67,992 research outputs found
Analytical solutions for Navier-Stokes equations with -Caputo fractional derivative
This work aims to use the homotopy analysis method to obtain analytical
solutions of linear time-fractional Navier-Stokes equations with cylindrical
coordinates and of a system of nonlinear time-fractional Navier-Stokes
equations with Cartesian coordinates. These equations are described in the
-Caputo time-fractional derivative. The solutions obtained for
time-fractional Navier-Stokes equations are graphically presented.Comment: 17 pages, 8 figures. arXiv admin note: text overlap with
arXiv:2004.0236
Zeros of Dirichlet Polynomials via a Density Criterion
We obtain a necessary and sufficient condition in order that a semi-plane of
the form , , is free of zeros of a given Dirichlet
polynomial. The result may be considered a natural generalization of a
well-known criterion for the truth of the Riemann hypothesis due to
B\'aez-Duarte. An analog for the case of Dirichlet polynomials of a result of
Burnol which is closely related to B\'aez-Duarte's one is also established
Magnetosphere-Ionosphere Coupling and Field-Aligned Currents
It is presented in this paper a review of one of several interactions between
the magnetosphere and the ionosphere through the field-aligned currents (FACs).
Some characteristics and physical implications of the currents flowing in a
plane perpendicular to the magnetic field at high latitudes are discussed. The
behavior of this system as an electric circuit is explained, where momentum and
energy are transferred via Poynting flux from the magnetosphere into the
ionosphere.Comment: 5 pages, 4 figures; Revista Brasileira de Ensino de F\'isica (2014
Hilfer-Katugampola fractional derivative
We propose a new fractional derivative, the Hilfer-Katugampola fractional
derivative. Motivated by the Hilfer derivative this formulation interpolates
the well-known fractional derivatives of Hilfer, Hilfer-Hadamard,
Riemann-Liouville, Hadamard, Caputo, Caputo-Hadamard, Liouville, Weyl,
generalized and Caputo-type. As an application, we consider a nonlinear
fractional differential equation with an initial condition using this new
formulation. We show that this equation is equivalent to a Volterra integral
equation and demonstrate the existence and uniqueness of solution to the
nonlinear initial value problem.Comment: 21 page
Impact Angle Control of Interplanetary Shock Geoeffectiveness
We use OpenGGCM global MHD simulations to study the nightside magnetospheric,
magnetotail, and ionospheric responses to interplanetary (IP) fa st forward
shocks. Three cases are presented in this study: two inclined oblique shocks,
here after IOS-1 and IOS-2, where the latter has a Mach number twice stronger
than the former. Both shocks have impact angles of 30 in relation to the
Sun-Earth line. Lastly, we choose a frontal perpendicular shock, FPS, whose
shock normal is along the Sun-Earth line, with the same Mach number as IOS-1.
We find that, in the IOS-1 case, due to the north-south asymmetry, the
magnetotail is deflected southward, leading to a mild compression. The
geomagnetic activity observed in the nightside ionosphere is then weak. On the
other hand, in the head-on case, the FPS compresses the magnetotail from both
sides symmetrically. This compression triggers a substorm allowing a larger
amount of stored energy in the magnetotail to be released to the nightside
ionosphere, resulting in stronger geomagnetic activity. By comparing IOS-2 and
FPS, we find that, despite the IOS-2 having a larger Mach number, the FPS leads
to a larger geomagnetic response in the nightside ionosphere. As a result, we
conclude that IP shocks with similar upstream conditions, such as magnetic
field, speed, density, and Mach number, can have different geoeffectiveness,
depending on their shock normal orientation.Comment: 12 pages, 5 figures in Journal of Geophysical Research (2015
Impact Angle Control of Interplanetary Shock Geoeffectiveness: A Statistical Study
We present a survey of interplanetary (IP) shocks using Wind and ACE
satellite data from January 1995 to December 2013 to study how IP shock
geoeffectiveness is controlled by IP shock impact angles. A shock list covering
one and a half solar cycle is compiled. The yearly number of IP shocks is found
to correlate well with the monthly sunspot number. We use data from SuperMAG, a
large chain with more than 300 geomagnetic stations, to study geoeffectiveness
triggered by IP shocks. The SuperMAG SML index, an enhanced version of the
familiar AL index, is used in our statistical analysis. The jumps of the SML
index triggered by IP shock impacts on the Earth's magnetosphere is
investigated in terms of IP shock orientation and speed. We find that, in
general, strong (high speed) and almost frontal (small impact angle) shocks are
more geoeffective than inclined shocks with low speed. The strongest
correlation (correlation coefficient R = 0.70) occurs for fixed IP shock speed
and varying the IP shock impact angle. We attribute this result, predicted
previously with simulations, to the fact that frontal shocks compress the
magnetosphere symmetrically from all sides, which is a favorable condition for
the release of magnetic energy stored in the magnetotail, which in turn can
produce moderate to strong auroral substorms, which are then observed by ground
based magnetometers.Comment: 8 pages, 5 figures, Journal of Geophysical Research (2015
Entanglement modes and topological phase transitions in superconductors
Topological insulators and topological superconductors display various
topological phases that are characterized by different Chern numbers or by
gapless edge states. In this work we show that various quantum information
methods such as the von Neumann entropy, entanglement spectrum, fidelity, and
fidelity spectrum may be used to detect and distinguish topological phases and
their transitions. As an example we consider a two-dimensional -wave
superconductor, with Rashba spin-orbit coupling and a Zeeman term. The nature
of the phases and their changes are clarified by the eigenvectors of the
-space reduced density matrix. We show that in the topologically nontrivial
phases the highest weight eigenvector is fully aligned with the triplet pairing
state. A signature of the various phase transitions between two points on the
parameter space is encoded in the -space fidelity operator.Comment: 17 pages, 19 figure
Sign regularity of Maclaurin coefficients of functions in the Laguerre-P\'olya class
We prove that the signs of the Maclaurin coefficients of a wide class of
entire functions that belong to the Laguerre-P\'olya class posses a regular
behaviour.Comment: 12 page
Child mortality in Penna ageing model
Assuming the deleterious mutations in the Penna ageing model to affect mainly
the young ages, we get an enhanced mortality at very young age, followed by a
minimum of the mortality, and then the usual exponential increase of mortality
with age.Comment: To pages including one figur
On the existence and stability for non-instantaneuos impulsive fractional integrodifferential equation
In this paper, by means of Banach fixed point theorem, we investigate the
existence and Ulam--Hyers--Rassias stability of the non-instantaneous impulsive
integrodifferential equation by means of -Hilfer fractional derivative.
In this sense, some examples are presented, in order to consolidate the results
obtained.Comment: 15 page
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