Sensitivity indices for multivariate outputs

We define and study a generalization of Sobol sensitivity indices for the case of a vector output.     

A version of Hörmander’s theorem for the fractional Brownian motion

It is shown that the law of an SDE driven by fractional Brownian motion with Hurst parameter greater than 1/2 has a smooth density with respect to Lebesgue measure, provided that the driving vector fields satisfy Hörmander’s condition. The main new ingredient of the proof is an extension of Norris’ lemma to this situation.     

Stationary Analysis of a Fluid Queue Driven by Some Countable State Space Markov Chain

Motivated by queueing systems playing a key role in the performance evaluation of telecommunication networks, we analyze in this paper the stationary behavior of a fluid queue, when the instantaneous input rate is driven by a continuous-time Markov chain with finite or infinite state space. In the case of an infinite state space and for particular classes of Markov chains with a countable state space, such as quasi birth and death processes or Markov chains of the G/M/1 type, we develop an algorithm to compute the stationary probability distribution function of the buffer level in the fluid queue. This algorithm relies on simple recurrence relations satisfied by key characteristics of an auxiliary queueing system with normalized input rates.      

Exciton swapping in a twisted graphene bilayer as a solid-state realization of a two-brane model

It is shown that exciton swapping between two graphene sheets may occur under specific conditions. A magnetically tunable optical filter is described to demonstrate this new effect. Mathematically, it is shown that two turbostratic graphene layers can be described as a “noncommutative” two-sheeted (2 +?1)-spacetime thanks to a formalism previously introduced for the study of braneworlds in high energy physics. The Hamiltonian of the model contains a coupling term connecting the two layers which is similar to the coupling existing between two braneworlds at a quantum level. In the present case, this term is related to a K-K ^′ intervalley coupling. In addition, the experimental observation of this effect could be a way to assess the relevance of some theoretical concepts of the braneworld hypothesis.     

Finite size effects on structure and magnetism in mass-selected CoPt nanoparticles

In this paper, the one-way absorption property in one-dimensional dielectric/metal photonic crystal structure with a dielectric defect layer is studied. The effects of incident angle and state of polarization on one-way absorption behaviour of the anti-resonant (AR) mode are investigated. The normally incident wave from left to right propagation is totally allowed to penetrate to the structure but right to left propagation totally reflected at the same wavelength. It is found that, with increasing of the incident angle, the AR mode shifts to the lower wavelengths and its intensity decreases. Simultaneously, another AR mode with reversed one-way property appears at higher wavelength. The one-way behaviour on absorption is observed at the both states of polarizations but is localized on different wavelengths. Those effects, are suggesting that the proposed structure can be used as a direction sense polarization splitter or reflector/antireflector device.     

Boson Mott insulators at finite temperatures

We discuss the finite temperature properties of ultracold bosons in optical lattices in the presence of an additional, smoothly varying potential, as in current experiments. Three regimes emerge in the phase diagram: a low-temperature Mott regime similar to the zero-temperature quantum phase, an intermediate regime where Mott insulator features persist, but where superfluidity is absent, and a thermal regime where features of the Mott insulator state have disappeared. We obtain the thermodynamic functions of the Mott phase in the latter cases. The results are used to estimate the temperatures achieved by adiabatic loading in current experiments. We point out the crucial role of the trapping potential in determining the final temperature, and suggest a scheme for further cooling by adiabatic decompression.     

Direct observation of a "devil's staircase" in wave-particle interaction

We report the experimental observation of a "devil's staircase" in a time-dependent system considered as a paradigm for the transition to large-scale chaos in the universality class of Hamiltonian systems. A test electron beam is used to observe its non-self-consistent interaction with externally excited wave(s) in a traveling wave tube (TWT). A trochoidal energy analyzer records the beam energy distribution at the output of the interaction line. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The resonant velocity domain associated to a single wave is observed, as well as the transition to large-scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a "devil's staircase" behavior for increasing excitation amplitude, due to the nonlinear forcing by the second wave on the pendulum-like motion of a charged particle in one electrostatic wave.     

Quasi-solitonic behavior of self-written waveguides created by photopolymerization

We investigated the condition of unique self-written channel and multichannel propagation inside bulk photopolymerizable materials. Light was introduced in the medium by a single-mode optical fiber. At a very low beam power of 5 muW , a unique uniform-channel waveguide without any broadening was obtained by polymerization. When the input power is increased to 100 muW , the guide becomes chaotic and multichannel. We connected two fibers separated by a 1-cm distance. The results open the door to studies of the optical and electro-optical properties of photopolymerized guides doped by nonlinear optical chromophores and to possible applications in integrated optical devices.     

Dispersive estimates and the 2D cubic NLS equation

We prove that the initial value problem for the 2D cubic semi-linear Schrödinger equation is well-posed in the Besov space B _0, ^∞2 (?²). For this, we rely on some new dispersive inequalities derived from bilinear restriction theorems.