Happy New Year

This is the first issue of EPJ D in 2001, the new century in the new millennium! This is therefore appropriate timing for introducing some modifications in the journal. However, there is no need for a revolution. EPJ D is a healthy journal, which receives an increasing flow of excellent papers, but it is our continuing concern to adapt the journal to the evolution of science and to publish a better journal. So what's new in 2001? By examining the list of topics covered by EPJ D, you will find changes. To emphasize a few active fields, new sections have been added so that physicists working on these subjects can find immediately the papers belonging to their domain. For example, there is presently a large community working on quantum gases and Bose-Einstein condensation. For this community and those working on laser cooling of atoms, molecules, ions, we have created a section Laser Cooling and Quantum Gas. In the same manner, to satisfy those interested in quantum information, entanglement, quantum cryptography, we have extended the Quantum Optics section to Quantum Optics and Quantum Information. A new section has also been created for Ultrafast Phenomena and for the processes occurring in High Intensity Fields. The introduction of this section is triggered by the rapid development of femtosecond lasers and their numerous applications ranging from time-resolved spectroscopy of biological molecules to X-ray generation. Another new and exciting field, bringing even more interdisciplinary into our journal is molecules of biological interest in the gas phase. Finally, the section Nonlinear Dynamics has been polished. It is now the natural place to publish results dealing the fundamental aspects of chaotic systems and the manifestation of these phenomena in Atoms, Molecules and Optics. However, these new sections do not mean that EPJ D is now only devoted to a few fashionable subjects. Papers dealing with more traditional topics are obviously highly welcomed and they should find their place in one of the other sections. We have also decided to have regular publication of topical issues. We plan to publish two topical issues each year. In 2001, the topics of these issues will be Clusters and Femtosecond Spectroscopy. Another evolution concerns the Rapid Notes. Although they have existed since the start of the journal and they correspond to a regular demand of our community (fast publication of short papers, less than 4 pages, describing important advances), the EPJ D Rapid Notes were not very popular. We wish to make them more attractive. First, by increasing the rapidity of publication: our aim is to publish a Rapid Note 3 months at most after its reception by the editorial office. For this purpose the Editors, the Editorial Office and the Publisher will give the highest priority to these Rapid Notes. Second, by using a different lay-out to separate and distinguish them from the other papers of the same issue. Furthermore, if you wish to communicate with an editor it will be no longer necessary to look for his email address. To achieve better connections between authors and editors, every editor can now be reached through the electronic address first name.last name@epjd.org. The mail will be directly forwarded towards his personal address. Finally, we expect that 2001 will be the real beginning of a new type of publication that combines the possibilities of the printed journal and of the on-line edition. First as soon as a paper is accepted and proofread, it will appear on the on-line version by using the Digital Object Identifier (DOI) system, and can therefore be quoted. There are however additional advantages. For example, it is now possible to have a short paper published in the printed journal and an extended version on-line, with supplementary material (tables, figures, complements) and possibly various multimedia documents. Obviously, if there are additional materials in the on-line version, this will be mentioned on the printed version. Technical information is available hereafter. We hope that all these small advances will make the journal more attractive. However, what makes a journal alive are really the authors. Therefore, we wish you many results, many discoveries and we hope that you will provide us with lots of excellent papers. Happy New Year! The publisher informs the authors of the possibility to published “electronic-only" materials. Electronic-only material is designed to provide supplementary information which is either too voluminous to be printed or is designed specifically for the Web, such as illustration in colour. Electronic-only material may include but is not restricted to: •(Large) tables • Appendices • Programmes • Images, videos For more information on the submission of this material, (file requirements, etc.), please contact the production office at: articles@edpsciences.org     

Refractive index profiles of LiNbO3: Ti waveguides

Eight LiNbO₃: Ti waveguides have been fabricated under differing conditions. The effective refractive indices of guided modes have been measured and successfully fitted to Gaussian index profiles. The change of refractive index and titanium concentration are related by a power law, the exponents being different for the extraordinary and the ordinary beam.     

Interaction of C60 with carbon nanotubes and graphite

The interaction of C60 with single-wall carbon nanotubes (SWNTs) and graphite is studied experimentally by thermal desorption spectroscopy and theoretically by molecular-mechanics and molecular-dynamics calculations. The van der Waals parameters and force field for C60-graphene and C60-SWNT interactions are derived from the low-coverage C60 binding energy to the graphite surface. We use these to compare the efficiency of different mechanisms by which C60 can be encapsulated into SWNTs.     

A unified expression of elastic–plastic notch stress–strain calculation in bodies subjected to multiaxial cyclic loading

In this paper, a simplified thermodynamics analysis of cyclic plastic deformation is performed in order to establish an energy transition relation for describing the elastic–plastic stress and strain behavior of the notch-tip material element in bodies subjected to multiaxial cyclic loads. Based on the thermodynamics analysis, it is deduced that in the case of elastic–plastic deformation, Neuber’s rule inevitably overestimates the actual stress and strain at the notch tip, while the equivalent strain energy density (ESED) method tends to underestimate the actual notch-tip stress and strain. According to the actual energy conversion occurring in the notch-tip material element during cyclic plastic deformation, a unified expression for estimating the elastic–plastic notch stress–strain responses in bodies subjected to multiaxial cyclic loads is developed, of which Neuber’s rule and the ESED method become two particular cases, i.e. upper and lower bound limits of the notch stress and strain estimations. This expression is verified experimentally under both proportional and non-proportional multiaxial cyclic loads and a good agreement between the calculated and the measured notch strains has been achieved. It is also shown that in the case of multiaxial cyclic loading, the unified expression distinctly improves the accuracy of the notch-tip stress–strain estimations in comparison with Neuber’s rule and the ESED method. The unified expression of the notch stress–strain calculation developed in this paper can thus provide a more logical approximate approach for estimating the elastic–plastic notch-tip stress and strain responses of components subjected to lengthy multiaxial cyclic loading histories for local strain approach-based fatigue-crack-initiation life prediction.     

Tiling Convex Polygons with Congruent Equilateral Triangles

We study the sets $\mathcal{T}_{v}=\{m \in\{1,2,\ldots\}: \mbox{there is a convex polygon in }\mathbb{R}^{2}\mbox{ that has }v\mbox{ vertices and can be tiled with $m$ congruent equilateral triangles}\}$ , v=3,4,5,6. $\mathcal{T}_{3}$ , $\mathcal{T}_{4}$ , and $\mathcal{T}_{6}$ can be quoted completely. The complement $\{1,2,\ldots\} \setminus\mathcal{T}_{5}$ of $\mathcal{T}_{5}$ turns out to be a subset of Euler’s numeri idonei. As a consequence, $\{1,2,\ldots\} \setminus\mathcal{T}_{5}$ can be characterized with up to two exceptions, and a complete characterization is given under the assumption of the Generalized Riemann Hypothesis.     

A new wavelet multigrid method

The standard multigrid procedure performs poorly or may break down when used to solve certain problems, such as elliptic problems with discontinuous or highly oscillatory coefficients. The method discussed in this paper solves this problem by using a wavelet transform and Schur complements to obtain the necessary coarse grid, interpolation, and restriction operators. A factorized sparse approximate inverse is used to improve the efficiency of the resulting method. Numerical examples are presented to demonstrate the versatility of the method.     

Approximate Euclidean Steiner Trees

An approximate Steiner tree is a Steiner tree on a given set of terminals in Euclidean space such that the angles at the Steiner points are within a specified error from \(120^{\circ }\). This notion arises in numerical approximations of minimum Steiner trees. We investigate the worst-case relative error of the length of an approximate Steiner tree compared to the shortest tree with the same topology. It has been conjectured that this relative error is at most linear in the maximum error at the angles, independent of the number of terminals. We verify this conjecture for the two-dimensional case as long as the maximum angle error is sufficiently small in terms of the number of terminals. In the two-dimensional case we derive a lower bound for the relative error in length. This bound is linear in terms of the maximum angle error when the angle error is sufficiently small in terms of the number of terminals. We find improved estimates of the relative error in length for larger values of the maximum angle error and calculate exact values in the plane for three and four terminals.     

Convexity in finite metric spaces

A subsetS of a metric space (X,d) is calledd-convex if for any pair of pointsx,y S each pointz X withd(x,z) +d(z,y) =d(x,y) belongs toS. We give some results and open questions concerning isometric and convexity-preserving embeddings of finite metric spaces into standard spaces and the number ofd-convex sets of a finite metric space.