Search results for "Power series"

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.

Construction of O-minimal Structures from Quasianalytic Classes

2012

I present the method of constructing o-minimal structures based on local reduction of singularities for quasianalytic classes.

Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets

2006

We consider the set W of double zeros in (0,1) for power series with coefficients in {-1,0,1}. We prove that W is disconnected, and estimate the minimum of W with high accuracy. We also show that [2^(-1/2)-e,1) is contained in W for some small, but explicit e>0 (this was only known for e=0). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine fractals.

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…

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…

Complex singularities and PDEs

2015

In this paper we give a review on the computational methods used to capture and characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the classical singularity tracking method and give an example of application using the Burgers equation as a case study. This method is based on the analysis of the Fourier spectrum of the solution and it allows to determine and characterize the complex singularity closest to the real domain. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Padé approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the s…

Evolution of initial stage fluctuations in the glasma

2021

We perform a calculation of the one- and two-point correlation functions of energy density and axial charge deposited in the glasma in the initial stage of a heavy ion collision at finite proper time. We do this by describing the initial stage of heavy ion collisions in terms of freely evolving classical fields whose dynamics obey the linearized Yang-Mills equations. Our approach allows us to systematically resum the contributions of high momentum modes that would make a power series expansion in proper time divergent. We evaluate the field correlators in the McLerran-Venugopalan model using the glasma graph approximation, but our approach for the time dependence can be applied to a general…

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…

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.

A rank theorem for analytic maps between power series spaces

1994