Mimetic Finite Difference methods for Hamiltonian wave equations in 2D

In this paper we consider the numerical solution of the Hamiltonian wave equation in two spatial dimension. We use the Mimetic Finite Difference (MFD) method to approximate the continuous problem combined with a symplectic integration in time to integrate the semi-discrete Hamiltonian system. The main characteristic of MFD methods, when applied to stationary problems, is to mimic important properties of the continuous system. This approach, associated with a symplectic method for the time integration yields a full numerical procedure suitable to integrate Hamiltonian problems. A complete theoretical analysis of the method and some numerical simulations are developed in the paper.Comment: 26 pages, 8 figure

Numerical Methods for the Nonlocal Wave Equation of the Peridynamics

In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering because seems to provide an effective approach to modeling mechanical systems avoiding spatial discontinuous derivatives and body singularities. In particular, we will consider the linear model of peridynamics in a one-dimensional spatial domain. Here we will review some numerical techniques to solve this equation and propose some new computational methods of higher order in space; moreover we will see how to apply the methods studied for the linear model to the nonlinear one. Also a spectral method for the spatial discretization of the linear problem will be discussed. Several numerical tests will be given in order to validate our results

A space-time discretization of a nonlinear peridynamic model on a 2D lamina

Peridynamics is a nonlocal theory for dynamic fracture analysis consisting in a second order in time partial integro-differential equation. In this paper, we consider a nonlinear model of peridynamics in a two-dimensional spatial domain. We implement a spectral method for the space discretization based on the Fourier expansion of the solution while we consider the Newmark-$\beta$ method for the time marching. This computational approach takes advantages from the convolutional form of the peridynamic operator and from the use of the discrete Fourier transform. We show a convergence result for the fully discrete approximation and study the stability of the method applied to the linear peridynamic model. Finally, we perform several numerical tests and comparisons to validate our results and provide simulations implementing a volume penalization technique to avoid the limitation of periodic boundary conditions due to the spectral approach

Computation of Eigenvalues for Nonlocal Models by Spectral Methods

The purpose of this work is to study spectral methods to approximate the eigenvalues of nonlocal integral operators. Indeed, even if the spatial domain is an interval, it is very challenging to obtain closed analytical expressions for the eigenpairs of peridynamic operators. Our approach is based on the weak formulation of eigenvalue problem and we consider as orthogonal basis to compute the eigenvalues a set of Fourier trigonometric or Chebyshev polynomials. We show the order of convergence for eigenvalues and eigenfunctions in $L^2$-norm, and finally, we perform some numerical simulations to compare the two proposed methods

Sweeping-jet active flow control actuation effects on boundary layer separation on airfoil at ultralow Reynolds

Airfoils incur large drag penalty and a drop of lift production when operated at high angles of attack. Active flow control has a potential for improving the aerodynamic efficiency of airfoils at off-design operating conditions. Several simulations with Nektar++ CFD have been performed with intent to show the ability of sweeping jet active flow control method to improve performances of an airfoil at low Reynolds conditions. A sweeping jet is an output of a fluidic oscillator with no mobile parts which is able to make the fluid that goes through it to oscillate at its nozzle in a very stable way. This device has been previously successfully tested on airfoils with a deflected flap, with the intention of attach the boundary layer until the trailing edge. In this study, single sweeping jet on a 2D NACA0012 airfoil has been mathematically parameterized, with multiple degrees of freedom whose effect on the solution has been studied. In order to do so, a structured mesh containing the airfoil has been firstly studied and then modified with the aim of placing the jet on the airfoil’s upper surface. Baseline calculations show that at Re=1000 and with an angle of attack of 9o, the boundary layer detaches at 35% of the chord approximately. This study focuses on the effects on the boundary layer of the parameters of the sweeping-jet: the position, momentum coefficient, oscillation amplitude, frequency and opening angle have been modified. The sweeping jet has been studied in two configurations: the first one pointing normal to the airfoil’s upper surface and oscillating in the XY plane, and the second one near tangential to the upper surface of the airfoil, that is, the jet’s principal direction is almost the stream-wise direction. It oscillates on z-axis, but due to the fact that most experiments have been carried out in 2D, the frequency behaviour will be simulated represented by making the output velocity oscillate on its magnitude. The tangential configuration has been found to give the sweeping jet the authority to control flow by reattaching the boundary layer and significantly increase the lift coefficient of the airfoil. Also, it has been found a strong relationship between the jet’s position over the upper surface of the airfoil and the trajectory of the fluid, which is determinant on the aerodynamic characteristics of a wing. Finally, a quasi-3D study has been carried out, due to the importance found on previous studies of the span-wise distance between two consecutive jets on a finite wing. Taking advantage of the homogeneity of the z direction in this experiment, in order to analyze the stability to span-wise-dependent perturbations a unimodal Fourier expansion of varying wave-number has been used in the span-wise direction, which reduces the computational cost significantly. Also, this has allowed the authors to study the stability of the system depending on the span dimension.Els perfils alars pateixen un greu augment d’arrosegament i pèrdua de sustentació quan operen a grans angles d’atac. El control actiu t é un gran potencial de millorar l’efici ència aerodinàmica als perfils ’off-design’ que operen aquestes condicions.En aquest estudi s’- han dut a terme m´ ultiples simulacions mitjanc¸ant el software CFD Nektar++ per a demostrar l’habilitat que t é el sweeping jet per millorar les condicions a un Reynolds baix. El sweeping jet és un possible output d’un oscil lador fluídic sense parts m` obils que és capac¸ d’aconseguir que el fluid que passa através d’ell oscil li a la tovera d’una manera estable. Aquest dispositiu ja ha estat provat pr èvia i reeixidament en perfils amb fald ó (Flaps), amb la clara intenci ó de sostenir el fluxe fins a la vora final d’aquest (trailing edge). En aquest estudi, un únic jet en un perfil 2D NACA0012 s’ha parametritzat, amb certes variables com a graus de llibertat per tal d’estudiar-ne el seu efecte. En primer lloc s’ha treballat una malla estructurada la qual s’ha reestructurat posteriorment amb l’objectiu d’incloure el jet sobre del perfil. Les simulacions demostren com amb el perfil cru sense jet, a Re=1000 i un angle d’atac a 9o, la capa límit es desprén al 35% de la corda aproximadament. Els principals paràmetres modificats i testejats del jet han estat: la posici ´ o, el coeficient de moment, l’amplitud d’oscil laci ´ o, la freq ¨uència i l’angle d’apertura de la sortida del jet. El sweeping jet s’ha estudiat en dues configuracions: la primera apuntant perpendicular a l’extradós i oscil lant al pl à XY, i la segona quasi-tangencialment a l’extradós, és a dir, que la seva direcci ó principal és similar a la direcci ó stream-wise. En base a aquests resultats, hem obtingut que el jet tangencial permet tenir un control sobre el fluxe fent-lo reenganxarse un altre cop al perfil i augmentant significativament la sustentaci´ o. També s’ha trobat una forta relaci ó entre la posici ó del jet sobre el perfil amb la traject ` oria del fluid, el qualés determinant per a les característiques aerodinàmiques del perfil alar. Finalment, s’ha dut a terme un estudi en quasi-3D degut a l’import ància trobada en altres articles amb respecte a la dist ància d’amplada entre dos jets consecutius en un ala finita. Aprofitant la homogeneitat en la direcci ó Z del nostre estudi, s’ha utilitzat una expansió de Fourier unimodal de nombre d’ona variable en la direcci ó span-wise per tal d’estudiar l’evoluci ó dels paràmetres en direcci ó Z, el qual fa reduir el temps d’obtenci ó de resultats. Aix` o, a més, ha possibilitat als autors la capacitat d’estudi d’estabilitat de l’ala en funci ó de la seva amplada

Analysis of a long-duration AR throughout five solar rotations: Magnetic properties and ejective events

Coronal mass ejections (CMEs), which are among the most magnificent solar eruptions, are a major driver of space weather and can thus affect diverse human technologies. Different processes have been proposed to explain the initiation and release of CMEs from solar active regions (ARs), without reaching consensus on which is the predominant scenario, and thus rendering impossible to accurately predict when a CME is going to erupt from a given AR. To investigate AR magnetic properties that favor CMEs production, we employ multi-spacecraft data to analyze a long duration AR (NOAA 11089, 11100, 11106, 11112 and 11121) throughout its complete lifetime, spanning five Carrington rotations from July to November 2010. We use data from the Solar Dynamics Observatory to study the evolution of the AR magnetic properties during the five near-side passages, and a proxy to follow the magnetic flux changes when no magnetograms are available, i.e. during far-side transits. The ejectivity is studied by characterizing the angular widths, speeds and masses of 108 CMEs that we associated to the AR, when examining a 124-day period. Such an ejectivity tracking was possible thanks to the multi-viewpoint images provided by the Solar-Terrestrial Relations Observatory and Solar and Heliospheric Observatory in a quasi-quadrature configuration. We also inspected the X-ray flares registered by the GOES satellite and found 162 to be associated to the AR under study. Given the substantial number of ejections studied, we use a statistical approach instead of a single-event analysis. We found three well defined periods of very high CMEs activity and two periods with no mass ejections that are preceded or accompanied by characteristic changes in the AR magnetic flux, free magnetic energy and/or presence of electric currents. Our large sample of CMEs and long term study of a single AR, provide further evidence relating AR magnetic activity to CME and Flare production.Fil: Iglesias, Francisco Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Tecnológica Nacional. Facultad Regional de Mendoza; ArgentinaFil: Cremades Fernandez, Maria Hebe. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Tecnológica Nacional. Facultad Regional de Mendoza; ArgentinaFil: Merenda, Luciano A.. Universidad Tecnológica Nacional. Facultad Regional de Mendoza; ArgentinaFil: Mandrini, Cristina Hemilse. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Lopez Fuentes, Marcelo Claudio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Instituto de Ciencias Astronómicas, de la Tierra y del Espacio. Universidad Nacional de San Juan. Instituto de Ciencias Astronómicas, de la Tierra y del Espacio; ArgentinaFil: Lopez Fuentes, Marcelo Claudio. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Ugarte Urra, Ignacio. Spece Sciences División. Naval Research Laboratory; Estados Unido

The Digital Millennium Copyright Act: The Future of the Safe Harbor Provision

Inspired by the current federal case, Viacom v. YouTube, this discussion delves into the history and creation of the Digital Millennium Act (DMCA), the court cases which set the foundation for the ongoing Viacom v . YouTube case, and an in-depth discussion on the growth of technology and the Internet with how it is affecting copyright holders. This article culminates with an analysis on how the DMCA is applied to the current Internet landscape and offers potential solutions to solve the battle between Internet Service Providers and copyright holders

A common framework for single-molecule localization using sequential structured illumination

Localization of single fluorescent molecules is key for physicochemical and biophysical measurements, such as single-molecule tracking and super-resolution imaging by single-molecule localization microscopy. Over the last two decades, several methods have been developed in which the position of a single emitter is interrogated with a sequence of spatially modulated patterns of light. Among them, the recent MINFLUX technique outstands for achieving a ∼10-fold improvement compared with wide-field camera-based single-molecule localization, reaching ∼1–2 nm localization precision at moderate photon counts. Here, we present a common framework for this type of measurement. Using the Cramér-Rao bound as a limit for the achievable localization precision, we benchmark reported methods, including recent developments, such as MINFLUX and MINSTED, and long-established methods, such as orbital tracking. In addition, we characterize two new proposed schemes, orbital tracking and raster scanning, with a minimum of intensity. Overall, we found that approaches using an intensity minimum have a similar performance in the central region of the excitation pattern, independent of the geometry of the excitation pattern, and that they outperform methods featuring an intensity maximum.Fil: Masullo, Luciano Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Centro de Investigaciones en Bionanociencias "Elizabeth Jares Erijman"; ArgentinaFil: Lopez, Lucía Fernanda. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Centro de Investigaciones en Bionanociencias "Elizabeth Jares Erijman"; ArgentinaFil: Stefani, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Centro de Investigaciones en Bionanociencias "Elizabeth Jares Erijman"; Argentin

Autosomal Recessive Hypercholesterolemia Protein Interacts with and Regulates the Cell Surface Level of Alzheimer's Amyloid β Precursor Protein *

The familial Alzheimer's disease gene product amyloid beta protein precursor (A beta PP) is sequentially processed by beta- and gamma-secretases to generate the A beta peptide. Although much is known about the biochemical pathway leading to A beta formation, because extracellular aggregates of A beta peptides are considered the cause of Alzheimer's disease, the biological role of A beta PP processing is only recently being investigated. Cleavage of A beta PP by gamma-secretase releases, together with A beta, a COOH-terminal A beta PP intracellular domain, termed AID. Hoping to gain clues about proteins that regulates A beta PP processing and function, we used the yeast two-hybrid system to identify proteins that interact with the AID region of A beta PP. One of the interactors isolated is the autosomal recessive hypercholesterolemia (ARH) adapter protein. This molecular interaction is confirmed in vitro and in vivo by fluorescence resonance energy transfer and in cell lysates. Moreover, we show that reduction of ARH expression by RNA interference results in increased levels of cell membrane A beta PP. These data assert a physiological role for ARH in A beta PP internalization, transport, and/or processing