Search results for "Numerical integration"
showing 10 items of 43 documents
Nonlinear effects in optical pumping of a cold and slow atomic beam
2015
By photoionizing hyperfine (HF) levels of the Cs state $6{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}$ in a slow and cold atom beam, we find how their population depends on the excitation laser power. The long time (around $180\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s})$ spent by the slow atoms inside the resonant laser beam is large enough to enable exploration of a unique atom-light interaction regime heavily affected by time-dependent optical pumping. We demonstrate that, under such conditions, the onset of nonlinear effects in the population dynamics and optical pumping occurs at excitation laser intensities much smaller than the conventional respective saturation values. The ev…
Correction: Generalized Langevin dynamics: construction and numerical integration of non-Markovian particle-based models.
2018
Correction for ‘Generalized Langevin dynamics: construction and numerical integration of non-Markovian particle-based models’ by Gerhard Jung et al., Soft Matter, 2018, DOI: 10.1039/c8sm01817k.
Analysis of negative-resistance oscillators with piecewise nonlinearity
1977
An iterative method of solution of negative-resistance oscillators with piecewise-analytical characteristics is presented. The method allows the determination of the frequency and the harmonic content of the waveform as a function of the circuit parameters and bias of the nonlinear device. An application of the method, extended to the second order, for a polynomial characteristic limited by two straight lines is also reported. The results are compared with those obtained by numerical integration.
The Magnus expansion and some of its applications
2008
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem, shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to build up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of prese…
A new algorithm for the kinetic data analysis
2000
Abstract In this paper, a new algorithm for the kinetic data analysis is presented. The main objective of the algorithm is to retrieve the maximum information concerned with a multi-response complex chemical system evolving in time, in order to retrieve the rate constants (calibration problem) or the initial concentration of species. As a difference with other data treatments found in the literature, the algorithm is able to estimate the uniqueness and reliability of the calculated rate constants. This task is carried out by analyzing of the principal components of the sensitivity coefficients with regard to the rate constants. The analysis allows understanding whether the located stationar…
Laser induced thermal profiles in thermally and optically thin films
1988
The temperature field generated by the weak absorption of a gaussian laser beam in an optically and thermally thin film bounded by two transparent plates is discussed. An analytical solution of the problem is presented together with an algorithm for the numerical integration. The influence of the finite thermal conductivity of the plates is shown in an example.
Dynamic integration of classifiers in the space of principal components
2003
Recent research has shown the integration of multiple classifiers to be one of the most important directions in machine learning and data mining. It was shown that, for an ensemble to be successful, it should consist of accurate and diverse base classifiers. However, it is also important that the integration procedure in the ensemble should properly utilize the ensemble diversity. In this paper, we present an algorithm for the dynamic integration of classifiers in the space of extracted features (FEDIC). It is based on the technique of dynamic integration, in which local accuracy estimates are calculated for each base classifier of an ensemble, in the neighborhood of a new instance to be pr…
xloops - Automated Feynman diagram calculation
1998
The program package xloops, a general, model independent tool for the calculation of high energy processes up to the two-loop level, is introduced. xloops calculates massive one- and two-loop Feynman diagrams in the standard model and related theories both analytically and numerically. A user-friendly Xwindows frontend is part of the package. xloops relies on the application of parallel space techniques. The treatment of tensor structure and the separation of divergences in analytic expressions is described in this scheme. All analytic calculations are performed with Maple. We describe the mathematical methods and computer algebra techniques xloops uses and give a brief introduction how to …
Benefits of solvent concentration pulses in retention time modelling of liquid chromatography
2019
The advantages and disadvantages of the use of isocratic experimental designs including transient increments of organic solvent (i.e., pulses) in the mobile phase(s) of lowest elution strength are explored with modelling purposes. For retained solutes, this type of mixed design offers similar or better predictive capability than gradient designs, shorter measurement time than pure isocratic designs, and retention model parameters that agree with those derived from pure isocratic experiments, with similar uncertainties. The predicted retention times are comparable to those offered by models adjusted from pure isocratic designs, and the solvent waste is appreciably lower. Under a practical st…
Estimation of significant solvent concentration ranges and its application to the enhancement of the accuracy of gradient predictions.
2004
Abstract The solvent concentration range actually useful for gradient predictions is significantly narrower than the total range scanned in a gradient run. This range, called “solvent informative range” (SIR), if known with the highest accuracy, allows to predict gradient retention times ( t g ) with minimal error. The small size of the SIR supports the application of the linear solvent strength theory (LSST). Furthermore, LSST allows a closed-form solution to the integral required to predict gradient retention times, which eliminates numerical integration, needed with other retention models. A methodology that calculates the SIR by applying error analysis, and uses it to improve the accura…