Search results for "Power series"

Description of intermodulation generation of nonlinear responses beyond the validity of the power series expansion

2021

Weakly nonlinear responses are commonly described by a power series expansion. However, intermodulation distortion products that cannot be described by a power series have been observed in a variety of physical systems. As the power series description is only applicable within its radius of convergence, we choose an alternative approach based on Fourier coefficients to describe intermodulation levels beyond the convergence of the power series. The description over a wide power range allows us to make a decision about models and to determine previously inaccessible model parameters. We apply the approach to data obtained from the characterization of the nonlinear dielectric susceptibility of…

Analytical solution for the diffusion of a capacitor discharge generated magnetic field pulse in a conductor

2016

Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-sim…

Analytic curves in power series rings

1990

Complex singularities in KdV solutions

2016

In the small dispersion regime, the KdV solution exhibits rapid oscillations in its spatio-temporal dependence. We show that these oscillations are caused by the presence of complex singularities that approach the real axis. We give a numerical estimate of the asymptotic dynamics of the poles.

Mahonian STAT on words

2016

In 2000, Babson and Steingrimsson introduced the notion of what is now known as a permutation vincular pattern, and based on it they re-defined known Mahonian statistics and introduced new ones, proving or conjecturing their Mahonity. These conjectures were proved by Foata and Zeilberger in 2001, and by Foata and Randrianarivony in 2006.In 2010, Burstein refined some of these results by giving a bijection between permutations with a fixed value for the major index and those with the same value for STAT , where STAT is one of the statistics defined and proved to be Mahonian in the 2000 Babson and Steingrimsson's paper. Several other statistics are preserved as well by Burstein's bijection.At…

Convergence of iterative methods in perturbation theory

1995

We discuss iterative KAM type methods for eigenvalue problems in finite dimensions. We compare their convergence properties with those of straight forward power series expansions.

Bohr radii of vector valued holomorphic functions

2012

Abstract Motivated by the scalar case we study Bohr radii of the N -dimensional polydisc D N for holomorphic functions defined on D N with values in Banach spaces.

Extracting the impact parameter dependence of the nPDFs from the EKS98 and EPS09 global fits

2013

As all the globally fitted nuclear PDFs (nPDFs) have been so far impact parameter independent, it has not been possible to calculate the hard process cross sections in different centrality classes consistently with the global analyses. In \cite{Helenius:2012wd} we have offered a solution to this problem by determining two spatially dependent nPDF sets, \texttt{EPS09s} and \texttt{EKS98s}, using the $A$-systematics of the earlier global fits EPS09 and EKS98 and an assumption that the spatial dependence can be written as a power series of the nuclear thickness function. For a data comparison, we have calculated the nuclear modification factor of inclusive neutral pion production in d+Au colli…

New Accurate Fit of an Extended Set of Saturation Data for the ν3 Band of SF6: Comparison of Hamiltonians in the Spherical and Cubic Tensor Formalisms

2000

An extended set of 321 frequencies of vibration-rotation lines of the nu(3) band of SF(6) has been measured by saturation spectroscopy using various isotopic species of CO(2). A least-squares fit of these data has been performed using an effective Hamiltonian written either with a spherical tensor or with a cubic tensor formalism. We have derived correspondence formulas between the parameters in the two approaches and checked that both formalisms give the same results up to the seventh order. Corrected parameters are given for the fit with a fifth-order Hamiltonian. An accurate representation of the band is obtained at the tenth order (standard deviation approximately 12 kHz) with a remarka…

Impact-parameter dependent nuclear parton distribution functions: EPS09s and EKS98s and their applications in nuclear hard processes

2012

We determine the spatial (impact parameter) dependence of nuclear parton distribution functions (nPDFs) using the $A$-dependence of the spatially independent (averaged) global fits EPS09 and EKS98. We work under the assumption that the spatial dependence can be formulated as a power series of the nuclear thickness functions $T_A$. To reproduce the $A$-dependence over the entire $x$ range we need terms up to $[T_A]^4$. As an outcome, we release two sets, EPS09s (LO, NLO, error sets) and EKS98s, of spatially dependent nPDFs for public use. We also discuss the implementation of these into the existing calculations. With our results, the centrality dependence of nuclear hard-process observables…