Search results for "approximation"
showing 10 items of 818 documents
Analysis and control of a seven mode truncation of the Kolmogorov flow with drag.
2008
The transition from laminar to chaotic motion in a viscous fluid flow is investigated by analyzing a seven dimensional dynamical system obtained by a truncation of the Fourier modes for the Kolmogorov flow with drag friction. Analytical expressions of the bifurcation curves are obtained and a sequence of period doubling bifurcations are numerically observed as the Reynoplds number is increased for fixed values of the drag parameter. An adaptive stabilization of the system trajectories to an equilibrium point or to a periodic orbit is obtained through a model reference approach which makes the control global.
Linear Response Theory with finite-range interactions
2021
International audience; This review focuses on the calculation of infinite nuclear matter response functions using phenomenological finite-range interactions, equipped or not with tensor terms. These include Gogny and Nakada families, which are commonly used in the literature. Because of the finite-range, the main technical difficulty stems from the exchange terms of the particle–hole interaction. We first present results based on the so-called Landau and Landau-like approximations of the particle–hole interaction. Then, we review two methods which in principle provide numerically exact response functions. The first one is based on a multipolar expansion of both the particle–hole interactio…
Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the…
2021
Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to self-pulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around classical solutions do not reach a quantum-statistical stationary state, which prevents adopting the simple and reliable methods used for stationary quantum systems. Here we put forward a general and efficient method to compute two-time correlations and corresponding spectral densities of time-periodic open quantum systems within the usual linearized (Gaussian) approximation for their dynamics. Using Floquet theory we show how the quantum Langevin equations for…
Two-laser multiphoton adiabatic passage in the frame of the Floquet theory. Applications to (1+1) and (2+1) STIRAP
1998
We develop an adiabatic two-mode Floquet theory to analyse multiphoton coherent population transfer in N-level systems by two delayed laser pulses, which is a generalization of the three-state stimulated Raman adiabatic passage (STIRAP). The main point is that, under conditions of non-crossing and adiabaticity, the outcome and feasibility of a STIRAP process can be determined by the analysis of two features: (i) the lifting of degeneracy of dressed states at the beginning and at the end of the laser pulses, and (ii) the connectivity of these degeneracy-lifted branches in the quasienergy diagram. Both features can be determined by stationnary perturbation theory in the Floquet representation…
Prediction and Surveillance Sampling Assessment in Plant Nurseries and Fields
2022
In this paper, we propose a structured additive regression (STAR) model for modeling the occurrence of a disease in fields or nurseries. The methodological approach involves a Gaussian field (GF) affected by a spatial process represented by an approximation to a Gaussian Markov random field (GMRF). This modeling allows the building of maps with prediction probabilities regarding the presence of a disease in plants using Bayesian kriging. The advantage of this modeling is its computational benefit when compared with known spatial hierarchical models and with the Bayesian inference based on Markov chain Monte Carlo (MCMC) methods. Inference through the use of the integrated nested Laplace app…
On natural convection in a single and two zone rectangular enclosure
1992
Abstract Convective heat transfer was investigated numerically for rectangular enclosures both undivided and divided in two zones by a vertical partition, and having opposite isothermal walls at different temperatures. The aspect ratio was varied from 0.1 to 16 and the Rayleigh number from 3.5 ∗ 10 3 to ∗ 10 7 (non-partitioned enclosures) and from 1.0 ∗ 10 5 to 1.6 ∗ 10 8 (partitioned enclosures). The thickness and conductivity of the partition were varied. The end wall thermal boundary conditions were adiabatic or LTP (Linear Temperature Profile). The continuity, momentum and energy equations for a 2-D laminar steady flow were solved under the Boussinesq approximation by using a finite-dif…
One-dimensional Mixed MHD Convection
2006
The parallel, fully developed flow of an electrically conducting fluid between plane parallel walls under the simultaneous influence of a driving pressure head, buoyancy, and magnetohydrodynamic (MHD) forces is studied. The fluid is assumed to be internally heated and the flow is modeled as one-dimensional and incompressible, while the Boussinesq approximation is adopted for the buoyancy terms. Analytical solutions are obtained for temperature, velocity and electrical potential under different electrical boundary conditions, forced to natural convection intensity ratios and values of the magnetic induction. Generalized working charts are presented which synthetically describe the system''s …
Route to chaos in the weakly stratified Kolmogorov flow
2019
We consider a two-dimensional fluid exposed to Kolmogorov’s forcing cos(ny) and heated from above. The stabilizing effects of temperature are taken into account using the Boussinesq approximation. The fluid with no temperature stratification has been widely studied and, although relying on strong simplifications, it is considered an important tool for the theoretical and experimental study of transition to turbulence. In this paper, we are interested in the set of transitions leading the temperature stratified fluid from the laminar solution [U∝cos(ny),0, T ∝ y] to more complex states until the onset of chaotic states. We will consider Reynolds numbers 0 < Re ≤ 30, while the Richardson numb…
Visco-elastic behavior through fractional calculus: an easier method for best fitting experimental results
2011
In capturing visco-elastic behavior, experimental tests play a fundamental rule, since they allow to build up theoretical constitutive laws very useful for simulating their own behavior. The main challenge is representing the visco-elastic materials through simple models, in order to spread their use. However, the wide used models for capturing both relaxation and creep tests are combinations of simple models as Maxwell and/or Kelvin, that depend on several parameters for fitting both creep and relaxation tests. This paper, following Nutting and Gemant idea of fitting experimental data through a power law function, aims at stressing the validity of fractional model. In fact, as soon as rela…