Search results for "numerical [Methods]"
showing 10 items of 500 documents
A fully adaptive wavelet algorithm for parabolic partial differential equations
2001
We present a fully adaptive numerical scheme for the resolution of parabolic equations. It is based on wavelet approximations of functions and operators. Following the numerical analysis in the case of linear equations, we derive a numerical algorithm essentially based on convolution operators that can be efficiently implemented as soon as a natural condition on the space of approximation is satisfied. The algorithm is extended to semi-linear equations with time dependent (adapted) spaces of approximation. Numerical experiments deal with the heat equation as well as the Burgers equation.
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.
Avoiding strange attractors in efficient parametric families of iterative methods for solving nonlinear problems
2019
[EN] Searching zeros of nonlinear functions often employs iterative procedures. In this paper, we construct several families of iterative methods with memory from one without memory, that is, we have increased the order of convergence without adding new functional evaluations. The main aim of this manuscript yields in the advantage that the use of real multidimensional dynamics gives us to decide among the different classes designed and, afterwards, to select its most stable members. Moreover, we have found some elements of the family whose behavior includes strange attractors of different kinds that must be avoided in practice. In this sense, Feigenbaum diagrams have resulted an extremely …
Numerical simulation of reciprocating turbulent flow in a plane channel
2009
Direct numerical simulation results were obtained for oscillatory flow with zero time mean (reciprocating flow) in a plane channel using a finite volume method, Crank-Nicolson time stepping and central approximation of the advection terms. A pressure gradient varying co-sinusoidally in time was imposed as the forcing term, and its frequency and amplitude were made to vary so as to span a range of regimes from purely laminar to fully turbulent. For the limiting cases of reciprocating laminar flow and steady-state turbulent flow, numerical results were validated against analytical solutions and classic experimental literature data, respectively. For general reciprocating flows, predictions we…
Three-dimensional linear stability analysis of the flow in a liquid spherical droplet driven by an alternating magnetic field
2003
The paper presents a numerical stability analysis of the flow driven by an alternating (AC) magnetic field in an electromagnetically levitated liquid metal droplet. The basic axisymmetric flow is found to become unstable at Reynolds numbers in the order of 100. The critical Reynolds number Rec and the corresponding most unstable azimuthal wave number m are found for several configurations of the magnetic field depending on the skin-depth d. For a uniform external AC magnetic field the azimuthal wave number of the most unstable mode is m=3. An additional steady (DC) magnetic field imposed along the axis of symmetry increases the stability of the flow.
A study of turbulent heat transfer in curved pipes by numerical simulation
2013
Abstract Turbulent heat transfer in curved pipes was studied by numerical simulation. Two curvatures δ (pipe radius a/curvature radius c) were considered, 0.1 and 0.3; results were also obtained for a straight pipe (δ = 0) for comparison purposes. A tract of pipe 5 diameters in length was chosen as the computational domain and was discretized by finite volume multiblock-structured grids of ∼5.3 × 106 hexahedral cells. Fully developed conditions were assumed; the friction velocity Reynolds number was 500, corresponding to bulk Reynolds numbers between 12 630 and ∼17 350 according to the curvature, while the Prandtl number was 0.86 (representative of saturated liquid water at 58 bar). Simulat…
Momentum transport and bed shear stress distribution in a meandering bend: Experimental analysis in a laboratory flume
2015
The paper concerns the mechanisms underlying the distribution of the bed shear stress in meandering bends. Literature indicates that cross-stream circulation strongly affects the redistribution of the downstream velocity, but the feedback between them is still poorly understood. The aim of this paper is to gain some insight into how the momentum transport by cross-stream circulation contributes to the bed shear stress redistribution. Experimental analysis, based on a detailed dataset collected in a large-amplitude meandering laboratory flume, is presented. From these data an evaluation is made of the terms in the depth-averaged momentum equations and the analysis is especially devoted to te…
Revealing the pace of river landscape evolution during the Quaternary: recent developments in numerical dating methods
2016
During the last twenty years, several technical developments have considerably intensified the use of numerical dating methods for the Quaternary. The study of fluvial archives has greatly benefited from these enhancements, opening new dating horizons for a range of archives at distinct time scales and thereby providing new insights into previously unanswered questions. In this contribution, we separately present the state of the art of five numerical dating methods that are frequently used in the fluvial context: radiocarbon, Luminescence, Electron Spin Resonance (ESR), 230Th/U and terrestrial cosmogenic nuclides (TCN) dating. We focus on the major recent developments for each technique th…
Analytic CCSD(T) second derivatives
1997
A general-purpose implementation of analytic CCSD(T) second derivatives is presented. Its applicability is demonstrated by calculations of vibration-rotation interaction constants for the astrophysically important molecule cyclopropenylidene (C3H2) in which the required cubic force constants have been determined by numerical differentiation of analytically evaluated second derivatives of the energy.