Secant and conjugate direction methods in optimisation

Not Availabl

Robust shape control in a sendzimir cold-rolling steel mill

The shape control problem for a Sendzimir 20-roll cold rolling steel mill is characterised by operation over a wide range of conditions arising from roll changes, changes in rolling schedules and changes in material gauge, width and hardness. Previous approaches to the problem suggest storing a large number of precompensator matrices to cater for the full range of operating conditions. This paper, on the other hand, attempts to synthesise a controller which is optimally robust to changes in the conditions associated with the rolling cluster, resulting in a reduced storage requirement for the controlling computer. The performance of the robust controller is evaluated via nonlinear simulation

Optimal damping profiles for a heaving buoy wave-energy converter

This paper explores optimal damping profiles for a heaving buoy wave energy converter (WEC). The approach is mathematical and the model of Eidsmoen (1995) is used as a basis. In order to permit analytical development, the model is initially simplified and an optimal damping profile is determined using numerical optimization. Having found the optimal damping profile, a semi-analytical solution methodology is developed to determine the optimal damping parameters. Finally, the procedure is validated on the original model and some aspects related to the control problem are addressed

Historical Evolution of theWave Resource and Energy Production off the Chilean Coast over the 20th Century

The wave energy resource in the Chilean coast shows particularly profitable characteristics for wave energy production, with relatively high mean wave power and low inter-annual resource variability. This combination is as interesting as unusual, since high energetic locations are usually also highly variable, such as the west coast of Ireland. Long-term wave resource variations are also an important aspect when designing wave energy converters (WECs), which are often neglected in resource assessment. The present paper studies the long-term resource variability of the Chilean coast, dividing the 20th century into five do-decades and analysing the variations between the different do-decades. To that end, the ERA20C reanalysis of the European Centre for Medium-Range Weather Forecasts is calibrated versus the ERA-Interim reanalysis and validated against buoy measurements collected in different points of the Chilean coast. Historical resource variations off the Chilean coast are compared to resource variations off the west coast in Ireland, showing a significantly more consistent wave resource. In addition, the impact of historical wave resource variations on a realistic WEC, similar to the Corpower device, is studied, comparing the results to those obtained off the west coast of Ireland. The annual power production off the Chilean coast is demonstrated to be remarkably more regular over the 20th century, with variations of just 1% between the different do-decades.The authors with the Centre for Ocean Energy Research in Maynooth University are supported by Science Foundation Ireland under Grant No. 13/IA/1886. It is also supported by grant CGL2016-76561-R, MINECO/ERDF, UE. Additional funding was received from the University of Basque Country (UPV/EHU, GIU17/002)

Normal Mode Determination of Perovskite Crystal Structures with Octahedral Rotations: Theory and Applications

Nuclear site analysis methods are used to enumerate the normal modes of $ABX_{3}$ perovskite polymorphs with octahedral rotations. We provide the modes of the fourteen subgroups of the cubic aristotype describing the Glazer octahedral tilt patterns, which are obtained from rotations of the $BX_{6}$ octahedra with different sense and amplitude about high symmetry axes. We tabulate all normal modes of each tilt system and specify the contribution of each atomic species to the mode displacement pattern, elucidating the physical meaning of the symmetry unique modes. We have systematically generated 705 schematic atomic displacement patterns for the normal modes of all 15 (14 rotated + 1 unrotated) Glazer tilt systems. We show through some illustrative examples how to use these tables to identify the octahedral rotations, symmetric breathing, and first-order Jahn-Teller anti-symmetric breathing distortions of the $BX_{6}$ octahedra, and the associated Raman selection rules. We anticipate that these tables and schematics will be useful in understanding the lattice dynamics of bulk perovskites and would serve as reference point in elucidating the atomic origin of a wide range of physical properties in synthetic perovskite thin films and superlattices.Comment: 17 pages, 3 figures, 17 tables. Supporting information accessed through link specified within manuscrip

Consistency analysis of Kaluza-Klein geometric sigma models

Geometric sigma models are purely geometric theories of scalar fields coupled to gravity. Geometrically, these scalars represent the very coordinates of space-time, and, as such, can be gauged away. A particular theory is built over a given metric field configuration which becomes the vacuum of the theory. Kaluza-Klein theories of the kind have been shown to be free of the classical cosmological constant problem, and to give massless gauge fields after dimensional reduction. In this paper, the consistency of dimensional reduction, as well as the stability of the internal excitations, are analyzed. Choosing the internal space in the form of a group manifold, one meets no inconsistencies in the dimensional reduction procedure. As an example, the SO(n) groups are analyzed, with the result that the mass matrix of the internal excitations necessarily possesses negative modes. In the case of coset spaces, the consistency of dimensional reduction rules out all but the stable mode, although the full vacuum stability remains an open problem.Comment: 13 pages, RevTe

Antineutrino Geophysics with Liquid Scintillator Detectors

Detecting the antineutrinos emitted by the decay of radioactive elements in the mantle and crust could provide a direct measurement of the total abundance of uranium and thorium in the Earth. In calculating the antineutrino flux at specific sites, the local geology of the crust and the background from the world's nuclear power reactors are important considerations. Employing a global crustal map, with type and thickness data, and using recent estimates of the uranium and thorium distribution in the Earth, we calculate the antineutrino event rate for two new neutrino detectors. We show that spectral features allow terrestrial antineutrino events to be identified above reactor antineutrino backgrounds and that the uranium and thorium contributions can be separately determined.Comment: Published paper differs from original submitted preprint because reviewers suggested updated continental crust U/Th abundances. Kamioka geographical location error was in preprint, partially corrected in published version. This version is the same as the published paper, with Kamioka fully corrected. Because of recent interest in this topic, this version is being made available, despite this work being 8 years ol

Formation and Structure of Low Density Exo-Neptunes

Kepler has found hundreds of Neptune-size (2-6 R_Earth) planet candidates within 0.5 AU of their stars. The nature of the vast majority of these planets is not known because their masses have not been measured. Using theoretical models of planet formation, evolution and structure, we explore the range of minimum plausible masses for low-density exo-Neptunes. We focus on highly irradiated planets with T_eq>=500K. We consider two separate formation pathways for low-mass planets with voluminous atmospheres of light gases: core nucleated accretion and outgassing of hydrogen from dissociated ices. We show that Neptune-size planets at T_eq=500K with masses as small as a few times that of Earth can plausibly be formed core nucleated accretion coupled with subsequent inward migration. We also derive a limiting low-density mass-radius relation for rocky planets with outgassed hydrogen envelopes but no surface water. Rocky planets with outgassed hydrogen envelopes typically have computed radii well below 3 R_Earth. For both planets with H/He envelopes from core nucleated accretion and planets with outgassed hydrogen envelopes, we employ planet interior models to map the range of planet mass--envelope mass--equilibrium temperature parameter space that is consistent with Neptune-size planet radii. Atmospheric mass loss mediates which corners of this parameter space are populated by actual planets and ultimately governs the minimum plausible mass at a specified transit radius. We find that Kepler's 2-6 R_Earth planet candidates at T_eq=500--1000K could potentially have masses less than ~4 M_Earth. Although our quantitative results depend on several assumptions, our qualitative finding that warm Neptune-size planets can have masses substantially smaller than those given by interpolating the masses and radii of planets within our Solar System is robust.Comment: 17 pages, 9 figures, accepted for publication in Ap

Single-crossover dynamics: finite versus infinite populations

Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes continuous time and single crossover events. The corresponding nonlinear system of differential equations permits a closed solution, both in terms of the type frequencies and via linkage disequilibria of all orders. To include stochastic effects, we then consider the corresponding finite-population model, the Moran model with single crossovers, and examine it both analytically and by means of simulations. Particular emphasis is on the connection with the deterministic solution. If there is only recombination and every pair of recombined offspring replaces their pair of parents (i.e., there is no resampling), then the {\em expected} type frequencies in the finite population, of arbitrary size, equal the type frequencies in the infinite population. If resampling is included, the stochastic process converges, in the infinite-population limit, to the deterministic dynamics, which turns out to be a good approximation already for populations of moderate size.Comment: 21 pages, 4 figure

The origin of the Moon within a terrestrial synestia

The giant impact hypothesis remains the leading theory for lunar origin. However, current models struggle to explain the Moon's composition and isotopic similarity with Earth. Here we present a new lunar origin model. High-energy, high-angular momentum giant impacts can create a post-impact structure that exceeds the corotation limit (CoRoL), which defines the hottest thermal state and angular momentum possible for a corotating body. In a typical super-CoRoL body, traditional definitions of mantle, atmosphere and disk are not appropriate, and the body forms a new type of planetary structure, named a synestia. Using simulations of cooling synestias combined with dynamic, thermodynamic and geochemical calculations, we show that satellite formation from a synestia can produce the main features of our Moon. We find that cooling drives mixing of the structure, and condensation generates moonlets that orbit within the synestia, surrounded by tens of bars of bulk silicate Earth (BSE) vapor. The moonlets and growing moon are heated by the vapor until the first major element (Si) begins to vaporize and buffer the temperature. Moonlets equilibrate with BSE vapor at the temperature of silicate vaporization and the pressure of the structure, establishing the lunar isotopic composition and pattern of moderately volatile elements. Eventually, the cooling synestia recedes within the lunar orbit, terminating the main stage of lunar accretion. Our model shifts the paradigm for lunar origin from specifying a certain impact scenario to achieving a Moon-forming synestia. Giant impacts that produce potential Moon-forming synestias were common at the end of terrestrial planet formation.Comment: Accepted for publication in Journal of Geophysical Research: Planets. Main text: 44 pages, 24 figures. Supplement: 16 pages, 5 figures, 3 table