381 research outputs found
Estimation of drift and diffusion functions from time series data: A maximum likelihood framework
Complex systems are characterized by a huge number of degrees of freedom
often interacting in a non-linear manner. In many cases macroscopic states,
however, can be characterized by a small number of order parameters that obey
stochastic dynamics in time. Recently techniques for the estimation of the
corresponding stochastic differential equations from measured data have been
introduced. This contribution develops a framework for the estimation of the
functions and their respective (Bayesian posterior) confidence regions based on
likelihood estimators. In succession approximations are introduced that
significantly improve the efficiency of the estimation procedure. While being
consistent with standard approaches to the problem this contribution solves
important problems concerning the applicability and the accuracy of estimated
parameters.Comment: 18 pages, 2 figure
Urolithiasis in a Patient Ingesting Pure Silica: A Scanning Electron Microscopy Study
A patient who repeatedly produced urinary calculi, had consumed about 3g of cristobalite (SiO2) per day for many years. Investigations using scanning electron microscopy revealed minute particles containing silicon in the core of the stone as well as in urine sediment. A mechanism similar to that proposed for the effect of silicon-containing drugs against gastric ulcer, may play a role in this formation of silicon-containing urinary stones
Groundwater seepage landscapes from distant and local sources in experiments and on Mars
© 2014 Author(s). Valleys with theater-shaped heads can form due to the seepage of groundwater and as a result of knickpoint (waterfall) erosion generated by overland flow. This ambiguity in the mechanism of formation hampers the interpretation of such valleys on Mars, particularly since there is limited knowledge of material properties. Moreover, the hydrological implications of a groundwater or surface water origin are important for our understanding of the evolution of surface features on Mars, and a quantification of valley morphologies at the landscape scale may provide diagnostic insights on the formative hydrological conditions. However, flow patterns and the resulting landscapes produced by different sources of groundwater are poorly understood. We aim to improve the understanding of the formation of entire valley landscapes through seepage processes from different groundwater sources that will provide a framework of landscape metrics for the interpretation of such systems. We study groundwater seepage from a distant source of groundwater and from infiltration of local precipitation in a series of sandbox experiments and combine our results with previous experiments and observations of the Martian surface. Key results are that groundwater flow piracy acts on valleys fed by a distant groundwater source and results in a sparsely dissected landscape of many small and a few large valleys. In contrast, valleys fed by a local groundwater source, i.e., nearby infiltration, result in a densely dissected landscape. In addition, valleys fed by a distant groundwater source grow towards that source, while valleys with a local source grow in a broad range of directions and have a strong tendency to bifurcate, particularly on flatter surfaces. We consider these results with respect to two Martian cases: Louros Valles shows properties of seepage by a local source of groundwater and Nirgal Vallis shows evidence of a distant source, which we interpret as groundwater flow from Tharsis
Stochastische Modellierung komplexer Systeme:Von den theoretischen Grundlagen zur Simulation athmosphärischer Windfelder
Ein erster Schwerpunkt dieser Arbeit liegt auf Methoden zur statistischen Analyse der Dynamik komplexer Systeme. Die Grundlage bildet hierbei ein von Friedrich und Peinke entwickeltes Verfahren zum Schätzen von Drift- und Diffusionsfunktionen aus Messdaten. Im Anschluss daran werden Continuous Time Random Walks (CTRWs) betrachtet, die die Modellierung von nicht-Markov-Prozessen, die im Ensemble anomales Diffusionsverhalten zeigen, ermöglichen. Insbesondere wird ein Algorithmus zur numerischen Simulation stetiger Trajektorien solcher Prozesse eingeführt. Auf der Basis von CTRWs wird schließlich ein Modell für atmosphärische Windfelder, die für eine bessere Charakterisierung von Windkraftanlagen in der atmosphärischen Grenzschicht benötigt werden, entwickelt, das einige intermittente Eigenschaften der atmosphärischen Turbulenz reproduzieren kann. Die Arbeit schließt mit ersten Ergebnissen von Tests dieses Windfeldmodells an aktuellen Windkraftanlagen
Searching for optimal variables in real multivariate stochastic data
By implementing a recent technique for the determination of stochastic
eigendirections of two coupled stochastic variables, we investigate the
evolution of fluctuations of NO2 concentrations at two monitoring stations in
the city of Lisbon, Portugal. We analyze the stochastic part of the
measurements recorded at the monitoring stations by means of a method where the
two concentrations are considered as stochastic variables evolving according to
a system of coupled stochastic differential equations. Analysis of their
structure allows for transforming the set of measured variables to a set of
derived variables, one of them with reduced stochasticity. For the specific
case of NO2 concentration measures, the set of derived variables are well
approximated by a global rotation of the original set of measured variables. We
conclude that the stochastic sources at each station are independent from each
other and typically have amplitudes of the order of the deterministic
contributions. Such findings show significant limitations when predicting such
quantities. Still, we briefly discuss how predictive power can be increased in
general in the light of our methods
Wind Energy and the Turbulent Nature of the Atmospheric Boundary Layer
Wind turbines operate in the atmospheric boundary layer, where they are
exposed to the turbulent atmospheric flows. As the response time of wind
turbine is typically in the range of seconds, they are affected by the small
scale intermittent properties of the turbulent wind. Consequently, basic
features which are known for small-scale homogeneous isotropic turbulence, and
in particular the well-known intermittency problem, have an important impact on
the wind energy conversion process. We report on basic research results
concerning the small-scale intermittent properties of atmospheric flows and
their impact on the wind energy conversion process. The analysis of wind data
shows strongly intermittent statistics of wind fluctuations. To achieve
numerical modeling a data-driven superposition model is proposed. For the
experimental reproduction and adjustment of intermittent flows a so-called
active grid setup is presented. Its ability is shown to generate reproducible
properties of atmospheric flows on the smaller scales of the laboratory
conditions of a wind tunnel. As an application example the response dynamics of
different anemometer types are tested. To achieve a proper understanding of the
impact of intermittent turbulent inflow properties on wind turbines we present
methods of numerical and stochastic modeling, and compare the results to
measurement data. As a summarizing result we find that atmospheric turbulence
imposes its intermittent features on the complete wind energy conversion
process. Intermittent turbulence features are not only present in atmospheric
wind, but are also dominant in the loads on the turbine, i.e. rotor torque and
thrust, and in the electrical power output signal. We conclude that profound
knowledge of turbulent statistics and the application of suitable numerical as
well as experimental methods are necessary to grasp these unique features (...)Comment: Accepted by the Journal of Turbulence on May 17, 201
- …