On upstream influence in supersonic flows

The general problem of propagation of three-dimensional disturbances in viscous supersonic flows is considered in the framework of characteristic analysis. Unlike previous results for linear disturbances we deduce a condition determining nonlinear characteristic surfaces which is exact and therefore allows both qualitative and quantitative studies of the speed of propagation as a function of various physical phenomena. These include negative and adverse pressure gradients, and effects of wall cooling and suction–blowing, which are studied in this work as an illustration of the general theory

QCD Saturation Equations including Dipole-Dipole Correlation

We derive two coupled non-linear evolution equations corresponding to the truncation of the Balitsky infinite hierarchy of saturation equations after inclusion of dipole-dipole correlations, i.e. one step beyond the Balitsky-Kovchegov (BK) equation. We exhibit an exact solution for maximal correlation which still satisfies the same asymptotic geometric scaling as BK but with the S-matrix going to 1/2 (instead of 0) in the full saturation region.Comment: 4 pages, no figure. Comment, references and acknowledgment adde

Fronts in passive scalar turbulence

The evolution of scalar fields transported by turbulent flow is characterized by the presence of fronts, which rule the small-scale statistics of scalar fluctuations. With the aid of numerical simulations, it is shown that: isotropy is not recovered, in the classical sense, at small scales; scaling exponents are universal with respect to the scalar injection mechanisms; high-order exponents saturate to a constant value; non-mature fronts dominate the statistics of intense fluctuations. Results on the statistics inside the plateaux, where fluctuations are weak, are also presented. Finally, we analyze the statistics of scalar dissipation and scalar fluxes.Comment: 18 pages, 27 figure

Reggeon Interactions in Perturbative QCD

We study the pairwise interaction of reggeized gluons and quarks in the Regge limit of perturbative QCD. The interactions are represented as integral kernels in the transverse momentum space and as operators in the impact parameter space. We observe conformal symmetry and holomorphic factorization in all cases.Comment: 13 pages LATEX, 2 figures using package FEYNMAN, N4-9

Mandelstam cuts and light-like Wilson loops in N=4 SUSY

We perform an analytic continuation of the two-loop remainder function for the six-point planar MHV amplitude in N=4 SUSY, found by Goncharov, Spradlin, Vergu and Volovich from the light-like Wilson loop representation. The remainder function is continued into a physical region, where all but two energy invariants are negative. It turns out to be pure imaginary in the multi-Regge kinematics, which is in an agreement with the predictions based on the Steinmann relations for the Regge poles and Mandelstam cut contributions. The leading term reproduces correctly the expression calculated by one of the authors in the BFKL approach, while the subleading term presents a result, that was not yet found with the use of the unitarity techniques. This supports the applicability of the Wilson loop approach to the planar MHV amplitudes in N=4 SUSY.Comment: 11 pages, 4 figure

BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes

After a brief review of the BFKL approach to Regge processes in QCD and in supersymmetric (SUSY) gauge theories we propose a strategy for calculating the next-to-next-to-leading order corrections to the BFKL kernel. They can be obtained in terms of various cross-sections for Reggeized gluon interactions. The corresponding amplitudes can be calculated in the framework of the effective action for high energy scattering. In the case of N=4 SUSY it is also possible to use the Bern-Dixon-Smirnov (BDS) ansatz. For this purpose the analytic properties of the BDS amplitudes at high energies are investigated, in order to verify their self-consistency. It is found that, for the number of external particles being larger than five, these amplitudes, beyond one loop, are not in agreement with the BFKL approach which predicts the existence of Regge cuts in some physical channels.Comment: 41 pages, expanded version with many clarifications and new references, conclusions unchanged. Note adde

QCD traveling waves beyond leading logarithms

We derive the asymptotic traveling-wave solutions of the nonlinear 1-dimensional Balitsky-Kovchegov QCD equation for rapidity evolution in momentum-space, with 1-loop running coupling constant and equipped with the Balitsky-Kovchegov-Kuraev-Lipatov kernel at next-to-leading logarithmic accuracy, conveniently regularized by different resummation schemes. Traveling waves allow to define "universality classes" of asymptotic solutions, i.e. independent of initial conditions and of the nonlinear damping. A dependence on the resummation scheme remains, which is analyzed in terms of geometric scaling properties.Comment: 10 pages, 5 figures; typos corrected, references updated, final Phys.Rev. D versio

Quark-nucleon dynamics and Deep Virtual Compton Scattering

We consider deeply virtual Compton scattering and deep inelastic scattering in presence of Regge exchanges that are part of the non-perturbative quark-nucleon amplitude. In particular we discuss contribution from the Pomeron exchange and demonstrate how it leads to Regge scaling of the Compton amplitude. Comparison with HERA data is given.Comment: 12 pages, 5 figure