Arc Sequence Research Articles

Characterization of the network of a transport infrastructure

Networks (whatever their nature: telecommunications, freight transport, energy or people) are studied from several points of view, they have a fundamental role in the existence of the territory as well as in its development. The transport networks are of great diversity depending on the mode of transport to which they belong. The transport infrastructure network is characterized by arcs and nodes. Both arcs and nodes have characteristics that must be connected to the means of transport that use it. In order to carry out the transport in the relationship (𝑖,𝑗) ∈ 𝑅 for a given network (𝐾,𝐷), the sequence of arcs connecting to node 𝑖 ∈ 𝐾 to the node 𝑗 ∈ 𝐾 must be chosen (in the case of the network appropriate to the request). If the nodes 𝑖,𝑗 are neighbors the arc will constitute the shortest sequence of arcs.

Energy-optimal trajectories for skid-steer rovers

This paper presents the energy-optimal trajectories for skid-steer rovers on hard ground, without obstacles. We obtain 29 trajectory structures that are sufficient to describe minimum-energy motion, which are enumerated and described geometrically; 28 of these structures are composed of sequences of circular arcs and straight lines; there is also a special structure called whirls consisting of different circular arcs. Our analysis identifies that the turns in the trajectory structures (aside from whirls) are all circular arcs of a particular turning radius, R′, the turning radius at which the inner wheels of a skid-steer rover are not commanded to turn. This work demonstrates its paramount importance in energy-optimal path planning. There has been a lack of analytical energy-optimal trajectory generation for skid-steer rovers, and we address this problem by a novel approach. The equivalency theorem presented in this work shows that all minimum-energy solutions follow the same path irrespective of velocity constraints that may or may not be imposed. This non-intuitive result stems from the fact that with this model of the system the total energy is fully parameterized by the geometry of the path alone. With this equivalency in mind, one can choose velocity constraints to enforce constant power consumption, thus transforming the energy-optimal problem into an equivalent time-optimal problem. Pontryagin’s Minimum Principle can then be used to solve the problem. Accordingly, the extremal paths are obtained and enumerated to find the minimum-energy path. Furthermore, our experimental results by using Husky UGV provide the experimental support for the equivalency theorem.

Kinematical Approach to the Drilling Mechanisms for n-Sided Polygonal Holes

Abstract The present analysis addresses the generation of regular polygonal paths with any number of sides, odd or even, by use of special rotors revolving with uniquely prescribed motions inside fixed polygonal holes of guidance, which may be coincident or similar to the paths to be traced. The whole rotation motion of the rotor is considered composed of a sequence of Cardan motions so that the active profile of contact is formed by a polycentric sequence of circular arcs. It is shown and proved that the guidance polygon and the target polygon may coincide in the hypothesis of an odd number n of sides, whereas the guidance profile must be larger than the one to be generated for n even, in which case two equal concentric polygons rotated of π/n between each other may be simultaneously generated by two particular points of the rotors. These devices are very useful to drill blind polygonal holes, providing the rotors of proper cutting tools and driving them by constant-speed motors through homokinetic joints.

Volcanogenic massive sulfide (VMS) deposits of the Dunnage Zone of the Newfoundland Appalachians: setting, styles, key advances, and future research

The Dunnage Zone of the Newfoundland Appalachians hosts diverse Cambrian–Ordovician volcanogenic massive sulfide (VMS) deposits. The peri-Laurentian Notre Dame Subzone contains Cu–Zn–Au mafic and bimodal mafic deposits in ∼501–485 Ma ophiolitic rocks and Zn–Pb–Cu–(Au–Ag) deposits in ∼471–465 Ma bimodal rifted continental arc sequences (e.g., Buchans). The peri-Gondwanan rocks of the Exploits Subzone host Zn–Pb–Cu–(Au–Ag) bimodal felsic, felsic siliciclastic, and Zn–Ag–Au hybrid bimodal felsic deposits in the ∼513–486 Ma Victoria Lake supergroup; Cu–Zn bimodal felsic to bimodal mafic deposits of the ∼486 Ma Wild Bight Group; and Cu–(Au) mafic siliciclastic deposits of the ∼466 Ma Great Burnt Lake/South Pond belt. Regardless of age or stratigraphic hosts, all VMS deposits are associated with specific magmatic assemblages and extensional tectonism (i.e., rifting). Gold-enriched deposits of the Rambler-Ming district are associated with felsic rocks that formed via slab melting and subsequent melt-mantle wedge interaction, which likely enhanced precious metal enrichment in these deposits. Whereas many deposits exhaled on the seafloor, some deposits formed via subseafloor replacement of host units or as re-sedimented sulfides generated in sediment-gravity flows. Metals in the deposits were derived from leaching of underlying footwall rocks; however, Au–Ag- and epithermal suite element-enriched deposits show evidence for metal contributions from magmatic hydrothermal fluids. Sulfur in deposits was derived predominantly from leaching of H2S from underlying footwall rocks and from thermochemical sulfate reduction of seawater sulfate, with lesser input from bacteria-derived H2S and magmatic-hydrothermal-derived H2S. Despite recent research advances and historic mining, numerous questions remain unresolved and provide opportunities for future study.

THE CURVE ARC AS A STRUCTURE ELEMENT OF AN OBJECT CONTOUR IN THE IMAGE TO BE RECOGNIZED

Context. The proposed article relates to the field of visual information processing in a computer environment, more precisely to the determination the parameters of the interest object in the image, in particular, the contour of the interest object In most cases, the contour of an object is a simply connected sequence of curve arcs.
 Objective. The purpose and subject of the study is to find and to propose such a definition of the digital curve arc, as the most important element of the object contour in the recognizable image, which does not contradict modern neurophysiological conceptions about visual perception, and to recognize the object contour as a sequence of the digital curve arcs.
 Method. The representation of the image in the form of a structural model is used, one of the structural elements of which is the contour of the object, consisting of digital curve arcs. Also, the image is considered as a cellular complex which corresponds to modern ideas about human visual perception.
 Results. The new definition for arc of a digital curve as a sequence of digital straight segments is proposed, which does not contradict to modern concepts of neurophysiology. In contrast to the known definitions of a curve arc, the proposed definition of a digital curve arc makes it possible to determine the start and end points of the arc. According to the description of the contour of an object as a simply connected closed sequence of line segments, it is proposed to construct a description of the contour as a sequence of arcs of digital curves.
 Conclusions. The use of the proposed definition of the digital curve arc in image processing makes it possible to recognize the contour of an object in an image and present it in a form close to visual perception. For best results, the use of variable resolution in image processing algorithms is recommended.

Data-Driven Adaptive Optimal Control Under Model Uncertainty: An Application to Cold Atmospheric Plasmas

Cold atmospheric plasmas (CAPs) are increasingly used for applications requiring the processing of heat- and pressure-sensitive (bio)materials. A key challenge in model-based control of CAPs arises from the high-computational requirements of theoretical plasma models as well as lack of mechanistic understanding of plasma-surface interactions. Thus, control strategies that rely on simple, physics-based models that can be adapted to mitigate plant-model mismatch will be particularly advantageous for CAP applications. This article presents an optimal control approach for controlling the nonlinear and cumulative effects of CAPs delivered to a target surface using a simple system model. Through parsimonious input parameterization, the solution to the optimal control problem (OCP) is given by an arc sequence that does not include any singular arcs. A data-driven adaptive algorithm based on modifier adaptation is proposed to deal with the structural plant-model mismatch by estimating the mismatch in the cost and constraints of the OCP. The adaptive approach is shown to converge to a Karush–Kuhn–Tucker (KKT) point of the OCP for the true system. Moreover, a control strategy based on feedback linearization and derivative estimation is proposed for online tracking of path constraints in the presence of disturbances and model uncertainty. The proposed approach is demonstrated by simulations and real-time control experiments on a kilohertz-excited atmospheric pressure plasma jet in helium, in which the plasma treatment time is minimized while delivering a desired amount of nonlinear thermal effects to the target surface.

Adaptive Global Solutions to Single-Input Optimal Control Problems via Gaussian Processes

Optimal control problems are found in state and parameter estimation, experimental design, and model-based control for complex dynamical systems. Parsimonious input parameterization is an approach for obtaining solutions to these problems, which comprises two tasks: the first corresponds to the generation of arc sequences and the second consists in the computation of optimal values of a small number of decision variables for each sequence. This paper proposes an adaptive method for global solutions to single-input optimal control problems that accounts for the mismatch between the true system and its model by using Gaussian processes to represent the mismatch in the cost and constraints for an arc sequence. This adaptive approach converges to the global solution for the true system and ensures constraint satisfaction with a prespecified probability. The proposed approach is illustrated by a simulation example of a reaction system.

Spacecraft Rendezvous in Closed Keplerian Orbits Using Constant Radial Thrust Acceleration

An analytical solution for spacecraft rendezvous within closed Keplerian orbits is presented using continuous radial thrust. The two spacecraft are assumed to be initially placed within the same closed orbit with arbitrary phase angle separation. The target spacecraft is assumed to always remain in the same initial orbit. The chaser vehicle, however, uses a judiciously designed maneuver sequence comprising constant-acceleration radial thrust phases interspersed with coast phases. Importantly, the proposed maneuver design is analytically characterized by one or two (depending on whether the parking orbit is circular or elliptical, respectively) nonlinear algebraic equations that determine the time intervals for the different phases. The set of initial conditions from which rendezvous is feasible is also characterized. Additionally, orbit rotation (that is, changing the orbit argument of periapsis in plane) is also demonstrated for the elliptical parking orbit case. Finally, the remarkable emergence of the golden and silver ratios, as well as their connections to Kepler’s triangle, is demonstrated for a specific sequence of thrust and coast arcs.

Efficient Global Solutions to Single-Input Optimal Control Problems via Approximation by Sum-of-Squares Polynomials

Optimal control problems are prevalent in model-based control, state and parameter estimation, and experimental design for complex dynamical systems. An approach for obtaining solutions to these problems is based on the notion of parsimonious input parameterization and comprises two tasks: the enumeration of arc sequences followed by the computation of optimal values of a small number of decision variables for each sequence. This article proposes an efficient global solution method for single-input optimal control problems for nonlinear dynamical systems with a potentially large number of states or complex dynamics via sum-of-squares polynomials and parallel computing. The method approximates the problem for a given arc sequence as a polynomial optimization problem that can be efficiently solved to global optimality via semidefinite programming. It is established that the difference between the cost obtained by the proposed method and the globally optimal cost of the original problem is bounded and depends on the polynomial approximation error. The method is illustrated by simulation examples of a reaction system and a rocket.

The surface and subsurface integrity in coupled operation of fused deposited modeling and centrifugal disk finishing

PurposeThis paper aims to investigate the effect of centrifugal disk finishing (CDF) technique on the surface and subsurface characteristics of the fused deposited modeling (FDM) parts in both theoretical and experimental aspects. From theoretical aspect, a novel theoretical model is developed as a function of layer deposition orientation, layer thickness, finishing working time, density ratio and hardness ratio to estimate the surface roughness profile of FDM part at different finishing conditions and finishing time intervals. Meanwhile, from the experimental aspect, an experimental campaign was performed under different mechanical and mechanical-chemical finishing conditions to verify the theoretical model and also assess the surface and subsurface characteristics of the polished parts.Design/methodology/approachThe theoretical model commences with an approximation of surface profile of the FDM part through a sequence of parabola arcs, continues with the calculation of reference line and machined surface profile and leads to a formulation of surface roughness of as-printed and polished surface. In the experimental section, the FDM parts are polished under dry, pure water, 25% and 50% volumetric aqueous acetone solutions finishing conditions through CDF technique.FindingsThe comparison between experimental and theoretical results reveals 9% mean absolute error between theoretical and experimental results. Meanwhile, Rq reduction percentage of polished parts under dry, pure water, 25% and 50% aqueous acetone solutions are 66.1%, 54.5%, 56.9% and 67.2%, respectively. The scanning electron microscopy results reveal severe layer damage in dry finishing condition, while the application of 50% aqueous acetone as a polishing solution completely eliminates layer damage. Another promising finding was sticky material phenomenon on the surface of polished part under 25% finishing condition. The Shore hardness test illustrates that the surface hardness improvement of the polished parts under dry, pure water, 25% and 50% aqueous acetone solutions finishing conditions are 8.4%, 2.25%, 4.36% and 10.8%, respectively. The results also revealed that the dimension variation of polished parts under dry, pure water, 25% and 50% aqueous acetone solutions are 0.634%, 0.525%, 0.545% and 0.608%, respectively. The edge profile radius of the as-printed part is 134 µm, while the edge profiles radius of the polished parts under dry, pure water, 25% aqueous acetone solution and 50% aqueous acetone solution are 785.5 µm, 545.5 µm, 623.5 µm and 721.5 µm, respectively, at the polishing time of 720 min.Originality/valueThis paper fulfills an identified need to study the benefits of the mechanical-chemical polishing technique in comparison to mechanical and chemical polishing strategy of the FDM parts for the first time. Beside the experimental campaign, the novel analytical formulation of surface roughness as a function of mechanical properties of abrasive media and FDM part and finishing specifications provides a valuable insight in the case of material-removal processes.

Review of Geochronologic and Geochemical Data of the Greater Antilles Volcanic Arc and Implications for the Evolution of Oceanic Arcs

AbstractThe Greater Antilles islands of Cuba, Hispaniola, Puerto Rico and Jamaica plus the Virgin Islands host fragments of the fossil convergent margin that records Cretaceous subduction (operated for about 90 m.y.) of the American plates beneath the Caribbean plate and ensuing arc‐continent collision in Late Cretaceous‐Eocene time. The “soft” collision between the Greater Antilles Arc (GAA) and the Bahamas platform (and the margin of the Maya Block in western Cuba) preserved much of the convergent margin. This fossil geosystem represents an excellent natural laboratory for studying the formation and evolution of an intra‐oceanic convergent margin. We compiled geochronologic (664 ages) and geochemical data (more than 1,500 analyses) for GAA igneous and metamorphic rocks. The data was classified with a simple fourfold subdivision: fore‐arc mélange, fore‐arc ophiolite, magmatic arc, and retro‐arc to inspect the evolution of GAA through its entire lifespan. The onset of subduction recorded by fore‐arc units, together with the oldest magmatic arc sequence shows that the GAA started in Early Cretaceous time and ceased in Paleogene time. The arc was locally affected (retro‐arc region in Hispaniola) by the Caribbean Large Igneous Province (CLIP) in Early Cretaceous and strongly in Late Cretaceous time. Despite multiple biases in the database presented here, this work is intended to help overcome some of the obstacles and motivate systematic study of the GAA. Our results encourage exploration of offshore regions, especially in the east where the forearc is submerged. Offshore explorations are also encouraged in the south, to investigate relations with the CLIP.

The composite Triassic\u2013Eocene Poshteh pluton, eastern Iran, an Eo-Cimmerian element south of the main Paleotethys suture

The composite Poshteh Pluton, at the northeastern margin of the Central Iranian Microplate near Taybad in eastern Iran, is positioned at a critical tectonic junction, south of the inferred main Paleotethys suture and along the major regional Doruneh Fault system. It consists of two distinct intrusions. Quartz monzonite is dated in this study by zircon U–Pb ID-TIMS to 215.8 ± 0.5 Ma, an age that coincides with the time of closure of the Paleotethys during the late collisional stages of the Eo-Cimmerian Orogeny. It is geochemically very similar to coeval plutons present along and north of the Paleotethys suture, where they intruded Carboniferous-Permian arc sequences, ophiolites and flysch. The Poshteh quartz monzonite is located south of the suture in a position similar to the Anarak and related complexes further west, which previously have been interpreted as reflecting Mesozoic and Cenozoic disruption of the Eo-Cimmerian Orogen by extensional and transtensional processes. The Triassic quartz monzonite was subsequently invaded by granite at 41.23 ± 0.31 Ma. The emplacement was in part structurally controlled by the Doruneh Fault system and associated to hydrothermal alteration and Fe mineralization. The granite is thus a coeval member of a widespread late Eocene to Oligocene plutonic suite in the region, and likely the result of delamination and melting of the subcontinental lithosphere.

Phase equilibria and microstructural constraints on the high‐T building of the Kohistan island arc: The Jijal garnet granulites, northern Pakistan

AbstractThe Kohistan island arc represents a >50 km thick and completely exposed Late Cretaceous–Eocene Neo‐Tethyan island arc sequence between the Indian and Eurasian plates in the western Himalaya. At the base of the Kohistan Arc, the Jijal Complex exposes a continuous sequence from ultramafic upper mantle rocks to mafic rocks of the lower crust across the Moho transition zone. In the shallower mafic section of the Jijal Complex, widespread garnet–clinopyroxene gabbros are uniform in assemblage but show a spectrum of microstructural variation involving two distinguishable styles of garnet growth. Uncertainty surrounds the genetic origin of these equilibria across the sequence which have been variably proposed to derive either from (a) dehydration melting of amphibole‐bearing precursor rocks, (b) subsolidus recrystallization of gabbronorite, or (c) primary magmatic crystallization. Owing to extensive high‐T re‐equilibration, compositional records of magmatic precursors and the pre‐peak evolution across the complex have been erased. However, quantitative textural analysis evidences a progressively increasing departure from microstructural randomness from deep to shallow levels of the upper Jijal Complex. This is interpreted to reflect the increased propensity for shallow garnet–clinopyroxene gabbros to have been derived from solid‐state recrystallization of a cumulate gabbronorite precursor, resulting in the development of coronitic garnet microstructures. In the deepest portions of the mafic sequence, both cumulate textures and thermodynamic modelling attest to the basal levels of the Kohistan arc crust at ~10–14 kbar crystallizing primary magmatic garnet and clinopyroxene from low H2O (<6 wt%) basaltic–andesitic melts. Granulite facies metamorphism and re‐equilibration across the whole upper Jijal Complex—shown via phase equilibrium modelling to be associated with over‐accretion in the mid‐arc crust and a pressure increase of 2–3 kbar to 850–1,050℃ and 11–14 kbar—was followed by a period of approximately isobaric cooling across ~200℃ and amphibolitization. Compositions of low‐volume leucosome‐hosted garnet indicate melting occurred prior to, or during, this re‐equilibration period and melt reintegration simulations suggest that dehydration melting of amphibole‐bearing precursors played only a minor role in the genesis of the Jijal garnet–clinopyroxene gabbros. By combining field relationships, petrological and textural analysis, interpretations of mineral compositions, and phase equilibrium modelling, we therefore provide detailed constraints on crustal thickening and the thermal evolution of the lowermost arc crust.

The Chongón/Colonche orocline transrotational bending and the coeval opening of the Progreso basin in southwestern Ecuador

Integration of geological and geophysical studies of Progreso Basin in SW Ecuador provided a unique opportunity to propose an unorthodox model for the Progreso Basin opening within a strike slip regime. Shearing couple transrotation of the Chongón/Colonche (C/C) orocline bending accounted for the atypical, isosceles triangle shape, Progreso Basin opening during the Oligocene oblique convergence amid the Farallon and South America plates. Transrotation commenced with the sinistral strike slip reactivation of the Paleocene Chongón-Jipijapa-Jama (CJJ) Suture. This suture is inferred based on field kinematics of Cretaceous outcrops in the Santa Elena Peninsula and published high resolution potential field maps. The reactivated suture worked as the sinistral La Cruz (LCF) Fault and their “en echelon” synthetic Riedels C/CF, Consuelo (COF), and Carrizal (CAF) faults accommodated most of the basin heterogeneous transtension and transrotation. While the synthetic Riedels migrated northward along the La Cruz Fault, a narrow segment of the Paleogene foredeep and the intra-oceanic arc sequence of the C/C High attached to the Estancia Hills was scrapped off and rotated. The shearing couple between the “en echelon” Riedels enhanced the transrotation and transtension and triggered the counterclockwise crustal rotation of the C/C High. The subvertical block rotation involved significant lithospheric decoupling of this high that set off the C/C Orocline development and coeval opening of the Progreso Basin.Early Zapotal Formation deposition characterized by alluvial fan aggradation rapidly filled the graben between the Consuelo and Carrizal faults as the Consuelo Fault underwent strain hardening and confining. In doing so, the sediment input by the active alluvial fan complex spilled over the Carrizal Fault displaying down lapping and progradation along the hanging wall. Its listric behavior on other hand, set off the tilting of the pre-extensional Paleogene sequences, which in turn caused the onlapping and diachronous deposition of the Zapotal Formation toward the La Cruz Fault. Protracted marine incursion and deposition of a fine grained siliciclastic sequence that encompassed the whole Oligocene took place around the already opened basin toward the south.Early Miocene breakup of the Farallon Plate not only increased the convergence rate but also gradually changed the convergence from oblique to orthogonal. Multiple intraformational unconformities and high sedimentation and subsidence rates in the Dos Bocas Formation documented this change. Recurrent deposition of the diatomaceous Villingota Formation suggested episodic upwelling in the basin enriched by the high siliceous tuffs supply from the coeval Saraguro Arc volcanism in the Western Cordillera. Basin transtension terminated during Late Miocene inception of the Rodeo and Playas synthetic Riedels to the reactivated Pallatanga Suture known as the dextral Chingual-Cosanga-Pallatanga-Puna (CCPP) fault system. However, as this fault continued into the Gulf of Guayaquil, the transtension was transferred to this area. Hitherto, the Progreso Basin underwent a sagging phase characterized by the onlapping of the Subibaja and Progreso formations against the La Cruz Fault High as well as a localized, subtle tectonic inversion due to space problems linked to the synthetic Riedels inception.

Geochemistry, U[sbnd]Pb geochronology, and Sr-Nd-Hf isotope systematics of a SW-NE transect in the southern Peninsular Ranges batholith, Mexico: Cretaceous magmatism developed on a juvenile island-arc crust

The Peninsular Ranges batholith (PRB) is a North American Cordillera segment with a protracted record of subduction-related magmatism (177–92 Ma). However, such a record is regionally fragmented, showing broad petrologic variations challenging to integrate into a coherent geologic evolution history. Here, we present a petrogenetic study of Cretaceous plutons in the southern PRB along the Sierra El Arco-San Francisquito transect (SW-NE) perpendicular to the paleotrench. The Middle Jurassic-Early Cretaceous (166–140 Ma) magmatism developed as an island arc with sedimentary rocks of intra-arc and oceanic marginal basins. At the Sierra El Arco, the Calmallí pluton intruded the Jurassic arc sequence. The basic to intermediate rocks of the Calmallí pluton show εSrt (average –3.6), εNdt (average +3.3), and εHft values (average +6.0) that suggest an origin from mantle-derived melts with minor contamination. These rocks display almost flat rare earth elements (REE) patterns and Eu anomalies suggesting plagioclase fractionation. East of the Calmallí pluton from the Piedra Blanca to the San Francisquito region, granodiorite and granite (100–92 Ma) are continuously exposed. The εSrt (average +3.1), εNdt (average +1.1), and εHft (average +2.6) isotopic signatures in the acid rocks suggest a mantle-derived melt genesis with increased contamination. Most granodioritic and granitic rocks display a characteristic depleted-HREE pattern without Eu anomalies, suggesting differentiation under the influence of garnet. The Jurassic-Cretaceous (166–92 Ma) magmatism displays an εSrt vs. εNdt correlation trend, indicating progressive contamination of mantle-derived magmas with a recycled crust. SrNd and NdHf isotopic mixing curves suggest the assimilation of the metasedimentary Triassic basement of NW Mexico instead of the considerably older and isotopically evolved Precambrian basement. The integration of this work with data from NW Mexico suggests a continuous magmatic activity from the Middle Jurassic to the Late Cretaceous. We consider the geochemical, isotopic, and temporal variation of the PRB indicative of natural heterogeneities along the trench axis of a long-lived arc system (crustal thickness and paleogeography) due to continuous subduction of the Farallon plate below the North American plate.

An Approximation of Bézier Curves by a Sequence of Circular Arcs

Some researches have investigated that a Bézier curve can be treated as circular arcs. This work is to proposea new scheme for approximating an arbitrary degree Bézier curve by a sequence of circular arcs. The sequenceof circular arcs represents the shape of the given Bézier curve which cannot be expressed using any other algebraicapproximation schemes. The technique used for segmentation is to simply investigate the inner anglesand the tangent vectors along the corresponding circles. It is obvious that a Bézier curve can be subdivided intothe form of subcurves. Hence, a given Bézier curve can be expressed by a sequence of calculated points on thecurve corresponding to a parametric variable t. Although the resulting points can be used in the circular arcconstruction, some duplicate and irrelevant vertices should be removed. Then, the sequence of inner angles arecalculated and clustered from a sequence of consecutive pixels. As a result, the output dots are now appropriateto determine the optimal circular path. Finally, a sequence of circular segments of a Bézier curve can be approximatedwith the pre-defined resolution satisfaction. Furthermore, the result of the circular arc representationis not exceeding a user-specified tolerance. Examples of approximated nth-degree Bézier curves by circular arcsare shown to illustrate efficiency of the new method.

Geochemistry and provenance of lower Permian sedimentary rocks, Nambucca Block, southern New England Orogen

It is well documented that sediments record geochemical signatures that reflect the composition and tectonic setting of the rocks providing the detritus for them. This is true of the turbidites in the Nambucca Block that record compositions that vary from basaltic to rhyodacitic but are dominantly andesitic to dacitic. They show chondrite and N-MORB patterns, characteristic of calc-alkaline, continental arc rocks, namely light REE (av. La/Yb) N = 6.3) and Th enrichment, Ti, Nb and Ta depletion, and substantial within plate components (Nb/Yb; 0.65–5.16; x = 3.15). Rare occurrences of rocks with intra-oceanic island arc affinities and felsic volcanic rocks showing tectonic fabrics occur, indicating more distal sources contributed detritus. Most detritus in the turbidites has been derived from the calc-alkaline, continental rocks of the Keepit arc, some from the subduction–accretion sequences of the Tablelands Complex. CIA [Al2O3/(Al2O3+Na2O + K2O + CaO)×100] values (48–83; x = 68) indicate that erosion of these arc sequences occurred during glacial, temperate and humid conditions at different times. Further, index of chemical variability values (0.3–1.85; x = 0.85) reveal a compositional maturity and a high percentage of clays in the source rocks suggesting a passive tectonic setting in which minimal uplift and extensive weathering took place. KEY POINTS Metasediments in the Nambucca Block record geochemical signatures typical of calc-alkaline, continental, arc rocks. Detritus in metasediments was derived from the Keepit arc and Tablelands Complex, southern New England Orogen. Source rocks were subjected to glacial, temperate and humid conditions at different times.

Comment to "Porphyry-related high-sulfidation mineralization early in Central American Arc Development: Cerro Quema deposit, Azuero Peninsula, Panama" by Perelló et al., (2020)

The Cerro Quema Au-Cu deposit is hosted by a dacite dome complex of the Río Quema Formation, a Late Campanian-Maastrichtian volcano-sedimentary sequence of the Panamanian magmatic arc. Its formational age is constrained at ~49 Ma by field evidences, crosscutting relationships and 40Ar/39Ar geochronology (Corral et al., 2016, Corral, 2021). The recent molybdenite Re-Os dates by Perelló et al. (2020) claim that ore is spatially and temporally related to the host volcanic domes at ~71 Ma. After a thorough review of the geologic, geochemical and geochronological data from the Cerro Quema area, it is concluded that the Re-Os dates of Perelló et al. (2020) are not representative of the Cerro Quema formational age. Their proposed formational age at ~71 Ma is significantly older than the age of the host rock (~67 Ma). Furthermore, they invoke a previously unrecognized regional-scale magmatic event solely based on their molybdenite Re-Os dates. Instead, the Cerro Quema genetic model discussed here, in which magmatic-hydrothermal fluids derived from porphyry copper-like intrusions associated with the Valle Rico batholith produced the Au-Cu mineralization at ~49 Ma, is consistent with the geology, geochemistry and geochronology of the Azuero Peninsula.

Tectonic history of the Grenville-age Trenton Prong inlier, Central Appalachians, USA: evidence from SHRIMP U–Pb geochronology

New zircon U–Pb geochronologic data from the Grenville-age Trenton Prong provide information on the age of magmatism, timing of metamorphism, and post-metamorphic history of the inlier. Diorite gneiss (1318 ± 13 Ma) of the Colonial Lake Suite temporally correlates to magmatic arc sequences that formed along the eastern margin of Laurentia at <1.4 Ga. Metasedimentary gneisses yielded detrital zircon ages of ca. 1319–1133 Ma and ca. 1370–1207, consistent with sediment derived from a similar local source of Laurentian affinity. A small population of zircon (either detrital or igneous in origin) in one sample yielded ages of ca. 1074–1037 Ma. Possible interpretations for their formation are explored. Ca. 1060 Ma overgrowths on zircon in the northern part of the inlier constrain the timing of granulite-facies metamorphism to the Ottawan phase of the Grenvillian Orogeny. The undeformed Assunpink Creek Granite (1041 ± 6 Ma) intruded country rocks as small bodies of late-orogenic syenogranite. It provides a minimum age for amphibolite-facies metamorphism and Ottawan orogenesis elsewhere in the inlier. Regionally, zircon rim ages of ca. 1010–960 Ma record continued thermal activity during the Rigolet phase of the orogen that resulted in migmatization of paragneiss at ca. 1004 Ma and juxtaposition of upper- and mid-crustal rocks during orogenic collapse. The lithologic ages and tectonic history of the Trenton Prong correlate to those in other Appalachian Mesoproterozoic inliers and parts of the Canadian Grenville Province, confirming it is not an exotic terrane that was accreted to eastern Laurentia during Grenvillian orogenesis.

Semi-analytical and extremal solutions for design and synthesis of powered descent and landing trajectories

Semi-analytical solutions to the optimal control problem for 3-dimensional fuel-efficient planetary landing trajectories with constant exhaust velocity and limited mass-flow rate in a drag-existing central Newtonian field are presented. The first-order optimality conditions reduce the problem to a Hamiltonian canonical system for the design and synthesis of feasible and extremal planetary entry, descent, and landing trajectories. The proposed solutions allow us to describe the state vector and Lagrange multipliers in terms of time and switching function's characteristics to determine the number and sequence of thrust arcs. These solutions can be adjusted for manoeuvres near other celestial bodies for which a central gravitational acceleration can be dominant. The paper describes new extremal trajectories, which are based on the analysis of first- and second-order optimality conditions. The results of this work can be used to support mission design analysis and synthesis of fuel-efficient trajectories.