Search results for "numeri"
showing 10 items of 2138 documents
Eliminating Artificial Boundary Conditions in Time-Dependent Density Functional Theory Using Fourier Contour Deformation
2023
We present an efficient method for propagating the time-dependent Kohn-Sham equations in free space, based on the recently introduced Fourier contour deformation (FCD) approach. For potentials which are constant outside a bounded domain, FCD yields a high-order accurate numerical solution of the time-dependent Schrödinger equation directly in free space, without the need for artificial boundary conditions. Of the many existing artificial boundary condition schemes, FCD is most similar to an exact nonlocal transparent boundary condition, but it works directly on Cartesian grids in any dimension, and runs on top of the fast Fourier transform rather than fast algorithms for the application of …
The strictly-correlated electron functional for spherically symmetric systems revisited
2017
The strong-interaction limit of the Hohenberg-Kohn functional defines a multimarginal optimal transport problem with Coulomb cost. From physical arguments, the solution of this limit is expected to yield strictly-correlated particle positions, related to each other by co-motion functions (or optimal maps), but the existence of such a deterministic solution in the general three-dimensional case is still an open question. A conjecture for the co-motion functions for radially symmetric densities was presented in Phys.~Rev.~A {\bf 75}, 042511 (2007), and later used to build approximate exchange-correlation functionals for electrons confined in low-density quantum dots. Colombo and Stra [Math.~M…
Periodic behaviour in heterogeneous chemical reactions
1992
Abstract The authors present an analytical and numerical analysis for a solid-gas oxidation process represented by a set of coupled reaction rates equations. The equations describe the time evolution of four elementary process that govern the overall heterogeneous kinetics. The description formation of a new oxide unit considers: (1) an internal interface (oxide-metal) reaction by which an activated complex is formed; (2) the dissolution of the complex produce a chemical element σ; (3) the diffusion of σ through the oxide layer; and (4) an external interface (oxide-gas) reaction. The results reported here delinate the parameter region where chemical oscillations are present.
Implementation of local chiral interactions in the hyperspherical harmonics formalism
2021
With the goal of using chiral interactions at various orders to explore properties of the few-body nuclear systems, we write the recently developed local chiral interactions as spherical irreducible tensors and implement them in the hyperspherical harmonics expansion method. We devote particular attention to three-body forces at next-to-next-to leading order, which play an important role in reproducing experimental data. We check our implementation by benchmarking the ground-state properties of $^3$H, $^3$He and $^4$He against the available Monte Carlo calculations. We then confirm their order-by-order truncation error estimates and further investigate uncertainties in the charge radii obta…
Characterization of chromatographic peaks using the linearly modified Gaussian model. Comparison with the bi-Gaussian and the Foley and Dorsey approa…
2017
To characterize column performance in liquid chromatography, several parameters must be obtained from experimental data. These parameters can be computed through the numerical integration of the net signal to calculate the moments after subtraction of the baseline. This requires the establishment of the peak integration limits. The whole process introduces significant uncertainty. For this reason, several alternative procedures have been proposed to measure the area, mean time and variance, based on the assumption that the chromatographic peak can be described with a mathematical function. This allows the calculation of the peak position and variance making use of the values of the experime…
Limits of multi-linear gradient optimisation in reversed-phase liquid chromatography
2005
Abstract The concept of limiting peak purity was applied to quantify the degree of completion of the separation capability of a chromatographic system using multi-linear gradients. The objective was to check whether the complexity of a gradient program deserves be increased to enhance resolution by inserting more linear segments, or on the contrary, no significant improvements can be expected under more complex gradients. A set of 19 isoindole derivatives of primary amino acids was selected to test the performance of isocratic, single linear and multi-linear gradients. Accurate simulated chromatograms were obtained via numerical integration of the general equation of gradient elution, using…
Analytical-numerical methods for investigation of hidden oscillations in nonlinear control systems
2011
The method of harmonic linearization, numerical methods, and the applied bifurcation the- ory together discover new opportunities for analysis of oscillations of control systems. In the present survey analytical-numerical algorithms for hidden oscillation localization are discussed. Examples of hidden attrac- tor localization in Chua's circuit and counterexamples construction to Aizerman's conjecture and Kalman's conjecture are considered.
Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems
2018
The paper is concerned with reliable space-time IgA schemes for parabolic initial-boundary value problems. We deduce a posteriori error estimates and investigate their applicability to space-time IgA approximations. Since the derivation is based on purely functional arguments, the estimates do not contain mesh dependent constants and are valid for any approximation from the admissible (energy) class. In particular, they imply estimates for discrete norms associated with stabilised space-time IgA approximations. Finally, we illustrate the reliability and efficiency of presented error estimates for the approximate solutions recovered with IgA techniques on a model example.
Systematisation of Systems Solving Physics Boundary Value Problems
2020
A general conservation law that defines a class of physical field theories is constructed. First, the notion of a general field is introduced as a formal sum of differential forms on a Minkowski manifold. By the action principle the conservation law is defined for such a general field. By construction, particular field notions of physics, e.g., magnetic flux, electric field strength, stress, strain etc. become instances of the general field. Hence, the differential equations that constitute physical field theories become also instances of the general conservation law. The general field and the general conservation law together correspond to a large class of relativistic hyperbolic physical …
Approximating hidden chaotic attractors via parameter switching.
2018
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …