20,252 research outputs found
An optimal penalty method for a hyperbolic system modeling the edge plasma transport in a tokamak
The penalization method is used to take account of obstacles, such as the
limiter, in a tokamak. Because of the magnetic confinement of the plasma in a
tokamak, the transport occurs essentially in the direction parallel to the
magnetic field lines. We study a 1D nonlinear hyperbolic system as a simplified
model of the plasma transport in the area close to the wall. A penalization
which cuts the flux term of the momentum is studied. We show numerically that
this penalization creates a Dirac measure at the plasma-limiter interface which
prevents us from defining the transport term in the usual distribution sense.
Hence, a new penalty method is proposed for this hyperbolic system. For this
penalty method, an asymptotic expansion and numerical tests give an optimal
rate of convergence without spurious boundary layer. Another two-fields
penalization has also been implemented and the numerical convergence analysis
when the penalization parameter tends to reveals the presence of a boundary
layer
Asymptotic-preserving methods for an anisotropic model of electrical potential in a tokamak
A 2D nonlinear model for the electrical potential in the edge plasma in a
tokamak generates a stiff problem due to the low resistivity in the direction
parallel to the magnetic field lines. An asymptotic-preserving method based on
a micro-macro decomposition is studied in order to have a well-posed problem,
even when the parallel resistivity goes to . Numerical tests with a finite
difference scheme show a bounded condition number for the linearised discrete
problem solved at each time step, which confirms the theoretical analysis on
the continuous problem.Comment: 8 page
Regulating nitrogen pollution with risk averse farmers under hidden information and moral hazard.
An experimental study of particle sedimentation using ultrasonic speckle velocimetry
Ultrasonic speckle velocimetry (USV) is a non-invasive technique that allows the measurement of fluid velocity in flow and also that of powders under sedimentation. To improve the USV method, we studied the sedimentation of polymethyl methacrylate and silica particles in water. Then, we built a sedimentation cell and characterized the diameter distribution of the particles. Subsequently, we carried out a specific study to optimize the USV procedure, the signal processing and data analysis. Space and temporal resolution and USV dynamics are also discussed with regard to the optimization conditions. We found that USV is a useful technique to measure velocities between 10−5 and 1 m s−1, using appropriate ultrasonic transducers. The space resolution is fixed by the length and the percentage of overlapping of the analyzed speckle windows and varies between 48 and 536 μm for the different studied particle families. Furthermore, we found that a 0.1 ns temporal resolution
could be obtained after a zero padding signal processing. In the context of our sedimentation experiments, we showed that the velocities measured by USV are in close agreement with those measured by particle image velocimetry and theory
Excitation and resonant enhancement of axisymmetric internal wave modes
To date, axisymmetric internal wave fields, which have relevance to
atmospheric internal wave fields generated by storm cells and oceanic
near-inertial wave fields generated by surface storms, have been experimentally
realized using an oscillating sphere or torus as the source. Here, we use a
novel wave generator configuration capable of exciting axisymmetric internal
wave fields of arbitrary radial form to generate axisymmetric internal wave
modes. After establishing the theoretical background for axisymmetric mode
propagation, taking into account lateral and vertical confinement, and also
accounting for the effects of weak viscosity, we experimentally generate and
study modes of different order. We characterize the efficiency of the wave
generator through careful measurement of the wave amplitude based upon group
velocity arguments. This established, we investigate the ability of vertical
confinement to induce resonance, identifying a series of experimental resonant
peaks that agree well with theoretical predictions. In the vicinity of
resonance, the wave fields undergo a transition to non-linear behaviour that is
initiated on the central axis of the domain and proceeds to erode the wave
field throughout the domain.Comment: 15 pages, 9 figure
Investigation of flow structures involved in sound generation by two- and three-dimensional cavity flows
Proper Orthogonal Decomposition and Stochastic Estimation are combined to shed some light on the link between organized flow structures and noise generation by turbulent flows. Proper Orthogonal Decomposition (POD) is firstly used to extract selected flow events. Based on the knowledge of these structures, the Quadratic Stochastic Estimation of the acoustic pressure field is secondly performed. Both procedures are successively applied to two- and three-dimensional numerical databases of a flow over a cavity. It is demonstrated that POD can extract selected aerodynamic events which can be associated with selected frequencies in the acoustic spectra. Reconstructed acoustic fields also indicate the aerodynamic events which are responsible of the main energy of the noise emission. Such mathematical tools offer new perspectives in analysing flow structures involved in sound generation by turbulent flows and in the experimental design of a flow control strategy
Effective material parameter retrieval for thin sheets: theory and application to graphene, thin silver films, and single-layer metamaterials
An important tool in the field of metamaterials is the extraction of
effective material parameters from simulated or measured scattering parameters
of a sample. Here we discuss a retrieval method for thin-film structures that
can be approximated by a two-dimensional scattering sheet. We determine the
effective sheet conductivity from the scattering parameters and we point out
the importance of the magnetic sheet current to avoid an overdetermined
inversion problem. Subsequently, we present two applications of the sheet
retrieval method. First, we determine the effective sheet conductivity of thin
silver films and we compare the resulting conductivities with the sheet
conductivity of graphene. Second, we apply the method to a cut-wire
metamaterial with an electric dipole resonance. The method is valid for
thin-film structures such as two-dimensional metamaterials and
frequency-selective surfaces and can be easily generalized for anisotropic or
chiral media.Comment: 5 pages, 5 figure
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