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We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
In this paper we develop a QCD motivated model for both hard and soft interactions at high energies. In this model the long distance behavior of the scattering amplitude is determined by the approximate solution to the non-linear evolution…
In the first part of this talk, I will summarize recent developments in the study of the chiral-odd spin-dependent parton distributions h_1(x,Q^2) and h_L(x,Q^2) of the nucleon, in particular, (i) Next-to- leading order Q^2 evolution of…
We study the long-time behavior of solutions to a class of evolution equations arising from random-time changes driven by subordinators. Our focus is on fractional diffusion equations involving mixed local and nonlocal operators. By…
We consider dihadron fragmentation functions, describing the fragmentation of a parton in two unpolarized hadrons, and in particular extended dihadron fragmentation functions, explicitly dependent on the invariant mass, $M_h$, of the hadron…
We prove controllability results for abstract systems of weakly coupled $N$ evolution equations in cascade by a reduced number of boundary or locally distributed controls ranging from a single up to $N-1$ controls. We give applications to…
We derive a generalized form of Altarelli-Parisi equations to decribe the time evolution of parton distributions in a nuclear medium. In the framework of the leading logarithmic approximation, we obtain a set of coupled integro-…
A two-dimensional extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities is derived. Prior work has demonstrated that the emergent dynamics of these systems is characterized by a…
We calculate the small-$x$ evolution of protons with finite size by solving numerically the JIMWLK evolution equation. The initial condition is constrained by the HERA measurements of charm reduced cross section and of exclusive vector…
Central to understanding the nonpertubative, intrinsic partonic nature of hadron structure are the concepts of transverse momentum dependent (TMD) parton distribution and fragmentation functions. A TMD factorization approach to the…
We study the small-$x$ asymptotics of unpolarized generalized parton distributions (GPDs) and generalized transverse momentum distributions (GTMDs). Unlike the previous works in the literature, we consider the case of non-zero (but small)…
We discuss QCD evolution equations for two and three particle correlation functions of quarks and gluon fields in a hadron which describe development of the momentum distribution of a parton system with a change of the wave length of a…
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a…
Using a recursive algorithm to solve the renormalization group equations of N=1 QCD (DGLAP), we describe the most general supersymmetric evolution of the parton distributions. The analysis involves the regular DGLAP evolution, a partial…
Misprints and numerical coefficients corrected, a bit of phenomenology and one figure added. The case for the linear evolution of the unitarized structure functions made stronger.
We develop efficient group-theoretical approach to the problem of classification of evolution equations that admit non-local transformation groups (quasi-local symmetries), i.e., groups involving integrals of the dependent variable. We…
We consider the one-dimensional local reggeon theory describing the leading pomeron with the conformal spin $l=0$ and two subdominant pomerons with $l=\pm 2$. The dependence of the propagators of pomerons and the $hA$ amplitude on rapidity…
The method of multiscale analysis is constructed for dicrete systems of evolution equations for which the problem is that of the far behavior of an input boundary datum. Discrete slow space variables are introduced in a general setting and…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
An approach to stochastic evolution equations based on a simple generalization of known embedding theorems is presented. It allows for the inclusion of problems which have nonlinear non monotone operators. This is used to discuss the…