At this line the mode-locked intervals trace up a complete Devil's Staircase whose complementary set is a Cantor set with universal fractal dimension D approx. 0.87. Below criticality there is room for quasiperiodic orbits, whose measure is given by an exponent ..beta.. approx. 0.34 which can be related to D through a scaling relation, just as for second order phase transitions. The Lebesgue measure serves as an order parameter for the transition to chaos. The resistively shunted Josephson junction, and charge density waves (CDWs) in rf electric fields are usually described by the differential equation of the damped driven pendulum. The 2d return map for this equation collapses to ld circle map at and below the transition to chaos. The theoretical results on universal behavior, derived here and elsewhere, can thus readily be checked experimentally by studying real physical systems. Recent experiments on Josephson junctions and CDWs indicating the predicted fractal scaling of mode-locking at criticality are reviewed
Hastings-Levitov aggregation in the small-particle limit
We establish some scaling limits for a model of planar aggregation. The model is described by the composition of a sequence of independent and identically distributed random conformal maps, each corresponding to the addition of one particle. We study the limit of small particle size and rapid aggregation. The process of growing clusters converges, in the sense of Caratheodory, to an inflating disc. A more refined analysis reveals, within the cluster, a tree structure of branching fingers, whose radial component increases deterministically with time. The arguments of any finite sample of fingers, tracked inwards, perform coalescing Brownian motions. The arguments of any finite sample of gaps between the fingers, tracked outwards, also perform coalescing Brownian motions. These properties are closely related to the evolution of harmonic measure on the boundary of the cluster, which is shown to converge to the Brownian web
Modeling Water and Nitrogen Behavior in the Soil-Plant System
A set of dynamic mathematical relations is
developed for the major variables of soil water,
nitrate, ammonium, available organic nitrogen,
and plant growth and nitrogen uptake. Daily
climatic conditions are used to control evapotranspiration
and modify the rates of plant
growth and soil processes. Inputs of irrigation
water and fertilizer can be controlled to reduce
leaching of nitrate
On two-dimensionalization of three-dimensional turbulence in shell models
Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model,
the signatures of so-called two-dimensionalization effect of three-dimensional
incompressible, homogeneous, isotropic fully developed unforced turbulence have
been studied and reproduced. Within the framework of shell models we have
obtained the following results: (i) progressive steepening of the energy
spectrum with increased strength of the rotation, and, (ii) depletion in the
energy flux of the forward forward cascade, sometimes leading to an inverse
cascade. The presence of extended self-similarity and self-similar PDFs for
longitudinal velocity differences are also presented for the rotating 3D
turbulence case
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