Noble internal transport barriers and radial subdiffusion of toroidal magnetic lines

Single trajectories of magnetic line motion indicate the persistence of a central protected plasma core, surrounded by a chaotic shell enclosed in a double-sided transport barrier : the latter is identified as being composed of two Cantori located on two successive "most-noble" numbers values of the perturbed safety factor, and forming an internal transport barrier (ITB). Magnetic lines which succeed to escape across this barrier begin to wander in a wide chaotic sea extending up to a very robust barrier (as long as L<1) which is identified mathematically as a robust KAM surface at the plasma edge. In this case the motion is shown to be intermittent, with long stages of pseudo-trapping in the chaotic shell, or of sticking around island remnants, as expected for a continuous time random walk.Comment: TEX file, 84 pages including 32 color figures. Higher quality figures can be seen on the PDF file at http://membres.lycos.fr/fusionbfr/JHM/Tokamap/JSP.pd

Trajectory structures and transport

The special problem of transport in 2-dimensional divergence-free stochastic velocity fields is studied by developing a statistical approach, the nested subensemble method. The nonlinear process of trapping determined by such fields generates trajectory structures whose statistical characteristics are determined. These structures strongly influence the transport.Comment: Latex file 19 pages, includes 12 EPS figures. Extended version of the invited talk at the ITCPP, Santorini, 200

Graphene-coated holey metal films: tunable molecular sensing by surface plasmon resonance

We report on the enhancement of surface plasmon resonances in a holey bidimensional grating of subwavelength size, drilled in a gold thin film coated by a graphene sheet. The enhancement originates from the coupling between charge carriers in graphene and gold surface plasmons. The main plasmon resonance peak is located around 1.5 microns. A lower constraint on the gold-induced doping concentration of graphene is specified and the interest of this architecture for molecular sensing is also highlighted.Comment: 5 pages, 4 figures, Final version. Published in Applied Physics Letter

Statistical properties of an ensemble of vortices interacting with a turbulent field

We develop an analytical formalism to determine the statistical properties of a system consisting of an ensemble of vortices with random position in plane interacting with a turbulent field. We calculate the generating functional by path-integral methods. The function space is the statistical ensemble composed of two parts, the first one representing the vortices influenced by the turbulence and the second one the turbulent field scattered by the randomly placed vortices.Comment: Third version; Important corrections in the normalization for the gas of vortices, et

The asymptotic quasi-stationary states of the two-dimensional magnetically confined plasma and of the planetary atmosphere

We derive the differential equation governing the asymptotic quasi-stationary states of the two dimensional plasma immersed in a strong confining magnetic field and of the planetary atmosphere. These two systems are related by the property that there is an intrinsic constant length: the Larmor radius and respectively the Rossby radius and a condensate of the vorticity field in the unperturbed state related to the cyclotronic gyration and respectively to the Coriolis frequency. Although the closest physical model is the Charney-Hasegawa-Mima (CHM) equation, our model is more general and is related to the system consisting of a discrete set of point-like vortices interacting in plane by a short range potential. A field-theoretical formalism is developed for describing the continuous version of this system. The action functional can be written in the Bogomolnyi form (emphasizing the role of Self-Duality of the asymptotic states) but the minimum energy is no more topological and the asymptotic structures appear to be non-stationary, which is a major difference with respect to traditional topological vortex solutions. Versions of this field theory are discussed and we find arguments in favor of a particular form of the equation. We comment upon the significant difference between the CHM fluid/plasma and the Euler fluid and respectively the Abelian-Higgs vortex models.Comment: Latex 126 pages, 7 eps figures included. Discussion on various forms of the equatio

On the ill/well-posedness and nonlinear instability of the magneto-geostrophic equations

We consider an active scalar equation that is motivated by a model for magneto-geostrophic dynamics and the geodynamo. We prove that the non-diffusive equation is ill-posed in the sense of Hadamard in Sobolev spaces. In contrast, the critically diffusive equation is well-posed. In this case we give an example of a steady state that is nonlinearly unstable, and hence produces a dynamo effect in the sense of an exponentially growing magnetic field.Comment: We have modified the definition of Lipschitz well-posedness, in order to allow for a possible loss in regularity of the solution ma

Towards Classification of Phase Transitions in Reaction--Diffusion Models

Equilibrium phase transitions are associated with rearrangements of minima of a (Lagrangian) potential. Treatment of non-equilibrium systems requires doubling of degrees of freedom, which may be often interpreted as a transition from the ``coordinate'' to the ``phase'' space representation. As a result, one has to deal with the Hamiltonian formulation of the field theory instead of the Lagrangian one. We suggest a classification scheme of phase transitions in reaction-diffusion models based on the topology of the phase portraits of corresponding Hamiltonians. In models with an absorbing state such a topology is fully determined by intersecting curves of zero ``energy''. We identify four families of topologically distinct classes of phase portraits stable upon RG transformations.Comment: 14 pages, 9 figure

Prototyping the Semantics of a DSL using ASF+SDF: Link to Formal Verification of DSL Models

A formal definition of the semantics of a domain-specific language (DSL) is a key prerequisite for the verification of the correctness of models specified using such a DSL and of transformations applied to these models. For this reason, we implemented a prototype of the semantics of a DSL for the specification of systems consisting of concurrent, communicating objects. Using this prototype, models specified in the DSL can be transformed to labeled transition systems (LTS). This approach of transforming models to LTSs allows us to apply existing tools for visualization and verification to models with little or no further effort. The prototype is implemented using the ASF+SDF Meta-Environment, an IDE for the algebraic specification language ASF+SDF, which offers efficient execution of the transformation as well as the ability to read models and produce LTSs without any additional pre or post processing.Comment: In Proceedings AMMSE 2011, arXiv:1106.596

Chemotherapy-Response Monitoring of Breast Cancer Patients Using Quantitative Ultrasound-Based Intra-Tumour Heterogeneities

© 2017 The Author(s). Anti-cancer therapies including chemotherapy aim to induce tumour cell death. Cell death introduces alterations in cell morphology and tissue micro-structures that cause measurable changes in tissue echogenicity. This study investigated the effectiveness of quantitative ultrasound (QUS) parametric imaging to characterize intra-tumour heterogeneity and monitor the pathological response of breast cancer to chemotherapy in a large cohort of patients (n = 100). Results demonstrated that QUS imaging can non-invasively monitor pathological response and outcome of breast cancer patients to chemotherapy early following treatment initiation. Specifically, QUS biomarkers quantifying spatial heterogeneities in size, concentration and spacing of acoustic scatterers could predict treatment responses of patients with cross-validated accuracies of 82 ± 0.7%, 86 ± 0.7% and 85 ± 0.9% and areas under the receiver operating characteristic (ROC) curve of 0.75 ± 0.1, 0.80 ± 0.1 and 0.89 ± 0.1 at 1, 4 and 8 weeks after the start of treatment, respectively. The patients classified as responders and non-responders using QUS biomarkers demonstrated significantly different survivals, in good agreement with clinical and pathological endpoints. The results form a basis for using early predictive information on survival-linked patient response to facilitate adapting standard anti-cancer treatments on an individual patient basis