645 research outputs found
Voltage and current spectra for matrix power converters
Matrix power converters are used for transforming one alternating-current power supply to another, with different peak voltage and frequency. There are three input lines, with sinusoidally varying voltages which are 120â—¦ out of phase one from another, and the output is to be delivered as a similar three-phase supply. The matrix converter switches rapidly, to connect each output line in sequence to each of the input lines in an attempt to synthesize the prescribed output voltages. The switching is carried out at high frequency and it is of practical importance to know
the frequency spectra of the output voltages and of the input and output currents. We determine in this paper these spectra using a new method, which has significant advantages over the prior default method (a multiple Fourier series technique), leading to a considerably more direct calculation. In particular, the determination of the input current spectrum is feasible here, whereas it would be a significantly more daunting procedure using the prior method instead
Scarring and the statistics of tunnelling
We show that the statistics of tunnelling can be dramatically affected by
scarring and derive distributions quantifying this effect. Strong deviations
from the prediction of random matrix theory can be explained quantitatively by
modifying the Gaussian distribution which describes wavefunction statistics.
The modified distribution depends on classical parameters which are determined
completely by linearised dynamics around a periodic orbit. This distribution
generalises the scarring theory of Kaplan [Phys. Rev. Lett. {\bf 80}, 2582
(1998)] to describe the statistics of the components of the wavefunction in a
complete basis, rather than overlaps with single Gaussian wavepackets. In
particular it is shown that correlations in the components of the wavefunction
are present, which can strongly influence tunnelling-rate statistics. The
resulting distribution for tunnelling rates is tested successfully on a
two-dimensional double-well potential.Comment: 20 pages, 4 figures, submitted to Ann. Phy
A Matrix Element for Chaotic Tunnelling Rates and Scarring Intensities
It is shown that tunnelling splittings in ergodic double wells and resonant
widths in ergodic metastable wells can be approximated as easily-calculated
matrix elements involving the wavefunction in the neighbourhood of a certain
real orbit. This orbit is a continuation of the complex orbit which crosses the
barrier with minimum imaginary action. The matrix element is computed by
integrating across the orbit in a surface of section representation, and uses
only the wavefunction in the allowed region and the stability properties of the
orbit. When the real orbit is periodic, the matrix element is a natural measure
of the degree of scarring of the wavefunction. This scarring measure is
canonically invariant and independent of the choice of surface of section,
within semiclassical error. The result can alternatively be interpretated as
the autocorrelation function of the state with respect to a transfer operator
which quantises a certain complex surface of section mapping. The formula
provides an efficient numerical method to compute tunnelling rates while
avoiding the need for the exceedingly precise diagonalisation endemic to
numerical tunnelling calculations.Comment: Submitted to Annals of Physics. This work has been submitted to
Academic Press for possible publicatio
Classical orbit bifurcation and quantum interference in mesoscopic magnetoconductance
We study the magnetoconductance of electrons through a mesoscopic channel
with antidots. Through quantum interference effects, the conductance maxima as
functions of the magnetic field strength and the antidot radius (regulated by
the applied gate voltage) exhibit characteristic dislocations that have been
observed experimentally. Using the semiclassical periodic orbit theory, we
relate these dislocations directly to bifurcations of the leading classes of
periodic orbits.Comment: 4 pages, including 5 figures. Revised version with clarified
discussion and minor editorial change
A simple hourly wind power simulation for the South-West region of Western Australia using MERRA data
A simple simulator capable of generating synthetic hourly values of wind power was developed for the South West region of Western Australia. The global Modern Era Retrospective Analysis for Research and Applications (MERRA) atmospheric database was used to calibrate the simulation with wind speeds 50m above ground level. Analysis of the MERRA data indicated that the normalised residual of hourly wind speed had a double exponential distribution. A translated square-root transformation function yn=(√(1.96+ ye )−1.4)/0.302 was used to convert this to a normal-like distribution so that autoregressive (AR) time series analysis could be used. There was a significant dependency in this time series on the last three hours, so a third order AR model was used to generate hourly 50m wind speed residuals. The MERRA daily average 50m wind speed was found to have a Weibull-like distribution, so a square root conversion was used on the data to obtain a normal distribution. The time series for this distribution was found to have a significant dependency on the values for the last two days, so a second order AR model was also used in the simulation to generate synthetic time series values for the square root of the daily average wind speed. Seasonal, daily, diurnal, and hourly components were added to generate synthetic time series values of total 50m wind speed. To scale this wind speed to turbine hub height, a time varying wind shear factor model was created and calibrated using measured data at a coastal and an inland site. Standard wind turbine power curves were modified to produce an estimate of wind farm power output from the hub-height wind speed. Comparison with measured grid supervisory control and data acquisition (SCADA) data indicated that the simulation generated conservative power output values. The simulation was compared to two other models: a Weibull distribution model, and an AR model with normally distributed residuals. The statistical fit with the SCADA data was found to be closer than these two models. Spatial correlation using only the MERRA data was found to be higher than the SCADA data, indicating that there is still a further source of variability to be accounted for. Hence the simulation spatial correlation was calibrated to previously reported findings, which were similar to the SCADA data
Regular-to-chaotic tunneling rates using a fictitious integrable system
We derive a formula predicting dynamical tunneling rates from regular states
to the chaotic sea in systems with a mixed phase space. Our approach is based
on the introduction of a fictitious integrable system that resembles the
regular dynamics within the island. For the standard map and other kicked
systems we find agreement with numerical results for all regular states in a
regime where resonance-assisted tunneling is not relevant.Comment: 4 pages, 4 figure
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