A point is normal for almost all maps βx+α mod 1 or generalized β-transformations

We consider the map Tα,β(x):=βx+αmod1, which admits a unique probability measure μα,β of maximal entropy. For x[0,1], we show that the orbit of x is μα,β-normal for almost all (α,β)[0,1)×(1,∞) (with respect to Lebesgue measure). Nevertheless, we construct analytic curves in [0,1)×(1,∞) along which the orbit of x=0 is μα,β-normal at no more than one point. These curves are disjoint and fill the set [0,1)×(1,∞). We also study the generalized β-transformations (in particular, the tent map). We show that the critical orbit x=1 is normal with respect to the measure of maximal entropy for almost all

Multicanonical Parallel Tempering

We present a novel implementation of the parallel tempering Monte Carlo method in a multicanonical ensemble. Multicanonical weights are derived by a self-consistent iterative process using a Boltzmann inversion of global energy histograms. This procedure gives rise to a much broader overlap of thermodynamic-property histograms; fewer replicas are necessary in parallel tempering simulations, and the acceptance of trial swap moves can be made arbitrarily high. We demonstrate the usefulness of the method in the context of a grand-multicanonical ensemble, where we use multicanonical simulations in energy space with the addition of an unmodified chemical potential term in particle-number space. Several possible implementations are discussed, and the best choice is presented in the context of the liquid-gas phase transition of the Lennard-Jones fluid. A substantial decrease in the necessary number of replicas can be achieved through the proposed method, thereby providing a higher efficiency and the possibility of parallelization.Comment: 8 pages, 3 figure, accepted by J Chem Phy

Non-Markovian dynamics in pulsed and continuous wave atom lasers

The dynamics of atom lasers with a continuous output coupler based on two-photon Raman transitions is investigated. With the help of the time-convolutionless projection operator technique the quantum master equations for pulsed and continuous wave (cw) atom lasers are derived. In the case of the pulsed atom laser the power of the time-convolutionless projection operator technique is demonstrated through comparison with the exact solution. It is shown that in an intermediate coupling regime where the Born-Markov approximation fails the results of this algorithm agree with the exact solution. To study the dynamics of a continuous wave atom laser a pump mechanism is included in the model. Whereas the pump mechanism is treated within the Born-Markov approximation, the output coupling leads to non-Markovian effects. The solution of the master equation resulting from the time-convolutionless projection operator technique exhibits strong oscillations in the occupation number of the Bose-Einstein condensate. These oscillations are traced back to a quantum interference which is due to the non-Markovian dynamics and which decays slowly in time as a result of the dispersion relation for massive particles

Pair distribution function and structure factor of spherical particles

The availability of neutron spallation-source instruments that provide total scattering powder diffraction has led to an increased application of real-space structure analysis using the pair distribution function. Currently, the analytical treatment of finite size effects within pair distribution refinement procedures is limited. To that end, an envelope function is derived which transforms the pair distribution function of an infinite solid into that of a spherical particle with the same crystal structure. Distributions of particle sizes are then considered, and the associated envelope function is used to predict the particle size distribution of an experimental sample of gold nanoparticles from its pair distribution function alone. Finally, complementing the wealth of existing diffraction analysis, the peak broadening for the structure factor of spherical particles, expressed as a convolution derived from the envelope functions, is calculated exactly for all particle size distributions considered, and peak maxima, offsets, and asymmetries are discussed.Comment: 7 pages, 6 figure

Étude du colmatage de membranes d'osmose inverse utilisées pour la préparation des eaux de dialyse rénale

L'osmose inverse est l'élément clef de la production d'eau ultrapure servant dans la préparation du liquide de dialyse rénale. Le vieillissement des membranes d'osmose inverse se traduit par une dérive croissante de la conductivité en sortie de membrane et par une augmentation de la teneur en bactéries dans le perméat délivré en sortie d'osmose inverse, entraînant un risque de contamination pour le patient.Les suivis en conductivité et numérations bactériennes dans la chaîne de production d'eau osmosée de l'Hôpital de Colmar (France) montre un fort dysfonctionnement au niveau des prétraitements et notamment du charbon actif, siège d'une importante prolifération bactérienne (2.3 103 colonies pour 100 ml en amont du charbon actif , 1.1 105 pour 100 ml en aval). Une étude de corrélations entre entrée et sortie d'osmoseurs montre que la forte teneur en germes en sortie du charbon actif est directement responsable de la présence des bactéries dans le perméat.Des tests hydrauliques effectués sur les membranes après quatre années d'utilisation intensive (6500 heures par an), permettent d'identifier les mécanismes prépondérants de vieillissement et de colmatage des membranes utilisées à l'hôpital de Colmar (compaction, formation d'un dépôt et altération de structure).Afin d'identifier les substances colmatantes non retenues par le prétraitement, le film colmatant est analysé par analyse élémentaire, spectrophotométrie infrarouge, diffraction X et zêtamétrie, ce qui nous a permis de mettre en évidence la présence notamment d'argiles, de silice et de substances humiques.The use of reverse osmosis to produce ultrapure water for kidney patients is very prevalent at the present time. About 20000 patients are treated every day in France and the cost of treatment is estimated at 10 thousand million French francs. The patients are provided with a permeate which in principle contains neither ions nor bacteria, which can cause disease and irreversible alteration of the upper-arm articulations. After several months of utilization, the presence of a foulant deposit and biofilm proliferation is often noted on the thin layered active surface of the polyamide membranes. In many cases, the membrane may become irreversibly fouled and require replacement.The aim of this work was to determine the causes of membrane fouling at a reverse osmosis plant in "Hôpital Pasteur" (Colmar, France). First we analyzed the ion-rejection capacity of membranes and the evolution of conductivity over 200 weeks. We observed an increasing drift in conductivity, which could not be halted by cleaning and regeneration procedures. In the second phase of the study, we carried out microbiological studies at many sampling points of the ultrapure water plant in "Hôpital Pasteur". We noted a very important proliferation of bacteria downstream of the pretreatments. The activated charcoal unit is responsible for this problem (2.3 x 103 UFC / 100 mL upstream from the activated charcoal bed, 1.1 x 105 UFC / 100 mL downstream). We noted an important dysfunction in the pretreatment, essentially attributable to the activated charcoal (bacteria) and the resins (silica).We performed tests with x-ray diffraction as a rapid method to determine the crystalline forms present. In the foulant deposits, we found quartz and clay. Infrared spectroscopy is useful in determining the type of organic constituents; in our deposits we noted the presence of humic materials. The analysis of those deposits gave essentially carbon and silicon. The foulant deposits were of organic and crystalline origins

Time-Delay Interferometry

Equal-arm interferometric detectors of gravitational radiation allow phase measurements many orders of magnitude below the intrinsic phase stability of the laser injecting light into their arms. This is because the noise in the laser light is common to both arms, experiencing exactly the same delay, and thus cancels when it is differenced at the photo detector. In this situation, much lower level secondary noises then set overall performance. If, however, the two arms have different lengths (as will necessarily be the case with space-borne interferometers), the laser noise experiences different delays in the two arms and will hence not directly cancel at the detector. In order to solve this problem, a technique involving heterodyne interferometry with unequal arm lengths and independent phase-difference readouts has been proposed. It relies on properly time-shifting and linearly combining independent Doppler measurements, and for this reason it has been called Time-Delay Interferometry (or TDI). This article provides an overview of the theory and mathematical foundations of TDI as it will be implemented by the forthcoming space-based interferometers such as the Laser Interferometer Space Antenna (LISA) mission. We have purposely left out from this first version of our ``Living Review'' article on TDI all the results of more practical and experimental nature, as well as all the aspects of TDI that the data analysts will need to account for when analyzing the LISA TDI data combinations. Our forthcoming ``second edition'' of this review paper will include these topics.Comment: 51 pages, 11 figures. To appear in: Living Reviews. Added conten

Parity and Time Reversal in the Spin-Rotation Interaction

A recently reported discrepancy between experimental and theoretical values of the muon's g-2 factor is interpreted as due to small violations of the conservation of P and T in the spin-rotation coupling. The experiments place an upper limit on these violations and on the weight change of spinning gyroscopes.Comment: 3 page

The Old Bailey proceedings and the representation of crime and criminal justice in eighteenth-century London

The Proceedings of the Old Bailey, published accounts of felony trials held at London’s central criminal court, were a remarkable publishing phenomenon. First published in 1674, they quickly became a regular periodical, with editions published eight times a year following each session of the court. Despite the huge number of trial reports (some 50,000 in the eighteenth century), the Proceedings, also known as the “Sessions Papers”, have formed the basis of several important studies in social history, dating back to Dorothy George’s seminal London Life in the Eighteenth Century (1925). Their recent publication online, however, has not only made them more widely available, but also changed the way historians consult them, leading to greater use of both quantitative analysis, using the statistics function, and qualitative examination of their language, through keyword searching. In the context of recent renewed interest in the history of crime and criminal justice, for which this is the most important source available in this period, the growing use of the Proceedings raises questions about their reliability, and, by extension, the motivations for their original publication. Historians generally consider the Proceedings to present accurate, if often incomplete, accounts of courtroom proceedings. From this source, along with manuscript judicial records, criminal biographies (including the Ordinary’s Accounts), polemical pamphlets such as Henry Fielding’s Enquiry into the Causes of the Late Increase of Robbers (1751), and of course the satirical prints of William Hogarth, they have constructed a picture of eighteenth-century London as a city overwhelmed by periodic crime waves and of a policing and judicial system which was forced into wide-ranging reforms in order to meet this challenge

Phase chaos in the anisotropic complex Ginzburg-Landau Equation

Of the various interesting solutions found in the two-dimensional complex Ginzburg-Landau equation for anisotropic systems, the phase-chaotic states show particularly novel features. They exist in a broader parameter range than in the isotropic case, and often even broader than in one dimension. They typically represent the global attractor of the system. There exist two variants of phase chaos: a quasi-one dimensional and a two-dimensional solution. The transition to defect chaos is of intermittent type.Comment: 4 pages RevTeX, 5 figures, little changes in figures and references, typos removed, accepted as Rapid Commun. in Phys. Rev.

Exploring Spirituality in Teaching Within a Christian School Context Through Collaborative Action Research

This article reports on a collaborative action research project conducted in New Zealand, during 2012, exploring spirituality in teaching within a Christian school context. The experienced primary school teacher participant chose to take action around the issue of personal fear and insecurity which were believed to be hindering professional growth and relationships. Through self-directed inquiry, critical reflective journaling, Bible study, fellowship and prayer with trusted friends, the teacher experienced a renewed sense of peace and freedom in Christ. This personal transformation was believed to be influential on subsequent professional practice, assisting the teacher to become more relational, responsive and compassionate. The findings provide a rich description of the participant’s spirituality, the lived reality of a person’s spiritual life. This report will be of interest to teachers, teacher-leaders and teacher-educators who desire to explore Christian spirituality through practitioner-led inquiry