Vibration induced electric dipole in a weakly bound molecular complex

A strong electric susceptibility is measured as a function of temperature in a molecular dimer which is weakly bound by a pair of hydrogen bonds. This system is a remarkable example where the dominant term in the susceptibility is due to a vibration induced electric dipole. As a consequence, the averaged square of the dipole moment varies linearly with the temperature and the susceptibility does not follow the usual 1/T Curie law. this spectacular effect demonstrates the importance of dynamics to interpret the properties of weakly bound complexes.     

Femtosecond optical vortices in air

We examine the robustness of ultrashort optical vortices propagating freely in the atmosphere. We first approximate the stability regions of femtosecond spinning pulses as a function of their topological charge. Next, we numerically demonstrate that atmospheric optical vortices are capable of conveying high power levels in air over hundreds of meters before they break up into filaments.     

Stability of rocksalt (111) polar surfaces: beyond the octopole

Stable polar oxide surfaces must be simultaneously electrostatically compensated and in thermodynamic equilibrium with the environment. As a paradigm, the MgO(111)-p(2x2) reconstructed surface is shown to involve combinations of Mg-covered terminations with peculiar insulating electronic structure, favored in O-poor conditions, and the O-terminated octopole, stabler in more O-rich environments. Such a picture, which could not have been foreseen by either experiments or simulations separately, goes beyond the Wolf model and reconciles the theory with the experimental data taken in variable thermodynamic conditions.     

Addition patterns in carbon allotropes: independence numbers and d-codes in the Klein and related graphs

The problem of predicting stoichiometries and patterns of chemical addition to a carbon framework, subject solely to the restriction that each addend excludes neighboring sites up to some distance d, is equivalent to determination of d-codes of a graph, and for d = 2 to determination of maximum independent sets. Sizes, symmetries, and numbers of d-codes are found for the all-heptagon Klein graph (prototype for "plumber's nightmare" carbon) and for three related graphs. The independence number of the Klein graph is 23, which increases to 24 for a related, but sterically relaxed, all-heptagon network with the same number of vertices and modified adjacencies. Expansion of the Klein graph and its relaxed analogue by insertion of hexagonal faces to form leapfrog graphs also allows all heptagons to achieve their maximum of 3 addends. Consideration of the pi system that is the complement of the addition pattern imposes a closed-shell requirement on the adjacency spectrum, which typically reduces the size of acceptable independent sets. The closed-shell independence numbers of the Klein graph and its relaxed analogue are 18 and 20, respectively.     

Singular Limit and Homogenization for Flame Propagation in Periodic Excitable Media

This paper is concerned with a class of singular equations modelling the combustion of premixed gases in periodic media. The model involves two parameters: the period of the medium |L| and a singular parameter related to the activation energy. The existence of pulsating travelling fronts for fixed and |L| was proved by Berestycki & Hamel in [BH]. In the present paper, we investigate the behaviour of such solutions when More precisely, we establish that pulsating travelling fronts behave like travelling waves, when the period |L| is small and . We also study the convergence of the solution, as goes to zero (and |L| is fixed), toward a solution of a free boundary problem.     

Rate Optimality of Wavelet Series Approximations of Fractional Brownian Motion

Consider the fractional Brownian motion process $B_H(t), t\in [0,T]$, with parameter $H\in (0,1)$. Meyer, Sellan and Taqqu have developed several random wavelet representations for $B_H(t)$, of the form $\sum_{k=0}^\infty U_k(t)\epsilon_k$ where $\epsilon_k$ are Gaussian random variables and where the functions $U_k$ are not random. Based on the results of Kühn and Linde, we say that the approximation $\sum_{k=0}^n U_k(t)\epsilon_k$ of $B_H(t)$ is optimal if $$ \displaystyle \left( E \sup_{t\in [0,T]} \left| \sum_{k=n}^\infty U_k(t) \epsilon_k\right|^2 \right)^{1/2} =O \left( n^{-H} (1+\log n)^{1/2} \right), $$ as $n\rightarrow\infty$. We show that the random wavelet representations given in Meyer, Sellan and Taqqu are optimal.     

The filtering approach to solvent peak suppression in MRS: a critical review

Suppressing the solvent peak is important in many applications of biomedical NMR spectroscopy in order to quantify the metabolites with a great accuracy. Among the postprocessing methods proposed in the literature, many deal with the concept of filtering. However, several proposals lack a theoretical perspective and some have not been explicitly applied to quantification problems. The present article is intended to bridge this gap: five methods are analyzed from a theoretical perspective. Subsequently the different methods are applied to the same set of data, and then the latter are quantified using the model fitting method AMARES. With our set, the scheme proposed by T. Sundin et al. (J. Magn. Reson. 139(2), 189-204 (1999)) proved to be the most reliable method.