On the role of the chaotic velocity in relativistic kinetic theory

In this paper we revisit the concept of chaotic velocity within the context of relativistic kinetic theory. Its importance as the key ingredient which allows to clearly distinguish convective and dissipative effects is discussed to some detail. Also, by addressing the case of the two component mixture, the relevance of the barycentric comoving frame is established and thus the convenience for the introduction of peculiar velocities for each species. The fact that the decomposition of molecular velocity in systematic and peculiar components does not alter the covariance of the theory is emphasized. Moreover, we show that within an equivalent decomposition into space-like and time-like tensors, based on a generalization of the relative velocity concept, the Lorentz factor for the chaotic velocity can be expressed explicitly as an invariant quantity. This idea, based on Ellis' theorem, allows to foresee a natural generalization to the general relativistic case.Comment: 12 pages, 2 figure

Relaxation time for the temperature in a dilute binary mixture from classical kinetic theory

The system of our interest is a dilute binary mixture, in which we consider that the species have different temperatures as an initial condition. To study their time evolution, we use the full version of the Boltzmann equation, under the hypothesis of partial local equilibrium for both species. Neither a diffusion force nor mass diffusion appears in the system. We also estimate the time in which the temperatures of the components reach the full local equilibrium. In solving the Boltzmann equation, we imposed no assumptions on the collision term. We work out its solution by using the well known Chapman-Enskog method to first order in the gradients. The time in which the temperatures relax is obtained following Landau's original idea. The result is that the relaxation time for the temperatures is much smaller than the characteristic hydrodynamical times but greater than a collisional time. The main conclusion is that there is no need to study binary mixtures with different temperatures when hydrodynamical properties are sought

Entropy Production in Relativistic Binary Mixtures

In this paper we calculate the entropy production of a relativistic binary mixture of inert dilute gases using kinetic theory. For this purpose we use the covariant form of Boltzmann's equation which, when suitably transformed, yields a formal expression for such quantity. Its physical meaning is extracted when the distribution function is expanded in the gradients using the well-known Chapman-Enskog method. Retaining the terms to first order, consistently with Linear Irreversible Thermodynamics we show that indeed, the entropy production can be expressed as a bilinear form of products between the fluxes and their corresponding forces. The implications of this result are thoroughly discussed

Empirical Ground-Motion Prediction Equations for Northern Italy Using Weak- and Strong-Motion Amplitudes, Frequency Content, and Duration Parameters

The goals of this work are to review the Northern-Italy ground-motion prediction equations (GMPEs) for amplitude parameters and to propose new GMPEs for frequency content and duration parameters. Approximately 10,000 weak and strong waveforms have been collected merging information from different neighboring regional seismic networks operating in the last 30 yr throughout Northern Italy. New ground-motion models, calibrated for epicentral distances ≤100 km and for both local (ML) and moment magnitude (Mw), have been developed starting from a high quality dataset (624 waveforms) that consists of 82 selected earthquakes with ML and Mw up to 6.3 and 6.5, respectively. The vertical component and the maximum of the two horizontal components of motion have been considered, for both acceleration (peak ground horizontal acceleration [PGHA] and peak ground vertical acceleration [PGVA]) and velocity (peak ground horizontal velocity [PGHV] and peak ground vertical velocity [PGVV]) data. In order to make comparisons with the most commonly used prediction equations for the Italian territory (Sabetta and Pugliese, 1996 [hereafter, SP96] and Ambraseys et al. 2005a,b [hereafter, AM05]) the coefficients for acceleration response spectra (spectral horizontal acceleration [SHA] and spectral vertical acceleration [SVA]) and for pseudovelocity response spectra (pseudospectral horizontal velocity [PSHV] and pseudospectral vertical velocity [PSVV]) have been calculated for 12 periods ranging between 0.04 and 2 sec and for 14 periods ranging between 0.04 and 4 sec, respectively. Finally, empirical relations for Arias intensities (IA), Housner intensities (IH), and strong motion duration (DV) have also been calibrated. The site classification based on Eurocode (hereafter, EC8) classes has been used (ENV, 1998, 2002). The coefficients of the models have been determined using functional forms with an independent magnitude decay rate and applying the random effects model (Abrahamson and Youngs, 1992; Joyner and Boore, 1993) that allow the determination of the interevent, interstation, and record-to-record components of variance. The goodness of fit between observed and predicted values has been evaluated using the maximum likelihood approach as in Spudich et al. (1999). Comparing the proposed GMPEs with SP96 and AM05, it is possible to observe a faster decay of predicted ground motion, in particular for distances greater than 25 km and magnitudes higher than 5.0. The result is an improvement in fit of about one order of size for magnitudes spanning from 3.5 to 4.5

Empirical ground motion prediction equations for northern italy using weak and strong motion amplitudes, frequency content and duration parameters

The aims of this work are to review the Northern-Italy ground motion prediction equations (hereinafter GMPEs) for amplitude parameters and to propose new GMPEs for frequency content and duration parameters. Approximately 10.000 weak and strong waveforms have been collected merging information from different neighbouring regional seismic networks operating in the last 30 years throughout Northern Italy. New ground motion models, calibrated for epicentral distances ≤ 100 km and for both local (Ml) and moment magnitude (Mw), have been developed starting from a high quality dataset (624 waveforms) which consists of 82 selected earthquakes with Ml and Mw up to 6.3 and 6.5 respectively. The vertical component and the maximum of the two horizontal components of motion have been considered, for both acceleration (PGHA and PGVA) and velocity (PGHV and PGVV) data. In order to make comparisons with the most commonly used prediction equations for the Italian territory (Sabetta and Pugliese, 1996 and Ambraseys et al. 2005a,b hereinafter named SP96 and AM05) the coefficients for acceleration response spectra (SHA and SVA) and for pseudo velocity response spectra (PSHV and PSVV) have been calculated for 12 periods ranging between 0.04 s and 2 s and for 14 periods ranging between 0.04 s and 4 s respectively. Finally, empirical relations for Arias and Housner Intensities (IA, IH) and strong motion duration (DV) have also been calibrated. The site classification based on Eurocode (hereinafter EC8) classes has been used (ENV, 1998). The coefficients of the models have been determined using functional forms with an independent magnitude decay rate and applying the random effects model (Abrahamson and Youngs, 1992; Joyner and Boore, 1993) that allow the determination of the inter-event, inter-station and record-to-record components of variance. The goodness of fit between observed and predicted values has been evaluated using the maximum likelihood approach as in Spudich et al. (1999). Comparing the proposed GMPEs both with SP96 and AM05 it is possible to observe a faster decay of predicted ground motion, in particular for distances greater than 25 km and magnitudes higher than 5.0. The result is a fit improvement of about one order of size for magnitudes spanning from 3.5 to 4.5

Generation of induced Pluripotent Stem Cells (UNIBSi008-A, UNIBSi008-B, UNIBSi008-C) from an Ataxia-Telangiectasia (AT) patient carrying a novel homozygous deletion in ATM gene.

Abstract Using a Sendai Virus based vector delivering Yamanaka Factors, we generated induced Pluripotent Stem Cells (iPSCs) from peripheral blood mononuclear cells of a patient affected by Ataxia Telangiectasia (AT), caused by a novel homozygous deletion in ATM, spanning exons 5 to 7. Three clones were fully characterized for pluripotency and capability to differentiate. These clones preserved the causative mutation of parental cells and genomic stability over time (>100 passages). Furthermore, in AT derived iPSCs we confirmed the impaired DNA damage response after ionizing radiation. All these data underline potential usefulness of our clones as in vitro AT disease model

Estimating Nuisance Parameters in Inverse Problems

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is variable projection, where nonlinear least squares problems which are linear in some parameters can be very efficiently optimized. In this paper, we extend the idea of projecting out a subset over the variables to a broad class of maximum likelihood (ML) and maximum a posteriori likelihood (MAP) problems with nuisance parameters, such as variance or degrees of freedom. As a result, we are able to incorporate nuisance parameter estimation into large-scale constrained and unconstrained inverse problem formulations. We apply the approach to a variety of problems, including estimation of unknown variance parameters in the Gaussian model, degree of freedom (d.o.f.) parameter estimation in the context of robust inverse problems, automatic calibration, and optimal experimental design. Using numerical examples, we demonstrate improvement in recovery of primary parameters for several large- scale inverse problems. The proposed approach is compatible with a wide variety of algorithms and formulations, and its implementation requires only minor modifications to existing algorithms.Comment: 16 pages, 5 figure