Observables for spacetimes with two Killing field symmetries

The Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied from a Hamiltonian point of view. The complexified Ashtekar canonical variables are used, and the symmetry reduction is performed directly in the Hamiltonian theory. The reduced system corresponds to the field equations of the SL(2,R) chiral model with additional constraints. On the classical phase space, a method of obtaining an infinite number of constants of the motion, or observables, is given. The procedure involves writing the Hamiltonian evolution equations as a single `zero curvature' equation, and then employing techniques used in the study of two dimensional integrable models. Two infinite sets of observables are obtained explicitly as functionals of the phase space variables. One set carries sl(2,R) Lie algebra indices and forms an infinite dimensional Poisson algebra, while the other is formed from traces of SL(2,R) holonomies that commute with one another. The restriction of the (complex) observables to the Euclidean and Lorentzian sectors is discussed. It is also shown that the sl(2,R) observables can be associated with a solution generating technique which is linked to that given by Geroch.Comment: 23 pages (LateX-RevTeX), Alberta-Thy-55-9

Amyloid-based nanosensors and nanodevices

This journal is © The Royal Society of Chemistry 2014Self-assembling amyloid-like peptides and proteins give rise to promising biomaterials with potential applications in many fields. Amyloid structures are formed by the process of molecular recognition and self-assembly, wherein a peptide or protein monomer spontaneously self-associates into dimers and oligomers and subsequently into supramolecular aggregates, finally resulting in condensed fibrils. Mature amyloid fibrils possess a quasi-crystalline structure featuring a characteristic fiber diffraction pattern and have well-defined properties, in contrast to many amorphous protein aggregates that arise when proteins misfold. Core sequences of four to seven amino acids have been identified within natural amyloid proteins. They are capable to form amyloid fibers and fibrils and have been used as amyloid model structures, simplifying the investigations on amyloid structures due to their small size. Recent studies have highlighted the use of self-assembled amyloid-based fibers as nanomaterials. Here, we discuss the latest advances and the major challenges in developing amyloids for future applications in nanotechnology and nanomedicine, with the focus on development of sensors to study protein–ligand interactions.This work is supported by the Institute of Bioengineering and Nanotechnology (Biomedical Research Council, Agency for Science, Technology and Research, Singapore). Dr Ivo C. Martins acknowledges the funding from the Portuguese Foundation for Science and Technology (project PTDC/SAU-ENB/117013/2010 and program Investigador FCT, Research Contract IF/00772/2013)

Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

Differentially rotating disks of dust: Arbitrary rotation law

In this paper, solutions to the Ernst equation are investigated that depend on two real analytic functions defined on the interval [0,1]. These solutions are introduced by a suitable limiting process of Backlund transformations applied to seed solutions of the Weyl class. It turns out that this class of solutions contains the general relativistic gravitational field of an arbitrary differentially rotating disk of dust, for which a continuous transition to some Newtonian disk exists. It will be shown how for given boundary conditions (i. e. proper surface mass density or angular velocity of the disk) the gravitational field can be approximated in terms of the above solutions. Furthermore, particular examples will be discussed, including disks with a realistic profile for the angular velocity and more exotic disks possessing two spatially separated ergoregions.Comment: 23 pages, 3 figures, submitted to 'General Relativity and Gravitation

Riccati parameter modes from Newtonian free damping motion by supersymmetry

We determine the class of damped modes \tilde{y} which are related to the common free damping modes y by supersymmetry. They are obtained by employing the factorization of Newton's differential equation of motion for the free damped oscillator by means of the general solution of the corresponding Riccati equation together with Witten's method of constructing the supersymmetric partner operator. This procedure leads to one-parameter families of (transient) modes for each of the three types of free damping, corresponding to a particular type of %time-dependent angular frequency. %time-dependent, antirestoring acceleration (adding up to the usual Hooke restoring acceleration) of the form a(t)=\frac{2\gamma ^2}{(\gamma t+1)^{2}}\tilde{y}, where \gamma is the family parameter that has been chosen as the inverse of the Riccati integration constant. In supersymmetric terms, they represent all those one Riccati parameter damping modes having the same Newtonian free damping partner modeComment: 6 pages, twocolumn, 6 figures, only first 3 publishe

'They're battle scars, I wear them well': A phenomenological exploration of young women's experiences of building resilience following adversity in adolescence

This is an Author's Accepted Manuscript of an article published in Journal of Youth Studies, 13(3), 273 - 290, 2010 [copyright Taylor & Francis], available online at: http://www.tandfonline.com/10.1080/13676260903520886.This phenomenological study explored young women's accounts of building resilience following chains of adverse life experiences in adolescence. Six participants were interviewed, aged 20–25 years. Most had, or were receiving, a university education. They described their recovery from adversity as starting with certain pivotal moments, followed by both short-term and longer-term strategies. Short-term strategies tended to offer respite from distress and emotional comfort, increased clarity about their experiences and social affirmation. Recovery involved gaining new perspectives on their adverse situation and recovering a positive self-image through three longer-term strategies. These involved making visible progress in their education, rebuilding relationships with family and friends, and participating in the ‘normalizing’ activities and developmental projects of adolescence. Participants believed that they were stronger and more compassionate although positive achievements co-existed with some regrets. Most perceived the adversity as catalyzing personal growth. These accounts of resilience revealed the complex psychosocial processes and resources available to some adolescents

Dirichlet Boundary Value Problems of the Ernst Equation

We demonstrate how the solution to an exterior Dirichlet boundary value problem of the axisymmetric, stationary Einstein equations can be found in terms of generalized solutions of the Backlund type. The proof that this generalization procedure is valid is given, which also proves conjectures about earlier representations of the gravitational field corresponding to rotating disks of dust in terms of Backlund type solutions.Comment: 22 pages, to appear in Phys. Rev. D, Correction of a misprint in equation (4

Composition of the Innermost Core Collapse Supernova Ejecta

With presently known input physics and computer simulations in 1D, a self-consistent treatment of core collapse supernovae does not yet lead to successful explosions, while 2D models show some promise. Thus, there are strong indications that the delayed neutrino mechanism works combined with a multi-D convection treatment for unstable layers. On the other hand there is a need to provide correct nucleosynthesis abundances for the progressing field of galactic evolution and observations of low metallicity stars. The innermost ejecta is directly affected by the explosion mechanism, i.e. most strongly the yields of Fe-group nuclei for which an induced piston or thermal bomb treatment will not provide the correct yields because the effect of neutrino interactions is not included. We apply parameterized variations to the neutrino scattering cross sections and alternatively, parameterized variations are applied to the neutrino absorption cross sections on nucleons in the ``gain region''. We find that both measures lead to similar results, causing explosions and a Ye>0.5 in the innermost ejected layers, due to the combined effect of a short weak interaction time scale and a negligible electron degeneracy, unveiling the proton-neutron mass difference. We include all weak interactions (electron and positron capture, beta-decay, neutrino and antineutrino capture on nuclei, and neutrino and antineutrino capture on nucleons) and present first nucleosynthesis results for these innermost ejected layers to discuss how they improve predictions for Fe-group nuclei. The proton-rich environment results in enhanced abundances of 45Sc, 49Ti, and 64Zn as requested by chemical evolution studies and observations of low metallicity stars as well as appreciable production of nuclei in the mass range up to A=80.Comment: 13 pages, 8 figures. Final versio

Power-Law Sensitivity to Initial Conditions within a Logistic-like Family of Maps: Fractality and Nonextensivity

Power-law sensitivity to initial conditions, characterizing the behaviour of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection with the family of nonlinear 1D logistic-like maps $x_{t+1} = 1 - a | x_t |^z, (z > 1; 0 < a \le 2; t=0,1,2,...)$ The main ingredient of our approach is the generalized deviation law \lim_{\Delta x(0) -> 0} \Delta x(t) / \Delta x(0)} = [1+(1-q)\lambda_q t]^{1/(1-q)} (equal to $e^{\lambda_1 t}$ for q=1, and proportional, for large t, to $t^{1/(1-q)}$ for $q \ne 1; q \in R$ is the entropic index appearing in the recently introduced nonextensive generalized statistics). The relation between the parameter q and the fractal dimension d_f of the onset-to-chaos attractor is revealed: q appears to monotonically decrease from 1 (Boltzmann-Gibbs, extensive, limit) to -infinity when d_f varies from 1 (nonfractal, ergodic-like, limit) to zero.Comment: LaTeX, 6 pages , 5 figure

A Measurement of the Angular Power Spectrum of the CMB Temperature Anisotropy from the 2003 Flight of Boomerang

We report on observations of the Cosmic Microwave Background (CMB) obtained during the January 2003 flight of Boomerang . These results are derived from 195 hours of observation with four 145 GHz Polarization Sensitive Bolometer (PSB) pairs, identical in design to the four 143 GHz Planck HFI polarized pixels. The data include 75 hours of observations distributed over 1.84% of the sky with an additional 120 hours concentrated on the central portion of the field, itself representing 0.22% of the full sky. From these data we derive an estimate of the angular power spectrum of temperature fluctuations of the CMB in 24 bands over the multipole range (50 < l < 1500). A series of features, consistent with those expected from acoustic oscillations in the primordial photon-baryon fluid, are clearly evident in the power spectrum, as is the exponential damping of power on scales smaller than the photon mean free path at the epoch of last scattering (l > 900). As a consistency check, the collaboration has performed two fully independent analyses of the time ordered data, which are found to be in excellent agreement.Comment: 11 pages, 7 figures, 3 tables. High resolution figures and data are available at http://cmb.phys.cwru.edu/boomerang/ and http://oberon.roma1.infn.it/boomerang/b2