Detecting and imaging dielectric objects from real data: A shape-based approach

In this paper we investigate the performance of a shape-reconstruction technique as tested on the ‘Marseille data’. This approach, which is based on a level set technique, offers several advantages compared to other approaches, as for example well-defined boundaries and the incorporation of an intrinsic regularization in the form of a priori assumptions regarding the general structures in the medium. The level set strategy (which is an implicit representation of the shapes) frees us from topological restrictions during this reconstruction process. Our algorithm is aiming at, not only detecting the objects, but simultaneously determining their approximate locations, sizes and dielectric properties. The numerical experiments show the utility of this method.     

Long time behavior of heat kernels of operators with unbounded drift terms

Given a second-order elliptic operator on Rd, with bounded diffusion coefficients and unbounded drift, which is the generator of a strongly continuous semigroup on L²(Rd) represented by an integral, we study the time behavior of the integral kernel and prove estimates on its decay at infinity. If the diffusion coefficients are symmetric, a local lower estimate is also proved.     

Hydrodynamic interaction between a pair of bubbles ascending in shear-thinning inelastic fluids

The interaction of two bubbles rising in shear-thinning inelastic fluids was studied. The experimental results were complemented by numerical simulations conducted with the arbitrary Lagrangian–Eulerian technique. Different initial alignments of the bubble pair were considered. Similarities and differences with the Newtonian fluids were found. The most noticeable difference is the so-called drafting–kissing–tumbling (DKT) process: for the case of bubbles rising in thinning fluids, the tumbling phase does not occur and the pair tends to form a stable doublet. The DKT process is also influenced by the amount of inertia and deformability of the individual bubbles and the initial angle between them. The experimental and numerical results suggest that the thinning wake formed behind the bubbles plays an important role in the speed of the pair and the formation of clusters in thinning fluids.     

Exploring the structural and electronic properties of nitrogen-containing exohydrogenated carbon nanotubes: a quantum chemistry study

Saturated nanotubes consisting of 2–10 and 20 layers of cyclic units of six-membered rings, each one having a pyrimidine-like framework (i.e., –C–C–C–N–C–N–), were studied by quantum chemistry methods using Density Functional Theory (DFT) at the B3LYP/6-31G* level of theory. Four different nanotube (NT) configurations were theoretically studied in this work. They were formed by covalently arranging each layer over the other, with uniform relative rotations of 0°, 60°, 120°, and 180° with respect to each of the layers. Different structures can be created by modulating the relative rotation as layers are added to the main nanostructure. NTs with a relative rotation of 60° showed both greater stabilities and highest potential for catalytic activity. All of them showed band gaps of around 0.2 eV. Charges and other properties can be controlled by appropriate layer arrangement. The studied families of NTs have a very small diameter and could find potential applications in chemistry, physics, and medicine.     

Tracking control of high-performance robots via stabilizing controllers for uncertain systems

The development of flexible manufacturing systems calls for industrial robots characterized by robustness of performance with regard to the variations of the loads and real time specification of the trajectory in the work space. In this paper, the design of a feedback controller guaranteeing such performance is considered. At first, the manipulator dynamics are embedded into a larger class of uncertain dynamical systems and a class of feedback controls is proposed that guarantees uniform ultimate boundedness of the tracking error. Successively, the methodology is specialized for the case of robotic manipulators to track trajectories described in task-oriented coordinates; the proposed control algorithm operates without requiring any explicit coordinate transformation.     

A version of Stöber synthesis enabling the facile prediction of silica nanospheres size for the fabrication of opal photonic crystals

A sol-gel synthesis procedure based on the method proposed by Stöber et al. (J Colloid Interface Sci 26:302–315, 1968) has been adopted for the one-step preparation of mono-dispersed silica nanospheres. An excellent control of the particle diameter over a wide range is obtained by varying the amount of silicon alkoxide only, while the concentration of all other components is kept fixed: this allows the fabrication of artificial opals with a finely tuned and precisely predictable lattice parameter.     

Noise effects of reducing traffic flow through a Spanish city

Towards the end of 1999, the building of one of the main communication routes in Spain was finished, the A-3 motorway, which connects Madrid and Valencia. So far, this road was running through the town Motilla de Palancar, province of Cuenca. The opening of the last section of the motorway on 3 December 1999, re-routes all the traffic passing through the town. This study makes a comparative of the noise levels before and after the opening of the motorway that goes through Motilla de Palancar.     

Asymptotic analysis of the Krawtchouk polynomials by the WKB method

We analyze the Krawtchouk polynomials K _n (x,N,p,q) asymptotically. We use singular perturbation methods to analyze them for N→∞, with appropriate scalings of the two variables x and n. In particular, the WKB method and asymptotic matching are used. We obtain asymptotic approximations valid in the whole domain [0,N]×[0,N], involving some special functions. We give numerical examples showing the accuracy of our formulas.      

On classical electrodynamics of point particles and mass renormalization: Some preliminary results

Apparently, no rigorous results exist for the dynamics of a classical point particle interacting with the electromagnetic field, as described by the standard Maxwell-Lorentz equations. Some results are given here for the corresponding linearized system (dipole approximation) in the presence of a mechanical linear restoring force. We consider a regularization of the system (Pauli-Fierz model), and explicitly solve the Cauchy problem in terms of normal modes. Then we study the limit of the particle's motion as the regularization is removed. We prove that the particle's motion corresponding to smooth initial data for the field has a well-defined limit if mass is renormalized, while the motion is trivial (i.e. the particle does not move at all) if mass is not renormalized. Moreover, the limit particle's motion corresponding to an interesting class of initial data satifies exactly the Abraham-Lorentz-Dirac equation. Finally, for generic initial data the limit motion is runaway.