159 research outputs found
Small scale behavior of financial data
A new approach is presented to describe the change in the statistics of the
log return distribution of financial data as a function of the timescale. To
this purpose a measure is introduced, which quantifies the distance of a
considered distribution to a reference distribution. The existence of a small
timescale regime is demonstrated, which exhibits different properties compared
to the normal timescale regime. This regime seems to be universal for
individual stocks. It is shown that the existence of this small timescale
regime is not dependent on the special choice of the distance measure or the
reference distribution. These findings have important implications for risk
analysis, in particular for the probability of extreme events.Comment: 4 pages, 6 figures Calculations for the turbulence data sets were
redone using the log return as the increment definition in order to provide
better comparison to the results for financial asset
Towards a Simplified Dynamic Wake Model using POD Analysis
We apply the proper orthogonal decomposition (POD) to large eddy simulation
data of a wind turbine wake in a turbulent atmospheric boundary layer. The
turbine is modeled as an actuator disk. Our analyis mainly focuses on the
question whether POD could be a useful tool to develop a simplified dynamic
wake model. The extracted POD modes are used to obtain approximate descriptions
of the velocity field. To assess the quality of these POD reconstructions, we
define simple measures which are believed to be relevant for a sequential
turbine in the wake such as the energy flux through a disk in the wake. It is
shown that only a few modes are necessary to capture basic dynamical aspects of
these measures even though only a small part of the turbulent kinetic energy is
restored. Furthermore, we show that the importance of the individual modes
depends on the measure chosen. Therefore, the optimal choice of modes for a
possible model could in principle depend on the application of interest. We
additionally present a possible interpretation of the POD modes relating them
to specific properties of the wake. For example the first mode is related to
the horizontal large scale movement. Besides yielding a deeper understanding,
this also enables us to view our results in comparison to existing dynamic wake
models
Self-Organized Synchronization and Voltage Stability in Networks of Synchronous Machines
The integration of renewable energy sources in the course of the energy
transition is accompanied by grid decentralization and fluctuating power
feed-in characteristics. This raises new challenges for power system stability
and design. We intend to investigate power system stability from the viewpoint
of self-organized synchronization aspects. In this approach, the power grid is
represented by a network of synchronous machines. We supplement the classical
Kuramoto-like network model, which assumes constant voltages, with dynamical
voltage equations, and thus obtain an extended version, that incorporates the
coupled categories voltage stability and rotor angle synchronization. We
compare disturbance scenarios in small systems simulated on the basis of both
classical and extended model and we discuss resultant implications and possible
applications to complex modern power grids.Comment: 9 pages, 9 figure
The Langevin Approach: An R Package for Modeling Markov Processes
We describe an R package developed by the research group Turbulence, Wind
energy and Stochastics (TWiSt) at the Carl von Ossietzky University of
Oldenburg, which extracts the (stochastic) evolution equation underlying a set
of data or measurements. The method can be directly applied to data sets with
one or two stochastic variables. Examples for the one-dimensional and
two-dimensional cases are provided. This framework is valid under a small set
of conditions which are explicitly presented and which imply simple preliminary
test procedures to the data. For Markovian processes involving Gaussian white
noise, a stochastic differential equation is derived straightforwardly from the
time series and captures the full dynamical properties of the underlying
process. Still, even in the case such conditions are not fulfilled, there are
alternative versions of this method which we discuss briefly and provide the
user with the necessary bibliography
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