Vacuum Polarization and Casimir Energy of a Dirac Field Induced by a Scalar Potential in One Spatial Dimension

We investigate the vacuum polarization and the Casimir energy of a Dirac field coupled to a scalar potential in one spatial dimension. Both of these effects have a common cause which is the distortion of the spectrum due to the coupling with the background field. Choosing the potential to be a symmetrical square-well, the problem becomes exactly solvable and we can find the whole spectrum of the system, analytically. We show that the total number of states and the total density remain unchanged as compared with the free case, as one expects. Furthermore, since the positive- and negative-energy eigenstates of the fermion are fermion-number conjugates of each other and there is no zero-energy bound state, the total density and the total number of negative and positive states remain unchanged, separately. Therefore, the vacuum polarization in this model is zero for any choice of the parameters of the potential. It is important to note that although the vacuum polarization is zero due to the symmetries of the model, the Casimir energy of the system is not zero in general. In the graph of the Casimir energy as a function of the depth of the well there is a maximum approximately when the bound energy levels change direction and move back towards their continuum of origin. The Casimir energy for a fixed value of the depth is a linear function of the width and is always positive. Moreover, the Casimir energy density (the energy density of all the negative-energy states) and the energy density of all the positive-energy states are exactly the mirror images of each other. Finally, computing the total energy of a valence fermion present in the lowest fermionic bound state, taking into account the Casimir energy, we find that the lowest bound state is almost always unstable for the scalar potential.Comment: 16 pages, 7 figure

An Investigation of the Casimir Energy for a Fermion Coupled to the Sine-Gordon Soliton with Parity Decomposition

We consider a fermion chirally coupled to a prescribed pseudoscalar field in the form of the soliton of the sine-Gordon model and calculate and investigate the Casimir energy and all of the relevant quantities for each parity channel, separately. We present and use a simple prescription to construct the simultaneous eigenstates of the Hamiltonian and parity in the continua from the scattering states. We also use a prescription we had introduced earlier to calculate unique expressions for the phase shifts and check their consistency with both the weak and strong forms of the Levinson theorem. In the graphs of the total and parity decomposed Casimir energies as a function of the parameters of the pseudoscalar field distinctive deformations appear whenever a fermionic bound state energy level with definite parity crosses the line of zero energy. However, the latter graphs reveal some properties of the system which cannot be seen from the graph of the total Casimir energy. Finally we consider a system consisting of a valence fermion in the ground state and find that the most energetically favorable configuration is the one with a soliton of winding number one, and this conclusion does not hold for each parity, separately.Comment: 13 pages, 8 figure

Charged Black Holes in Einsteinian Quartic Gravity

In this paper, we studied Einsteinian quartic gravity minimally coupled to electrodynamics in four dimensions. First, by variation action, we obtain the field equations, and by integration, we obtain a nonlinear third-order differential equation for the metric function and as well as the electromagnetic potential. Then, in the context of the Maxwell field, we discussed the conditions under which the charged black hole exists. Then, we have demonstrated the thermodynamics and stability of the solution for the case of positive coupling of quartic theory. Finally, we showed that the charged black hole solutions of EQG (unlike GR and like ECG) have no inner horizon and do not conform to the extremal bound of GR. Also, the uniqueness of BH solutions in this theory does not work anymore.Comment: 13 pages, 6 figure

A Tutorial on Machine Learning for Failure Management in Optical Networks

Failure management plays a role of capital importance in optical networks to avoid service disruptions and to satisfy customers' service level agreements. Machine learning (ML) promises to revolutionize the (mostly manual and human-driven) approaches in which failure management in optical networks has been traditionally managed, by introducing automated methods for failure prediction, detection, localization, and identification. This tutorial provides a gentle introduction to some ML techniques that have been recently applied in the field of the optical-network failure management. It then introduces a taxonomy to classify failure-management tasks and discusses possible applications of ML for these failure management tasks. Finally, for a reader interested in more implementative details, we provide a step-by-step description of how to solve a representative example of a practical failure-management task

Lingulodinium machaerophorum expansion over the last centuries in the Caspian Sea reflects global warming

This article is made available through the Brunel Open Access Publishing Fund. Copyright @ Author(s) 2012. This work is distributed under the Creative Commons Attribution 3.0 License.We analysed dinoflagellate cyst assemblages in four short sediment cores, two of them dated by radionuclides, taken in the south basin of the Caspian Sea. The interpretation of the four sequences is supported by a collection of 27 lagoonal or marine surface sediment samples. A sharp increase in the biomass of the dinocyst occurs after 1967, especially owing to Lingulodinium machaerophorum. Considering nine other cores covering parts or the whole of Holocene, this species started to develop in the Caspian Sea only during the last three millennia. By analysing instrumental data and collating existing reconstructions of sea level changes over the last few millennia, we show that the main forcing of the increase of L. machaerophorum percentages and of the recent dinocyst abundance is global climate change, especially sea surface temperature increase. Sea level fluctuations likely have a minor impact. We argue that the Caspian Sea has entered the Anthropocene

NANO MANIPULATION WITH RECTANGULAR CANTILEVER OF ATOMIC FORCE MICROSCOPE (AFM) IN A VIRTUAL REALITY ENVIRONMENT

One of the problems of working with AFM in nano environment is lack of simultaneous image feedback. For solving this problem, a virtual reality environment (VR) is designed. For this purpose, a nano manipulation environment is implemented and then, through examining and analyzing the forces existing between probe tips and nanoparticle, the process of nanoparticle driving is added to this environment. In the first step of nano manipulation operations, the dimensions of the base plan as well as the exact place of nanoparticles on that plan needs to be defined so that the user can identify the place of the origin and nanoparticles' destination. The second step in simulation is driving the nanoparticle. In this process, the AFM probe tip starts moving toward nanoparticle with a constant speed of V and after touching it and applying F resultant force from probe tip side on nano particles and increasing up to critical value (F ), it overcomes contract and frictional forces existing between the particle and base plane. In this moment, the probe tip starts moving along with nanoparticle and as a result the nanoparticle is transferred to the pre-determined place by the user. Thus the user may observe the manipulation process

Background and Anomaly Learning Methods for Static Gamma-ray Detectors

Static gamma-ray detector systems that are deployed outdoors for radiological monitoring purposes experience time- and spatially-varying natural backgrounds and encounters with man-made nuisance sources. In order to be sensitive to illicit sources, such systems must be able to distinguish those sources from benign variations due to, e.g., weather and human activity. In addition to fluctuations due to non-threats, each detector has its own response and energy resolution, so providing a large network of detectors with predetermined background and source templates can be an onerous task. Instead, we propose that static detectors use simple physics-informed algorithms to automatically learn the background and nuisance source signatures, which can them be used to bootstrap and feed into more complex algorithms. Specifically, we show that non-negative matrix factorization (NMF) can be used to distinguish static background from the effects of increased concentrations of radon progeny due to rainfall. We also show that a simple process of using multiple gross count rate filters can be used in real time to classify or ``triage'' spectra according to whether they belong to static, rain, or anomalous categories for processing with other algorithms. If a rain sensor is available, we propose a method to incorporate that signal as well. Two clustering methods for anomalous spectra are proposed, one using Kullback-Leibler divergence and the other using regularized NMF, with the goal of finding clusters of similar spectral anomalies that can be used to build anomaly templates. Finally we describe the issues involved in the implementation of some of these algorithms on deployed sensor nodes, including the need to monitor the background models for long-term drifting due to physical changes in the environment or changes in detector performance.Comment: 12 pages, 6 figures, accepted for publication in IEEE Transactions on Nuclear Scienc

A highly efficient green synthesis of 1, 8-dioxo-octahydroxanthenes

SmCl3 (20 mol%) has been used as an efficient catalyst for reaction between aromatic aldehydes and 5,5-dimethyl-1,3-cyclohexanedione at 120°C to give 1,8-dioxo-octahydroxanthene derivatives in high yield. The same reaction in water, at room temperature gave only the open chain analogue of 1,8-dioxo-octahydroxanthene. Use of eco-friendly green Lewis acid, readily available catalyst and easy isolation of the product makes this a convenient method for the synthesis of either of the products