8,390 research outputs found
Coherent anti-Stokes Raman spectroscopy (CARS) selection rules, depolarization ratios and rotational structure
No full textBy putting the non-linear susceptibility tensors in irreducible spherical form it is found that orientation averaging, selection rules, and the angular dependence of intensity on field polarizations all follow in a straightforward way. These spherical tensor techniques are used to treat coherent anti-Stokes Raman scattering (CARS) in detail and a comparison is made with conventional Raman scattering. The selection rules for both processes are shown to be the same. The paper concludes with a brief discussion of the rotational structure in CARS
Drop deformation in stokes flow through converging channels
No full textThis work presents an application of a direct BEM formulation for drop
deformation and interaction in Stokes flows through converging channels. Parametric
studies are conducted to investigate the effect, on drop deformation, of the channel’s
convergence ratio, the drop-fluid viscosity ratio, the interfacial tension and the initial
relative position of the drops
Large-scale adaptive mantle convection simulation
No full textA new generation, parallel adaptive-mesh mantle convection code, Rhea, is described and benchmarked. Rhea targets large-scale mantle convection simulations on parallel computers, and thus has been developed with a strong focus on computational efficiency and parallel scalability of both mesh handling and numerical solvers. Rhea builds mantle convection solvers on a collection of parallel octree-based adaptive finite element libraries that support new distributed data structures and parallel algorithms for dynamic coarsening, refinement, rebalancing and repartitioning of the mesh. In this study we demonstrate scalability to 122 880 compute cores and verify correctness of the implementation. We present the numerical approximation and convergence properties using 3-D benchmark problems and other tests for variable-viscosity Stokes flow and thermal convection
Hydrostatic Stokes Equations With Non-smooth Date For Mixed Boundary Conditions
No full textThe main subject of this work is to study the concept of very weak solution for the hydrostatic Stokes system with mixed boundary conditions (non-smooth Neumann conditions on the rigid surface and homogeneous Dirichlet conditions elsewhere on the boundary). In the Stokes framework, this concept has been studied by Conca [Rev. Mat. Apl. 10 (1989)] imposing non-smooth Dirichlet boundary conditions. In this paper, we introduce the dual problem that turns out to be a hydrostatic Stokes system with non-free divergence condition. First, we obtain strong regularity for this dual problem (which can be viewed as a generalisation of the regularity results for the hydrostatic Stokes system with free divergence condition obtained by Ziane [Appl. Anal. 58 (1995)]). Afterwards, we prove existence and uniqueness of very weak solution for the (primal) problem. As a consequence of this result, the existence of strong solution for the non-stationary hydrostatic Navier-Stokes equations is proved, weakening the hypothesis over the time derivative of the wind stress tensor imposed by Guillén-González, Masmoudi and Rodríguez-Bellido [Differential Integral Equations 50 (2001)]. © 2004 Elsevier SAS. All rights reserved.216807826Amrouche, C., Girault, V., Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension (1994) Czechoslovak Math. J., 44 (119), pp. 109-140Azérad, P., Guillén, F., Mathematical justification of the hydrostatic approximation in the Primitive Equations of qeophysical fluid dynamics (2001) SIAM J. Math. Anal., 33 (4), pp. 847-859Besson, O., Laydi, M.R., Some estimates for the anisotropic Navier-Stokes equations and for the hydrostatic approximation (1992) M2AN-Mod. Math. Ana. Nume., 7, pp. 855-865Cattabriga, L., Sur un problema al contorno relativo al sistema di equazioni di Stokes (1961) Rend. Mat. Sem. Univ. Padova, 31, pp. 308-340Chacón, T., Guillén, F., An intrinsic analysis of existence of solutions for the hydrostatic approximation of the Navier-Stokes equations (2000) C. R. Acad. Sci. Paris, Série I, 330, pp. 841-846Conca, C., Stokes equations with non-smooth data (1989) Revista de Matemáticas Aplicadas, 10, pp. 115-122Girault, V., Raviart, P.A., (1986) Finite Element Methods for Navier-Stokes Equations, , Berlin: Springer-VerlagGuillén-González, F., Rodríguez-Bellido, M.A., On the strong solutions of the Primitive Equations in 2D domains (2002) Nonlin. Anal., 50, pp. 621-646Guillén-González, F., Masmoudi, N., Rodríguez-Bellido, M.A., Anisotropic estimates and strong solutions of the Primitive Equations (2001) Differential Integral Equations, 14 (11), pp. 1381-1408Lewandowski, R., (1997) Analyse Mathématique et Océanographie, , MassonLions, J.L., Magenes, E., (1969) Problèmes aux Limites Non Homogènes et Applications, 1. , Paris: DunodLions, J.L., Temam, R., Wang, S., New formulation of the primitive equations of the atmosphere and applications (1992) Nonlinearity, 5, pp. 237-288Lions, J.L., Temam, R., Wang, S., On the equations of the large scale ocean (1992) Nonlinearity, 5, pp. 1007-1053Pedlosky, J., (1987) Geophysical Fluid Dynamics, , Berlin: Springer-VerlagTemam, R., (1977) Navier-Stokes Equations: Theory and Numerical Analysis, , Amsterdam: North HollandZiane, M., Regularity results for Stokes type systems (1995) Appl. Anal., 58, pp. 263-29
Deep anisotropic dry etching of silicon microstructures by high-density plasmas
No full textThis thesis deals with the dry etching of deep anisotropic microstructures in monocrystalline silicon by high-density plasmas. High aspect ratio trenches are necessary in the fabrication of sensitive inertial devices such as accellerometers and gyroscopes. The etching of silicon in fluorine-based plasmas is isotropic. To obtain anisotropy the addition of sidewall passivation is necessary. This is achieved with both oxygen passivation at low temperatures and fluorocarbon passivation at room temperature. A quantitative approach was pursued to explain the etching mechanism. The etch results were analysed using the measured plasma species fluxes and the surface composition. Moreover, the transport of the plasma species in narrow anisotropic structures is a fundamental factor determining the etch rate and the profile evolution. The experimental methods such as the etching equipment, plasma diagnostics, surface analysis and sample preparation are described in chapter 2. Three etching processes were investigated: the cryogenic etching process with oxygen passivation at low temperatures, the Bosch process with fluorocarbon passivation at room temperature and the novel triple pulse process that was developed in our laboratory. The polymer deposition mechanism and the characteristic role of the ions are also explained. The cryogenic etching process is discussed in chapter 3. Fluorine radicals, oxygen radicals and ion bombardment are responsible for the three main sub-processes, that is, etching, sidewall passivation and depassivation of the trench bottom, respectively. Etching experiments with an extremely low ion-to-radical flux ratio were used to reveal the etching mechanism. Crystal orientation dependent etching leading to Si(111) crystal facets is observed in a surface kinetics controlled regime. By varying the plasma conditions it is possible to adjust the etching mechanism from fluorine-limited to ion-limited. Controlled etching is obtained because the etching is tuned from aspect ratio dependent in the fluorine-limited domain to aspect ratio independent in the ion-limited domain. The transport of radicals in high aspect ratio trenches is an important limiting factor and was investigated with special structures. The etch results are described by an analytic model that is based on the surface site balance of fluorine and oxygen radicals. The results are further explained with a Monte Carlo simulation model. The Bosch process is clarified in chapter 4. The anisotropy of the etched structures is controlled by balancing the etching and passivation pulse. However, the maximal obtainable aspect ratio is limited by convergence of the trench sidewalls due to excessive passivation. The maximal obtainable aspect ratio increases if the ion-to-radical flux ratio increases. The transport of ions is an important limiting factor in the depassivation of the bottom of the trench. Divergence of the ion beam leads to a reduction of the ion flux, so that the fluorocarbon passivation is insufficiently removed near the base of the sidewalls. The average ion angle was measured and correlated to the maximal obtainable aspect ratio. The Bosch process was improved at the depassivation side with the triple pulse process and at the passivation side with preferential sidewall deposition. The triple pulse process that is described in chapter 5 has the aim to improve the depassivation in deep trenches. The three main sub-processes are decoupled using a separate depassivation pulse directly after the etching and passivation pulses. The fluorocarbon passivation is efficiently removed with low-pressure, high-density, oxygen-based plasmas. The investigated plasma chemistries include O2, CO2 and SO2. The triple pulse process leads to better profile control with a straight trench bottom. However, the maximal obtainable aspect ratio is comparable to the Bosch process because a larger etch depth and a small lateral etch cancel out. The polymer deposition mechanism is treated in chapter 6 with the aim to understand the fluorocarbon passivation in deep trenches. The deposition on plane surfaces and on special structures was investigated to distinguish between the radical-induced and ion-enhanced components. A simple analytical model, which explains the main deposition characteristics, was developed. Preferential sidewall deposition is obtained for higher ion fluxes and higher bias voltages where sputtering plays an important role. In this case no fluorocarbon passivation has to be removed from the bottom of the trench. The trench profile was optimised in the Bosch process by tuning the bias voltage during etching and passivation independently. It resulted in perfectly anisotropic trenches but the maximal obtainable aspect ratio was still limited by a small lateral etch. The characteristic role of the ions in the etching mechanism is explained in chapter 7. Ion-induced etching of both SiC in a SF6-O2 plasma and Si in a Cl2 plasma were investigated. The impact of the ions on the profile evolution can be examined more explicitly because spontaneous chemical reactions are absent for these plasma-material systems. The etching mechanism varies from fluorine-limited to ion-limited depending on the radical-to-ion flux ratio. Microtrenches are observed for an ion-limited etching mechanism. Fluorine-limited SiC etching is aspect ratio dependent in contrast to ion-limited SiC etching, which is aspect ratio independent. The etching of high aspect ratio SiC structures is limited by the positive sidewall taper. This is presumably caused by insufficient removal of the thin fluorocarbon layer on the surface. Si etching in a Cl2 plasma is always aspect ratio independent in contrast to SiC etching because of the low reaction probability. The conclusions and recommendations of this thesis are given in chapter 8.Applied Science
Stationary Stokes, Oseen and Navier-Stokes equations with singular data
No full text56 pagesThe concept of very weak solution introduced by Giga [20] for the Stokes equations has been hardly studied in the last years for either the Navier-Stokes equations or the Navier-Stokes type equations. We treat the stationary Stokes, Oseen and Navier-Stokes system in the case of a bounded open set, connected of class C1;1 of R3. Taking the duality method introduced by Lions & Magenes in [28] and Giga in [20] up again for open sets of class C1 (see also Necas [31] chapter 4 that consider the Hilbertian case p = 2 for general elliptic operators), we give a simpler proof of the existence of a very weak solution for stationary Oseen and Navier-Stokes equations when data are not regular enough, based on density arguments and a functional framework adequate for de¯ning more rigourously the traces of non regular vector ¯elds. In the stationary Navier-Stokes case, the results will be valid for external forces non necessarily small which let us extend the uniqueness class of solutions for these equations. Considering more regular data, regu- larity results in fractional Sobolev spaces will also be discussed for the three systems. All these results can be extended to other dimensions
Assessment of Models for Near Wall Behavior and Swirling Flows in Nuclear Reactor Sub-system Simulations
No full textAccurate simulation of turbulence remains one of the most challenging problems in nuclear reactor analysis and design. Due to limitations in computing resources, Reynolds averaged Navier Stokes models (RANS) continue to play an important role in reactor simulations. The Consortium for advanced simulations of light water reactors (CASL) is a Department of Energy technology hub that is investing in research and developmentof a state-of-the-art computational fluid dynamics capabilityto meet the challenges of turbulent simulation of nuclear reactors. In this presentation, we assess several RANS eddy viscosity models appropriate for single-phase incompressible turbulent flows. Specifically, we compare the single equation Splalart-Allmaras to several variations of the model. The assessment takes into consideration elements of full system reactor cores such as complex geometries, heterogeneous meshes, swirling flow, near wall flow behavior, heat transfer and robustness issues. The goal of this strategically oriented assessment is to provide an accurate and robust turbulent simulation capability for the CASL community. Metrics of performance will be constructed by comparing different models on a strategically chosen set of problems that represent reactor core sub-systems
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Observation of anomalous low J-value Stokes and anti-Stokes lines in stimulated rotational Raman scattering over long air paths
No full textAnomalous low-J-value Stokes and anti-Stokes lines in stimulated rotational Raman scattering are observed with large Fresnel number, linearly polarized beams. Forced light scattering at the rotational intermodulation frequency is also observed. Dynamics of the Stokes-anti-Stokes coupling will be discussed. 5 refs., 2 figs
Improved regularity criterion for the 3D Navier–Stokes equations via the gradient of one velocity component
No full textIn this paper, we study regularity of weak solutions to the incompressible Navier–Stokes equations in R3× (0 , T). The main goal is to establish the regularity criterion via the gradient of one velocity component in some multiplier spaces. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG
Very weak solutions for the Stokes equations
No full text6 pagesThe concept of very weak solution introduced by Giga [9] for the Stokes equations has been intensively studied in the last years for the Navier-Stokes equations. However, a more rigorous study about the existence of traces for non regular vector fields is necessary in order to make a precise extension of the Stokes result to the Navier-Stokes case. Such study and a new and simpler proof of the existence of very weak solution for Stokes equations are made, based on density arguments and an adequate functional framework. We also obtain regularity results in fractional Sobolev spaces. All these results are obtained in the case of a bounded open set, connected of class of and can be extended to Laplace's equation and to other dimensions
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