Imaging electron trajectories in a laser-wakefield cavity using betatron X-ray radiation

We demonstrate that betatron x-ray radiation accurately provides direct imaging of electrons trajectories accelerated in laser wakefields. Experimental far field x-ray beam profiles reveal that electrons can follow similar transverse trajectories with typical excursions of 1.5 microm+/-0.5 microm in the plane of laser polarization and 0.7 microm+/-0.2 microm in the plane perpendicular.     

Energy level and band alignment for GaAs-alkylthiol monolayer-Hg junctions from electrical transport and photoemission experiments

A series of p- and n-GaAs-S-C(n)H(2n+1) || Hg junctions are prepared, and the electronic transport through them is measured. From current-voltage measurements, we find that, for n-GaAs, transport occurs by both thermionic emission and tunneling, with the former dominating at low forward bias and the latter dominating at higher forward bias. For p-GaAs, tunneling dominates at all bias voltages. By combining the analysis of the transport data with results from direct and inverse photoemission spectroscopy, we deduce an energy band diagram of the system, including the tunnel barrier and, with this barrier and within the Simmons tunneling model, extract an effective mass value of 1.5-1.6m(e) for the electronic carriers that cross the junctions. We find that transport is well-described by lowest unoccupied and highest occupied states at 1.3-1.4 eV above and 2.0-2.2 eV below the Fermi level. At the same time, the photoemission data indicate that there are continua of states from the conduction band minimum and the valence band maximum, the density of which varies with energy. On the basis of our results, it appears likely that, for both types of junctions, electrons are the main carrier type, although holes may contribute significantly to the transport in the p-GaAs system.     

Theoretical study of the reduction mechanism of sulfoxides by thiols

Theoretical computations have been carried out to investigate the reaction mechanism of the sulfoxide reduction by thiols in solution. This reaction is a suitable model for enzymatic processes involving methionine sulfoxide reductases (Msrs). Recent investigations on the Msr mechanism have clearly shown that a sulfenic acid intermediate is formed on the catalytic cysteine of the active site concomitantly to the methionine product. In contrast, experimental studies for the reaction of a number of thiols and sulfoxides in solution did not observe sulfenic acid formation. Only, a disulfide was identified as the final product of the process. The present study has been carried out at the MP2/6-311+G(3d2f,2df,2p)//B3LYP/6-311G(d,p) level of theory. The solvent effect in DMSO has been incorporated using a discrete-continuum model. The calculations provide a basic mechanistic framework that allows discussion on the apparent discrepancy existing between experimental data in solution and in the enzymes. They show that, in the early steps of the process in solution, a sulfurane intermediate is formed the rate of which is limiting. Then, a proton transfer from a second thiol molecule to the sulfurane leads to the formation of either a sulfenic acid or a disulfide though the latter is much more stable than the former. If a sulfenic acid is formed in solution, it should react with a thiol molecule making its experimental detection difficult or even unfeasible.     

Sensitivity of rough differential equations: An approach through the Omega lemma

The Itô map gives the solution of a Rough Differential Equation, a generalization of an Ordinary Differential Equation driven by an irregular path, when existence and uniqueness hold. By studying how a path is transformed through the vector field which is integrated, we prove that the Itô map is Hölder or Lipschitz continuous with respect to all its parameters. This result unifies and weakens the hypotheses of the regularity results already established in the literature.     

Estimation of the bias parameter of the skew random walk and application to the skew Brownian motion

We study the asymptotic property of simple estimator of the parameter of a skew Brownian motion when one observes its positions on a fixed grid—or equivalently of a simple random walk with a bias at 0. This estimator, nothing more than the maximum likelihood estimator, is based only on the number of passages of the random walk at 0. It is very simple to set up, is consistent and is asymptotically mixed normal. We believe that this simplified framework is helpful to understand the asymptotic behavior of the maximum likelihood of the skew Brownian motion observed at discrete times which is studied in a companion paper.     

Reachability analysis of linear systems using support functions

This work is concerned with the algorithmic reachability analysis of continuous-time linear systems with constrained initial states and inputs. We propose an approach for computing an over-approximation of the set of states reachable on a bounded time interval. The main contribution over previous works is that it allows us to consider systems whose sets of initial states and inputs are given by arbitrary compact convex sets represented by their support functions. We actually compute two over-approximations of the reachable set. The first one is given by the union of convex sets with computable support functions. As the representation of convex sets by their support function is not suitable for some tasks, we derive from this first over-approximation a second one given by the union of polyhedrons. The overall computational complexity of our approach is comparable to the complexity of the most competitive available specialized algorithms for reachability analysis of linear systems using zonotopes or ellipsoids. The effectiveness of our approach is demonstrated on several examples.