Artificial boundary conditions on polyhedral truncation surfaces for three-dimensional elasticity systemsConditions aux limites artificielles sur des surfaces polyhédrales de troncature pour des systèmes d'élasticité tridimensionalle

For a three-dimensional exterior problem in the framework of anisotropic elasticity, artificial boundary conditions are constructed on a polyhedral truncation surface. These conditions do not need an explicit formula for the fundamental matrix. An approach to adapt the shape of truncation surfaces to the shape of the enclosed cavity is discussed. To cite this article: S. Langer et al., C. R. Mecanique 332 (2004).     

Dynamical investigation of railway vehicles on a curved track

The main objective of this article is an examination of railway vehicle dynamics during motion along a curved track. Two main aspects are presented in the paper. First, two different methods used while investigating multi-rigid body systems such as railway vehicles are discussed, i.e. the quasi-statical (or kineto-statical) and dynamical approaches. Second, two practical problems dealing with vehicle motion along a curved track are investigated. The problems under consideration refer to vibrations as well as stability, examined via finding obtained with the author's software as a result of numerical simulation. The work has both a practical and a cognitive character. The aim of the investigations is firstly to indicate the limitations of quasi-statical (and kineto-statical) methods and secondly to study the problems which cannot be treated by these methods. Two specific problems of the type investigated using a dynamical approach are the influence of track geometrical irregularities on the evaluation of vehicle ride properties and limit cycle occurrence during vehicle curve negotiation. Due to the renewed interest in the rapid passenger railway, the investigations take into consideration curves of large radii introduced along railway routes for increased velocities. Furthermore, it is shown under which conditions the obtained results may have an important practical application. This concerns the influence of vehicle suspension parameters as well as conditions of motion (speed, superelevation, curve radius, transition curve existence) on limit cycle occurrence. The limited value of conclusions dealing with vehicle ride properties obtained while using quasi-statical (kineto-statical) methods is proved through quantitative analysis. The problem of the influence of geometrical irregularities on wheel-rail pair wear is also pointed out.     

Monochromatic surface waves on impermeable boundaries in two-component poroelastic media

The dispersion relation for surface waves on an impermeable boundary of a fully saturated poroelastic medium is investigated numerically over the whole range of applicable frequencies. To this aim a linear simplified model of a two-component poroelastic medium is used. Similarly to the classical Biot’s model, it is a continuum mechanical model but it is much simpler due to the lack of coupling of stresses. However, results for bulk waves following for these two models agree very well indeed which motivates the application of the simplified model in the analysis of surface waves. In the whole range of frequencies there exist two modes of surface waves corresponding to the classical Rayleigh and Stoneley waves. The numerical results for velocities and attenuations of these waves are shown for different values of the bulk permeability coefficient in different ranges of frequencies. In particular, we expose the low and high frequency limits, and demonstrate the existence of the Stoneley wave in the whole range of frequencies as well as the leaky character of the Rayleigh wave.     

The influence of process parameters on the laser-induced coloring of titanium

This paper presents the results of the measurements and analysis of the influence of laser process parameters on the color obtained. The study was conducted for titanium (Grade 2) using a commercially available industrial pulsed fiber laser. It was determined how a variety of different laser process parameters, such as laser power, the scanning speed of the material, the temperature of the material, the size of the marked area, and the position of the sample, relative to both the focal plane and the center of the working field of the system, affect the repeatability of the colors created. For an objective assessment of color changes, an optical spectrometer and the CIE color difference parameter $\Delta E_{ab}^{*}$ were used. Our paper explains why the tolerance of process parameters highly depends on the specific color. Additionally, a comparison of the results for titanium with those obtained for stainless steel in a previous study is presented. Based on this analysis, a number of necessary modifications are proposed to laser systems commonly used for monochrome marking in order to improve repeatability in color marking.     

Effect of one-, two-, and three-body atom loss processes on superpositions of phase states in Bose-Josephson junctions

In a two-mode Bose-Josephson junction formed by a binary mixture of ultracold atoms, macroscopic superpositions of phase states are produced during the time evolution after a sudden quench to zero of the coupling amplitude. Using quantum trajectories and an exact diagonalization of the master equation, we study the effect of one-, two-, and three-body atom losses on the superpositions by analyzing separately the amount of quantum correlations in each subspace with fixed atom number. The quantum correlations useful for atom interferometry are estimated using the quantum Fisher information. We identify the choice of parameters leading to the largest Fisher information, thereby showing that, for all kinds of loss processes, quantum correlations can be partially protected from decoherence when the losses are strongly asymmetric in the two modes.     

A note on Hecke eigenvalues of Hermitian Siegel Eisenstein series

In this note we compute Hecke eigenvalues of Siegel Eisenstein series on the unitary group \(\operatorname{U}(2,2)\) induced from a character. We do this for Hecke operators at primes not dividing the level of the Eisenstein series.     

The Trefoil

Dixon’s elliptic functions parameterize the real sextic trefoil curve by arc length and the complex curve as an embedded Platonic surface with 18 (or 108) faces.     

A Note on Recent Papers by Grafakos and Teschl,and Estrada

We indicate how recent results of Grafakos and Teschl (J Fourier Anal Appl 19:167–179, 2013), and Estrada (J Fourier Anal Appl 20:301–320, 2014), relating the Fourier transform of a radial function in \(\mathbb R^n\) and the Fourier transform of the same function in \(\mathbb R^{n+2}\) and \(\mathbb R^{n+1}\) , respectively, are located within known results on transplantation for Hankel transforms.     

Reaching generalized critical values of a polynomial

Let $f: \mathbb K ^n \rightarrow \mathbb K $ be a polynomial, $\mathbb K =\mathbb R , \,\mathbb C $ . We give an algorithm to compute the set of generalized critical values. The algorithm uses a finite dimensional space of rational arcs along which we can reach all generalized critical values of $f$ .