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The effects of saturation and unitarization for hadron-hadron scattering at LHC energies are explored in several models. It is shown that different choices of saturation parameters lead to sizable differences in the energy dependence of…
We use an orthonormal frame approach to provide a general framework for the first order hyperbolic reduction of the Einstein equations coupled to a fairly generic class of matter models. Our analysis covers the special cases of dust and…
The paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov-type…
In this paper we prove a new optimal bound on the logarithmic slope of the elastic slope when: elastic cross section and differential cross sections in forward and backward directions are known from experimental data. The results on the…
We give a phenomenological analysis of the behavior of inelastic, elastic and total cross-sections of the high energy $\textit{pp}$ interaction. In particular, we argue that the universal picture of behavior of cross-sections and their…
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…
The asymptotic behavior of the elastic scattering amplitude by the exchange of graviton between two scalar particles at high energies and fixed momentum transfers is reconsidered in the Logunov-Tavkhelidze equation in the linearized…
At high energy, exclusive meson photo- and electro-production give access to the structure of hadronic matter. At low momentum transfers, the exchange of a few Regge trajectories leads to a comprehensive account of the cross-sections. Among…
We present a simple variational framework for planar elastica that enables distributed energies, such as gravitational loading or magnetic body torques, to be incorporated in a modular and unified manner. The formulation is based on…
It is shown that, for a wide class of functions with physical interest as forward scattering amplitudes, integral dispersion relations can be replaced by derivative forms without any high-energy approximation. The applicability of these…
The evolution equations for Green functions of the Reggeon Field Theory (RFT) are equivalent to those of the inclusive distributions for the reaction-diffusion system of classical particles. We use this equivalence to obtain numerically…
The processes of exclusive diffractive scattering $p+p\to p+p$, $\bar p+p\to\bar p+p$, and $\gamma^*+p\to V+p$ at high energies are considered in the framework of a unified Regge-eikonal model with a very simple reggeon structure of the…
In this paper we derive the high energy evolution equation in the Gribov-Zwanziger approach, for the confinement of quarks and gluons. We demonstrate that the new equation generates an exponential decrease of the scattering amplitude at…
Analysis of new experimental data obtained by the TOTEM and ATLAS Collaborations at the LHC together with old data obtained at the SPS and Tevatron colliders at small momentum transferin the framework of the high energy generalized…
In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for…
We prove a scattering result near certain steady states for a Hartree equation for a random field. This equation describes the evolution of a system of infinitely many particles. It is an analogous formulation of the usual Hartree equation…
The ISR and the 7 TeV LHC data indicate that the differential cross-section of elastic proton-proton scattering remains almost energy-independent at the transferred momentum $t\approx - 0.21\, \mathrm{GeV}^{2}$ at the level of $\approx 7.5…
Pattern-forming nonequilibrium systems are ubiquitous in nature, from driven quantum matter and biological life forms to atmospheric and interstellar gases. Identifying universal aspects of their far-from-equilibrium dynamics and statistics…
Recurrent representations for an electron transmission and reflection amplitudes for a one-dimensional chain are obtained. The linear differential equations for scattering amplitudes of an arbitrary potential are found.
We discuss a model which gives a `global' description of the wide variety of high-energy elastic and diffractive data that are presently available, particularly from the LHC experiments. The model is based on only one pomeron pole, but…