On the cut‐off phenomenon for the transitivity of randomly generated subgroups

Consider K ≥ 2 independent copies of the random walk on the symmetric group S_N starting from the identity and generated by the products of either independent uniform transpositions or independent uniform neighbor transpositions. At any time $n\in \mathbb{N}$, let G_n be the subgroup of S_N generated by the K positions of the chains. In the uniform transposition model, we prove that there is a cut‐off phenomenon at time N ln(N)/(2K) for the non‐existence of fixed point of G_n and for the transitivity of G_n, thus showing that these properties occur before the chains have reached equilibrium. In the uniform neighbor transposition model, a transition for the non‐existence of a fixed point of G_n appears at time of order $N^{1+\frac{2}{K}}$ (at least for K ≥ 3), but there is no cut‐off phenomenon. In the latter model, we recover a cut‐off phenomenon for the non‐existence of a fixed point at a time proportional to N by allowing the number K to be proportional to ln(N). The main tools of the proofs are spectral analysis and coupling techniques. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

Asynchronous sampling for ultrafast experiments with low momentum compaction at the ANKA ring

A high‐repetition‐rate pump–probe experiment is presented, based on the asynchronous sampling approach. The low‐α mode at the synchrotron ANKA can be used for a time resolution down to the picosecond limit for the time‐domain sampling of the coherent THz emission as well as for hard X‐ray pump–probe experiments, which probe structural dynamics in the condensed phase. It is shown that a synchronization of better than 1 ps is achieved, and examples of phonon dynamics of semiconductors are presented.     

Accelerated Poisson-Boltzmann calculations for static and dynamic systems

We report here an efficient implementation of the finite difference Poisson-Boltzmann solvent model based on the Modified Incomplete Cholsky Conjugate Gradient algorithm, which gives rather impressive performance for both static and dynamic systems. This is achieved by implementing the algorithm with Eisenstat's two optimizations, utilizing the electrostatic update in simulations, and applying prudent approximations, including: relaxing the convergence criterion, not updating Poisson-Boltzmann-related forces every step, and using electrostatic focusing. It is also possible to markedly accelerate the supporting routines that are used to set up the calculations and to obtain energies and forces. The resulting finite difference Poisson-Boltzmann method delivers efficiency comparable to the distance-dependent dielectric model for a system tested, HIV Protease, making it a strong candidate for solution-phase molecular dynamics simulations. Further, the finite difference method includes all intrasolute electrostatic interactions, whereas the distance dependent dielectric calculations use a 15-A cutoff. The speed of our numerical finite difference method is comparable to that of the pair-wise Generalized Born approximation to the Poisson-Boltzmann method.     

Photogenotoxicity of mammalian cells: a review of the different assays for in vitro testing

During the past several years, phototoxicity has been studied at the molecular level, and these studies have provided new insights in the field of DNA lesion characterization, DNA repair and cell response to ultraviolet (UV)-induced stress. The development of new antibiotics and antiinflammatory drugs has highlighted the necessity to develop the assessment of phototoxicity in the safety evaluation of new chemical compounds. This paper aims at reviewing the known molecular mechanisms of the cellular response to UV-induced stress, the in vitro methods that can be proposed and used to screen for toxicity of sunlight and the photosensitization process resulting from the activation of drugs by light. UV sources, biological systems and endpoints of interest in that particular objective are listed. Phototoxic effects span from the cytotoxic-apoptotic effect to the induction of primary DNA damage, DNA repair and a variety of stress genes acting on the cell cycle and the fate of the cell. Ultimately, it can lead to the induction of hereditary DNA modification. A variety of assays are proposed to specifically address all these particular consequences of UV-induced toxicity.     

One-step stereoselective synthesis and NMR chiral shift properties of a novel hexacoordinated phosphorus cation

[reaction: see text] Tropolone, binol, and PCl(5) react in CH(2)Cl(2) at reflux to generate in one step a novel C(2)-symmetric hexacoordinated phosphorus cation of configuration controlled by the binol ligand. It behaves as an efficient NMR chiral shift agent for chiral anionic phosphate and borate anions.     

Multiscale clustering in granular surface flows

We investigate steady granular surface flows in a rotating drum and demonstrate the existence of rigid clusters of grains embedded in the flowing layer. These clusters appear to be fractal and their size is power law distributed from the grain size scale up to the thickness of the flowing layer. The implications of the absence of a characteristic length scale on available theoretical models of dense granular flows are discussed. Finally, we suggest a possible explanation of the difference between velocity profiles observed in surface flows and in flows down a rough inclined plane.     

Spatial trapping of short pulses in Ti-indiffused LiNbO(3) waveguides

We show numerically and experimentally that spatial trapping can be induced in quadratic media even if the pump pulse's duration is shorter than the group-delay mismatch between fundamental wave and second-harmonic components. The influence of phase mismatch and pulse power on the trapping effect is discussed. Spatial, temporal, and spectral behaviors that accompany self-trapped propagation are highlighted.