Microcanonical thermostatistics analysis without histograms: cumulative distribution and Bayesian approaches

Microcanonical thermostatistics analysis has become an important tool to reveal essential aspects of phase transitions in complex systems. An efficient way to estimate the microcanonical inverse temperature $\beta(E)$ and the microcanonical entropy $S(E)$ is achieved with the statistical temperature weighted histogram analysis method (ST-WHAM). The strength of this method lies on its flexibility, as it can be used to analyse data produced by algorithms with generalised sampling weights. However, for any sampling weight, ST-WHAM requires the calculation of derivatives of energy histograms $H(E)$, which leads to non-trivial and tedious binning tasks for models with continuous energy spectrum such as those for biomolecular and colloidal systems. Here, we discuss two alternative methods that avoid the need for such energy binning to obtain continuous estimates for $H(E)$ in order to evaluate $\beta(E)$ by using ST-WHAM: (i) a series expansion to estimate probability densities from the empirical cumulative distribution function (CDF), and (ii) a Bayesian approach to model this CDF. Comparison with a simple linear regression method is also carried out. The performance of these approaches is evaluated considering coarse-grained protein models for folding and peptide aggregation.Comment: 9 pages, 11 figure

Density Matrix Renormalization Group for Dummies

We describe the Density Matrix Renormalization Group algorithms for time dependent and time independent Hamiltonians. This paper is a brief but comprehensive introduction to the subject for anyone willing to enter in the field or write the program source code from scratch.Comment: 29 pages, 9 figures. Published version. An open source version of the code can be found at http://qti.sns.it/dmrg/phome.htm

Heat flux evaluation in high temperature ring-on-ring contacts

A comprehensive methodology to investigate heat flux in a ring-on-ring tribometer is presented. Thermal fluxes under high contact pressures and temperature differences were evaluated through an experimental campaign and by a numerical procedure of inverse analysis applied to surface temperature measurements. An approximation of a two-dimensional time-dependent analytical solution for the temperature distribution was first developed and subsequently adapted to mimic the specific testing configuration characteristics; the problem was finally simplified to enable further inverse analysis. Experiments were performed using an innovative high temperature ring-on-ring tribometer. The evaluated contact heat transfer rates were reported as a function of normal load and temperature difference between the discs under steady-state conditions; the results reported here show that, in the present test configuration, the temperature difference has stronger influence than the applied load in terms of heat transfer induced by contact

Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime: I. Admissible 3+1 Splittings of Minkowski Spacetime and the Non-Inertial Rest Frames

By using the 3+1 point of view and parametrized Minkowski theories we develop the theory of {\it non-inertial} frames in Minkowski space-time. The transition from a non-inertial frame to another one is a gauge transformation connecting the respective notions of instantaneous 3-space (clock synchronization convention) and of the 3-coordinates inside them. As a particular case we get the extension of the inertial rest-frame instant form of dynamics to the non-inertial rest-frame one. We show that every isolated system can be described as an external decoupled non-covariant canonical center of mass (described by frozen Jacobi data) carrying a pole-dipole structure: the invariant mass and an effective spin. Moreover we identify the constraints eliminating the internal 3-center of mass inside the instantaneous 3-spaces. In the case of the isolated system of positive-energy scalar particles with Grassmann-valued electric charges plus the electro-magnetic field we obtain both Maxwell equations and their Hamiltonian description in non-inertial frames. Then by means of a non-covariant decomposition we define the non-inertial radiation gauge and we find the form of the non-covariant Coulomb potential. We identify the coordinate-dependent relativistic inertial potentials and we show that they have the correct Newtonian limit. In the second paper we will study properties of Maxwell equations in non-inertial frames like the wrap-up effect and the Faraday rotation in astrophysics. Also the 3+1 description without coordinate-singularities of the rotating disk and the Sagnac effect will be given, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system.Comment: This paper and the second one are an adaptation of arXiv 0812.3057 for publication on Int.J.Geom. Methods in Modern Phys. 77

X-ray sources and their optical counterparts in the globular cluster M 22

Using XMM-Newton EPIC imaging data, we have detected 50 low-luminosity X-ray sources in the field of view of M 22, where 5 +/- 3 of these sources are likely to be related to the cluster. Using differential optical photometry, we have identified probable counterparts to those sources belonging to the cluster. Using X-ray spectroscopic and timing studies, supported by the optical colours, we propose that the most central X-ray sources in the cluster are cataclysmic variables, millisecond pulsars, active binaries and a blue straggler. We also identify a cluster of galaxies behind this globular cluster.Comment: 11 pages, 7 figures, accepted for publication in A&

Spacetime geometries and light trapping in travelling refractive index perturbations

In the framework of transformation optics, we show that the propagation of a locally superluminal refractive index perturbation (RIP) in a Kerr medium can be described, in the eikonal approximation, by means of a stationary metric, which we prove to be of Gordon type. Under suitable hypotheses on the RIP, we obtain a stationary but not static metric, which is characterized by an ergosphere and by a peculiar behaviour of the geodesics, which are studied numerically, also accounting for material dispersion. Finally, the equation to be satisfied by an event horizon is also displayed and briefly discussed.Comment: 14 pages, 7 figure