Related papers: Modular resurgent structures
The renormalon singularities are a known source of the divergent behavior of asymptotic perturbative series from field theoretical models. These singularities live in the Borel plane and are responsible for ambiguities in the physical…
Turbulent suspensions of heavy particles in incompressible flows have gained much attention in recent years. A large amount of work focused on the impact that the inertia and the dissipative dynamics of the particles have on their dynamical…
A bracket is a function that assigns a number to each monomial in variables \tau_0, \tau_1, ... We show that any bracket satisfying the string and the dilaton relations gives rise to a power series lying in the algebra A generated by the…
Division-of-focal-plane modulation is a powerful technique for real-time polarization imaging. This technique, however, suffers from the non-uniformity of the performance of linear polarization filters and photodetectors. We study the…
We provide an overview of the tools and techniques of resurgence theory used in the Borel-Ecalle resummation method, which we then apply to the massless Wess-Zumino model. Starting from already known results on the anomalous dimension of…
Using high resolution Cluster satellite observations, we show that the turbulent solar wind is populated by magnetic discontinuities at different scales, going from proton down to electron scales. The structure of these layers resembles the…
Algebraic holonomic $\mathcal{D}$-modules on a complex line are classified by the associated topological data consisting of local systems with Stokes structure and the nearby and vanishing cycles at the singularities. The Fourier transform…
Assuming the asymptotic character of divergent perturbation series, we address the problem of ambiguity of a function determined by an asymptotic power expansion. We consider functions represented by an integral of the Laplace-Borel type,…
The full resurgent trans-series is found exactly in near-supersymmetric $\mathbb C P^1$ quantum mechanics. By expanding in powers of the SUSY breaking deformation parameter, we obtain the first and second expansion coefficients of the…
We consider formal power series defined through the functional q-equation of the q-Lagrange inversion. Under some assumptions, we obtain the asymptotic behavior of the coefficients of these power series. As a by-product, we show that, via…
In this paper we explore stochastical and statistical properties of so-called recurring spike induced Kasner sequences. Such sequences arise in recurring spike formation, which is needed together with the more familiar BKL scenario to yield…
We use well-resolved direct numerical simulations of high-Reynolds-number turbulence to study a fundamental statistical property of turbulence -- the asymmetry of velocity increments -- with likely implications on important dynamics. This…
We revisit the strong coupling limit of the cusp anomalous dimension in planar N=4 super Yang-Mills theory. It is known that the strong coupling expansion is asymptotic and non-Borel summable. As a consequence, the cusp anomalous dimension…
In paper I of this series on fluid turbulence we showed that exact resummations of the perturbative theory of the structure functions of velocity differences result in a finite (order by order) theory. These findings exclude any known…
The analytic contribution to the low energy expansion of Type II string amplitudes at genus-one is a power series in space-time derivatives with coefficients that are determined by integrals of modular functions over the complex structure…
When we have two expansions of physical quantity around two different points in parameter space, we can usually construct a family of functions, which interpolates the both expansions. In this paper we study analytic structures of such…
A method is developed for calculating effective sums of divergent series. This approach is a variant of the self-similar approximation theory. The novelty here is in using an algebraic transformation with a power providing the maximal…
The article is based on the differential properties of the inner generators (singularities) that occur while handling SP series (sum product series), power series whose Taylor coefficients can be written as sum-product combinations. It is…
Persistence modules are representations of products of totally ordered sets in the category of vector spaces. They appear naturally in the representation theory of algebras, but in recent years they have also found applications in other…
We study inverse factorial series and their relation to Stirling numbers of the first kind. We prove a special representation of the polylogarithm function in terms of series with such numbers. Using various identities for Stirling numbers…