Kinematic Orbits and the Structure of the Internal Space for Systems of Five or More Bodies

The internal space for a molecule, atom, or other n-body system can be conveniently parameterised by 3n-9 kinematic angles and three kinematic invariants. For a fixed set of kinematic invariants, the kinematic angles parameterise a subspace, called a kinematic orbit, of the n-body internal space. Building on an earlier analysis of the three- and four-body problems, we derive the form of these kinematic orbits (that is, their topology) for the general n-body problem. The case n=5 is studied in detail, along with the previously studied cases n=3,4.Comment: 38 pages, submitted to J. Phys.

Phase equilibrium modelling of the amphibolite to granulite facies transition in metabasic rocks (Ivrea Zone, NW Italy)

The development of thermodynamic models for tonalitic melt and the updated clinopyroxene and amphibole models now allow the use of phase equilibrium modelling to estimate P–T conditions and melt production for anatectic mafic and intermediate rock types at high‐temperature conditions. The Permian mid‐lower crustal section of the Ivrea Zone preserves a metamorphic field gradient from mid amphibolite facies to granulite facies, and thus records the onset of partial melting in metabasic rocks. Interlayered metabasic and metapelitic rocks allows the direct comparison of P–T estimates and partial melting between both rock types with the same metamorphic evolution. Pseudosections for metabasic compositions calculated in the Na2O–CaO–K2O–FeO–MgO–Al2O3–SiO2–H2O–TiO2–O (NCKFMASHTO) system are presented and compared with those of metapelitic rocks calculated with consistent endmember data and a–x models. The results presented in this study show that P–T conditions obtained by phase equilibria modelling of both metabasic and metapelitic rocks give consistent results within uncertainties, allowing integration of results obtained for both rock types. In combination, the calculations for both metabasic and metapelitic rocks allows an updated and more precisely constrained metamorphic field gradient for Val Strona di Omegna to be defined. The new field gradient has a slightly lower dP/dT which is in better agreement with the onset of crustal thinning of the Adriatic margin during the Permian inferred in recent studies

The limit of N=(2,2) superconformal minimal models

The limit of families of two-dimensional conformal field theories has recently attracted attention in the context of AdS/CFT dualities. In our work we analyse the limit of N=(2,2) superconformal minimal models when the central charge approaches c=3. The limiting theory is a non-rational N=(2,2) superconformal theory, in which there is a continuum of chiral primary fields. We determine the spectrum of the theory, the three-point functions on the sphere, and the disc one-point functions.Comment: 37 pages, 3 figures; v2: minor corrections in section 5.3, version to be published in JHE

Global environmental changes impact soil hydraulic functions through biophysical feedbacks

Although only representing 0.05% of global freshwater, or 0.001% of all global water, soil water supports all terrestrial biological life. Soil moisture behaviour in most models is constrained by hydraulic parameters that do not change. Here we argue that biological feedbacks from plants, macro‐fauna and the microbiome influence soil structure, and thus the soil hydraulic parameters and the soil water content signals we observe. Incorporating biological feedbacks into soil hydrological models is therefore important for understanding environmental change and its impacts on ecosystems. We anticipate that environmental change will accelerate and modify soil hydraulic function. Increasingly we understand the vital role that soil moisture exerts on the carbon cycle and other environmental threats such as heatwaves, droughts and floods, wildfires, regional precipitation patterns, disease regulation and infrastructure stability, in addition to agricultural production. Biological feedbacks may result in changes to soil hydraulic function that could be irreversible, resulting in alternative stable states (ASS) of soil moisture. To explore this, we need models that consider all the major feedbacks between soil properties and soil‐plant‐faunal‐microbial‐atmospheric processes, which is something we currently do not have. Therefore, a new direction is required to incorporate a dynamic description of soil structure and hydraulic property evolution into soil‐plant‐atmosphere, or land surface, models that consider feedbacks from land use and climate drivers of change, so as to better model ecosystem dynamics

Six supersoft X-ray binaries: system parameters and twin-jet outflows

A comparison is made between the properties of CAL 83, CAL 87, RX J0513.9-6951, 1E 0035.4-7230 (SMC 13), RX J0019.8+2156, and RX J0925.7-4758, all supersoft X-ray binaries. Spectra with the same resolution and wavelength coverage of these systems are compared and contrasted. Some new photometry is also presented. The equivalent widths of the principal emission lines of H and He II differ by more than an order of magnitude among these sources, although those of the highest ionization lines (e.g. O VI) are very similar. In individual systems, the velocity curves derived from various ions often differ in phasing and amplitude, but those whose phasing is consistent with the light curves (implying the lines are formed near the compact star) give masses of $\sim 1.2M_{\odot}$ and $\sim 0.5M_{\odot}$ for the degenerate and mass-losing stars, respectively. This finding is in conflict with currently prevailing theoretical models for supersoft binaries. The three highest luminosity sources show evidence of "jet" outflows, with velocities of $\sim 1-4 \times10^3 km/s$. In CAL 83 the shape of the He II 4686\AA profile continues to show evidence that these jets may precess with a period of $\sim 69$ days.Comment: 27 pages including 5 tables, plus 6 figures. To appear in Ap

Moyal star product approach to the Bohr-Sommerfeld approximation

The Bohr-Sommerfeld approximation to the eigenvalues of a one-dimensional quantum Hamiltonian is derived through order $\hbar^2$ (i.e., including the first correction term beyond the usual result) by means of the Moyal star product. The Hamiltonian need only have a Weyl transform (or symbol) that is a power series in $\hbar$, starting with $\hbar^0$, with a generic fixed point in phase space. The Hamiltonian is not restricted to the kinetic-plus-potential form. The method involves transforming the Hamiltonian to a normal form, in which it becomes a function of the harmonic oscillator Hamiltonian. Diagrammatic and other techniques with potential applications to other normal form problems are presented for manipulating higher order terms in the Moyal series.Comment: 27 pages, no figure

A limit cycle model for long-term optical variations of V Sagittae: The second example of accretion wind evolution

V Sagittae shows quasi-periodic optical high (soft X-ray off) and low (soft X-ray on) states with the total period of ~300 days. A binary model is presented to explain orbital light curves both for the high and low states as well as the transition mechanism between them. The binary model consists of a white dwarf (WD), a disk around the WD, and a lobe-filling main-sequence (MS) companion. In the optical high state, the mass transfer rate to the WD exceeds the critical rate of ~1 x 10^{-6} Msun/yr, and the WD blows an optically thick, massive wind. Surface layers of the disk are blown in the wind and the disk surface extends to the companion or over. As a result, optical luminosity of the disk increases by a magnitude because of its large irradiation effect. The massive wind completely obscures soft X-rays. This corresponds to the optical high/soft X-ray off state. The transition between optical high and low states is driven by an attenuation of the mass transfer from the secondary. As the mass supply stops, the WD wind weakens and eventually stops. The disk shrinks to a Roche lobe size and the optical magnitude drops. This phase corresponds to the optical low/soft X-ray on state. This cycle is repeated like a limit cycle. The WD can grow in mass at the critical rate and eventually reach the Chandrasekhar mass limit. This process is called ``accretion wind evolution,'' which is a key evolutionary process in a recently developed evolutionary scenario of Type Ia supernovae. This evolutionary process was first confirmed in the LMC supersoft X-ray source RX J0513.9$-$6951. Thus, V Sge is the second example of accretion wind evolution.Comment: to appear in ApJ, 33 pages including figure

Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties

In this article we apply the methods outlined in the previous paper of this series to the particular set of states obtained by choosing the complexifier to be a Laplace operator for each edge of a graph. The corresponding coherent state transform was introduced by Hall for one edge and generalized by Ashtekar, Lewandowski, Marolf, Mour\~ao and Thiemann to arbitrary, finite, piecewise analytic graphs. However, both of these works were incomplete with respect to the following two issues : (a) The focus was on the unitarity of the transform and left the properties of the corresponding coherent states themselves untouched. (b) While these states depend in some sense on complexified connections, it remained unclear what the complexification was in terms of the coordinates of the underlying real phase space. In this paper we resolve these issues, in particular, we prove that this family of states satisfies all the usual properties : i) Peakedness in the configuration, momentum and phase space (or Bargmann-Segal) representation, ii) Saturation of the unquenched Heisenberg uncertainty bound. iii) (Over)completeness. These states therefore comprise a candidate family for the semi-classical analysis of canonical quantum gravity and quantum gauge theory coupled to quantum gravity, enable error-controlled approximations and set a new starting point for {\it numerical canonical quantum general relativity and gauge theory}. The text is supplemented by an appendix which contains extensive graphics in order to give a feeling for the so far unknown peakedness properties of the states constructed.Comment: 70 pages, LATEX, 29 figure

Programmable active memories in real-time tasks: implementing data-driven triggers for LHC experiments

The future Large Hadron Collider (LHC), to be built at CERN, presents among other technological challenges a formidable problem of real-time data analysis. At a primary event rate of 40 MHz, a multi-stage trigger system has to analyze data to decide which is the fraction of events that should be preserved on permanent storage for further analysis. We report on implementations of local algorithms for feature extraction as part of triggering, using the detectors of the proposed ATLAS experiment as a model. The algorithms were implemented for a decision frequency of 100 kHz, on different data-driven programmable devices based on structures of field- programmable gate arrays and memories. The implementations were demonstrated at full speed with emulated input, and were also integrated into a prototype detector running in a test beam at CERN, in June 1994