121,314 research outputs found
Simulation of Chua's Circuit by Means of Interval Analysis
The Chua's circuit is a paradigm for nonlinear scientific studies. It is
usually simulated by means of numerical methods under IEEE 754-2008 standard.
Although the error propagation problem is well known, little attention has been
given to the relationship between this error and inequalities presented in
Chua's circuit model. Taking the average of round mode towards and
, we showed a qualitative change on the dynamics of Chua's circuit.Comment: 6th International Conference on Nonlinear Science and Complexity -
S\~ao Jos\'e dos Campos, 2016, p. 1-
Inline self-diffraction dispersion-scan of over octave-spanning pulses in the single-cycle regime
We present an implementation of dispersion-scan based on self-diffraction (SD
d-scan) and apply it to the measurement of over octave-spanning sub-4-fs
pulses. The results are compared with second-harmonic generation (SHG) d-scan.
The efficiency of the SD process is derived theoretically and compared with the
spectral response retrieved by the d-scan algorithm. The new SD d-scan has a
robust inline setup and enables measuring pulses with over-octave spectra,
single-cycle durations and wavelength ranges beyond those of SHG crystals, such
as the ultraviolet and the deep-ultraviolet.Comment: 8 pages, 5 figure
High harmonic generation in crystals using Maximally Localized Wannier functions
In this work, the nonlinear optical response, and in particular, the high
harmonic generation of semiconductors is addressed by using the Wannier gauge.
One of the main problems in the time evolution of the Semiconductor Bloch
equations resides in the fact that the dipole couplings between different bands
can diverge and have a random phase along the reciprocal space and this leads
to numerical instability. To address this problem, we propose the use of the
Maximally Localized Wannier functions that provide a framework to map ab-initio
calculations to an effective tight-binding Hamiltonian with great accuracy. We
show that working in the Wannier gauge, the basis set in which the Bloch
functions are constructed directly from the Wannier functions, the dipole
couplings become smooth along the reciprocal space thus avoiding the problem of
random phases. High harmonic generation spectrum is computed for a 2D monolayer
of hBN as a numerical demonstration
Information entropy of classical versus explosive percolation
We study the Shannon entropy of the cluster size distribution in classical as
well as explosive percolation, in order to estimate the uncertainty in the
sizes of randomly chosen clusters. At the critical point the cluster size
distribution is a power-law, i.e. there are clusters of all sizes, so one
expects the information entropy to attain a maximum. As expected, our results
show that the entropy attains a maximum at this point for classical
percolation. Surprisingly, for explosive percolation the maximum entropy does
not match the critical point. Moreover, we show that it is possible determine
the critical point without using the conventional order parameter, just
analysing the entropy's derivatives.Comment: 6 pages, 6 figure
Autonomous thermal machine for amplification and control of energetic coherence
We present a model for an autonomous quantum thermal machine comprised of two
qubits capable of manipulating and even amplifying the local coherence in a
non-degenerate external system. The machine uses only thermal resources,
namely, contact with two heat baths at different temperatures, and the external
system has a non-zero initial amount of coherence. The method we propose allows
for an interconversion between energy, both work and heat, and coherence in an
autonomous configuration working in out-of-equilibrium conditions. This model
raises interesting questions about the role of fundamental limitations on
transformations involving coherence and opens up new possibilities in the
manipulation of coherence by autonomous thermal machines.Comment: v1: 5 + 3 pages, 2 figures. v2: Restructured version with several new
results and a new appendix, 11 + 14 pages, 4 + 3 figures. v3: Improved and
corrected version with new discussions, 8 + 8 pages, 4 + 3 figure
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