Power law in a gauge-invariant cut-off regularisation

We study one-loop quantum corrections of a compactified Abelian 5d gauge field theory. We use a cut-off regularisation procedure which respects the symmetries of the model, i.e. gauge invariance, exhibits the expected power-like divergences and therefore allows the derivation of power-law behavior of the effective 4d gauge coupling in a coherent manner.Comment: 5 pages, 1 figure, 5 graphs, few references added, to appear in Phys.Rev. Rapid Communication

Femtosecond Self-Reconfiguration of Laser-Induced Plasma Patterns in Dielectrics

Laser-induced modification of transparent solids by intense femtosecond laser pulses allows fast integration of nanophotonic and nanofluidic devices with controlled optical properties. So far, the local and dynamic nature of the interactions between plasma and light needed to correctly explain nanograting fabrication on dielectric surfaces has been missing in the theoretical models. With our numerical approach, we show that a self-consistent dynamic treatment of the plasma formation and its interaction with light triggers an ultrafast reconfiguration of the periodic plasma patterns on a field-cycle time scale. Within this framework, a simple stability analysis of the local interactions explains how the laser-induced plasma patterns change their orientation with respect to the incident light polarization, when a certain energy density threshold is reached. Moreover, the reconfigured sub-wavelength plasma structures grow into the bulk of the sample and agree with the experimental findings of self-organized volume nanogratings. Mode coupling of the incident and transversally scattered light with the periodic plasma structures is sufficient to initiate the growth and the self-organization of the characteristic pattern with a periodicity of a half-wavelength in the medium.Comment: 8 pages, 7 figure

Using distributed magnetometry in navigation of heavy launchers and space vehicles

Recently, a new technique has emerged to address the general problem of reconstructing the inertial velocity of a rigid body moving in a magnetically disturbed region. The contribution of this paper is to apply the developed method, in a prospective spirit, to a case of space navigation in view of estimating the performance improvement that could be obtained using state-of-the-art magnetometer technology onboard heavy launchers and other space vehicles. The main underlying idea of the approach is to estimate the inertial velocity by readings of the magnetic field at spatially distributed (known) locations on the rigid body. Mathematically, through a chain-rule differentiation involving variables commonly appearing in classic inertial navigation, an estimate of this velocity can be obtained. In this paper, we show the potential of this method in the field of navigation of heavy launchers passing through particular regions of the Earth magnetosphere as considered, e.g., for upcoming Galileo missions. Numerical results based on the specifications of candidate embedded magnetic sensors stress the relevance of the approach

Dynamical rate equation model for femtosecond laser-induced breakdown in dielectrics

Experimental and theoretical studies of laser-induced breakdown in dielectrics provide conflicting conclusions about the possibility to trigger ionization avalanche on the subpicosecond time scale and the relative importance of carrier-impact ionization over field ionization. On the one hand, current models based on a single ionization-rate equation do not account for the gradual heating of the charge carriers, which, for short laser pulses, might not be sufficient to start an avalanche. On the other hand, kinetic models based on microscopic collision probabilities have led to variable outcomes that do not necessarily match experimental observations as a whole. In this paper, we present a rate-equation model that accounts for the avalanche process phenomenologically by using an auxiliary differential equation to track the gradual heating of the charge carriers and define the collisional impact rate dynamically. The computational simplicity of this dynamical rate-equation model offers the flexibility to extract effective values from experimental data. This is demonstrated by matching the experimental scaling trends for the laser-induced damage threshold of several dielectric materials for pulse durations ranging from a few fs to a few ps. Through numerical analysis, we show that the proposed model gives results comparable to those obtained with multiple rate equations and identify potential advantages for the development of large-scale, three-dimensional electromagnetic methods for the modeling of laser-induced breakdown in transparent media

Asymptotic expansion of the optimal control under logarithmic penalty: worked example and open problems

We discuss the problem of expansion of optimal control, state and costate when a logarithmic penalty is applied to constraints. We show that, in a simple case, that the variation of (a regular) junction point, and of the optimal control, state and costate is of order \eps\log \eps, where \eps is the penalty parameter

Multiple hepatosplenic abscesses in an immunocompetent host

Sphingomonas paucimobilis, a gram-negative organism, mainly infects immunocompromised hosts due to its low virulence. Patients with such an infection usually have contact with healthcare. Meningitis, peritonitis, visceral abscess, septic arthritis, septicemia, post-traumatic endophthalmitis, and keratitis are among the documented complications of Sphingomonas paucimobilis infection. Such an infection is rarely seen in the literature as the one causing splenic and liver abscess and that too in an immunocompetent host. We present a case of a 23-year-old immunocompetent male, who presented with fever and other constitutional symptoms with recent onset of abdominal pain and fullness. Splenic and liver abscesses were detected on radiology with the growth of only Sphingomonas on blood culture and negative reports for other organisms excluding the differentials, proving S.mobilis being the cause of the abscesses. The patient was managed on broad-spectrum antibiotics and additional medications for symptomatic relief. The patient gradually improved over 7 days of hospitalization. This case report mainly focuses on Sphingomonas paucimobilis infection, which is rarely seen and documented, and surprisingly in an immunocompetent host causing life-threatening infections and abscesses. Even though it’s a rare and a low virulence organism, such a presentation must not be overlooked. A regular and focused laboratory workup for detection and management, with adequate antibiotic treatment, is a must to avoid a poor prognosis

Hybrid copula mixed models for combining case-control and cohort studies in meta-analysis of diagnostic tests

Copula mixed models for trivariate (or bivariate) meta-analysis of diagnostic test accuracy studies accounting (or not) for disease prevalence have been proposed in the biostatistics literature to synthesize information. However, many systematic reviews often include case-control and cohort studies, so one can either focus on the bivariate meta-analysis of the case-control studies or the trivariate meta-analysis of the cohort studies, as only the latter contains information on disease prevalence. In order to remedy this situation of wasting data we propose a hybrid copula mixed model via a combination of the bivariate and trivariate copula mixed model for the data from the case-control studies and cohort studies, respectively. Hence, this hybrid model can account for study design and also due to its generality can deal with dependence in the joint tails. We apply the proposed hybrid copula mixed model to a review of the performance of contemporary diagnostic imaging modalities for detecting metastases in patients with melanoma

Computation of order conditions for symplectic partitioned Runge-Kutta schemes with application to optimal control

We discuss the derivation of order conditions for the discretization of (unconstrained) optimal control problems, when the scheme for the state equation is of Runge-Kutta type. This problem appears to be essentially the one of checking order conditions for symplectic partitioned Runge-Kutta schemes. We show that the the computations using bi-coloured trees are naturally expressed in this case in terms of oriented free tree. This gives a way to compute them by an appropriate computer program. Our software is able to compute conditions up to order 7 (we display them up to order 6). The results are in accordance with those of Hager (where they were computed for order up to 4) as well as those of Murua where the number of conditions up to order 7 is stated

Asymptotic expansion of the optimal control under logarithmic penalty: worked example and open problems

We discuss the problem of expansion of optimal control, state and costate when a logarithmic penalty is applied to constraints. We show that, in a simple case, that the variation of (a regular) junction point, and of the optimal control, state and costate is of order \eps\log \eps, where \eps is the penalty parameter