On correlations and discreteness in non-linear QCD evolution

We consider modifications of the standard non-linear QCD evolution in an attempt to account for some of the missing ingredients discussed recently, such as correlations, discreteness in gluon emission and Pomeron loops. The evolution is numerically performed using the Balitsky-Kovchegov equation on individual configurations defined by a given initial value of the saturation scale, for reduced rapidities $y=(\alpha_s N_c/\pi) Y<10$. We consider the effects of averaging over configurations as a way to implement correlations, using three types of Gaussian averaging around a mean saturation scale. Further, we heuristically mimic discreteness in gluon emission by considering a modified evolution in which the tails of the gluon distributions are cut-off. The approach to scaling and the behavior of the saturation scale with rapidity in these modified evolutions are studied and compared with the standard mean-field results. For the large but finite values of rapidity explored, no strong quantitative difference in scaling for transverse momenta around the saturation scale is observed. At larger transverse momenta, the influence of the modifications in the evolution seems most noticeable in the first steps of the evolution. No influence on the rapidity behavior of the saturation scale due to the averaging procedure is found. In the cut-off evolution the rapidity evolution of the saturation scale is slowed down and strongly depends on the value of the cut-off. Our results stress the need to go beyond simple modifications of evolution by developing proper theoretical tools that implement such recently discussed ingredients.Comment: 20 pages, LaTeX, 18 eps figures included using epsfig; changes in v3: new kind of averaging added, 5 new plots, discussions and conclusions extended, final versio

Study of the derivative expansions for the nuclear structure functions

We study the convergence of the series expansions sometimes used in the analysis of the nuclear effects in Deep Inelastic Scattering (DIS) proccesses induced by leptons. The recent advances in statistics and quality of the data, in particular for neutrinos calls for a good control of the theoretical uncertainties of the models used in the analysis. Using realistic nuclear spectral functions which include nucleon correlations, we find that the convergence of the derivative expansions to the full results is poor except at very low values of $x$

Nuclear Structure Functions at Small x from Inelastic Shadowing and Diffraction

Nuclear structure functions at small x and small or moderate $Q^2$ are studied using the relation with diffraction on nucleons which arises from Gribov's Reggeon Calculus. A reasonable description of experimental data is obtained with no fitted parameters. A comparison with other models and predictions for future lepton-ion colliders are provided. Consequences for the reduction of multiplicities in nucleus-nucleus collisions at energies of RHIC and LHC are examined.Comment: LaTeX, 32 pages, 14 eps figures included using epsfig; 1 reference update

Nuclear size and rapidity dependence of the saturation scale from QCD evolution and experimental data

The solutions of the Balitsky-Kovchegov evolution equations are studied numerically and compared with known analytical estimations. The rapidity and nuclear size dependences of the saturation scale are obtained for the cases of fixed and running coupling constant. These same dependences are studied in experimental data, on lepton-nucleus, deuteron-nucleus and nucleus-nucleus collisions, through geometric scaling and compared with the theoretical calculations.Comment: 8 pages, 8 figures. Contribution based on talks given by J. G. Milhano and C. A. Salgado to the proceedings of ``Hard Probes 2004'', Ericeira (Portugal), November 4-10, 200

On improving robot image-based visual servoing based on dual-rate reference filtering control strategy

It is well known that the use of multi-rate control techniques have improved the performance of many systems in general, and robotic systems, in particular. The main contribution of this paper is the generalization of the Reference Filtering control strategy from a dual-rate point of view, improving its inherent properties by overcoming the problem of sensor latency. In the paper, we discuss and analyze the improvements introduced by the novel dual-rate reference filtering control strategy in terms of convergence time, reachability and robustness. More specifically, we discuss the capability to solve positioning tasks, when hardware limitations are present with large sampling rates. In addition, a comparison is made between the single-rate and the proposed dual-rate control strategies to prove the advantages of the latter approach. A complete set-up has been prepared for validation, including a six degree of freedom (DOF) industrial manipulator, a smart camera and embedded hardware used as a high level controller.This work was supported by VALi+d Program (Generalitat Valenciana), DIVISAMOS Project (Spanish Ministry, DPI-2009-14744-C03-01), PROMETEO Program (Conselleria d'Educacio, Generalitat Valenciana) and SAFEBUS: Ministry of Economy and Competitivity, IPT-2011-1165-370000).Solanes Galbis, JE.; Muñoz Benavent, P.; Girbés, V.; Armesto Ángel, L.; Tornero Montserrat, J. (2015). On improving robot image-based visual servoing based on dual-rate reference filtering control strategy. Robotica. 1-18. https://doi.org/10.1017/S0263574715000454S11

On Hierarchy and Equivalence of Relativistic Equations for Massive Fields

A non-canonical correspondence of the complete sets of solutions to the Dirac and Klein-Gordon free equations in Minkowski space-time is established. This allows for a novel viewpoint on the relationship of relativistic equations for different spins and on the origin of spinor transformations. In particular, starting from a solution to the Dirac equation, one obtains a chain of other solutions to both Dirac and Klein-Gordon equations. A comparison with the massless case is performed, and examples of non-trivial singular solutions are presented. A generalization to Riemannian space-time and inclusion of interactions are briefly discussed.Comment: 7 pages, twocolumn. Problem of construction the hierarchy of solutions in the massive case reformulate

Scattering of shock waves in QCD

The cross section of heavy-ion collisions is represented as a double functional integral with the saddle point being the classical solution of the Yang-Mills equations with boundary conditions/sources in the form of two shock waves corresponding to the two colliding ions. I develop the expansion of this classical solution in powers of the commutator of the Wilson lines describing the colliding particles and calculate the first two terms of the expansion.Comment: 23 pages, 13 figure