Related papers: Unified derivation of evolution equations
This research is concerned with evolution equations and their forward-backward discretizations. Our first contribution is an estimation for the distance between iterates of sequences generated by forward-backward schemes, useful in the…
We formulate the momentum-space Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for structure functions measurable in deeply inelastic scattering. We construct a six-dimensional basis of structure functions that…
This paper presents an operational framework for the computation of the discretized solutions for relativistic equations of Klein-Gordon and Dirac type. The proposed method relies on the construction of an evolution-type operador from the…
We revisit the evolution of generalised parton distributions (GPDs) at the leading order in the strong coupling constant $\alpha_s$ for all of the twist-2 quark and gluon operators. We rederive the relevant one-loop evolution kernels,…
Stochastic processes described by evolution equations in the universality class of the FKPP equation may be approximately factorized into a linear stochastic part and a nonlinear deterministic part. We prove this factorization on a model…
We develop a variational technique for some wide classes of nonlinear evolutions. The novelty here is that we derive the main information directly from the corresponding Euler-Lagrange equations. In particular, we prove that not only the…
The Fortran package QCD-PEGASUS is presented. This program provides fast, flexible and accurate solutions of the evolution equations for unpolarized and polarized parton distributions of hadrons in perturbative QCD. The evolution is…
Continuous time random walks are non-Markovian stochastic processes, which are only partly characterized by single-time probability distributions. We derive a closed evolution equation for joint two-point probability density functions of a…
We consider three classical models of biological evolution: (i) the Moran process, an example of a reducible Markov Chain; (ii) the Kimura Equation, a particular case of a degenerated Fokker-Planck Diffusion; (iii) the Replicator Equation,…
We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting…
Recently, various evolutionary partial differential equations (PDEs) with a mixed derivative have been emerged and drawn much attention. Nonetheless, their PDE-theoretical and numerical studies are still in their early stage. In this paper,…
The cross section for transverse momentum dependent double parton scattering involves transverse momentum dependent double parton distributions (DTMDs). In the region of perturbative transverse momentum the DTMDs can be matched onto…
We show that the discrete operator stemming from the time and space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines…
Continuing with our analysis of parton distributions in the nucleon, we extend our light-front quark model in order to obtain both the helicity independent and helicity dependent parton distributions, analytically matching the results of…
We consider an evolution equation involving the fractional powers, of order $s \in (0,1)$, of a symmetric and uniformly elliptic second order operator and Caputo fractional time derivative of order $\gamma \in (1,2]$. Since it has been…
In this paper, we study the existence and uniqueness of solutions for several classes of stochastic evolution equations with non-Lipschitz coefficients, that is, backward stochastic evolution equations, stochastic Volterra type evolution…
The differential cross section for the dilepton production is calculated including Fermi motion of hadron constituents as well as emission from the ladders in the formalism of unintegrated parton distributions. We use unintegrated parton…
In this paper we use key elements of the Olver's approach to Hamiltonian evolution equations in partial derivatives and propose an algebraic construction appropriate for Hamiltonian evolution systems with constraints.
We show that, for certain evolution partial differential equations, the solution on a finite interval $(0,\ell)$ can be reconstructed as a superposition of restrictions to $(0,\ell)$ of solutions to two associated partial differential…
We show how generalized parton distributions (GPDs) can be determined in the case where hadrons are described in terms of their partonic degrees of freedom through solutions of dynamical equations. We demonstrate our approach on the example…