Tri-polarized spectrum sensing based on an experimental outdoor-to-indoor cognitive-radio scenario

Compared to classical spatially separated multiple antenna system, cross-polarized co-located antenna systems are an interesting way to reduce equipment size while reducing the inter-antenna correlation. In this paper the spectrum sensing of a Cognitive Radio (CR) system taking advantage of polarization diversity under Rayleigh fading is investigated and compared to an equivalent system using spatial diversity. This analysis is based on a theoretical formulation applied to a real-world scenario. For this purpose, an outdoor-to-indoor measurement campaign at a frequency of 3.5 GHz is realized, where an indoor secondary user senses the signals received from an outdoor primary base station. The signals received at each antenna are first combined and then applied to an energy detector. The theoretical expressions are simulated in the measurement context. The detection probability behavior as a function of distance between the Primary Transmitter (PTx) and the Secondary Terminal (STE) and the inter-antenna correlation effect on the sensing performance are studied.     

Molecular Frame Photoemission： Probe of the Photoionization Dynamics for Molecules in the Gas Phase

Molecular frame photoemission is a very sensitive probe of the photoionization （PI） dynamics of molecules. This paper reports a comparative study of non-resonant and resonant photoionization of D2 induced by VUV circularly polarized synchrotron radiation at SOLEIL at the level of the molecular frame photoelectron angular distributions （MFPADs）. We use the vector correlation method which combines imaging and time-of-flight resolved electron-ion coincidence techniques, and a generalized formalism for the expression of the Ⅰ（χ, θe, Фe） MFPADs, where χ is the orientation of the molecular axis with respect to the light quantization axis and （θe, Фe） the electron emission direction in the molecular frame. Selected MFPADs for a molecule aligned parallel or perpendicular to linearly polarized light, or perpendicular to the propagation axis of circularly polarized light, are presented for dissociative photoionization （DPI） of D2 at two photon excitation energies, hv=19 eV, where direct PI is the only channel opened, and hv=32.5 eV, i.e. in the region involving resonant excitation of Q1 and Q2 doubly excited state series. We discuss in particular the properties of the circular dichroism characterizing photoemission in the molecular frame for direct and resonant PI. In the latter case, a remarkable behavior is observed which may be attributed to the interference occurring between undistinguishable autoionization decay channels.     

Measurement accuracy of a mono-fiber optical probe in a bubbly flow

The measurement accuracy of a mono-fiber optical probe is studied experimentally using isolated bubbles rising freely in a still liquid. The dwell time of the probe tip within the gas phase, which is obtained from both the optical probe signal and high-speed visualization, is compared with the value expected for a non-perturbed bubble. The difference originates mainly from the intrusive nature of the optical probe, which modifies the bubble behavior when it comes into contact with the probe tip. This interaction increases the dwell time if the bubble is pierced by the probe near its pole, and shortens it for piercing near the equator. The mean dwell time, obtained by averaging for various piercing locations, is shortened and the local void fraction indicated by the probe is thus underestimated. It is shown that the void fraction error can be correlated with a modified Weber number, and this correlation is helpful for sensor selection and for uncertainty estimate. In addition, the distribution of gas dwell time usually differs from the response expected for an ideal probe. This deviation results from the dependence of the dwell time error on the piercing location. The dwell time distribution can be used to infer the dependence of the dwell time on the piercing location. Finally, the deformation of long fibers during the bubble-probe interaction significantly increases the measurement error. Observed results are consistent with data of Andreotti (2009), which were measured in an airlift flow, suggesting that present results are applicable also to the case of moving liquid. Conclusions of this study could be applied also to conductivity probes or more generally to the interaction of a bubble with any kind of thin, intrusive sensor or fiber.     

A moment method for splashing and evaporation processes of polydisperse sprays

A new moment method for the modelling of polydisperse sprays is proposed that simultaneously takes into account the dispersion in droplet size and droplet velocity. For the derivation of this Eulerian method the kinetic spray equation is used which constitutes a partial differential equation for the probability density function of droplets. To reduce the complex kinetic spray equation to a form that can be managed with the available numerical procedures, moment transforms with respect to the droplet velocity and the droplet size are conducted. The resulting moment equations are closed by choosing an approximate probability density function which applies to polydisperse sprays. The method is successfully tested for configurations in which a polydisperse spray is either splashed, evaporated or effected by a Stokes drag force. The tests are organised in such a way that crossing of two spray distributions is always included. The new method is able to capture the polydisperse nature of sprays as well as the bi-(or multi-) modal character of the droplet velocity distribution function, for example, when droplets cross each other.     

Sobolev Periodic Solutions of Nonlinear Wave Equations in Higher Spatial Dimensions

We prove the existence of Cantor families of periodic solutions for nonlinear wave equations in higher spatial dimensions with periodic boundary conditions. We study both forced and autonomous PDEs. In the latter case our theorems generalize previous results of Bourgain to more general nonlinearities of class C ^k and assuming weaker non-resonance conditions. Our solutions have Sobolev regularity both in time and space. The proofs are based on a differentiable Nash–Moser iteration scheme, where it is sufficient to get estimates of interpolation-type for the inverse linearized operators. Our approach works also in presence of very large “clusters of small divisors”.     

Flow-induced polymer degradation probed by a high throughput microfluidic set-up

A complex fluid submitted to strong flows can endure irreversible changes in its structure. This is the case for long chain polymer additives that are commonly used as viscosity enhancers in industry, notably for oil recovery. These polymers break in solution when submitted to high deformation rates, eventually causing a serious viscosity loss. This problem of practical importance is though difficult to handle from a fundamental point of view given its complexity. We introduce here a new tool, based on microfluidic technology, for the screening of the degradation of solutions in the model situation of the flow through a constriction. We integrate two functions in a single set-up, a micro-fabricated constriction and an on-chip viscosimeter. This tool enables us to probe rapidly the viscosity loss imparted by flowing through the constriction at a given flow rate. Thanks to microfluidics, the sample preparation and measurement time are significantly lower than those implied by classical measurement protocols (reduction by up to two orders of magnitude). In addition, confinement provides control of the flow in terms of inertia. To illustrate the potential of this approach in a screening perspective, we use this tool to study the degradation of a series of semi-dilute aqueous solutions of PEO of varying molecular weights and concentrations. For each solution we identify a threshold flow rate for polymer degradation. The corresponding critical deformation rate decreases with molecular weight and concentration, as expected (the mass dependence is in line with previous reports and theories for dilute solutions). In addition we characterize the viscosity loss for larger deformation rates and find that, despite the polydispersity of our solutions, the observations for the various solutions can be roughly recast on a master curve by renormalization of the imposed deformation rates according to a law $M_w^{?1.7\pm 03}{c}^{?0.7\pm 03}$.     

The Manifold-Valued Dirichlet Problem for Symmetric Diffusions

Harmonic maps between two Riemannian manifolds M and N are often constructed as energy minimizing maps. This construction is extended for the Dirichlet problem to the case where the Riemannian energy functional on M is replaced by a more general Dirichlet form. We obtain weakly harmonic maps and prove that these maps send the diffusion to N-valued martingales. The basic tools are the reflected Dirichlet space and the stochastic calculus for Dirichlet processes.