Double-quantum filtered MAS NMR in the presence of chemical shielding anisotropies and direct dipolar and J couplings

Double-quantum filtered MAS NMR spectra of an isolated homonuclear spin-1/2 pair are considered, at and away from rotational resonance conditions. The pulse sequence used is the solid-state NMR equivalent of double-quantum filtered COSY, known from solution-state NMR. The 119Sn spin pair in [(chex3Sn)2S] is characterized by a difference in isotropic chemical shielding smaller than the two chemical shielding anisotropies and by direct dipolar and isotropic J-coupling constants of similar magnitudes. At rotational resonance, one-dimensional double-quantum filtered 119Sn lineshapes yield the relative orientation of the two 119Sn chemical shielding tensors. Good double-quantum filtration efficiencies are found at and away from rotational resonance conditions, despite the presence of large chemical shielding anisotropies. Numerical simulations illustrate the interplay of the direct dipolar and J-coupling pathways and identify the latter as the main pathway even at rotational resonance conditions.     

Disjoint Hamilton cycles in the random geometric graph

We consider the standard random geometric graph process in which n vertices are placed at random on the unit square and edges are sequentially added in increasing order of edge‐length. For fixed k?1, weprove that the first edge in the process that creates a k‐connected graph coincides a.a.s. with the first edge that causes the graph to contain k/2 pairwise edge‐disjoint Hamilton cycles (for even k), or (k?1)/2 Hamilton cycles plus one perfect matching, all of them pairwise edge‐disjoint (for odd k). This proves and extends a conjecture of Krivelevich and M ler. In the special case when k = 2, our result says that the first edge that makes the random geometric graph Hamiltonian is a.a.s. exactly the same one that gives 2‐connectivity, which answers a question of Penrose. (This result appeared in three independent preprints, one of which was a precursor to this article.) We prove our results with lengths measured using the ?_p norm for any p>1, and we also extend our result to higher dimensions. © 2011 Wiley Periodicals, Inc. J Graph Theory 68:299‐322, 2011     

Variations de champs gaussiens stationnaires: application a l'identification

Summary Let be a stationary Gaussian random field, with covariance R. For d=1 and d=2, families of variations are described. The convergence in mean square of these variations and a subsequent identification of a model for X are studied. Under suitable glocal conditions for R, the behaviour of these variations depends on the local behaviour of R near the origin. The differences between the case d=1 and d=2 are particularly emphasised: for d=1, there exists only one variation; for d=2, several families of variations are available which provided a useful tool for identifying different models: for example, Orstein-Uhlenbeck processes can be identified in mean square on , but not on .

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Variations de champs gaussiens stationnaires: application a l'identification

     

Probing structural integrity of single walled carbon nanotubes by dynamic and static compression

We report on a first study of single walled carbon nanotubes (SWCNTs) after application of dynamic (shock) compression. The experiments were conducted at 19 GPa and 36 GPa in a recovery assembly. For comparison, an experiment at a static pressure of 36 GPa was performed on the material from the same batch in a diamond anvil cell (DAC). After the high pressure treatment the samples were characterized by Raman spectroscopy and transmission electron microscopy (TEM). After exposure to 19 GPa of shock compression the CNT material exhibited substantial structural damage such as CNT wall disruption, opening of the tube along its axis (“unzipping”) and tube shortening (“cutting”). Dynamic compression to 36 GPa resulted in essentially complete CNT destruction whereas at least a fraction of the nanotubes was recovered after 36 GPa of static compression though severely damaged. The results of these shock wave experiments underline the prospect of using SWCNTs as reinforcing units in material WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

An improved On-Surface Radiation Condition for acoustic scattering problems in the high-frequency spectrum

This Note addresses the derivation of an improved On-Surface Radiation Condition for the numerical solution of the exterior Helmholtz equation at high-frequencies. This condition is built as an approximation of the Neumann-to-Dirichlet map by using a local regularization of its principal classical symbol in the gliding zone for modelling the creeping waves. The numerical simulation of this pseudodifferential operator is efficiently realized with a linear cost according to the dimension of the boundary element approximation space using suitable complex Padé approximants. A numerical example is provided. To cite this article: X. Antoine et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

A Note on the Morozov Principle via Lagrange Duality

Considering a general linear ill-posed equation, we explore the duality arising from the requirement that the discrepancy should take a given value based on the estimation of the noise level, as is notably the case when using the Morozov principle. We show that, under reasonable assumptions, the dual function is smooth, and that its maximization points out the appropriate value of Tikhonov’s regularization parameter. The numerical relevance of our approach is established by means of an illustrative example from nonparametric instrumental regression, a standard problem in statistics.     

On the existence of a minimum integer representation for?weighted voting systems

A basic problem in the theory of simple games and other fields is to study whether a simple game (Boolean function) is weighted (linearly separable). A second related problem consists in studying whether a weighted game has a minimum integer realization. In this paper we simultaneously analyze both problems by using linear programming. For less than 9 voters, we find that there are 154 weighted games without minimum integer realization, but all of them have minimum normalized realization. Isbell in 1958 was the first to find a weighted game without a minimum normalized realization, he needed to consider 12 voters to construct a game with such a property. The main result of this work proves the existence of weighted games with this property with less than 12 voters. This research was partially supported by Grant MTM 2006-06064 of “Ministerio de Ciencia y Tecnología y el Fondo Europeo de Desarrollo Regional” and SGRC 2005-00651 of “Generalitat de Catalunya”, and by the Spanish “Ministerio de Ciencia y Tecnología” programmes ALINEX (TIN2005-05446 and TIN2006-11345).     

Effective magnetic monopoles and universal conductance fluctuations

The observation of isolated positive and negative charges, but not isolated magnetic north and south poles, is an old puzzle. Instead, evidence of effective magnetic monopoles has been found in the abstract momentum space. Apart from Hall-related effects, few observable consequences of these abstract monopoles are known. Here, we show that it is possible to manipulate the monopoles by external magnetic fields and probe them by universal conductance fluctuation measurements in ferromagnets with strong spin-orbit coupling. The observed fluctuations are not noise, but reproducible quasiperiodic oscillations as a function of magnetization direction, a novel Berry phase fingerprint of the magnetic monopoles.     

DNA transport and delivery in thermal gradients near optofluidic resonators

Heat generation and its impact on DNA transport in the vicinity of an optofluidic silicon photonic crystal resonator are studied theoretically and experimentally. The temperature rise is measured to be as high as 57 K for 10 mW of input power. The resulting optical trapping and biomolecular sensing properties of these devices are shown to be strongly affected by the combination of buoyancy driven flow and thermophoresis. Specifically, the region around the electromagnetic hot spot is depleted in biomolecules because of a high free energy barrier.