Fast and accurate algorithm for the simulation of NMR spectra of large spin systems

The computational cost for the simulation of NMR spectra grows exponentially with the number of nuclei. Today, the memory available to store the Hamiltonian limits the size of the system that can be studied. Modern computers enable to tackle systems containing up to 13 spins [1], which obviously does not allow to study most molecules of interest in research. This issue can be addressed by identifying groups of spins or fragments that are not or only weakly interacting together, i.e., that only share weakly coupled spin pairs. Such a fragmentation is only permitted in the weak coupling regime, i.e., when the coupling interaction is weak compared to the difference in chemical shift of the coupled spins. Here, we propose a procedure that removes weak coupling interactions in order to split the spin system efficiently and to correct a posteriori for the effect of the neglected couplings. This approach yields accurate spectra when the adequate interactions are removed, i.e., between spins only involved in weak coupling interactions, but fails otherwise. As a result, the computational time for the simulation of 1D spectra grows linearly with the size of the spin system.     

Perfect extinction in subwavelength dual metallic transmitting gratings

We investigate the strong electromagnetic coupling that settles in dual metallic grating structures. This coupling is evidenced to lead to a perfect optical extinction in the transmission spectrum. The behavior of this perfect extinction that strongly depends on the longitudinal space and the lateral displacement between the two gratings can be explained by a simple model that describes the interference between a propagating mode and a couple of evanescent modes. The results show that the electromagnetic transmission of the structure can be tuned by controlling the position of this perfect transmission extinction and thus pave the way to new types of infrared tunable filters.     

Cellular resolution optical coherence microscopy with high acquisition speed for in-vivo human skin volumetric imaging

In this Letter, we report for the first time (to our knowledge) in-vivo volumetric optical coherence microscopy images of skin epidermal cells. We achieved micrometer-class resolution, 2 μm laterally and axially, with an acquisition speed of 23 K A-scans/s and over 90 dB sensitivity to a depth of 1 mm by employing a custom, liquid-lens-based, dynamic-focusing objective, a broadband light source, and a custom, astigmatism-corrected Czerny-Turner spectrometer with a high-speed complementary metal-oxide-semiconductor camera.     

Double-T metamaterial for parallel and normal transverse electric incident waves

Electric and magnetic hybridized plasmonic modes are obtained by stacking two T-shaped resonators. We show that head-to-toe configuration leads to inverse the hybridization. The frequency shift between the resonances is finely controlled by adjusting the gap between the two resonators. A negative refractive index close to -1 is numerically and experimentally demonstrated at 4.3 GHz for TE waves. This left-handed behavior is similar for parallel and normal TE incident wave vectors. The proposed double-T unit cell is well adapted for developing terahertz and IR metamaterials.     

Semi-Markov regime switching interest rate models and minimal entropy measure

In this paper, we present a discrete time regime switching binomial-like model of the term structure where the regime switches are governed by a discrete time semi-Markov process. We model the evolution of the prices of zero-coupon when given an initial term structure as in the model by Ho and Lee that we aim to extend. We discuss and derive conditions for the model to be arbitrage free and relate this to the notion of martingale measure. We explicitly show that due to the extra source of uncertainty coming from the underlying semi-Markov process, there are an infinite number of equivalent martingale measures. The notion of path independence is also studied in some detail, especially in the presence of regime switches. We deal with the market incompleteness by giving an explicit characterization of the minimal entropy martingale measure. We give an application to the pricing of a European bond option both in a Markov and semi-Markov framework. Finally, we draw some conclusions.     

Interval Methods for Model Qualification: Methodology and Advanced Application

An actual model in simulation (e.g. in chemistry) or control (e.g. in robotics) is often too complex to use, and sometimes impossible to obtain. To handle a system in practice, a simplification of the real model is often necessary. This simplification goes through some hypotheses made on the system or the modeling approach. These hypotheses are rarely verified whereas they could lead to an inadmissible model, over approximated for its use. In this paper, we propose a method that qualifies the simplification validity for all models that can be expressed by real-valued variables involved in closed-form relations and depending on parameters. We based our approach on a verification of a quality threshold on the hypothesis relevance. This method, based on interval analysis, checks the acceptance of the hypothesis in a full range of the whole model space, and gives bounds on the quality threshold and on the model parameters. Our approach is experimentally validated on a robotic application.     

An expeditious construction of 9-membered rings

9-Membered rings are readily constructed through a radical addition-cyclisation sequence on a 1,6-dien-3-ol system followed by a Grob-type fragmentation.     

Mutual Diffusion Driven NMR: a new approach for the analysis of mixtures by spatially resolved NMR spectroscopy

We introduce a new approach for resolving the NMR spectra of mixtures that relies on the mutual diffusion of dissolved species when a concentration gradient is established within the NMR tube. This is achieved by cooling down a biphasic mixture of triethylamine and deuterated water below its mixing temperature, where a single phase is expected. Until equilibrium is reached, a gradient of concentration, from ‘pure’ triethylamine to ‘pure’ water, establishes within the tube. The amount of time required to reach this equilibrium is controlled by the mutual diffusion coefficient of both species. Moreover, a gradient of concentration exists for each additional compound dissolved in this system, related to the partition coefficient for that compound in the original biphasic state. Using slice selective experiments, it was possible to measure these concentration gradients and use them to separate signals from all the present species. We show the results acquired for a mixture composed of n‐octanol, methanol, acetonitrile and benzene and compare them with those obtained by pulse field gradient NMR. Copyright © 2016 John Wiley & Sons, Ltd.     

Physical-chemistry of silica/alkaline silicate interactions during consolidation. Part 1: Effect of cation size

The purpose of this work is to identify the effect of the cation nature on mechanisms of the sand consolidation with alkaline silicate solution at low temperature (70 °C). Three diluted lithium, sodium and potassium silicate solutions with [Si] = 2.8 mol/l were used to agglomerate sand composed of grains which mean diameter is 340 μm. According to the cation, different behaviors were observed in terms of the drying time and the material cohesion. Essentially, the drying time increases with decreasing cation size. In contrast, the compressive strength raises when the cation size increases inducing intra-granular rupture highlighted by SEM observations. This could find an explanation in the cation hydration sphere of cations. The strength of the cation–water electrostatic interaction becomes less important as the size of the cations increase leading to more ionic bonds. Despite their strong consolidation, potassium-based materials have a high solubility in water. This result is consistent with the ionic nature of bonds.