Related papers: Initial conditions and evolution of off-diagonal d…
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
This paper is devoted to studying a system of coupled nonlinear first order history-dependent evolution inclusions in the framework of evolution triples of spaces. The multivalued terms are of the Clarke subgradient or of the convex…
In contrast to regular ordinary differential equations, the problem of accurately setting initial conditions just emerges in the context of differential-algebraic equations where the dynamic degree of freedom of the system is smaller than…
We present an analytical parametrization of the QCD description of the small x behaviour of parton distribution functions in the leading twist approximation of the Wilson operator product expansion, in the case of soft initial conditions.…
We report the evolution effects on jet energy loss with detailed balance. The initial conditions and parton evolution based on perturbative QCD in the chemical non-equilibrated medium and Bjorken expanding medium at RHIC are determined. The…
The evolution of random wave fields on the free surface is a complex process which is not completely understood nowadays. For the sake of simplicity in this study we will restrict our attention to the 2D physical problems only (i.e. 1D wave…
This work formally investigates the differential evolution indicators as a tool for ultrasonic tracking of elastic transformation and fracturing in randomly heterogeneous solids. Within the framework of periodic sensing, it is assumed that…
We discuss the scale dependence of a skewed parton distribution of the pion obtained from a generalized light-cone wave function overlap formula. Using a simple ansatz for the transverse momentum dependence of the light-cone wave function…
One can use more than one scale variable to define the family of surfaces in the space of parton splitting parameters that define the evolution of a parton shower. In an earlier paper, we developed this idea for electron-positron…
In this talk, we summarize how QCD evolution can be exploited to improve the treatment of transverse momentum dependent (TMD) parton distribution and fragmentation functions. The methods allow existing non-perturbative fits to be turned…
We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…
We have investigated skewed parton distributions in coordinate space. We found that their evolution can be described in a simple manner in terms of non-local, conformal operators introduced by Balitsky and Braun. The resulting formula is…
We characterize the time evolution of a d-dimensional probability distribution by the value of its final entropy. If it is near the maximally-possible value we call the evolution mixing, if it is near zero we say it is purifying. The…
We study damped wave propagation problems phrased as abstract evolution equations in Hilbert spaces. Under some general assumptions, including a natural compatibility condition for initial values, we establish exponential decay estimates…
We consider a thin droplet that spreads over a flat, horizontal and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes…
We propose a generalized diffusion equation for a flat Euclidean space subjected to a continuous infinitesimal scale transform. For the special cases of an algebraic or exponential expansion/contraction, governed by time-dependent scale…
We revisit the evolution of generalised parton distributions (GPDs) in momentum space. We formulate the evolution kernels at one-loop in perturbative QCD (pQCD) in a form suitable for numerical implementation and that allows for an accurate…
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-…
Recently, there have been some interesting developments involving off-forward parton distributions of the nucleon, deeply virtual Compton scattering, and hard diffractive vector-meson production. These developments are triggered by the…
In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic…