719 research outputs found
Darboux class of cosmological fluids with time-dependent adiabatic indices
A one-parameter family of time dependent adiabatic indices is introduced for
any given type of cosmological fluid of constant adiabatic index by a
mathematical method belonging to the class of Darboux transformations. The
procedure works for zero cosmological constant at the price of introducing a
new constant parameter related to the time dependence of the adiabatic index.
These fluids can be the real cosmological fluids that are encountered at
cosmological scales and they could be used as a simple and efficient
explanation for the recent experimental findings regarding the present day
accelerating universe. In addition, new types of cosmological scale factors,
corresponding to these fluids, are presentedComment: document with the following three latex files: 1) quhm.tex: 17 pages,
10 figs, 16 numbered refs, Honorable Mention GRF 2000, 2) errad.tex: Errata
and Addenda (EaA) of 5 pages with 2 figs enclosed, 3) analogy.tex: Negative
friction of Darboux cosmological fluids of 4 page
Existence of periodic orbits in nonlinear oscillators of Emden-Fowler form
The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is
mapped to an Emden-Fowler (EF) equation that is written as an autonomous
two-dimensional ODE system for which we provide the phase-space analysis and
the parametric solution. Through an invariant transformation we find periodic
solutions to a certain class of EF equations that pass an integrability
condition. We show that this condition is necessary to have periodic solutions
and via the ODE analysis we also find the sufficient condition for periodic
orbits. EF equations that do not pass integrability conditions can be made
integrable via an invariant transformation which also allows us to construct
periodic solutions to them. Two other nonlinear equations, a zero-frequency
Ermakov equation and a positive power Emden-Fowler equation are discussed in
the same contextComment: 13 pages, 5 figures, title changed and content extended, version
accepted at Phys. Lett.
Multifractal analyses of row sum signals of elementary cellular automata
We first apply the WT-MFDFA, MFDFA, and WTMM multifractal methods to binomial
multifractal time series of three different binomial parameters and find that
the WTMM method indicates an enhanced difference between the fractal components
than the known theoretical result. Next, we make use of the same methods for
the time series of the row sum signals of the two complementary ECA pairs of
rules (90,165) and (150,105) for ten initial conditions going from a single 1
in the central position up to a set of ten 1's covering the ten central
positions in the first row. Since the members of the pairs are actually similar
from the statistical point of view, we can check which method is the most
stable numerically by recording the differences provided by the methods between
the two members of the pairs for various important quantities of the scaling
analyses, such as the multifractal support, the most frequent Holder exponent,
and the Hurst exponent and considering as the better one the method that
provides the minimum differences. According to this criterion, our results show
that the MFDFA performs better than WT-MFDFA and WTMM in the case of the
multifractal support, while for the other two scaling parameters the WT-MFDFA
is the best. The employed set of initial conditions does not generate any
specific trend in the values of the multifractal parametersComment: 23 pages including an appendix and 11 figures, extended version
accepted for publication by Physica
Scaling analyses based on wavelet transforms for the Talbot effect
The fractal properties of the transverse Talbot images are analysed with two
well-known scaling methods, the wavelet transform modulus maxima (WTMM) and the
wavelet transform multifractal detrended fluctuation analysis (WT-MFDFA). We
use the widths of the singularity spectra, Delta alpha=alpha_H-alpha_min, as a
characteristic feature of these Talbot images. The tau scaling exponents of the
q moments are linear in q within the two methods, which proves the
monofractality of the transverse diffractive paraxial field in the case of
these imagesComment: 9 pages, 6 figures, version accepted at Physica
Shifted one-parameter supersymmetric family of quartic asymmetric double-well potentials
Extending our previous work (Rosu, Mancas, Chen, Ann.Phys. 343 (2014)
87-102), we define supersymmetric partner potentials through a particular
Riccati solution of the form F(x)=(x-c)^2-1, where c is a real shift parameter,
and work out the quartic double-well family of one-parameter isospectral
potentials obtained by using the corresponding general Riccati solution. For
these parametric double well potentials, we study how the localization
properties of the two wells depend on the parameter of the potentials for
various values of the shifting parameter. We also consider the supersymmetric
parametric family of the first double-well potential in the Razavy chain of
double well potentials corresponding to F(x)=(1/2)sinh 2x-2(1+sqrt 2)sinh
2x/[(1+sqrt 2) cosh 2x+1], both unshifted and shifted, to test and compare the
localization propertiesComment: 11 pages, 4 figures, published versio
Traveling wave solutions for wave equations with two exponential nonlinearities
We use a simple method that leads to the integrals involved in obtaining the
traveling wave solutions of wave equations with one and two exponential
nonlinearities. When the constant term in the integrand is zero, implicit
solutions in terms of hypergeometric functions are obtained while when that
term is nonzero all the basic traveling wave solutions of Liouville, Tzitzeica
and their variants, as well as sine/sinh-Gordon equations with important
applications in the phenomenology of nonlinear physics and dynamical systems
are found through a detailed study of the corresponding elliptic equationsComment: 9 pages, 7 figures, 42 references, version matching the published
articl
Multifractal properties of elementary cellular automata in a discrete wavelet approach of MF-DFA
In 2005, Nagler and Claussen (Phys. Rev. E 71 (2005) 067103) investigated the
time series of the elementary cellular automata (ECA) for possible
(multi)fractal behavior. They eliminated the polynomial background at^b through
the direct fitting of the polynomial coefficients a and b. We here reconsider
their work eliminating the polynomial trend by means of the multifractal-based
detrended fluctuation analysis (MF-DFA) in which the wavelet multiresolution
property is employed to filter out the trend in a more speedy way than the
direct polynomial fitting and also with respect to the wavelet transform
modulus maxima (WTMM) procedure. In the algorithm, the discrete fast wavelet
transform is used to calculate the trend as a local feature that enters the
so-called details signal. We illustrate our result for three representative ECA
rules: 90, 105, and 150. We confirm their multifractal behavior and provide our
results for the scaling parametersComment: 8 pages, 5 figures, 21 reference
Multifractal properties of elementary cellular automata in a discrete wavelet approach of MF-DFA
In 2005, Nagler and Claussen (Phys. Rev. E 71 (2005) 067103) investigated the
time series of the elementary cellular automata (ECA) for possible
(multi)fractal behavior. They eliminated the polynomial background at^b through
the direct fitting of the polynomial coefficients a and b. We here reconsider
their work eliminating the polynomial trend by means of the multifractal-based
detrended fluctuation analysis (MF-DFA) in which the wavelet multiresolution
property is employed to filter out the trend in a more speedy way than the
direct polynomial fitting and also with respect to the wavelet transform
modulus maxima (WTMM) procedure. In the algorithm, the discrete fast wavelet
transform is used to calculate the trend as a local feature that enters the
so-called details signal. We illustrate our result for three representative ECA
rules: 90, 105, and 150. We confirm their multifractal behavior and provide our
results for the scaling parametersComment: 8 pages, 5 figures, 21 reference
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