Related papers: Comparison of numerical solutions for Q^2 evolutio…
We consider evolutionary systems, i.e. systems of linear partial differential equations arising from the mathematical physics. For these systems there exists a general solution theory in exponentially weighted spaces which can be exploited…
We propose the formulation of a dihadron fragmentation function in terms of parton matrix elements. Under the collinear factorization approximation and facilitated by the cut-vertex technique, the two hadron inclusive cross section at…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Quark and gluon parton dihadron fragmentation functions and their evolution are studied in the process of e+e- annihilation. We provide definitions of such dihadron fragmentation functions in terms of parton matrix elements and derive the…
We present a new method to solve in a semianalytical way the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NLO order in the x-space. The method allows to construct an evolution operator expressed in form of a rapidly…
We present an evolution equation which simultaneously sums the leading BFKL and DGLAP logarithms for the integrated gluon distribution in terms of a single variable, namely the emission angle of the gluon. This form of evolution is…
We derive equations for the time evolution of the reduced density matrix of a collection of heavy quarks and antiquarks immersed in a quark gluon plasma. These equations, in their original form, rely on two approximations: the weak coupling…
This is the introductory part of my PhD thesis which consists of two parts, the separate introduction and four published articles. The introduction begins by a technically detailed description of the DGLAP evolution and the fast numerical…
It is the central goal of our studies to describe parton fragmentation in the hot and dense medium of a quark gluon plasma (QGP). Under the assumption that the medium is not static and homogeneous, knowledge about the temporal evolution of…
A new method of numerical solution for partial differential equations is proposed. The method is based on a fast matrix multiplication algorithm. Two-dimensional Poison equation is used for comparison of the proposed method with…
This is the second in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper the numerical methods used to solve the system of evolution…
The supersymmetric evolution of the fragmentation functions (or timelike evolution) within N=1 $QCD$ is discussed and predictions for the fragmentation functions of the theory (into final protons) are given. We use a backward running of the…
An approach is elaborated for calculation of "all loop" contributions to the non-singlet evolution kernels from the diagrams with renormalon chain insertions. Closed expressions are obtained for sums of contributions to kernels $P(z)$ for…
High-precision numerical scheme for nonlinear hyperbolic evolution equations is proposed based on the spectral method. The detail discretization processes are discussed in case of one-dimensional Klein-Gordon equations. In conclusion, a…
Using the conformal invariance the leading-log evolution of the off-forward structure function is reduced to the forward evolution described by the conventional DGLAP equation. The method relies on the fact that the anomalous dimensions of…
We present an algorithm for massive parton evolution which is based on the differentially accurate simulation of soft-gluon radiation by means of a non-trivial azimuthal angle dependence of the splitting functions. The kinematics mapping is…
We present a solution of the DGLAP evolution equations, written in terms of Sudakov form factors to describe the branching and no-branching probabilities, using a parton branching Monte Carlo method. We demonstrate numerically that this…
The Abelian decomposition of QCD reveals two types of gluons: color-neutral ``neurons" and color-carrying ``chromons". This classification does not alter the overall properties of QCD, but the investigation of different types of gluon…
We propose the formulation of a dihadron fragmentation function in terms of parton matrix elements. Under the collinear factorization approximation and facilitated by the cut-vertex technique, the two hadron inclusive cross section at…