Uniqueness results for direct and inverse scattering by infinite surfaces in a lossy medium

We consider the Dirichlet boundary-value problem for the Helmholtz equation, Au + x2u = 0, with Imx > 0. in an hrbitrary bounded or unbounded open set C c W. Assuming continuity of the solution up to the boundary and a bound on growth a infinity, that lu(x)l < Cexp (Slxl), for some C > 0 and S~< Imx, we prove that the homogeneous problem has only the trivial salution. With this resnlt we prove uniqueness results for direct and inverse problems of scattering by a bounded or infinite obstacle.

Tempo, magnitude e o mito do cinema moderno

Neste texto, irei abordar três filmes ambientados em Portugal, cujas locações oferecem uma visão privilegiada da função do tempo e da magnitude no cinema, os quais, por sua vez, nos permitem reavaliar as categorias de clássico, moderno e pós-moderno aplicadas a esse meio. Trata-se de O estado das coisas (Der Stand der Dinge, Wim Wenders, 1982), Terra estrangeira (Walter Salles and Daniela Thomas, 1995) e Mistérios de Lisboa (Raúl Ruiz, 2010). Neles, a cidade se compõe de círculos viciosos, espelhos, réplicas e mise-en-abyme que interrompem o movimento vertiginoso característico da cidade modernista do cinema dos anos 20. Curiosamente, é também o lugar em que a assim chamada estética pós-moderna finalmente encontra abrigo em contos auto-irônicos que expõem as insuficiências dos mecanismos narrativos no cinema. Para compensá-las, recorre-se a procedimentos de intermídia, tais como fotografias de polaroid em O estado das coisas ou um teatro de papelão em Mistérios de Lisboa, que transformam uma realidade incomensurável em miniaturas fáceis de enquadrar e manipular. O real assim diminuído, no entanto, se revela um simulacro decepcionante, um ersatz da memória que evidencia o caráter ilusório da teleologia cosmopolita. Em minha abordagem, começarei por examinar a gênese interligada e transnacional desses filmes que resultou em três visões correlatas mas muito diversas do fim da história e da narrativa, típico da estética pós-moderna. A seguir, irei considerar o miniaturismo intermedial como uma tentativa de congelar o tempo no interior do movimento, uma equação que inevitavelmente nos remete ao binário deleuziano tempo-movimento, que também irei revisitar com o fim de distingui-lo da oposição entre cinema clássico e moderno. Por fim, irei propor a stasis reflexiva e a inversão de escala como demonominadores comuns entre todos os projetos ditos modernos, que por esta razão, segundo creio, são mais confiáveis que a modernidade enquanto indicadores de valores artísticos e políticos.

Multiple, discrete arcs on sunward convecting field lines in the 14-15 MLT region

Ionospheric plasma flow measurements and simultaneous observations of thin (∼0.2° invariant latitude (ILAT)), multiple, longitudinally extended auroral arcs of transient nature within 74°-76° ILAT and 1030-1130 UT (∼14-15 MLT) on January 12, 1989, are reported. The auroral structures appeared within the luminous belt of strong 630.0-nm emissions located predominantly on sunward convecting field lines equatorward of the convection reversal boundary as identified by the European Incoherent Scatter UHF radar. The events occurred during a period of several hours quasi-steady solar wind speed (∼ 700 km s−1) and a radially orientated interplanetary magnetic field (IMF) with a weak northward tilt (IMF Bz>0). These typical dayside auroral features are related to previous studies of auroral activity related to the upward region 1 current in the postnoon sector. The discrete auroral events presented here may result from magnetosheath plasma injections into the low-latitude boundary layer (LLBL) and an associated dynamo mechanism. An alternative explanation invokes kinetic Alfvén waves, triggered either by Kelvin-Helmholtz instability at the inner (or outer) edge of the LLBL or by pressure pulse induced magnetopause surface waves.

Dynamic auroral structure in the vicinity of the polar cusp - multipoint observations during southward and northward IMF

The low- and high-latitude boundary layers of the earth's magnetosphere [low-latitude boundary layer (LLBL) and mantle] play important roles in transferring momentum and energy from the solar wind to the magnetosphere-ionosphere system. Particle precipitation, field-aligned current, auroral emission, ionospheric ion drift and ground magnetic perturbations are among the low-altitude parameters that show signatures of various plasma processes in the LLBL and the magnetopause current layer. Magnetic merging events, Kelvin-Helmholtz waves, and pressure pulses excited by the variable solar wind/magnetosheath plasma are examples of boundary phenomena that may be coupled to the ionosphere via field-aligned currents. Optical auroral observation, by photometry and all-sky TV cameras, is a unique technique for investigating the spatial and temporal structure of the electron precipitation associated with such phenomena. However, the distinction between the different boundary layer plasma populations cannot in general be unambiguously determined by optics alone. Additional information, such as satellite observations of particle boundaries and field-aligned currents, is needed in order to identify the plasma source(s) and the magnetosphere-ionosphere coupling mode(s). Two categories of auroral activity/structure in the vicinity of the polar cusp are discussed in this paper, based on combined ground and satellite data. In one case, the quasi-periodic sequence of auroral events at the polar cap boundary involves accelerated electrons (< 1 keV) moving poleward (< 1 km s-1) and azimuthally along the persistent cusp/cleft arc poleward boundary with velocities (< 4 km s-1), comparable to the local ionospheric ion drift during periods of southward IMF. A critical question is whether or not the optical events signify a corresponding plasma flow across the open/closed field line boundary in such cases. Near-simultaneous observations of magnetopause flux transfer events (FTEs) and such optical/ion drift events are reported. The reverse pattern of motion of discrete auroral forms is observed during positive interplanetary magnetic field (IMF) B(Z), i.e. equatorward motion into the cusp/cleft background arc from the poleward edge. Combined satellite and ground-based information for the latter cases indicate a source mechanism, poleward of the cusp at the high-latitude magnetopause or plasma mantle, giving rise to strong momentum transfer and electron precipitation structures within a approximately 200 km-wide latitudinal zone at the cusp/cleft poleward boundary. The striking similarities of auroral electrodynamics in the cleft/mantle region during northward and southward IMF indicate that a qualitatively similar solar wind-magnetosphere coupling mode is operating. It is suggested that, in both cases, the discrete auroral forms represent temporal/spatial structure of larger-scale convection over the polar magnetosphere.

Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.