Search results for "numerical methods"
showing 10 items of 51 documents
Etude numérique d'équations aux dérivées partielles non linéaires et dispersives
2011
Numerical analysis becomes a powerful resource in the study of partial differential equations (PDEs), allowing to illustrate existing theorems and find conjectures. By using sophisticated methods, questions which seem inaccessible before, like rapid oscillations or blow-up of solutions can be addressed in an approached way. Rapid oscillations in solutions are observed in dispersive PDEs without dissipation where solutions of the corresponding PDEs without dispersion present shocks. To solve numerically these oscillations, the use of efficient methods without using artificial numerical dissipation is necessary, in particular in the study of PDEs in some dimensions, done in this work. As stud…
Increasing understanding and confidence in THM simulations of engineered barrier systems
2020
Previous studies on the modelling of coupled thermo-hydro-mechanical (THM) processes in bentonite-based engineered barrier systems (EBSs) showed the sensitivity of the output quantities to changes in the input parameters. To investigate the effects of uncertainties on the modelling results, to improve the understanding of the coupled processes active in the repository near field and to gain in-depth understanding of model uncertainties of different codes, a sensitivity analysis and code comparison of EBS simulations was performed within the Task Force on Engineered Barrier Systems. The analysis included variations in material parameter values, boundary and initial conditions, considered phy…
Finite Element Simulation of Multilayer Metal Cylinder Head Gaskets
2006
ABAQUS gasket elements are an efficient and flexible tool to study gasket applications. Nevertheless the usage of the ABAQUS gasket elements is not limited to gasket analysis, but it provides an effective improvement in structural analysis. The results point out that both the predicted contact pressure and the predicted stress distribution depend on the mesh topology. Several combinations of mesh dimension and topology are investigated. The purpose is the definition of a calculation methodology and the demonstration of the application potentiality. Complex models analysis highlights that the set methodology constitutes a very effective tool for the design and optimization of gasket, cylinde…
Detection of the Lowest-Lying Odd-Parity Atomic Levels in Actinium
2020
Two lowest-energy odd-parity atomic levels of actinium, 7s27pP21/2o, 7s27pP23/2o, were observed via two-step resonant laser-ionization spectroscopy and their respective energies were measured to be 7477.36(4) and 12 276.59(2) cm-1. The lifetimes of these states were determined as 668(11) and 255(7) ns, respectively. In addition, we observed the effect of the hyperfine structure on the line for the transition to P23/2o. These properties were calculated using a hybrid approach that combines configuration interaction and coupled-cluster methods, in good agreement with the experiment. The data are of relevance for understanding the complex atomic spectra of actinides and for developing efficien…
Feedback Classification and Optimal Control with Applications to the Controlled Lotka-Volterra Model
2023
Let M be a σ-compact C^∞ manifold of dimension n ≥ 2 and consider a single-input control system: ẋ(t) = X (x(t)) + u(t) Y (x(t)), where X , Y are C^∞ vector fields on M. We prove that there exist an open set of pairs (X , Y ) for the C^∞ –Whitney topology such that they admit singular abnormal rays so that the spectrum of the projective singular Hamiltonian dynamics is feedback invariant. It is applied to controlled Lotka–Volterra dynamics where such rays are related to shifted equilibria of the free dynamics.
Some Improvements on Relativistic Positioning Systems
2018
[EN] We make some considerations about Relativistic Positioning Systems (RPS). Four satellites are needed to position a user. First of all we define the main concepts. Errors should be taken into account. Errors depend on the Jacobian transformation matrix. Its Jacobian is proportional to the tetrahedron volume whose vertexes are the four tips of the receiver-satellite unit vectors. If the four satellites are seen by the user on a circumference in the sky, then, the Jacobian and the tetrahedron volume vanish. The users we consider are spacecraft. Spacecraft to be positioned cannot be close to a null Jacobian satellites-user configuration. These regions have to be avoided choosing an appropr…
Size-intensive decomposition of orbital energy denominators
2000
We introduce an alternative to Almlöf and Häser’s Laplace transform decomposition of orbital energy denominators used in obtaining reduced scaling algorithms in perturbation theory based methods. The new decomposition is based on the Cholesky decomposition of positive semidefinite matrices. We show that orbital denominators have a particular short and size-intensive Cholesky decomposition. The main advantage in using the Cholesky decomposition, besides the shorter expansion, is the systematic improvement of the results without the penalties encountered in the Laplace transform decomposition when changing the number of integration points in order to control the convergence. Applications will…
Modeling Atmospheric Turbulence via Rapid Distortion Theory: Spectral Tensor of Velocity and Buoyancy
2017
Abstract A spectral tensor model is presented for turbulent fluctuations of wind velocity components and temperature, assuming uniform vertical gradients in mean temperature and mean wind speed. The model is built upon rapid distortion theory (RDT) following studies by Mann and by Hanazaki and Hunt, using the eddy lifetime parameterization of Mann to make the model stationary. The buoyant spectral tensor model is driven via five parameters: the viscous dissipation rate ε, length scale of energy-containing eddies L, a turbulence anisotropy parameter , gradient Richardson number (Ri) representing the local atmospheric stability, and the rate of destruction of temperature variance . Model outp…
The finite element method for the mechanically-based model of non-local continuum
2011
In this paper the finite element method (FEM) for the mechanically based non-local elastic continuum model is proposed. In such a model each volume element of the domain is considered mutually interacting with the others, beside classical interactions involved by the Cauchy stress field, by means of central body forces that are monotonically decreasing with their inter-distance and proportional to the product of the interacting volume elements. The constitutive relations of the long-range interactions involve the product of the relative displacement of the centroids of volume elements by a proper, distance-decaying function, which accounts for the decrement of the long-range interactions as…
Electrical conductance of carbon nanotubes with misaligned ends
2013
During a manufacturing process, when a straight carbon nanotube is placed on a substrate, e.g., production of transistors, its two ends are often misaligned. In this study, we investigate the effects of multiwall carbon nanotubes’ (MWCNTs) outer diameter and chirality on the change in conductance due to misalignment of the two ends. The length of the studied MWCNTs was 120 nm, while the diameters ranged between 4 and 7 nm. A mixed finite element-tight-binding approach was carefully designed to realize reduction in computational time by orders of magnitude in calculating the deformation-induced changes in the electrical transport properties of the nanotubes. Numerical results suggest that ar…