Similarity inner solutions for the Pulsar equation

Lie symmetries are applied to classify the source of the magnetic field for the Pulsar equation near to the surface of the neutron star. We find that there are six possible different admitted Lie algebras. We apply the corresponding Lie invariants to reduce the Pulsar equation close to the surface to an ordinary differential equation. This equation is solved either with the use of Lie symmetries or the application of the ARS algorithm for singularity analysis to write the analytic solution as a Laurent expansion. These solutions are called inner solutions.     

A very simple facility for reactor irradiations from 70–400°C

The formation and complete recrystallization of an amorphous silicon layer during highly intensive Ar ion implantation have been studied. Rutherford backscattering and electron microscopy techniques have shown some specific features of such a crystallization as compared with a conventional thermal annealing. A model of dynamic cascade annealing of secondary defects is suggested to account for the experimental results.     

The geometric nature of Lie and Noether symmetries

It is shown that the Lie and the Noether symmetries of the equations of motion of a dynamical system whose equations of motion in a Riemannian space are of the form [(x)\ddot]ⁱ+G_jkⁱ[(x)\dot]^j[(x)\dot] ^k+f(xⁱ)=0{\ddot{x}^{i}+\Gamma_{jk}^{i}\dot{x}^{j}\dot{x} ^{k}+f(x^{i})=0} where f(x ⁱ ) is an arbitrary function of its argument, are generated from the Lie algebra of special projective collineations and the homothetic algebra of the space respectively. Therefore the computation of Lie and Noether symmetries of a given dynamical system in these cases is reduced to the problem of computation of the special projective algebra of the space. It is noted that the Lie and Noether symmetry vectors are common to all dynamical systems moving in the same background space. The selection of the vectors which are Lie/Noether symmetries for a given dynamical system is done by means of a set of differential conditions involving the vectors and the potential function defining the dynamical system. The general results are applied to a number of different applications concerning (a) The motion in Euclidean space under the action of a general central potential (b) The motion in a space of constant curvature (c) The determination of the Lie and the Noether symmetries of class A Bianchi type hypersurface orthogonal spacetimes filled with a scalar field minimally coupled to gravity (d) The analytic computation of the Bianchi I metric when the scalar field has an exponential potential.     

Cosmological singularities and analytical solutions in varying vacuum cosmologies

We investigate the dynamical features of a large family of running vacuum cosmologies for which \(\Lambda \) evolves as a polynomial in the Hubble parameter. Specifically, using the critical point analysis we study the existence and the stability of singular solutions which describe de-Sitter, radiation and matter dominated eras. We find several classes of \(\Lambda (H)\) cosmologies for which new analytical solutions are given in terms of Laurent expansions. Finally, we show that the Milne universe and the \(R_{h}=ct\) model can be seen as perturbations around a specific \(\Lambda (H)\) model, but this model is unstable.     

Effectiveness of 2‐mercaptobenzothiazole, 8‐hydroxyquinoline and benzotriazole as corrosion inhibitors on AA 2024‐T3 assessed by electrochemical methods

In this study, the effectiveness of 2‐mercaptobenzothiazole (2‐MBT), 8‐hydroxyquinoline and benzotriazole as corrosion inhibitors for AA 2024‐T3 aluminium alloy was evaluated. The corrosion behaviour in the presence of each compound was investigated by image‐assisted electrochemical noise analysis, electrochemical impedance spectroscopy, potentiodynamic polarization and the split cell technique. It was found that 2‐MBT has superior inhibition properties compared with the other inhibitors. In particular, the specimens immersed in 3.5% NaCl in the presence of 2‐MBT displayed high values of noise resistance that were maintained for over 400 h of testing, and high values of low‐frequency impedance, measured after immersion for 24 h. The split cell technique and potentiodynamic polarization tests indicated that only 2‐MBT decreases significantly both the anodic and the cathodic reaction rates. Scanning electron microscopy observations and energy dispersive X‐ray measurements complement the findings from electrochemical measurements indicating that only 2‐MBT protects the second phase particles, preventing dealloying, trenching and initiation of corrosion. © 2015 The Authors. Surface and Interface Analysis published by John Wiley & Sons Ltd.     

Lie symmetries of geodesic equations and projective collineations

We prove a theorem which relates the Lie symmetries of the geodesic equations in a Riemannian space with the collineations of the metric. We apply the results to Einstein spaces and spaces of constant curvature. Finally with examples we show the use of the results.     

Conformally related metrics and Lagrangians and their physical interpretation in cosmology

Conformally related metrics and Lagrangians are considered in the context of scalar–tensor gravity cosmology. After the discussion of the problem, we pose a lemma in which we show that the field equations of two conformally related Lagrangians are also conformally related if and only if the corresponding Hamiltonian vanishes. Then we prove that to every non-minimally coupled scalar field, we may associate a unique minimally coupled scalar field in a conformally related space with an appropriate potential. The latter result implies that the field equations of a non-minimally coupled scalar field are the same at the conformal level with the field equations of the minimally coupled scalar field. This fact is relevant in order to select physical variables among conformally equivalent systems. Finally, we find that the above propositions can be extended to a general Riemannian space of $n$ n -dimensions.     

QKD Based on Symmetric Entangled Bernstein-Vazirani

This paper introduces a novel entanglement-based QKD protocol, that makes use of a modified symmetric version of the Bernstein-Vazirani algorithm, in order to achieve secure and efficient key distribution. Two variants of the protocol, one fully symmetric and one semi-symmetric, are presented. In both cases, the spatially separated Alice and Bob share multiple EPR pairs, each one qubit of the pair. The fully symmetric version allows both parties to input their tentative secret key from their respective location and acquire in the end a totally new and original key, an idea which was inspired by the Diffie-Hellman key exchange protocol. In the semi-symmetric version, Alice sends her chosen secret key to Bob (or vice versa). The performance of both protocols against an eavesdroppers attack is analyzed. Finally, in order to illustrate the operation of the protocols in practice, two small scale but detailed examples are given.     

Lie and Noether symmetries of geodesic equations and collineations

The Lie symmetries of the geodesic equations in a Riemannian space are computed in terms of the special projective group and its degenerates (affine vectors, homothetic vector and Killing vectors) of the metric. The Noether symmetries of the same equations are given in terms of the homothetic and the Killing vectors of the metric. It is shown that the geodesic equations in a Riemannian space admit three linear first integrals and two quadratic first integrals. We apply the results in the case of Einstein spaces, the Schwarzschild spacetime and the Friedman Robertson Walker spacetime. In each case the Lie and the Noether symmetries are computed explicitly together with the corresponding linear and quadratic first integrals.