Analytical solutions for Navier-Stokes equations with ψ\psi-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 $\psi$-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 $\Re(s)>r$, $r\in \mathbb{R}$, 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$^o$ 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 $p$-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 $k$-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 $k$-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

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 $\psi$-Hilfer fractional derivative. In this sense, some examples are presented, in order to consolidate the results obtained.Comment: 15 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