Search results for "Mathematica"
showing 10 items of 7971 documents
Stochastic dynamics of nonlinear systems with a fractional power-law nonlinear term: The fractional calculus approach
2011
Fractional power-law nonlinear drift arises in many applications of engineering interest, as in structures with nonlinear fluid viscous–elastic dampers. The probabilistic characterization of such structures under external Gaussian white noise excitation is still an open problem. This paper addresses the solution of such a nonlinear system providing the equation governing the evolution of the characteristic function, which involves the Riesz fractional operator. An efficient numerical procedure to handle the problem is also proposed.
Pseudo-force method for a stochastic analysis of nonlinear systems
1996
Nonlinear systems, driven by external white noise input processes and handled by means of pseudo-force theory, are transformed through simple coordinate transformation to quasi-linear systems. By means of Itô stochastic differential calculus for parametric processes, a finite hierarchy for the moment equations of these systems can be exactly obtained. Applications of this procedure to the first-order differential equation with cubic nonlinearity and to the Duffing oscillator show the versatility of the proposed method. The accuracy of the proposed procedure improves by making use of the classical equivalent linearization technique.
An Application of the Fixed Point Theory to the Study of Monotonic Solutions for Systems of Differential Equations
2020
In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete gauge spaces.
On critical behaviour in generalized Kadomtsev-Petviashvili equations
2016
International audience; An asymptotic description of the formation of dispersive shock waves in solutions to the generalized Kadomtsev–Petviashvili (KP) equation is conjectured. The asymptotic description based on a multiscales expansion is given in terms of a special solution to an ordinary differential equation of the Painlevé I hierarchy. Several examples are discussed numerically to provide strong evidence for the validity of the conjecture. The numerical study of the long time behaviour of these examples indicates persistence of dispersive shock waves in solutions to the (subcritical) KP equations, while in the supercritical KP equations a blow-up occurs after the formation of the disp…
Character Tables and Sylow Subgroups Revisited
2018
Suppose that G is a finite group. A classical and difficult problem is to determine how much the character table knows about the local structure of G and vice versa.
A Branch-Price-and-Cut Algorithm for the Min-Max k -Vehicle Windy Rural Postman Problem
2013
[EN] The min-max k -vehicles windy rural postman problem consists of minimizing the maximal distance traveled by a vehicle to find a set of balanced routes that jointly service all the required edges in a windy graph. This is a very difficult problem, for which a branch-and-cut algorithm has already been proposed, providing good results when the number of vehicles is small. In this article, we present a branch-price-and-cut method capable of obtaining optimal solutions for this problem when the number of vehicles is larger for the same set of required edges. Extensive computational results on instances from the literature are presented.
Analytical solution for multisingular vortex Gaussian beams: The mathematical theory of scattering modes
2016
We present a novel procedure to solve the Schr\"odinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal to propagation embedded in a Gaussian beam. We use the scattering modes, which are solutions of the paraxial wave equation that can be combined straightforwardly to express the initial condition and therefore permit to solve the problem. To construct the scattering modes one needs to obtain a particular set of polynomials, which play an analogous role than Laguerre polynomials for Laguerre-Gaussian modes. We demonstrate here the recurrence relations need…
Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering
2017
Abstract The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.
Electric and dielectric properties of nanostructured stoichiometric and excess-iron Ni–Zn ferrites
2013
In this paper, we report a study of the effect of excess iron on structural, microstructural, electric and dielectric properties of the nanostructured Ni–Zn ferrites Ni1−xZnxFe2+zO4−δ of different compositions with x = 0, 0.3, 0.5, 0.7, 1 and z = 0, 0.1. The structural and microstructural properties are estimated from x-ray diffraction and atomic force microscopy (AFM) data. The average grain size, evaluated from AFM topographical analysis, is found to be below 70 nm. The samples exhibit low values of dielectric constant and dielectric loss and a high resistivity. Contrary to earlier conclusions regarding microstructured Ni–Zn ferrites, in nanostructured Ni–Zn ferrites sintered at relativel…
Atomistic simulations of the FeK-edge EXAFS in FeF3using molecular dynamics and reverse Monte Carlo methods
2016
Atomistic simulations of the experimental Fe K-edge extended x-ray absorption fine structure (EXAFS) of rhombohedral (space group ) FeF3 at T = 300 K were performed using classical molecular dynamics and reverse Monte Carlo (RMC) methods. The use of two complementary theoretical approaches allowed us to account accurately for thermal disorder effects in EXAFS and to validate the developed force-field model, which was constructed as a sum of two-body Buckingham-type (Fe–F and F–F), three-body harmonic (Fe–F–Fe) and Coulomb potentials. We found that the shape of the Fe K-edge EXAFS spectrum of FeF3 is a more sensitive probe for the determination of potential parameters than the values of stru…