77,954 research outputs found
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
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-
Effects of systemic and non-systemic stresses on the thermal characteristics of corn
Experiments were conducted on corn plants using a calibrated spectroradiometer under field conditions in the indium antimonide channel (InSb, 2.8 to 5.6 mm) and the mercury cadmium telluride channel (HgCdTe, 7 to 14 mm). A ground cover experiment, an experiment on nonsystemic corn plants, and an experiment on systemic-stressed corn plants were included. The average spectral radiance temperature of corn plant populations was found (1) to be statistically significantly different for four healthy corn plant populations, (2) to increase with increased blight severity, and (3) to be statistically significantly different for varying rates of nitrogen applications
Characterizing Weak Chaos using Time Series of Lyapunov Exponents
We investigate chaos in mixed-phase-space Hamiltonian systems using time
series of the finite- time Lyapunov exponents. The methodology we propose uses
the number of Lyapunov exponents close to zero to define regimes of ordered
(stickiness), semi-ordered (or semi-chaotic), and strongly chaotic motion. The
dynamics is then investigated looking at the consecutive time spent in each
regime, the transition between different regimes, and the regions in the
phase-space associated to them. Applying our methodology to a chain of coupled
standard maps we obtain: (i) that it allows for an improved numerical
characterization of stickiness in high-dimensional Hamiltonian systems, when
compared to the previous analyses based on the distribution of recurrence
times; (ii) that the transition probabilities between different regimes are
determined by the phase-space volume associated to the corresponding regions;
(iii) the dependence of the Lyapunov exponents with the coupling strength.Comment: 8 pages, 6 figure
The Jacobi identity for Dirac-like brackets
For redundant second-class constraints the Dirac brackets cannot be defined
and new brackets must be introduced. We prove here that the Jacobi identity for
the new brackets must hold on the surface of the second-class constraints. In
order to illustrate our proof we work out explicitly the cases of a fractional
spin particle in 2+1 dimensions and the original Brink-Schwarz massless
superparticle in D=10 dimensions in a Lorentz covariant constraints separation.Comment: 14 pages, Latex. Final version to be published in Int. J. Mod. Phys.
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