Descripción: The factorization theorems are a generalization for J-biexpansive meromorphic operator-valued functions on an infinite-dimensional Hilbert space of the theorems on decomposition of J-expansive matrix functions on a finite-dimensional Hilbert space due to A. V. Efimov and V. P. Potapov [Uspekhi Mat. Nauk 28 (1973), 65-130; Trudy Moskov. Mat. Obšč. 4 (1955), 125-236]. They also generalize theorems on factorization of J-expansive meromorphic operator functions due to Ju. P. Ginzburg [Izv. Vysš. Učebn. Zaved. Matematika 32 (1963), 45-53]. Within the framework of generalized network theory, the results can be applied to the J-biexpansive real operators that characterize a Hilbert port. Application of the extraction procedure to a given real operator leads to its splitting into a product of real factors, corresponding to Hilbert ports of a simpler structure. This can be interpreted as an extension of the classical method of synthesis of passive n-ports by factor decomposition. © 1981.

Descripción: Factorization of J-biexpansive operator-valued functions on an infinite-dimensional Hilbert space is performed, to extract terms with an arbitrary number of poles of first order on the left and right half planes. Special emphasis is given to the case of reciprocal poles, which has an application to the synthesis of reciprocal passive linear systems as an extension of the classical synthesis of reciprocal n-ports by factor decomposition. © 1986.

Descripción: A factorization method is given to extract poles located on the imaginary axis for J-biexpansive meromorphic operator-valued functions acting on an infinite-dimensional Hilbert space. Decomposition of a real operator in terms of real factors, applicable to Hilbert ports, is also described, thus generalizing synthesis techniques originally developed for passive n-ports. © 1985.

Descripción: The spatial stability of similarity solutions for an incompressible fluid flowing along a channel with porous walls and driven by constant uniform suction along the walls is analyzed. This work extends the results of Durlofsky and Brady [Phys. Fluids 27, 1068 (1984)] to a wider class of similarity solutions, and examines the spatial stability of small amplitude perturbations of arbitrary shape, generated at the entrance of the channel. It is found that antisymmetric perturbations are the best candidates to destabilize the solutions. Temporally stable asymmetric solutions with flow reversal presented by Zaturska, Drazin, and Banks [Fluid Dyn. Res. 4, 151 (1988)] are found to be spatially unstable. The perturbed similarity solutions are also compared with fully bidimensional ones obtained with a finite difference code. The results confirm the importance of similarity solutions and the validity of the stability analysis in a region whose distance to the center of the channel is more than three times the channel half-width. © 2000 American Institute of Physics.

Descripción: Working within the domain of inviscid incompressible MHD theory, we found that a tangential discontinuity (TD) separating two uniform regions of different density, velocity and magnetic field may be Kelvin-Helmholtz (KH) stable and yet a study of a transition between the same constant regions given by a continuous velocity profile shows the presence of the instability with significant growth rates. Since the cause of the instability stems from the velocity gradient, and since a TD may be considered as the ultimate limit of such gradient, the statement comes as a surprise. In fact, a long wavelength (λ) boundary for the KH instability does not exist in ordinary liquids being instead a consequence of the presence of magnetic shear, a possibility that has passed unnoticed in the literature. It is shown that KH modes of a magnetic field configuration with constant direction do not have the long A boundary. A theoretical explanation of this feature and examples of the violation of the TD stability condition are given using a model that can be solved in closed form. Stability diagrams in the (kd, MA) plane are given (where kd = 2πd/λ, 2d is the velocity gradient length scale, and MA is the Alfvénic Mach number) that show both the well-known limit at small λs and the boundary for large but finite As noted here. Consequences of this issue are relevant for stability studies of the dayside magnetopause as the stability condition for a TD should be used with care in data analysis work.

Descripción: Compressibility has a strong influence on the stability of velocity shear layers when the difference of velocity ΔV across the flow becomes supersonic. The flanks of the Earth's magnetopause are normally supersonic Ms > 1, and super-Alfvénic MA > 1, depending on the distance from the dayside terminator (Ms and MA are the sonic and Alfvén Mach numbers of the magnetosheath plasma, respectively). The stability of MHD supersonic flows depends, also on several other features, such as the finite thickness Δ of the boundary layer, the relative orientation of velocity and magnetic fields, the density jump across the boundary and the magnetic shear angle. We analyze the MHD stability of some representative flank sites modeled after data from spacecraft crossings of the magnetopause under different interplanetary conditions, complementing these cases with extrapolations of likely conditions upstream, and downstream of the crossing site. Under northward interplanetary magnetic field conditions, there are solar wind regimes such that the near, but already supersonic, flank of the magnetopause may be locally stable. Stability is possible, e.g., when M s becomes larger than ∼1.2-1.4 while MA remains smaller than 1.2, and there is magnetic shear between the geomagnetic and the interplanetary magnetic field. Solar winds favouring local stability of the boundary layer are cold, not-too-dense plasmas, with strong magnetic fields, so that MA is smaller, while Ms is larger, than normal values of the magnetosheath flow. A gap between dayside and tail amplifying regions of Kelvin-Helmholtz disturbances over the magnetopause may exist when the above conditions are realized. © 2009 IOP Publishing Ltd.

Descripción: Fil:Gratton, F.T. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

Descripción: The Kelvin-Helmoltz instability (KH) with formation of vortices appears in a wide variety of terrestrial, interplanetary, and astrophysical contexts. We study a series of iterated rolled-up coherent plasma structures (15) that flow in the equatorial Earth's boundary layer (BL), observed on October 24, 2001. The data were recorded during a 1.5 hour-long Wind crossing of the BL at the dawn magnetospheric flank, tailward of the terminator (X≈-13 RE). The interplanetary magnetic field (IMF) was radially directed, almost antiparallel to the magnetosheath (MS) flow. This configuration is expected to be adverse to the KH instability because of the collinearity of field and flow, and the high compressibility of the MS. We analyze the BL stability with compressible MHD theory using continuous profiles for the physical quantities. Upstream, at near Earth sites, we input parameters derived from an exact MHD solution for collinear flows. Further downtail at Wind position we input measured parameters. The BL is found KH unstable in spite of unfavorable features of the external flow. On the experimental side, the passage of vortices is inferred from the presence of low density - hot plasma being accelerated to speeds higher than that of the contiguous MS. It is further supported by the peculiar correlation of relative motions (in the bulk velocity frame): cold-dense plasma drifts sunward, while hot-tenuous plasma moves tailward. This event differs from many other studies that reported BL vortices under strongly northward IMF orientations. This is a case of KH vortices observed under an almost radial IMF, with implicit significance for the more common Parker's spiral fields, and the problem of plasma entry in the magnetosphere.

Descripción: Fil:Gnavi, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

Descripción: The expanded bow shock on and around "the day the solar wind almost disappeared" (11 May 1999) allowed the Geotail spacecraft to make a practically uninterrupted 54-h-long magnetosheath pass near dusk (16:30-21:11 magnetic local time) at a radial distance of 24 to 30 RE (Earth radii). During most of this period, interplanetary parameters varied gradually and in such a way as to give rise to two extreme magnetosheath structures, one dominated by magnetohydrodynamic (MHD) effects and the other by gas dynamic effects. We focus attention on unusual features of electromagnetic ion wave activity in the former magnetosheath state, and compare these features with those in the latter. Magnetic fluctuations in the gas dynamic magnetosheath were dominated by compressional mirror mode waves, and left-and right-hand polarized electromagnetic ion cyclotron (EIC) waves transverse to the background field. In contrast, the MHD magnetosheath, lasting for over one day, was devoid of mirror oscillations and permeated instead by EIC waves of weak intensity. The weak wave intensity is related to the prevailing low solar wind dynamic pressures. Left-hand polarized EIC waves were replaced by bursts of right-hand polarized waves, which remained for many hours the only ion wave activity present. This activity occurred when the magnetosheath proton temperature anisotropy (=Tp, ⊥/Tp, ∥-1) became negative. This was because the weakened bow shock exposed the magnetosheath directly to the (negative) temperature anisotropy of the solar wind. Unlike the normal case studied in the literature, these right-hand waves were not by-products of left-hand polarized waves but derived their energy source directly from the magnetosheath temperature anisotropy. Brief entries into the low latitude boundary layer (LLBL) and duskside magnetosphere occurred under such inflated conditions that the magnetospheric magnetic pressure was insufficient to maintain pressure balance. In these crossings, the inner edge of the LLBL was flowing sunward. The study extends our knowledge of magnetosheath ion wave properties to the very low solar wind dynamic pressure regime. © European Geosciences Union 2005.