Search results for "approximation"
showing 10 items of 818 documents
Practical formula for the evaluation of high-order multiphoton absorption in thin nonlinear media
2009
We present an analytical formula for the fast and accurate evaluation of nonlinear absorption in materials exhibiting an admixture of different multiphoton processes. This approach is specifically addressed for its use in thin films when the slowly varying envelope approximation applies. The contribution of absorptions of distinct order is conveniently averaged in order to use well-known expressions for a single multiphoton process. In the latter case, therefore, our simple expression is reduced toward the exact solution.
Further results on H<inf>&#x221E;</inf> control of switched linear time-delay systems
2012
In this note, we study the problems of stability analysis and H ∞ controller synthesis of discrete-time switched systems with time-varying delay. The system under consideration is firstly transformed into an interconnection system. Based on the system transformation and the scaled small gain theorem, the asymptotic stability of the original system is examined via the version of the bounded realness of the transformed forward system. The aim of the proposed approach is to reduce conservatism, which is made possible by a precise approximation of the time-varying delay and the input-output approach. The proposed stability condition is demonstrated to be much less conservative than most existin…
Approximation of W1, Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian
2018
Abstract Let Ω ⊂ R n , n ≥ 4 , be a domain and 1 ≤ p [ n / 2 ] , where [ a ] stands for the integer part of a. We construct a homeomorphism f ∈ W 1 , p ( ( − 1 , 1 ) n , R n ) such that J f = det D f > 0 on a set of positive measure and J f 0 on a set of positive measure. It follows that there are no diffeomorphisms (or piecewise affine homeomorphisms) f k such that f k → f in W 1 , p .
Proximal-sensing-powered modelling of energy-water fluxes in a vineyard: A spatial resolution analysis
2021
Spatial resolution is a key parameter in energy–water surface flux modelling. In this research, scale effects are analyzed on fluxes modelled with the FEST-EWB model, by upscaling both its inputs and outputs separately. The main questions are: (a) if high-resolution remote sensing images are necessary to accurately model a heterogeneous area; and (b) whether and to what extent low-resolution modelling provides worse/better results than the upscaled results of high-resolution modelling. The study area is an experimental vineyard field where proximal sensing images were obtained by an airborne platform and verification fluxes were measured via a flux tower. Modelled fluxes are in line with th…
Description of x-ray beams using the fluorescence yields of a set of thick targets
1995
Quantitative methods in x-ray fluorescence analysis require a knowledge of the spectral distribution of the fluorescence-exciting beam. The use of XRF yield measurements of a set of thick pure element targets is proposed for the description of a fluorescence-exciting x-ray beam, without the need to obtain its spectral distribution. This new approach is derived theoretically and verified by comparing thin-target yields calculated from XRF yield measurements of thick pure element specimens with those obtained from a calculated spectral distribution. The difference between the two methods of obtaining the thin-target yields is within 9% relative error.
First Experiences on an Accurate SPH Method on GPUs
2017
It is well known that the standard formulation of the Smoothed Particle Hydrodynamics is usually poor when scattered data distribution is considered or when the approximation near the boundary occurs. Moreover, the method is computational demanding when a high number of data sites and evaluation points are employed. In this paper an enhanced version of the method is proposed improving the accuracy and the efficiency by using a HPC environment. Our implementation exploits the processing power of GPUs for the basic computational kernel resolution. The performance gain demonstrates the method to be accurate and suitable to deal with large sets of data.
Order-disorder-and order-order-transitions in AB and ABC block copolymers: description by a simple model
1996
Based on the description of AB-block copolymers as micellar structures given by Semenov, the phase diagram of AB-diblock copolymers is calculated taking the homogeneously mixed system as a reference state. The predicted value (χN)c = 10.385 for a symmetric AB-diblock copolymer compares very well to the result of the original Random Phase Approximation theory (10.495). The simplicity of the model allows its extension to predict order-order transitions in ABC-triblock copolymers.
Quasi-interpolating and Smoothing Local Splines
2015
In this chapter, local quasi-interpolating and smoothing splines are described. Although approximation properties of local spline are similar to properties of the global interpolating and smoothing splines, their design does not require the IIR filtering of the whole data array. The computation of a local spline value at some point utilizes only a few adjacent grid samples. Therefore, local splines can be used for real-time processing of signals and for the design of FIR filter banks generating wavelets and wavelet frames (Chaps. 12 and 14). In the chapter, local splines of different orders are designed and their approximation properties are established which are compared with the propertie…
Separatrix reconstruction to identify tipping points in an eco-epidemiological model
2018
Many ecological systems exhibit tipping points such that they suddenly shift from one state to another. These shifts can be devastating from an ecological point of view, and additionally have severe implications for the socio-economic system. They can be caused by overcritical perturbations of the state variables such as external shocks, disease emergence, or species removal. It is therefore important to be able to quantify the tipping points. Here we present a study of the tipping points by considering the basins of attraction of the stable equilibrium points. We address the question of finding the tipping points that lie on the separatrix surface, which partitions the space of system traj…
Time delay induced effects on control of linear systems under random excitation
2001
Recursive formulas in terms of statistics of the response of linear systems with time delay under normal white noise input are developed. Two alternative methods are presented, in order to capture the time delay effects. The first is given in an approximate solution obtained by expanding the control force in a Taylor series. The second, available for the stationary solution (if it exists) gets the variance of the controlled system, with time delay in an analytical form. The efficacy loss in terms of statistics of the response is discussed in detail.