Linear Zone Research Articles

A general mechanism to generate three limit cycles in planar Filippov systems with two zones

Discontinuous piecewise linear systems with two zones are considered. A general canonical form that includes all the possible configurations in planar linear systems is introduced and exploited. It is shown that the existence of a focus in one zone is sufficient to get three nested limit cycles, independently on the dynamics of the another linear zone. Perturbing a situation with only one hyperbolic limit cycle, two additional limit cycles are obtained by using an adequate parametric sector of the unfolding of a codimension-two focus-fold singularity.

Tectonic significance of Neoproterozoic magmatism of Nakora area, Malani igneous suite, Western Rajasthan, India

Three magmatic phases are distinguished in the Neoproterozoic Nakora Ring Complex (NRC) of Malani Igneous Suite (MIS), namely (a) Extrusive (b) Intrusive and (c) Dyke phase. Magmatism at NRC initiated with minor amount of (basic) basalt flows and followed by the extensive/voluminous acid (rhyolites-trachytes) flows. The ripple marks are observed at the Dadawari area of NRC in tuffaceous rhyolite flow which suggests the aqueous condition of flows deposition. The emplacement of the magma appears to have been controlled by a well defined NE-SW tectonic lineament and cut by radial pattern of dykes. These NE-SW tectonic lineaments are the linear zones of crustal weakness and high heat flow. The spheroidal and rapakivi structures in the Nakora acid volcanics indicate the relationship between genetic link and magma mixing. Basalt-trachyte-rhyolite association suggests that the large amount of heat is supplied to the crust from the magma chamber before the eruption. The field (elliptical/ring structures), mineralogical and geochemical characteristics of Nakora granites attest an alkaline character in their evolution and consistent with within plate tectonic setting. The emplacement of these granites and associated volcanics is controlled by ring structures, a manifestation of plume activity and cauldron subsidence, an evidence of extensional tectonic environment. NRC granites are the product of partial melting of rocks similar to banded gneiss from Kolar Schist Belt of India. The present investigations suggest that the magmatic suites of NRC rocks are derived from a crustal source and the required heat supplied from a mantle plume.

Age and eruptive center of the Paeroa Subgroup ignimbrites (Whakamaru Group) within the Taupo Volcanic Zone of New Zealand

We here explore the temporal and spatial relationships between the contrasting sources for two eruptive episodes that collectively represent the Whakamaru Group, the largest ignimbrite-forming sequence in the ∼2 m.y. history of the Taupo Volcanic Zone in New Zealand. At 349 ± 4 ka (weighted mean at 2σ), the >1500 km 3 widespread Whakamaru Group ignimbrites and ∼700 km 3 Rangitawa Tephra fallout were erupted in association with collapse of the 40 km long by 25 km wide rectilinear Whakamaru caldera. New 40 Ar/ 39 Ar age data presented here show that the co-magmatic >110 km 3 Paeroa Subgroup ignimbrites, previously included as part of the Whakamaru Group, are slightly younger and were erupted at 339 ± 5 ka (weighted mean at 2σ). New field evidence also presented here demonstrates that the Paeroa Subgroup ignimbrites came from a source geographically separated from vents for the widespread Whakamaru Group ignimbrites. The presence of co-ignimbrite lag breccias, sizes of vent-derived lithic clasts, thicknesses of exposed and subsurface deposits, and morphologies of deposits imply that eruptions of the Paeroa Subgroup occurred from a linear source (the Paeroa linear vent zone), coinciding with the present-day northeast-striking Paeroa fault, and outside (northeast) of the earlier Whakamaru caldera collapse area. No separate caldera has been recognized, although three nearby areas may have undergone eruption-related subsidence. Residual magma from the Whakamaru or adjacent Kapenga caldera areas may have migrated toward the Paeroa linear vent zone during eruptive episodes, resulting in subsidence in either, or both, of these areas. Shallow plutons are also inferred to lie beneath near source fault blocks (Paeroa and Te Weta) on each side of the fault, and eruption-related subsidence may have been expressed as movement across the Paeroa fault and localized subsidence in the southern Paeroa fault block. Subsequent secular, rift-related displacement along the Paeroa fault has obscured the Paeroa linear vent zone.

Role of the organic matter of a shale layer in the formation of its permeability at the early catagenic stage

The role of an important bulk component of high-carbon rocks (in particular, oil shale)—their concentrated organic matter (COM)—in the formation of epigenetic permeability is considered. Baltic kukersite shale (degree of transformation—early catagenesis) is used as an example. It is emphasized that the fluid permeability of this shale layer is manifested locally in tectonic disturbances, buried erosional valleys, and linear structural-deformation zones. The quality of shale in these zones deteriorates (the calorific value, the yield of tar, etc., decrease), and it is partially decarbonized (and decarbonated) and deformed; the shale acquires increased permeability, and its bed thickness decreases and marl varieties become more terrigenous. It is asserted that these phenomena were caused by the partial (and sometimes almost complete) loss of kukersite in the test sections of COM. The decrease of the organic matter caused the liberation of void space and then deformations, the disturbance of the integrity of layers, an increase in the permeability, and the loss of the status of fuels by the initial shale. The relationship of the degradation of the COM of shale with sulfate reduction processes in the underground hydrosphere at the early catagenic stage of the existence of a shale layer is substantiated.

Noose bifurcation and crossing tangency in reversible piecewise linear systems

The structure of the periodic orbits analysed in this paper was first reported in the Michelson system by Kent and Elgin (1991 Nonlinearity 4 1045–61), who gave it the name noose bifurcation. Recently, it has been found in a piecewise linear system with two linearity zones separated by a plane, which is called the separation plane. In this system, the orbits that take part in the noose bifurcation have two and four points of intersection with the separation plane, and they are arranged in two curves that are connected by a point where the periodic orbit has a crossing tangency with the separation plane. In this work, we analytically prove the local existence of the curve of periodic orbits with four intersections that emerges from the point corresponding to the crossing tangency. Moreover, we add a numerical study of the stability and bifurcations of the periodic orbits involved in the noose curve for the piecewise linear system and check that they exhibit the same configuration as that of the Michelson system.

A NEW ESTIMATE OF THE CHONDRULE COOLING RATE DEDUCED FROM AN ANALYSIS OF COMPOSITIONAL ZONING OF RELICT OLIVINE

Compositional zoning in chondrule phenocrysts records the crystallization environments in the early solar nebula. We modeled the growth of olivine phenocrysts from a silicate melt and proposed a new fractional crystallization model that provides a relation between the zoning profile and the cooling rate. In our model, we took elemental partitioning at a growing solid-liquid interface and time-dependent solute diffusion in the liquid into consideration. We assumed a local equilibrium condition, namely, that the compositions at the interface are equal to the equilibrium ones at a given temperature. We carried out numerical simulations of the fractional crystallization in one-dimensional planar geometry. The simulations revealed that under a constant cooling rate the growth velocity increases exponentially with time and a linear zoning profile forms in the solid as a result. We derived analytic formulae of the zoning profile, which reproduced the numerical results for wide ranges of crystallization conditions. The formulae provide a useful tool to estimate the cooling rate from the compositional zoning. Applying the formulae to low-FeO relict olivine grains in type II porphyritic chondrules observed by Wasson & Rubin, we estimate the cooling rate to be ~200-2000 K s?1, which is greater than that expected from furnace-based experiments by orders of magnitude. Appropriate solar nebula environments for such rapid cooling conditions are discussed.

The Pieniny klippen belt: its tectonic structure and evolution

Many mobile belts contain narrow (a few kilometres wide) and elongated (several hundreds and thousands kilometres long) zones characterized by complicated tectonic interiors and intensive rock metamorphism. Such zones are important components of the crustal structure; they determine the internal divisibility of the crust and act as accommodation areas or buffers between fragments of the crust which differ in origin and have specific evolution features. The article describes the paleo-evolution and characteristics of the Pieniny klippen belt, a major tectonic structure of the Carpathians and one of the largest linear tectonic zones in the Alpine-Himalayan folded belt.

Tectonic geomorphology of marine terraces: Santa Barbara fold belt, California

Uplifted marine terraces are common landforms in coastal regions where active tectonics are an important component of landscape evolution, such as along the coastal stretches of southern California. The pattern and elevation of shoreline angles on active folds provide information about rates of uplift and fold growth, which is important for defining tectonic models. A particularly impressive succession of marine terraces are developed across the Santa Barbara fold belt (SBFB) in southern California, which comprises an east-west linear zone of active folds and (mostly) blind faults on the coastal piedmont and in the Santa Barbara Channel. The fold belt is characterized by several flights of emergent late Pleistocene marine terraces uplifted and preserved on the flanks of active anticlines. At several locations along the fold belt, the first emergent marine terrace is numerically dated by methods that include uranium-series dating on terrace corals, 14 C dating on terrace shells and detrital charcoal, optically stimulated luminescence of marine terrace sands, and oxygen isotopic signatures (δ 18 O) of mollusks. Individual marine terraces have as many as four ages, using up to three different dating methods, providing confidence in terrace chronology. Ages of higher terraces are estimated assuming a constant rate of uplift for a particular flight. Of the 31 terraces, 22 formed during a time of falling sea level, with 9 forming at or near marine oxygen isotope stage (MIS) 3 or 5 highstands. Ages and rates of uplift of the first emergent terrace vary systematically from west (younger and higher) to east (older and lower). The first emergent marine terraces in the westernmost SBFB are approximately 45 ka (MIS 3), and the rate of local surface uplift is ∼2 m/k.y. In the central part of the belt, first emergent terraces date to 60–70 ka (MIS 5), and uplift rates decrease to ∼1.2 m/k.y. First emergent marine terraces preserved in the easternmost fold belt range from 70 ka to 105 ka (MIS 5), with rates of local surface uplift of ∼0.5 m/k.y. Lower rates of uplift in the eastern end of the fold belt result from the MIS 5 terrace being tilted down into the Carpinteria syncline. Rates of vertical uplift in the western end of the fold belt are about six times higher than previously reported, suggesting the seismic hazard is also greater.

Central Atlantic Igneous Province: Origin and mechanisms of formation

The paper considers various aspects of the formation of the Central Atlantic Igneous Province. Generation and eruption of enormous bodies of basic magmas over a short time interval (a few million years) are explained by the accumulation of thermal energy beneath the continental lithosphere. The thermal energy was transferred by heated matter or fluid flows from the lower mantle along separate channels or permeable zones and accumulated beneath the continental lithosphere of Pangea over a long period of time (tens of mil� lions of years) over a vast area. The large thickness of the lithosphere hindered melting. A change in the geo� dynamic regime with the onset of the breakdown of Pangea resulted in extension, formation of linear perme� able zones, local decompression, and, as a consequence, in generation and ascent of huge magma bodies along extended linear tectonically weakened zones. The homogeneity of igneous rocks is explained by the short time interval favorable for magma generation, when all the stored thermal energy had been exhausted.

The basement of the South American platform: Half Laurentian (N-NW) + half Gondwanan (E-SE) domains

The basement of the South American platform consists of two large distinct geologic domains: the Amazonian or pre-Tonian (N-NW portions) and the “Brasiliano” (or “Extra-Amazonian”, the central and eastern portions). These domains are separated by a set of two long linear fault zones, the Transbrasiliano lineament (NNE-SSW) to the south and the Araguaia lineament (NS) to the north.The Amazonian domain consists of large Archaean nuclei surrounded by Paleoproterozoic and Mesoproterozoic mobile belts of all of the systems of these eras. These mobile belts strike NNW-SSE, with indications of crustal growth from NNE to SSW, as recorded by the belts themselves as well as by subsequent anorogenic plutonism and cratonic covers. The western portion of the Amazonian domain and the basement inliers of the Andean orogenic belt present important affinities in terms of composition and crustal evolution. Most of the general framework and most of the Amazonian domain are akin to those recorded to the north in the Laurentian continent.The Brasiliano domain records a complex orogenic collage, representing branching systems of orogens, dated from tectonic cycles of the Tonian up to the Early Ordovician. This domain includes several minor cratonic nuclei formed of Archaean and Paleoproterozoic rock units, amalgamated by fold belts generated during (at least) five Wilsonian orogenic cycles. Crustal growth follows different centripetal processes because the vergences of the belts are towards the small cratonic nuclei. Aside from the cratons, several other pre-Neoproterozoic terranes were also amalgamated, and submitted to strong tectonic-thermal reactivations. Mesoproterozoic mobile belts have not been detected yet. The few geological records known from the Statherian and from the Mesoproterozoic were reset during the Neoproterozoic tectonism. At the end of the Neoproterozic orogenic cycles, a striking post-collisional scenario led by extrusional tectonics was in place. These processes reshaped the final structural framework of the Brasiliano provinces, distinguishing them from the Amazonian domain. The Brasiliano domain displays many compositional, structural and crustal evolution affinities with those of the westernmost part of the African continent.The more than 4500km long NNE-SSW Transbrasiliano lineament is the main record of the extrusional processes (from ca. 540Ma onwards) and displays evidence of seismic and faulting activities along the Phanerozoic. The Araguaia lineament is the final record of orogeny and collision, as the result of interactions between the Amazonian craton/plate and the backlands situated to the east in Neoproterozoic times (Colméia-Xambioá, Paranaiba and Granja terranes are good candidates).

Metal-assisted etching of silicon molds for electroforming

Ordered arrays of high-aspect-ratio micro/nanostructures in semiconductors stirred a huge scientific interest due to their unique one-dimensional physical morphology and the associated electrical, mechanical, chemical, optoelectronic, and thermal properties. Metal-assisted chemical etching enables fabrication of such high aspect ratio Si nanostructures with controlled diameter, shape, length, and packing density, but suffers from structure deformation and shape inconsistency due to uncontrolled migration of noble metal structures during etching. Hereby the authors prove that a Ti adhesion layer helps in stabilizing gold structures, preventing their migration on the wafer surface while not impeding the etching. Based on this finding, the authors demonstrate that the method can be used to fabricate linear Fresnel zone plates.

Spectral delineation of albite zone using ASTER data in Khetri Copper Belt

The Khetri Copper Belt is well known because of its economically viable Cu deposits. In this region, there is a linear narrow zone following a major crustal fracture. Along this zone, due to hydrothermal activity and subsequent alteration, a new rock, albitite has formed. The study presents an account of the spectral analysis of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) dataset for albitite mapping in the Khetri Copper Belt. Spectral angle mapper algorithm is applied on the ASTER data taking the ground sample reflectance spectra (VNIR–SWIR) and image derived spectra (TIR) as reference spectra. The albitite-classified areas are analyzed spatially and statistically to determine the extent of albitite zone in the study area. This research is to contribute to the better understanding of the spatial extent of the albitite zone which will assist in determining the potential for the mineralization in the area. The remote sensing approach of utilizing multichannel data offers the capability to resolve the key geological features of this geologically dynamic area.

Petrostructural evolution of ultramafic rocks of the Kalninsky chromite-bearing massif, Western Sayan

The Kalininsky ultramafic massif is a fragment of lower structural zone of the Kurtushiba ophiolitic belt in the extreme northeastern part of the Western Sayan. The massif is composed largely of rocks making up the dunite-garzburgite banded complex. The northeastern part of the massif is composed mainly of dunite with linear NW-trending chromite-bearing zones, the localization of which is controlled by banding of the dunite-harzburgite complex. Harzburgite and dunite are characterized by inhomogeneous structures and textures caused by nonuniform ductile deformation, which is expressed as heterogeneous extinction, kink bands, and syntectonic and annealing recrystallization. The petrostructural patterns of olivine in harzburgite and dunite provide evidence for three stages of ductile deformation. At the first stage under deep mantle-crustal conditions, the ductile flow of ultramafic rocks developed mainly in a regime of axial compression, high temperature (>1000°C), and low strain rate (ɛ 1000°C). The translational gliding in olivine proceeded largely along (010)[100] and was accompanied by diffusion creep. As the temperature rose, ductile deformation gave way to secondary recrystallization of annealing, which facilitated the growth of olivine grains free of dislocations owing to absorption of individual grains oriented adversely relative to the compression axis and deformed grains saturated with dislocations. As a result, dunite and harzburgite with a coarse-grained porphyroblastic microstructure have been formed. The third stage of ductile flow was apparently related to their transport along deep-seated thrust faults under settings of intense shear deformations at a high temperature (∼1000°C) and strain rate (ɛ >10−4 s−1). The ductile flow in olivine resulted in heterogeneous translational gliding along (010)[100] and accompanied by intense syntectonic recrystallization with the formation of a porphyroblastic microstructure. Chromite mineralization in dunite is controlled by internal banding. Intense ductile flow facilitated the metamorphic separation of linearbanded Cr-spinel segregations. Thus, the results of a petrostructural study show that ultramafic rocks of the Kalninsky massif, ascending to the upper lithosphere, underwent both axial and shear ductile deformations in the mantle and lower crust, and these deformations controlled chromite mineralization.

Control global del péndulo de furuta empleando redes neuronales artificiales y realimentación de variables de estado

En este artículo se presenta el modelado matemático para la planta conocida como Péndulo de Furuta mediante funciones de energía, teniendo en cuenta las dinámicas no lineales propias de los sistemas físicos y considerando los acoples existentes entre los dispositivos eléctricos y mecánicos. Se desarrolla un proceso de control basado en Realimentación de Variables de Estado (RVE) para el punto de equilibrio y se abordan dos temáticas para la zona no lineal de la planta. En primera instancia se implementan funciones que representan los estados energéticos de la planta en forma global y se establecen las regiones de operación (zona de ‘’Swing Up’’) y finalmente se emplean Redes Neuronales Artificiales (RNA) para emular el comportamiento de las funciones de energía. Finalmente se presenta la combinación de las técnicas de control, considerando las restricciones propias de los actuadores y sensores utilizados, además se realiza un estudio desde un ambiente simulado de los fenómenos físicos que pueden alterar el comportamiento del sistema y se verifica la capacidad, robustez y sensibilidad del controlador.

A Degradation Kinetic Study on Pyrolysis of Three Biomass Samples and Co-pyrolysis of Hazelnut Shell and Ultra-high Molecular Weight Polyethylene Blends Using a Silver Indicator

A kinetic study was proposed in pyrolysis process supplementary to thermo-gravimetric analysis. Three different biomasses, hazelnut shell, olive residue, and tea waste, and hazelnut shell and ultra-high molecular weight polyethylene mixture were analyzed kinetically in a batch-type tubular pyrolysis reactor. Reaction times were measured with the changing color of silver indicator, which was attached to the terminal of pyrolysis set up at various specified temperatures between 623 and 923 K. The Arrhenius plots were obtained and the activation energies (Ea ) of reaction values were calculated from the slope of linear curves. For pure biomass, two linear degradation zones were detected possibly belonging to cellulose and hemicellulose. In the case of hazelnut shell and ultra-high molecular weight polyethylene mixtures, linearity of Arrhenius plots were grasped with the modification of the pre-exponential factor of the basic Arrhenius equation. This type of kinetic method directly involves the basic parameters, namely, reaction time and temperature for supplementation of kinetic analysis.

Magnetic Resonance Imaging (MRI) Anatomy of the Ovine Lumbar Spine

Although the ovine spine is a useful research model for intervertebral disc pathology and vertebral surgery, there is little peer-reviewed information regarding the MRI anatomy of the ovine spine. To describe the lumbar spine MRI anatomy, 10 lumbar segments of cadaver ewes were imaged by 1.5-Tesla MR. Sagittal and transverse sequences were performed in T1 and T2 weighting (T1W, T2W), and the images were compared to gross anatomic sagittal and transverse sections performed through frozen spines. MRI was able to define most anatomic structures of the ovine spine in a similar way as can be imaged in humans. In both T1W and T2W, the signals of ovine IVDs were similar to those observed in humans. Salient anatomic features were identified: (1) a 2- to 3-mm linear zone of hypersignal was noticed on both extremities of the vertebral body parallel to the vertebral plates in sagittal planes; (2) the tendon of the crura of the diaphragm appeared as a hypointense circular structure between hypaxial muscles and the aorta and caudal vena cava; (3) dorsal and ventral longitudinal ligaments and ligamentum flavum were poorly imaged; (4) no ilio-lumbar ligament was present; (5) the spinal cord ended between S1-S2 level, and the peripheral white matter and central grey matter were easily distinguished on T1W and T2W images. This study provides useful reference images to researchers working with ovine models.

Spatial variations in 3He/4He ratios along a high strain rate zone, central Japan

A linear zone with high strain rates along the Japan Sea coast, the Niigata-Kobe Tectonic Zone (NKTZ), is considered to be associated with rheological heterogeneities in the lower crust and/or upper mantle. Helium isotope variations along the NKTZ reveal a close association with the geophysical evidence for rheological heterogeneities in the crust and mantle. In the southern NKTZ, the 3He/4He ratios lower than 3.4Ra (Ra denotes the atmospheric 3He/4He ratio of 1.4×10−6) could be interpreted as a two-component mixture of helium stored in aqueous fluids driven off the subducting oceanic crust and radiogenic crustal helium. Higher 3He/4He ratios are observed in the central NKTZ where Quaternary volcanoes and high-temperature hot springs are concentrated, suggesting that the 3He emanation manifest in the central NKTZ results from the effective transfer of mantle helium by intrusion and degassing of mantle-derived magma in the crust. In the northern NKTZ where two large inland earthquakes occurred recently, there appears to be many samples with 3He/4He ratios significantly higher than those observed in the fore-arc side of northeast Japan. A plausible source of mantle helium could be attributed to upward mobilization of aqueous fluids generated by dehydration of the subducting Pacific Plate slab.

On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry

Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewise-linear differential systems.New results are obtained for systems with three linearity zones without symmetry and having one equilibrium point in the central region. We also revisit the case of systems with only two linear zones giving shorter proofs of known results.A relevant application to the McKean piecewise linear model of a single neuron activity is included.

Reliable transport through a microfabricated X-junction surface-electrode ion trap

We report the design, fabrication and characterization of a microfabricated surface-electrode ion trap that supports controlled transport through the two-dimensional intersection of linear trapping zones arranged in a 90° cross. The trap is fabricated with very large scalable integration techniques which are compatible with scaling to a large quantum information processor. The shape of the radio-frequency electrodes is optimized with a genetic algorithm to reduce axial pseudopotential barriers and minimize ion heating during transport. Seventy-eight independent dc control electrodes enable fine control of the trapping potentials. We demonstrate reliable ion transport between junction legs and determine the rate of ion loss due to transport. Doppler-cooled ions survive more than 105 round-trip transits between junction legs without loss and more than 65 consecutive round trips without laser cooling.

Geological structure of Charity Shoal crater, Lake Ontario, revealed by multibeam bathymetry

Acoustic images of Charity Shoal in Lake Ontario, derived from a 1 × 1 m grid model of bathymetry assembled by the Canadian Hydrographic Service in 2010–2011, confirm the existence of a crater, as revealed by its surface morphology. With these higher quality data, it is possible to describe the crater in much greater detail, and arrive at a better interpretation of the geology than was possible using the earlier bathymetry of Lake Ontario. This new bathymetry of Charity Shoal reveals a continuous rim encircling an ovoid-shaped crater floor 1,200–1,500 m in diameter, with the crater floor being largely devoid of relief. Extending 3–4 km southwest of the crater is a ridge capped by a linear zone of unstratified debris that resembles a medial moraine. NE–SW erosional valleys cut across the crater rim in its southwestern sector. Apparently, glacial erosion has stripped the soil zone off stratified bedrock beneath the crater rim, exposing an intricate pattern of micro-ridges and grooves that bear the record of differential resistance to erosion of successive beds within the sequence of rock strata. Mapping of the shallow structure of the bedrock reveals a continuous ring anticline coinciding with the crater rim, with rock strata dipping gently in both directions away from the rim axis. In combination with existing evidence on the regional stratigraphy, these observations and interpretations are consistent with the Charity Shoal crater having formed in a shallow marine environment by an extraterrestrial impact event in the Middle Ordovician, followed by post-impact sedimentation, and much later, erosion during Pleistocene glaciations. Apparently, post-impact sediments infilled the crater and eventually covered the crater rim, leaving only a diminished structural expression of a crater having no more than 20 m of surface relief. Further details of crater history and origin, and a test of the hypothesis of impact, will likely come from acoustic reflection profiling and direct sampling.