On Hamiltonian balanced dynamics and the slowest invariant manifold

The concept of a slowest invariant manifold is investigated for the five-component model of Lorenz under conservative dynamics. It is shown that Lorenz's model is a two-degree-of-freedom canonical Hamiltonian system, consisting of a nonlinear vorticity-triad oscillator coupled to a linear gravity wave oscillator, whose solutions consist of regular and chaotic orbits. When either the Rossby number or the rotational Froude number is small, there is a formal separation of timescales, and one can speak of fast and slow motion. In the same regime, the coupling is weak, and the Kolmogorov–Arnold-Moser theorem is shown to apply. The chaotic orbits are inherently unbalanced and are confined to regions sandwiched between invariant tori consisting of quasi-periodic regular orbits. The regular orbits generally contain free fast motion, but a slowest invariant manifold may be geometrically defined as the set of all slow cores of invariant tori (defined by zero fast action) that are smoothly related to such cores in the uncoupled system. This slowest invariant manifold is not global; in fact, its structure is fractal; but it is of nearly full measure in the limit of weak coupling. It is also nonlinearly stable. As the coupling increases, the slowest invariant manifold shrinks until it disappears altogether. The results clarify previous definitions of a slowest invariant manifold and highlight the ambiguity in the definition of “slowness.” An asymptotic procedure, analogous to standard initialization techniques, is found to yield nonzero free fast motion even when the core solutions contain none. A hierarchy of Hamiltonian balanced models preserving the symmetries in the original low-order model is formulated; these models are compared with classic balanced models, asymptotically initialized solutions of the full system and the slowest invariant manifold defined by the core solutions. The analysis suggests that for sufficiently small Rossby or rotational Froude numbers, a stable slowest invariant manifold can be defined for this system, which has zero free gravity wave activity, but it cannot be defined everywhere. The implications of the results for more complex systems are discussed.

Attempted re-establishment of a sooty tern Onychoprion fuscatus breeding colony on Denis Island, Seychelles

Seychelles supports around three million nesting pairs of sooty terns. However, there have been recent declines and the colonies continue to face ongoing threats from habitat change and excessive commercial harvesting of their eggs, as well as potential threats by commercial fishing and climate change. A possible method to counter these threats is to re-establish breeding colonies on islands from which they have disappeared. An attempt was made to attract birds to a previously occupied island through habitat management, decoy birds and playback of recorded sooty tern calls. Habitat preparation involved predator eradication and tree removal to provide open ground with bare sandy areas and low herb vegetation. Overflying birds were attracted by broadcast calls, with some circling over and landing among the decoys. Large three-dimensional plastic models were superior to other models presented. This study demonstrated that large numbers of birds can be attracted by these means and that the birds then undertook behaviour associated with breeding, including egg laying by a few birds. However, after five seasons a breeding colony has not yet been established; one possible cause is the emergence of unexpected egg predators, common moorhen Gallinula chloropus and common myna Acridotheres tristis.

THE COMPTON-THICK SEYFERT 2 NUCLEUS OF NGC 3281: TORUS CONSTRAINTS FROM THE 9.7 mu m SILICATE ABSORPTION

We present mid-infrared (mid-IR) spectra of the Compton-thick Seyfert 2 galaxy NGC 3281, obtained with the Thermal-Region Camera Spectrograph at the Gemini-South telescope. The spectra present a very deep silicate absorption at 9.7 mu m, and [S IV] 10.5 mu m and [Ne II] 12.7 mu m ionic lines, but no evidence of polycyclic aromatic hydrocarbon emission. We find that the nuclear optical extinction is in the range 24 mag <= A(V) <= 83 mag. A temperature T = 300 K was found for the blackbody dust continuum component of the unresolved 65 pc nucleus and the region at 130 pc SE, while the region at 130 pc NW reveals a colder temperature (200 K). We describe the nuclear spectrum of NGC 3281 using a clumpy torus model that suggests that the nucleus of this galaxy hosts a dusty toroidal structure. According to this model, the ratio between the inner and outer radius of the torus in NGC 3281 is R(0)/R(d) = 20, with 14 clouds in the equatorial radius with optical depth of tau(V) = 40 mag. We would be looking in the direction of the torus equatorial radius (i = 60 degrees), which has outer radius of R(0) similar to 11 pc. The column density is N(H) approximate to 1.2 x 10(24) cm(-2) and the iron K alpha equivalent width (approximate to 0.5-1.2 keV) is used to check the torus geometry. Our findings indicate that the X-ray absorbing column density, which classifies NGC 3281 as a Compton-thick source, may also be responsible for the absorption at 9.7 mu m providing strong evidence that the silicate dust responsible for this absorption can be located in the active galactic nucleus torus.

Semiclassical evolution of dissipative Markovian systems

A semiclassical approximation for an evolving density operator, driven by a `closed` Hamiltonian operator and `open` Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra `open` term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further `small-chord` approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions.

Plasma confinement in tokamaks with robust torus

We present a non-linear symplectic map that describes the alterations of the magnetic field lines inside the tokamak plasma due to the presence of a robust torus (RT) at the plasma edge. This RT prevents the magnetic field lines from reaching the tokamak wall and reduces, in its vicinity, the islands and invariant curve destruction due to resonant perturbations. The map describes the equilibrium magnetic field lines perturbed by resonances created by ergodic magnetic limiters (EMLs). We present the results obtained for twist and non-twist mappings derived for monotonic and non-monotonic plasma current density radial profiles, respectively. Our results indicate that the RT implementation would decrease the field line transport at the tokamak plasma edge. (C) 2010 Elsevier B.V. All rights reserved.

Palaeodrainage on Marajo Island, northern Brazil, in relation to Holocene relative sea-level dynamics

A large area in northeastern Marajo Island, northern Brazil, has been characterized geomorphologically, applying information acquired from Landsat imagery. This study was combined with detailed sedimentologic analysis of continuous cores, which provided a record of depositional settings developed in this area through the Holocene. The results revealed well-preserved, meandering to anastomosed drainage networks of wide palaeochannels that were superimposed by a narrower palaeochannel system. In both cases, the sedimentary record consists of sands, heterolithic deposits and muds, locally rich in plant debris. The strata are organized into fining upward successions that reach approximately 18 m thick in the wide channels and 4 m thick in the narrow channels. Sedimentary features suggestive of a coastal location for the wider palaeochannels and reworking of sediments by tidal currents include the prevalence of well to moderately sorted, rounded to sub-rounded, fine- to medium-grained sands displaying foreset packages separated by mud couplets, suggestive of tidal cycles. The data presented herein point to a rise in relative sea level reaching the Lake Arari area during the early to late/mid Holocene. This event was followed by a relative sea level drop. Tectonics seem to have contributed to an overall lowering in relative sea level in the study area since the mid-Holocene, which does not follow the same pattern recorded in other areas along the northern Brazilian coast.

Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.

Is the meander growth in the Brazil Current system off Southeast Brazil due to baroclinic instability?

Temporally-growing frontal meandering and occasional eddy-shedding is observed in the Brazil Current (BC) as it flows adjacent to the Brazilian Coast. No study of the dynamics of this phenomenon has been conducted to date in the region between 22 degrees S and 25 degrees S. Within this latitude range, the flow over the intermediate continental slope is marked by a current inversion at a depth that is associated with the Intermediate Western Boundary Current (IWBC). A time series analysis of 10-current-meter mooring data was used to describe a mean vertical profile for the BC-IWBC jet and a typical meander vertical structure. The latter was obtained by an empirical orthogonal function (EOF) analysis that showed a single mode explaining 82% of the total variance. This mode structure decayed sharply with depth, revealing that the meandering is much more vigorous within the BC domain than it is in the IWBC region. As the spectral analysis of the mode amplitude time series revealed no significant periods, we searched for dominant wavelengths. This search was done via a spatial EOF analysis on 51 thermal front patterns derived from digitized AVHRR images. Four modes were statistically significant at the 95% confidence level. Modes 3 and 4, which together explained 18% of the total variance, are associated with 266 and 338-km vorticity waves, respectively. With this new information derived from the data, the [Johns, W.E., 1988. One-dimensional baroclinically unstable waves on the Gulf Stream potential vorticity gradient near Cape Hatteras. Dyn. Atmos. Oceans 11, 323-350] one-dimensional quasi-geostrophic model was applied to the interpolated mean BC-IWBC jet. The results indicated that the BC system is indeed baroclinically unstable and that the wavelengths depicted in the thermal front analysis are associated with the most unstable waves produced by the model. Growth rates were about 0.06 (0.05) days(-1) for the 266-km (338-km) wave. Moreover, phase speeds for these waves were low compared to the surface BC velocity and may account for remarks in the literature about growing standing or stationary meanders off southeast Brazil. The theoretical vertical structure modes associated with these waves resembled very closely to the one obtained for the current-meter mooring EOF analysis. We interpret this agreement as a confirmation that baroclinic instability is an important mechanism in meander growth in the BC system. (C) 2008 Elsevier B.V. All rights reserved.

Estratigrafia de sequências do intervalo aptiano ao albino na Bacia do Araripe, NE do Brasil

This study has as a main objective to make a detailed stratigraphic analysis of the Aptian-Albian interval in the east part of Araripe Basin, NE of Brazil which correspond, litostratigraphically, to Rio Da Batateira, Crato, Ipubi and Romualdo formations. The stratigraphic analysis was based on three different stages, the 1D, 2D and 3D analysis; these ones were adapted to the sequence stratigraphy concepts in order to create a chronostratigraphic framework for the study area within the basin. The database used in the present study contains field and well information, wells that belong to Santana Project, carried out by the Ministério de Minas e Energia- DNPM- CPRM from 1977 to 1978. The analysis 1D, which was done separately for each well and outcrop allowed the recognition of 13 sedimentary facies, mainly divided based on predominant litologies and sedimentary structures. Such facies are lithologically represented by pebble, sandstones, claystones, margas and evaporates; these facies are associated in order to characterize different depositional systems, that integrate from the continental environment (fluvial system and lacustre), paralic system (delta system and lagunar) to the marine environment (shelfenvironment). The first one, the fluvial system was divided into two subtypes: meandering fluvial system, characterized by fill channel and floodplain deposits; the facies of this system are associated vertically according to the textural thinning upward cycles (dirting-up trend pattern in well logs). Lacustrine environment is mainly related with the lithotypes of the Crato Formation, it shows a good distribution within the basin, been composed by green claystone deposits and calcareous laminated. Deltaic System represented by prodelta and delta front deposits which coarsening upward tendency. Lagunar system is characterised by the presence of anhydrite and gypsum deposits besides the black claystone deposits with vegetal fragments which do not contain a fauna typically marine. The marine platform system is composed by successions of black and gray claystone with fossiliferous fauna of Dinoflagellates (Spiniferites Mantell, Subtilisphaera Jain e Subtilisphaera Millipied genre) typical of this kind of depositional system. The sedimentary facies described are vertically arranged in cycles with progradational patterns which form textural coersening upward cycles and retrogradational, represented by textural thinning dowward cycles. Based in these cycles, in their stack pattern and the vertical change between these patterns, the systems tracks and the depositional sequences were recognized. The Low System Track (LST) and High System Track (HST) are composed by cycles with progradational stack pattern, whereas the Trangessive System Track (TST) is composed by retrogradational stack pattern cycles. The 2D stratigraphic analysis was done through the carrying out of two stratigraphic sections. For the selection of the datum the deepest maximum flooding surface was chosen, inside the Sequence 1, the execution of these sections allowed to understand the behaviour of six depositional systems along the study area, which were interpreted as cycles of second order or supercycles (cycles between 3 and 10 Ma), according to the Vail, et al (1977) classification. The Sequence 1, the oldest of the six identified is composed by the low, transgressive and high systems tracks. The first two system tracks are formed exclusively by fluvial deposits of the Rio da Batateira Formation whereas the third one includes deltaic and lacustrine deposits of the Crato Formation. The sequences 2 and 3 are formed by the transgressive systems tracks (lake spreading phase) and the highstand system track (lake backward phase). The TST of these sequences are formed by lacustrine deposits whereas HST contains deltaic deposits, indicating high rates of sedimentary supply at the time of it s deposition. The sequence 4 is composed by LST, TST and HST, The TST4 shows a significant fall of the lake base level, this track was developed in conditions of low relation between the creation rate of space of accommodation and the sedimentary influx. The TST4 marks the third phase of expansion of the lacustrine system in the section after the basin´s rift, the lacustrine system established in the previous track starts a backward phase in conditions that the sedimentary supply rate exceeds the creation rate of space accommodation. The sequence 5 was developed in two different phases, the first one is related with the latest expansion stage of the lake, (TST5), the basal track of this sequence. In this phase the base level of the lake rose considerably. The second phase (related to the TST5) indicates the end of the lacustrine domain in the Araripe Basin and the change to lagunar system ant tidal flat, with great portions in the supratidal. These systems were formed by restricted lagoons, with shallow level of water and with intermittent connections with the sea. This, was the phase when the Araripe Basin recorded the most several arid conditions of the whole interval studied, Aptian Albian, conditions that allow the formation of evaporitic deposits. The sequence 6 began its deposition after a significant fall of the sea (LST6). The sequence 6 is without any doubtlessly, the sequence that has deposits that prove the effective entrance of the sea into the Araripe Basin. The TST6, end of this sequence, represents the moment which the sea reaches its maximum level during the Aptian Albian time. The stratigraphic analysis of the Aptian Albian interval made possible the understanding that the main control in the development of the depositional sequences recognized in the Araripe Basin were the variations of the local base level, which are controlled itself by the climate changes

Mapeamento digital de análogos a reservatórios petrolíferos: exemplos para depósitos fluviais da Unidade Açu-3 - Bacia Potiguar

In the current work are presented the results about the study of digital mapping of analogs referents the fluvial oil reservoirs in the Açu Formation. With the regional recognizing in the south corner of Potiguar Basin was selected a area of 150 Km square in the west of Assu city. In this area was chosen the outcrops for the digital mapping and from the data fields and remote sensors were done the depositional architectural for the fluvial deposits, which it was named coarse meandering fluvial systems. In the deposits were individualized 3 (three) fluvial cycles, which they was separated by bounding surface of fifth order. Such cycles are preferentially sandy, with fining-upward sequence finished in flood plain deposits. Inner of the sandy levels of the filling channels were characterized least cycles, normaly incomplete, constituted by braided sandy bodies and bounding surfaces of fourth order. In the mapped area was chosen a outcrop with great exposition, where it was possible to see tipical deposits of filling channel and was in this outcrop that was done the digital mapping. In this outcrop was used diverse technics and tools, which they integrated sedimentological, altimetric (GPS, Total Station), LIDAR (Light Detection and Ranging), digital photomosaic of high resolution and of the inner geometries (Ground Penetration Radar) data sets. For the integrating, interpretation and visualization of data was used software GoCAD®. The final product of the outcrop digital mapping was the photorealistic model of part of the cliff (or slope) because the observed reflectors in the radargrams were absents. A part of bar oblique accretion was modeled according to GPR gride of 200x200 meters in the alluvial Assu river probable recent analog. With the data of inner geometries was developed the three-dimentional sedimentary architectural, where it was possible characterize sand sheet deposits and many hierarchy of braided channels. At last, simulations of sedimentary geometries and architectures of the Potiguar Basin Fluvial Reservoirs were done with PetBool software, in order to understand the capacity of this program in simulations with a lot of numbers of conditioning wells. In total, 45 simulations was acquired, where the time and the channel numbers increase in relation of the conditioning wells quantity. The deformation of the meanders was detected from the change of simulated dominion dimensions. The presence of this problem was because the relationship between the simulated dominion and the width of the meander

Estudos sedimentológicos e o contexto estrutural da formação Serra do Martins, nos platôs de Portalegre, Martins e Santana/RN

This dissertation deals with sedimentological and structural framework of the siliciclastic rock of the Serra do Martins Formation (FSM) in the Portalegre, Martins and Santana plateau, located to the south of Potiguar Basin, in the southwest and central Rio Grande do Norte state. This formation, regarded as of Oligo-Miocene age based on intrusive relations of the Miocene Macau volcanics, has a still disputable age due to the lack of appropriate bio and/or chronostratigraphic markers. The FSSM deposits crop out along 650 to 750 m high plateau, as a remanescent sedimentary cover directly overlying topographically uplifted pre-cambrian crystalline rocks. During the last decades, these deposits were interpreted according to a Tertiary paleoclimatic evolutionary model, associated to pedogenetic processes. The sedimentological characterization of the FSM was done through a detailed study of its facies, petrography and diagenetic features. The facies study was based on description of field relations, textures and structures, the piling up of the strata and their lateral variations. The FSM was deposited by an anastomosing to coarse-meandering fluvial system, including deposits of lag, cannel-fill, ouver-bank and flood plain. The petrographic composition of the sediments, coupled to their facies and paleocurrent directions, suggest a rather distal sourcearea, to the south of the present plateau. The diagenetic study identified an incipient grain mechanical compaction, pronounced dissolution of the framework, matrix and/or cement components, intense precipitation of kaolinite, silic and, eventually, iron oxides, besides mechanical infiltration of the clays. Most of these events, regarded in the literature as associated to near-surface conditions (eo or telodiagenesis), indicate the FSM sediments were never deeply buried. Topographic relations along longitudinal and transversal sections reaching the Potiguar Basin to the north identified regional dips that allow to discuss stratigraphic correlations between the FSM and the basin formations. The sedimentological features of the different units and the intrusive relations of the Macau volcanics were also considered in these correlations,which support the Oligo-Miocene age previously accepted for the FSM. Concerning the tectonic framework of the FSM, this work investigated the pre-cambrian to cretaceous heritage and the cenozoic deformation, allowing the recognition of pre-, sin and post-FSM structures. The crystalline basement, belonging to the Seridó Belt, displays NE and WNW foliation trends related to the Brasiliano-age ductile shear zones. In this terrain, brittle-ductile and brittle NE- and NW-trending structures, associated with extensional joints filled with pegmatites and quartz veins, are related to an E-W compression by the end of Brasiliano Cycle. The E-W joints and NE-trending fractures were reactivated by N-S to N-S to NW extension during late Jurassic to Cretaceous times, controlling the emplacement of the Rio Ceará-Mirim basic dyke swarm and the opening of the Potiguar rift basin

O graben de Palestina: contribuição à estratigrafia e estrutura do estágio rifte na bacia do Araripe, nordeste do Brasil

The Palestina Graben is one of the NE-trending asymmetric grabens of the Araripe Basin. This basin rests on the precambrian terrains of the Transversal Zone, Borborema Province, immediately to the south of the Patos Lineament. It is part of the Interior Basins province of Northeastern Brazil, being related to the fragmentation of the Gondwana supercontinent and the opening of the South Atlantic ocean. The Palestina Graben trends NE-SW and presents an asymmetric geometry, controled by the NW extensional eocretaceous strain. The graben borders display distinct geometries. The SE border is a flexural margin, characterized by the non conformity of the eopaleozoic Mauriti Formation (the oldest unit of the basin) overlying the crystalline basement, but also affected by normal faults with small displacements. On the opposite, the NW border is continuous and rectilinear, being marked by normal faults with major displacements, that control the general tilting of the layers to the NW. In this sense, the Mauriti Formation is overlain by the Brejo Santo, Missão Velha (which also occurs in the Brejo Santo-Mauriti horst, to the NW of the fault border) and Abaiara formations, the latter restricted to the graben. The interpretation of available gravity data and a seismic line indicates that the main fault has a variable dip slip component, defining two deeper portions within the graben, in which the sedimentary column can reach thicknesses of up to 2 km. Regarding to the stratigraphy of Araripe Basin in the study area, the sedimentary package includes three distinct tectonosequences. The Paleozoic Syneclisis Tectonosequence is composed by the Mauriti Formation, deposited by a braided fluvial system. The Jurassic Tectonosequence, whose tectonic setting is still debatable (initial stage of the Neocomian rift, or a pre-rift syneclisis ?), is represented by the Brejo Santo Formation, originated in a distal floodplain related to ephemeral drainages. The Rift Tectonosequence, of neocomian age, includes the Missão Velha Formation, whose lower section is related to a braided to meandering fluvial system, outlining the Rift Initiation Tectonic Systems Tract. The upper section of the Missão Velha Formation is separated from the latter by a major unconformity. This interval was originated by a braided fluvial system, overlain by the Abaiara Formation, a deltaic system fed by a meandering fluvial system. Both sections correspond to the Rift Climax Tectonic Systems Tract. In the area, NE-trending normal to oblique faults are associated with NW transfer faults, while ENE to E-W faults display dominant strike slip kinematics. Both NE and E-W fault sets exhibit clear heritage from the basement structures (in particular, shear zones), which must have been reactivated during the eocretaceous rifting. Faults with EW trends display a dominant sinistral shear sense, commonly found along reactivated segments of the Patos Lineament and satellyte structures. Usually subordinate, dextral directional movements, occur in faults striking NNW to NE. Within this framework bearing to the Palestina Graben, classical models with orthogonal extension or pull-apart style deserve some caution in their application. The Palestina Graben is not limited, in its extremeties, by E-W transcurrent zones (as it should be in the case of the pull-apart geometry), suggesting a model close to the classic style of orthogonal opening. At the same time, others, adjacent depocenters (like the Abaiara-Jenipapeiro semi-graben) display a transtensional style. The control by the basement structures explains such differences

Topological signatures in CMB temperature anisotropy maps

We propose an alternative formalism to simulate cosmic microwave background (CMB) temperature maps in Lambda CDM universes with nontrivial spatial topologies. This formalism avoids the need to explicitly compute the eigenmodes of the Laplacian operator in the spatial sections. Instead, the covariance matrix of the coefficients of the spherical harmonic decomposition of the temperature anisotropies is expressed in terms of the elements of the covering group of the space. We obtain a decomposition of the correlation matrix that isolates the topological contribution to the CMB temperature anisotropies out of the simply connected contribution. A further decomposition of the topological signature of the correlation matrix for an arbitrary topology allows us to compute it in terms of correlation matrices corresponding to simpler topologies, for which closed quadrature formulas might be derived. We also use this decomposition to show that CMB temperature maps of (not too large) multiply connected universes must show patterns of alignment, and propose a method to look for these patterns, thus opening the door to the development of new methods for detecting the topology of our Universe even when the injectivity radius of space is slightly larger than the radius of the last scattering surface. We illustrate all these features with the simplest examples, those of flat homogeneous manifolds, i.e., tori, with special attention given to the cylinder, i.e., T-1 topology.

Scaling invariance for the escape of particles from a periodically corrugated waveguide

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Labyrinthic standard non-twist map

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)