Statistical fluctuations | EPFL Graph Search

Statistical fluctuations are fluctuations in quantities derived from many identical random processes. They are fundamental and unavoidable. It can be proved that the relative fluctuations reduce as the square root of the number of identical processes. Statistical fluctuations are responsible for many results of statistical mechanics and thermodynamics, including phenomena such as shot noise in electronics. Description When a number of random processes occur, it can be shown that the outcomes fluctuate (vary in time) and that the fluctuations are inversely proportional to the square root of the number of processes. Examples As an example that will be familiar to all, if a fair coin is tossed many times and the number of heads and tails counted, the ratio of heads to tails will be very close to 1 (about as many heads as tails); but after only a few throws, outcomes with a significant excess of heads over tails or vice versa are common; if an experiment with a few th

Physical Mechanisms governing Self-Excited Pressure Oscillations in Francis Turbines

Andres Müller

The importance of renewable energy sources for the electrical power supply has grown rapidly in the past decades. Their often unpredictable nature however poses a threat to the stability of the existing electric grid. Hydroelectric powerplants play an important role in regulating the integration of renewable energy sources into the network by supplying on-demand load balancing as well as primary and secondary power network control. Therefore, the operating ranges of hydraulic machines has to be continuously extended, which potentially produces undesirable flow phenomena involving cavitation. An example is the formation of a gaseous volume in the swirling flow leaving a Francis turbine runner at off-design operating conditions. At high load, this so called vortex rope is shaped axisymmetrically and may enter a self-excited oscillation, measurable through significant fluctuations of the pressure throughout the system and the mechanical torque transferred to the generator. The main objective of the present work is the identification of the physical mechanisms governing this self-sustained, unstable behavior by measurement. Furthermore, the key parameters of numerical approaches using one-dimensional hydroacoustic flowmodels or CFD require experimental validation. For this purpose, the measurements provide a comprehensive data base of various flow and system parameters at varying operating conditions. Two test cases are studied, a small scale hydraulic circuit with a micro-turbine as well as a reduced scale physical model of an existing Francis turbine. On the first test case, the study of the flow rate fluctuations up- and downstream of the oscillating vortex rope in the draft tube, together with the volume of the cavity, revealed the destabilizing effect of the flow swirl in the draft tube inlet. The second test case accurately simulates the behavior of an actual hydraulic power plant. Investigations range from a local study of the flow field in the draft tube cone bymeans of LDV, PIV, high speed visualization and wall pressure measurements to a global analysis, considering the response of the hydraulic and mechanical system to the excitation by the vortex rope oscillation. Among the main observations is a periodical variation of the flow swirl in the draft tube, synchronized with the pressure oscillations. This is likely to be caused by a cyclically appearing volume of cavitation on the runner blades, modifying the relative flow angle at the outlet. The interaction of the blade cavitation and the vortex rope oscillation via the flow swirl is found to play a crucial role in the occurrence of self-excited pressure oscillations in Francis turbines.

EPFL2014

Disorder effects on the coupling strength of coupled photonic crystal slab cavities

Vincenzo Savona, Juan Pablo Vasco Cano

We study the effects of disorder on the coupling strength of coupled photonic crystal slab cavities by considering fully-3D electromagnetic calculations. Specifically, we investigate two coupled L3 cavities at 30 degrees and 60 degrees configurations, where the coupling strength J(or photon hopping) is extracted from the simulations in the presence of disorder. We found that the relative fluctuations of the photon hopping are more sensitive to disorder effects than the corresponding fluctuations in the eigen-frequencies of the coupled cavities. Furthermore, for the typical range of disorder in state-of-the-art devices, the J fluctuations are found to increase linearly as a function of the disorder amplitude. This allows one to set upper bounds to the amplitude of fabrication imperfections, for which the coupling predicted by design can still be expected, on average, in a fabricated device.

2018

Strain-Induced Band Gap Engineering in Selectively Grown GaN-(Al,Ga)N Core-Shell Nanowire Heterostructures

Anna Fontcuberta i Morral, Luca Francaviglia

We demonstrate the selective area growth of GaN-(Al,Ga)N core shell nanowire heterostructures directly on Si(111). Photoluminescence spectroscopy on as-grown nanowires reveals a strong blueshift of the GaN band gap from 3.40 to 3.64 eV at room temperature. Raman measurements relate this shift to compressive strain within the GaN core. On the nanoscale, cathodoluminescence spectroscopy and scanning transmission electron microscopy prove the homogeneity of strain-related luminescence along the nanowire axis and the absence of significant fluctuations within the shell, respectively. A comparison of the experimental findings with numerical simulations indicates the absence of a significant defect-related strain relaxation for all investigated structures, with a maximum compressive strain of -3.4% for a shell thickness of 50 nm. The accurate control of the nanowire dimensions, namely, core diameter, shell thickness, and nanowire period, via selective area growth allows a specific manipulation of the resulting strain within individual nanowires on the same sample. This, in turn, enables a spatially resolved adjustment of the GaN band gap with an energy range of 240 meV in a one-step growth process.

American Chemical Society2016

Physical Mechanisms governing Self-Excited Pressure Oscillations in Francis Turbines

Andres Müller

EPFL2014