Post-critical set and non existence of preserved meromorphic two-forms

We present a family of birational transformations in $CP_2$ depending on two, or three, parameters which does not, generically, preserve meromorphic two-forms. With the introduction of the orbit of the critical set (vanishing condition of the Jacobian), also called ``post-critical set'', we get some new structures, some "non-analytic" two-form which reduce to meromorphic two-forms for particular subvarieties in the parameter space. On these subvarieties, the iterates of the critical set have a polynomial growth in the \emph{degrees of the parameters}, while one has an exponential growth out of these subspaces. The analysis of our birational transformation in $CP_2$ is first carried out using Diller-Favre criterion in order to find the complexity reduction of the mapping. The integrable cases are found. The identification between the complexity growth and the topological entropy is, one more time, verified. We perform plots of the post-critical set, as well as calculations of Lyapunov exponents for many orbits, confirming that generically no meromorphic two-form can be preserved for this mapping. These birational transformations in $CP_2$, which, generically, do not preserve any meromorphic two-form, are extremely similar to other birational transformations we previously studied, which do preserve meromorphic two-forms. We note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned, but drastically different results as far as a more ``probabilistic'' approach of dynamical systems is concerned (Lyapunov exponents). With these examples we see that the existence of a preserved meromorphic two-form explains most of the (numerical) discrepancy between the topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure

First Gale Western Butte Capping-Unit Compositions, and Relationships to Earlier Units Along Curiosity's Traverse

The Curiosity rover has been traversing through the clay-bearing unit (Glen Torridon; GT), approaching Greenheugh pediment, a large, fan-shaped surface surrounding the mouth of Gediz Vallis on the lower slope of Mt. Sharp. The pediment unconformably overlies the underlying bedrock, and is hence younger than units of the Mt. Sharp group. Orbital imaging of the pediment has shown it to have a slightly lower albedo and higher thermal inertia than neighboring units, to be relatively retentive of craters (e.g., erosion resistant), and to exhibit curved bedforms suggestive of lithified eolian bedforms. No diagnostic spectral signature has been observed from orbit. Recent rover positions allowed remote imaging of the contact between Greenheugh pediment and the eroded Murray formation strata below it, showing that the pediment capping material is cross-bedded and relatively thin (1-3 m), and suggesting that the pediment may have been much larger at one time. As Curiosity approached the edge of the pediment, the team investigated two buttes named Central and Western. The latter butte contains dark capping material that initially looked similar to the pediment cap, but close inspection revealed important physical differences. Here we report on compositions from ChemCam of two float rocks that appear to have rolled down from the capping unit, and on potential relation-ships to other targets along the traverse of the rover

Problems and Aspects of Energy-Driven Wavefunction Collapse Models

Four problematic circumstances are considered, involving models which describe dynamical wavefunction collapse toward energy eigenstates, for which it is shown that wavefunction collapse of macroscopic objects does not work properly. In one case, a common particle position measuring situation, the apparatus evolves to a superposition of macroscopically distinguishable states (does not collapse to one of them as it should) because each such particle/apparatus/environment state has precisely the same energy spectrum. Second, assuming an experiment takes place involving collapse to one of two possible outcomes which is permanently recorded, it is shown in general that this can only happen in the unlikely case that the two apparatus states corresponding to the two outcomes have disjoint energy spectra. Next, the progressive narrowing of the energy spectrum due to the collapse mechanism is considered. This has the effect of broadening the time evolution of objects as the universe evolves. Two examples, one involving a precessing spin, the other involving creation of an excited state followed by its decay, are presented in the form of paradoxes. In both examples, the microscopic behavior predicted by standard quantum theory is significantly altered under energy-driven collapse, but this alteration is not observed by an apparatus when it is included in the quantum description. The resolution involves recognition that the statevector describing the apparatus does not collapse, but evolves to a superposition of macroscopically different states.Comment: 17 page

UK Large-scale Wind Power Programme from 1970 to 1990: the Carmarthen Bay experiments and the Musgrove Vertical-Axis Turbines

This article describes the development of the Musgrove Vertical Axis Wind Turbine (VAWT) concept, the UK ‘Carmarthen Bay’ wind turbine test programme, and UK government’s wind power programme to 1990. One of the most significant developments in the story of British wind power occurred during the 1970s, 1980s, and 1990s, with the development of the Musgrove vertical axis wind turbine and its inclusion within the UK Government’s wind turbine test programme. Evolving from a supervisor’s idea for an undergraduate project at Reading University, the Musgrove VAWT was once seen as an able competitor to the horizontal axis wind systems that were also being encouraged at the time by both the UK government and the Central Electricity Generating Board, the then nationalised electricity utility for England and Wales. During the 1980s and 1990s the most developed Musgrove VAWT system, along with three other commercial turbine designs was tested at Carmarthen Bay, South Wales as part of a national wind power test programme. From these developmental tests, operational data was collected and lessons learnt, which were incorporated into subsequent wind power operations.http://dx.doi.org/10.1260/03095240677860621

Core Overshoot: An Improved Treatment and Constraints from Seismic Data

We present a comprehensive set of stellar evolution models for Procyon A in an effort to guide future measurements of both traditional stellar parameters and seismic frequencies towards constraining the amount of core overshoot in Procyon A and possibly other stars. Current observational measurements of Procyon A when combined with traditional stellar modeling only place a large upper limit on overshoot of alphaOV < 1.1. By carrying out a detailed pulsation analysis, we further demonstrate, how p- and g-mode averaged spacings can be used to gain better estimates of the core size. For both p- and g-modes, the frequency spacings for models without overshoot are clearly separated from the models with overshoot. In addition, measurements of the l=0 averaged small p-mode spacings could be used to establish Procyon A's evolutionary stage. For a fixed implementation of overshoot and under favorable circumstances, the g-mode spacings can be used to determine the overshoot extent to an accuracy of +-0.05 Hp. However, we stress that considerable confusion is added due to the unknown treatment of the overshoot region. This ambiguity might be removed by analyzing many different stars. A simple non-local convection theory developed by Kuhfuss is implemented in our stellar evolution code and contrasted with the traditional approaches. We show that this theory supports a moderate increase of the amount of convective overshoot with stellar mass of Delta(alphaOV) = +0.10 between 1.5 Msun and 15 Msun. This theory places an upper limit on Procyon A's core overshoot extent of ~0.4 Hp which matches the limit imposed by Roxburgh's integral criterion.Comment: 45 pages, 26 figures, accepted in Ap

Quantum Theory and Time Asymmetry

The relation between quantum measurement and thermodynamically irreversible processes is investigated. The reduction of the state vector is fundamentally asymmetric in time and shows an observer-relatedness which may explain the double interpretation of the state vector as a representation of physical states as well as of information about them. The concept of relevance being used in all statistical theories of irreversible thermodynamics is shown to be based on the same observer-relatedness. Quantum theories of irreversible processes implicitly use an objectivized process of state vector reduction. The conditions for the reduction are discussed, and I speculate that the final (subjective) observer system might even be carried by a spacetime point.Comment: Latex version of a paper published in 1979 (with minor revisions), 18 page

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page

The Stratigraphy of Central and Western Butte and the Greenheugh Pediment Contact

The Greenheugh pediment at the base of Aeolis Mons (Mt. Sharp), which may truncate units in the Murray formation and is capped by a thin sandstone unit, appears to represent a major shift in climate history within Gale crater. The pediment appears to be an erosional remnant of potentially a much more extensive feature. Curiositys traverse through the southern extent of Glen Torridon (south of Vera Rubin ridge) has brought the rover in contact with several new stratigraphic units that lie beneath the pediment. These strata were visited at two outcrop-forming buttes (Central and Western butte- both remnants of the retreating pediment) south of an orbitally defined boundary marking the transition from the Fractured Clay-bearing Unit (fCU) and the fractured Intermediate Unit (fIU). Here we present preliminary interpretations of the stratigraphy within Central and Western buttes and propose the Western butte cap rocks do not match the pediment capping unit

Decoherence, the measurement problem, and interpretations of quantum mechanics

Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. This paper is intended to clarify key features of the decoherence program, including its more recent results, and to investigate their application and consequences in the context of the main interpretive approaches of quantum mechanics.Comment: 41 pages. Final published versio