Narrowband random excitation of a limit cycle system

The response of the Van der Pol oscillator to stationary narrowband Gaussian excitation is considered. The central frequency of excitation is taken to be in the neighborhood of the system limit cycle frequency. The solution is obtained using a non-Gaussian closure approximation on the probability density function of the response. The validity of the solution is examined with the help of a stochastic stability analysis. Solution based on Stratonovich''s quasistatic averaging technique is also obtained. The comparison of the theoretical solutions with the digital simulations shows that the theoretical estimates are reasonably good.

Qualitative theorem proving in linear constraints

We know, from the classical work of Tarski on real closed fields, that elimination is, in principle, a fundamental engine for mechanized deduction. But, in practice, the high complexity of elimination algorithms has limited their use in the realization of mechanical theorem proving. We advocate qualitative theorem proving, where elimination is attractive since most processes of reasoning take place through the elimination of middle terms, and because the computational complexity of the proof is not an issue. Indeed what we need is the existence of the proof and not its mechanization. In this paper, we treat the linear case and illustrate the power of this paradigm by giving extremely simple proofs of two central theorems in the complexity and geometry of linear programming.

NEW MASS LIMIT OF WHITE DWARFS

Is the Chandrasekhar mass limit for white dwarfs (WDs) set in stone? Not anymore, recent observations of over-luminous, peculiar type Ia supernovae can be explained if significantly super-Chandrasekhar WDs exist as their progenitors, thus barring them to be used as cosmic distance indicators. However, there is no estimate of a mass limit for these super-Chandrasekhar WD candidates yet. Can they be arbitrarily large? In fact, the answer is no! We arrive at this revelation by exploiting the flux freezing theorem in observed, accreting, magnetized WDs, which brings in Landau quantization of the underlying electron degenerate gas. This essay presents the calculations which pave the way for the ultimate (significantly super-Chandrasekhar) mass limit of WDs, heralding a paradigm shift 80 years after Chandrasekhar's discovery.

Upper bound solution for pullout capacity of vertical anchors in sand using finite elements and limit analysis

The horizontal pullout capacity of vertical anchors embedded in sand has been determined by using an upper bound theorem of the limit analysis in combination with finite elements. The numerical results are presented in nondimensional form to determine the pullout resistance for various combinations of embedment ratio of the anchor (H/B), internal friction angle (ϕ) of sand, and the anchor-soil interface friction angle (δ). The pullout resistance increases with increases in the values of embedment ratio, friction angle of sand and anchor-soil interface friction angle. As compared to earlier reported solutions in literature, the present solution provides a better upper bound on the ultimate collapse load.

Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis

The ultimate bearing capacity of a circular footing, placed over rock mass, is evaluated by using the lower bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization. The generalized Hoek-Brown (HB) failure criterion, but by keeping a constant value of the exponent, alpha = 0.5, was used. The failure criterion was smoothened both in the meridian and pi planes. The nonlinear optimization was carried out by employing an interior point method based on the logarithmic barrier function. The results for the obtained bearing capacity were presented in a non-dimensional form for different values of GSI, m(i), sigma(ci)/(gamma b) and q/sigma(ci). Failure patterns were also examined for a few cases. For validating the results, computations were also performed for a strip footing as well. The results obtained from the analysis compare well with the data reported in literature. Since the equilibrium conditions are precisely satisfied only at the centroids of the elements, not everywhere in the domain, the obtained lower bound solution will be approximate not true. (C) 2015 Elsevier Ltd. All rights reserved.

An arithmetical theorem for partially ordered sets

The simplest multiplicative systems in which arithmetical ideas can be defined are semigroups. For such systems irreducible (prime) elements can be introduced and conditions under which the fundamental theorem of arithmetic holds have been investigated (Clifford (3)). After identifying associates, the elements of the semigroup form a partially ordered set with respect to the ordinary division relation. This suggests the possibility of an analogous arithmetical result for abstract partially ordered sets. Although nothing corresponding to product exists in a partially ordered set, there is a notion similar to g.c.d. This is the meet operation, defined as greatest lower bound. Thus irreducible elements, namely those elements not expressible as meets of proper divisors can be introduced. The assumption of the ascending chain condition then implies that each element is representable as a reduced meet of irreducibles. The central problem of this thesis is to determine conditions on the structure of the partially ordered set in order that each element have a unique such representation.

Part I contains preliminary results and introduces the principal tools of the investigation. In the second part, basic properties of the lattice of ideals and the connection between its structure and the irreducible decompositions of elements are developed. The proofs of these results are identical with the corresponding ones for the lattice case (Dilworth (2)). The last part contains those results whose proofs are peculiar to partially ordered sets and also contains the proof of the main theorem.

Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem

Gough, John, 'Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem', Journal of Mathematical Physics. 47, 113509, (2006)

Quantum Flows as Markovian Limit of Emission, Absorption and Scattering Interactions

Gough, John, (2004) 'Quantum Flows as Markovian Limit of Emission, Absorption and Scattering Interactions', Communications in Mathematical Physics 254 pp.498-512 RAE2008

Oxygen isotopes from Phorcus (Osilinus) turbinatus shells as a proxy for sea surface temperature in the central Mediterranean: a case study from Malta.

The marine topshell, Phorcus (Osilinus) turbinatus, is a common component of many archaeological sites in the Mediterranean. This species has been successfully used as a palaeoclimate proxy in Italy. To test whether d18O from P. turbinatus shells can serve as a reliable palaeoclimate archive for other regions of the Mediterranean, we collected live P. turbinatus from the northeast coast of Malta each month for a year. The d18OSHELL values of the outermost growth increments of these live-collected shells ranged between-0.4 and+2.4‰. These values correspond to growing temperatures calculated from shell edge d18O of between 15 °C and 27 °C. Calculated shell edge sea surface temperatures are highly correlated with instrumental records of sea surface temperature recorded over the period of collection. The individuals analysed for this study are smaller than P. turbinatus from populations studied elsewhere in the Mediterranean. Nonetheless, d18OSHELL provides a robust record of sea surface temperatures, suggesting that smaller/younger shells in archaeological deposits can still provide reliable palaeothermometry records. This study extends the upper growth limit P. turbinatus by 2 °C compared with the previous studies of P. turbinatus in the Mediterranean and suggests that, contrary to the previous studies, growth shutdown does not occur in all P. turbinatus when sea surface temperatures exceed 25 °C. This may reflect the higher sample resolution that can be obtained from smaller/faster growing shells, or it may reflect actual higher growth tolerances of P. turbinatus populations in Malta. By showing that P. turbinatus precipitate their shells in d18O equilibrium with surrounding sea water, this study reinforces the potential for the stable isotope chemistry of P. turbinatus shells preserved in Mediterranean archaeological sites to provide a window into the climate and seasonality regimes of the past.

Pollen Season and Climate: Is the Timing of Birch Pollen Release in the UK Approaching its Limit?

In light of heightened interest in the response of pollen phenology to temperature, we investigated recent changes to the onset of Betula (birch) pollen seasons in central and southern England, including a test of predicted advancement of the Betula pollen season for London. We calculated onset of birch pollen seasons using daily airborne pollen data obtained at London, Plymouth and Worcester, determined trends in the start of the pollen season and compared timing of the birch pollen season with observed temperature patterns for the period 1995–2010. We found no overall change in the onset of birch pollen in the study period although there was evidence that the response to temperature was nonlinear and that a lower asymptotic start of the pollen season may exist. The start of the birch pollen season was strongly correlated with March mean temperature. These results reinforce previous findings showing that the timing of the birch pollen season in the UK is particularly sensitive to spring temperatures. The climate relationship shown here persists over both longer decadal-scale trends and shorter, seasonal trends as well as during periods of ‘sign-switching’ when cooler spring temperatures result in later start dates. These attributes, combined with the wide geographical coverage of airborne pollen monitoring sites, some with records extending back several decades, provide a powerful tool for the detection of climate change impacts, although local site factors and the requirement for winter chilling may be confounding factors.

The Teggiolo zone: a key to the Helvetic-Penninic connection (stratigraphy and tectonics in the Val Bavona, Ticino, Central Alps)

The Teggiolo zone is the sedimentary cover of the Antigorio nappe, one of the lowest tectonic units of the Penninic Central Alps. Detailed mapping, stratigraphic and structural analyses, and comparisons with less metamorphic series in several well-studied domains of the Alps, provide a new stratigraphic interpretation. The Teggiolo zone is comprised of several sedimentary cycles, separated by erosive surfaces and large stratigraphic gaps, which cover the time span from Triassic to Eocene. At Mid-Jurassic times it appears as an uplifted, partially emergent block, marking the southern limit of the main Helvetic basin (the Limiting South-Helvetic Rise LSHR). The main mass of the Teggiolo calcschists, whose base truncates the Triassic-Jurassic cycles and can erode the Antigorio basement, consists of fine-grained clastic sediments analogous to the deep-water flyschoid deposits of Late Cretaceous to Eocene age in the North-Penninic (or Valais s.l.) basins. Thus the Antigorio-Teggiolo domain occupies a crucial paleogeographic position, on the boundary between the Helvetic and Penninic realms: from Triassic to Early Cretaceous its affinity is with the Helvetic; at the end of Cretaceous it is incorporated into the North-Penninic basins. An unexpected result is the discovery of the important role played by complex formations of wildflysch type at the top of the Teggiolo zone. They contain blocks of various sizes. According to their nature, three different associations are distinguished that have specific vertical and lateral distributions. These blocks give clues to the existence of territories that have disappeared from the present-day level of observation and impose constraints on the kinematics of early folding and embryonic nappe emplacement. Tectonics produced several phases of superimposed folds and schistosities, more in the metasediments than in the gneissic basement. Older deformations that predate the amplification of the frontal hinge of the nappe generated the dominant schistosity and the km-wide Vanzèla isoclinal fold.

A Generalization of a Theorem of Boyd and Lawton

Ce mémoire s’applique à étudier d’abord, dans la première partie, la mesure de Mahler des polynômes à une seule variable. Il commence en donnant des définitions et quelques résultats pertinents pour le calcul de telle hauteur. Il aborde aussi le sujet de la question de Lehmer, la conjecture la plus célèbre dans le domaine, donne quelques exemples et résultats ayant pour but de résoudre la question. Ensuite, il y a l’extension de la mesure de Mahler sur les polynômes à plusieurs variables, une démarche semblable au premier cas de la mesure de Mahler, et le sujet des points limites avec quelques exemples. Dans la seconde partie, on commence par donner des définitions concernant un ordre supérieur de la mesure de Mahler, et des généralisations en passant des polynômes simples aux polynômes à plusieurs variables. La question de Lehmer existe aussi dans le domaine de la mesure de Mahler supérieure, mais avec des réponses totalement différentes. À la fin, on arrive à notre objectif, qui sera la démonstration de la généralisation d’un théorème de Boyd-Lawton, ce dernier met en évidence une relation entre la mesure de Mahler des polynômes à plusieurs variables avec la limite de la mesure de Mahler des polynômes à une seule variable. Ce résultat a des conséquences en termes de la conjecture de Lehmer et sert à clarifier la relation entre les valeurs de la mesure de Mahler des polynômes à une variable et celles des polynômes à plusieurs variables, qui, en effet, sont très différentes en nature.

Interactive quantum information theory

La théorie de l'information quantique s'est développée à une vitesse fulgurante au cours des vingt dernières années, avec des analogues et extensions des théorèmes de codage de source et de codage sur canal bruité pour la communication unidirectionnelle. Pour la communication interactive, un analogue quantique de la complexité de la communication a été développé, pour lequel les protocoles quantiques peuvent performer exponentiellement mieux que les meilleurs protocoles classiques pour certaines tâches classiques. Cependant, l'information quantique est beaucoup plus sensible au bruit que l'information classique. Il est donc impératif d'utiliser les ressources quantiques à leur plein potentiel. Dans cette thèse, nous étudions les protocoles quantiques interactifs du point de vue de la théorie de l'information et étudions les analogues du codage de source et du codage sur canal bruité. Le cadre considéré est celui de la complexité de la communication: Alice et Bob veulent faire un calcul quantique biparti tout en minimisant la quantité de communication échangée, sans égard au coût des calculs locaux. Nos résultats sont séparés en trois chapitres distincts, qui sont organisés de sorte à ce que chacun puisse être lu indépendamment. Étant donné le rôle central qu'elle occupe dans le contexte de la compression interactive, un chapitre est dédié à l'étude de la tâche de la redistribution d'état quantique. Nous prouvons des bornes inférieures sur les coûts de communication nécessaires dans un contexte interactif. Nous prouvons également des bornes atteignables avec un seul message, dans un contexte d'usage unique. Dans un chapitre subséquent, nous définissons une nouvelle notion de complexité de l'information quantique. Celle-ci caractérise la quantité d'information, plutôt que de communication, qu'Alice et Bob doivent échanger pour calculer une tâche bipartie. Nous prouvons beaucoup de propriétés structurelles pour cette quantité, et nous lui donnons une interprétation opérationnelle en tant que complexité de la communication quantique amortie. Dans le cas particulier d'entrées classiques, nous donnons une autre caractérisation permettant de quantifier le coût encouru par un protocole quantique qui oublie de l'information classique. Deux applications sont présentées: le premier résultat général de somme directe pour la complexité de la communication quantique à plus d'une ronde, ainsi qu'une borne optimale, à un terme polylogarithmique près, pour la complexité de la communication quantique avec un nombre de rondes limité pour la fonction « ensembles disjoints ». Dans un chapitre final, nous initions l'étude de la capacité interactive quantique pour les canaux bruités. Étant donné que les techniques pour distribuer de l'intrication sont bien étudiées, nous nous concentrons sur un modèle avec intrication préalable parfaite et communication classique bruitée. Nous démontrons que dans le cadre plus ardu des erreurs adversarielles, nous pouvons tolérer un taux d'erreur maximal de une demie moins epsilon, avec epsilon plus grand que zéro arbitrairement petit, et ce avec un taux de communication positif. Il s'ensuit que les canaux avec bruit aléatoire ayant une capacité positive pour la transmission unidirectionnelle ont une capacité positive pour la communication interactive quantique. Nous concluons avec une discussion de nos résultats et des directions futures pour ce programme de recherche sur une théorie de l'information quantique interactive.

Hydrogeological, Geophysical And Geochemical Studies In Parts Of Coastal And Midland Areas, Central Kerala - A Gis Approach

The present study deals with the different hydrogeological characteristics of the coastal region of central Kerala and a comparative analysis with corresponding hard rock terrain. The coastal regions lie in areas where the aquifer systems discharge groundwater ultimately into the sea. Groundwater development in such regions will require a precise understanding of the complex mechanism of the saline and fresh water relationship, so that the withdrawals are so regulated as to avoid situations leading to upcoming of the saline groundwater bodies as also to prevent migration of sea water ingress further inland. Coastal tracts of Kerala are formed by several drainage systems. Thick pile of semi-consolidated and consolidated sediments from Tertiary to Recent age underlies it. These sediments comprise phreatic and confined aquifer systems. The corresponding hard rock terrain is encountered with laterites and underlined by the Precambrian metamorphic rocks. Supply of water from hard rock terrain is rather limited. This may be due to the small pore size, low degree of interconnectivity and low extent of weathering of the country rocks. The groundwater storage is mostly controlled by the thickness and hydrological properties of the weathered zone and the aquifer geometry. The over exploitation of groundwater, beyond the ‘safe yield’ limit, cause undesirable effects like continuous reduction in groundwater levels, reduction in river flows, reduction in wetland surface, degradation of groundwater quality and many other environmental problems like drought, famine etc.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 2. pseudoenergy-based theory

This paper represents the second part of a study of semi-geostrophic (SG) geophysical fluid dynamics. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. The development of such balanced models is an area of great current interest. The goal of the present work is to extend a central body of QG theory, concerning the evolution of disturbances to prescribed basic states, to SG dynamics. Part 1 was based on the pseudomomentum; Part 2 is based on the pseudoenergy. A pseudoenergy invariant is a conserved quantity, of second order in disturbance amplitude relative to a prescribed steady basic state, which is related to the time symmetry of the system. We derive such an invariant for the semi-geostrophic equations, and use it to obtain: (i) a linear stability theorem analogous to Arnol'd's ‘first theorem’; and (ii) a small-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number. The results are derived for both the f-plane Boussinesq form of semi-geostrophic dynamics, and its extension to β-plane compressible flow by Magnusdottir & Schubert. Novel features particular to semi-geostrophic dynamics include apparently unnoticed lateral boundary stability criteria. Unlike the boundary stability criteria found in the first part of this study, however, these boundary criteria do not necessarily preclude the construction of provably stable basic states. The interior semi-geostrophic dynamics has an underlying Hamiltonian structure, which guarantees that symmetries in the system correspond naturally to the system's invariants. This is an important motivation for the theoretical approach used in this study. The connection between symmetries and conservation laws is made explicit using Noether's theorem applied to the Eulerian form of the Hamiltonian description of the interior dynamics.