Search results for "Power series"

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…

EPS09s and EKS98s: Impact parameter dependent nPDF sets

2013

In our recent study we have determined two new spatially dependent nuclear PDF (nPDF) sets, EPS09s and EKS98s. With these, the hard-process cross-sections can be calculated in different centrality classes consistently with the globally analyzed nPDFs for the first time. The sets were determined by exploiting the $A$-systematics of the globally fitted nPDF sets, EPS09 and EKS98. For the spatial dependence of the nPDFs we used a power series ansatz in the nuclear thickness function $T_A$. In this flash talk we introduce the framework, and present our NLO EPS09s-based predictions for the nuclear modification factor in four centrality classes for inclusive neutral pion production in p+Pb collis…

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…

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.

Some BBP-functions

2002

Estimates for the first and second Bohr radii of Reinhardt domains

2004

AbstractWe obtain general lower and upper estimates for the first and the second Bohr radii of bounded complete Reinhardt domains in Cn.

Generalised power series solutions of sub-analytic differential equations

2006

Abstract We show that if a solution y ( x ) of a sub-analytic differential equation admits an asymptotic expansion ∑ i = 1 ∞ c i x μ i , μ i ∈ R + , then the exponents μ i belong to a finitely generated semi-group of R + . We deduce a similar result for the components of non-oscillating trajectories of real analytic vector fields in dimension n. To cite this article: M. Matusinski, J.-P. Rolin, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

Consistent treatment of relativistic corrections in deuteron photodisintegration in a one-pion-exchange model

1992

Using a one-pion-exchange model for the nucleon-nucleon interaction the relativistic corrections to potential and to the electromagnetic operators are derived in a power expansion of (p/M). All corrections up to the order (p/M)3 are consistently included. Numerical results are shown for differential cross section and polarization observables for deuteron photodisintegration. A sizeable influence of relativistic effects on some observables is found even at low energies. A comparison of our operators with the expressions of other authors is given.

Analytic Continuation of the Kite Family

2019

We consider results for the master integrals of the kite family, given in terms of ELi-functions which are power series in the nome q of an elliptic curve. The analytic continuation of these results beyond the Euclidean region is reduced to the analytic continuation of the two period integrals which define q. We discuss the solution to the latter problem from the perspective of the Picard–Lefschetz formula.

Characteristic time scale of auroral electrojet data

1994

The structure function of the AE time series shows that the AE time series is self-affine such that the scaling exponent changes at the time scale of approximately 113 (±9) minutes. Autocorrelation function is shown to have scaling properties similar to those of the structure function. From this result it can be deduced that the time scale at which the scaling properties of the AE data change should equal the typical autocorrelation time of these data. We find the typical autocorrelation time of the AE data is 118 (±9) minutes. The characteristic time scale of the AE data appears as a spectral break in their power spectrum at a period of about twice the autocorrelation time.