Narrow Results

The following effects in the nearly forward ("soft") region of the LHC are proposed to be investigated:

• At small |t| the fine structure of the cone (Pomeron) should be scrutinized: (a) a break of the cone near t ≈ -0.1 GeV², due to the two-pion threshold, and required by t-channel unitarity, and (b) possible small-period oscillations between t = 0 and the dip region.

• In measuring the elastic pp scattering and total pp cross-section at the LHC, the experimentalists are urged to treat the total cross-section σ_t, the ratio ρ of real to imaginary part of the forward scattering amplitude, the forward slope B and the luminosity as free parameters, and to publish model-independent results on dN/dt.

• Of extreme interest are the details of the expected diffraction minimum in the differential cross-section. Its position, expected in the interval 0.4 < -t < 1 GeV² at the level of about 10^-2mb · GeV^-2–10^-1mb · GeV^-2, cannot be predicted unambiguously, and its depth, i.e. the ratio of dσ/dt at the minimum to that at the subsequent maximum (about -t = 5 GeV², which is about 5) is of great importance.

• The expected slow-down with increasing |t| of the shrinkage of the second cone (beyond the dip-bump), together with the transition from an exponential to a power decrease in -t, will be indicative of the transition from "soft" to "hard" physics. Explicit models are proposed to help in quantifying this transition.

• In a number of papers a limiting behavior, or saturation of the black disk limit (BDL), was predicted. This controversial phenomenon shows that the BDL may not be the ultimate limit, instead a transition from shadow to antishadow scattering may by typical of the LHC energy scale.

The Bialas–Bzdak model of elastic proton–proton scattering is generalized to the case when the real part of the parton–parton level forward scattering amplitude is nonvanishing. Such a generalization enables the model to describe well the dip region of the differential cross-section of elastic scattering at the intersecting storage rings (ISR) energies, and improves significantly the ability of the model to describe also the recent TOTEM data at LHC energy. Within this framework, both the increase of the total cross-section, as well as the decrease of the location of the dip with increasing colliding energies, is related to the increase of the quark–diquark distance and to the increase of the "fragility" of the protons with increasing energies. In addition, we present and test the validity of two new phenomenological relations: one of them relates the total p+p cross-section to an effective, model-independent proton radius, while the other relates the position of the dip in the differential elastic cross-section to the measured value of the total cross-section.

The Bialas–Bzdak model of elastic proton–proton scattering assumes a purely imaginary forward scattering amplitude, which consequently vanishes at the diffractive minima. We extended the model to arbitrarily large real parts in a way that constraints from unitarity are satisfied. The resulting model is able to describe elastic pp scattering not only at the lower ISR energies but also at in a statistically acceptable manner, both in the diffractive cone and in the region of the first diffractive minimum. The total cross-section as well as the differential cross-section of elastic proton–proton scattering is predicted for the future LHC energies of , 14, 15 TeV and also to 28 TeV. A nontrivial, significantly nonexponential feature of the differential cross-section of elastic proton–proton scattering is analyzed and the excitation function of the nonexponential behavior is predicted. The excitation function of the shadow profiles is discussed and related to saturation at small impact parameters.

We present a new model of human cardiac electromechanics for the left ventricle where electrophysiology is described by a Reaction–Eikonal model and which enables an off-line resolution of the reaction model, thus entailing a big saving of computational time. Subcellular dynamics is coupled with a model of tissue mechanics, which is in turn coupled with a Windkessel model for blood circulation. Our numerical results show that the proposed model is able to provide a physiological response to changes in certain variables (end-diastolic volume, total peripheral resistance, contractility). We also show that our model is able to reproduce with high accuracy and with a considerably lower computational time the results that we would obtain if the monodomain model should be used in place of the Eikonal model.

A phenomenological method of analysis for heavy-ion elastic scattering data at intermediate energies is proposed within the framework of the optical limit approximation of the Glauber multiple scattering theory. The essential point of our method is to evaluate the NN scattering amplitude in terms of a phenomenological effective NN potential the parameters of which are varied to fit the experimental data. It is applied to analyze ¹²C–¹²C elastic scattering data in the energy range of 25–200 MeV/nucleon with a good degree of success.

We present a Coulomb-modified eikonal model formalism based on hyperbolic trajectory for heavy-ion elastic scattering. This formalism has been applied satisfactorily to elastic scatterings of the ¹²C + ¹²C system at E_lab=240, 360 and 1016 MeV. The presence of a nuclear rainbow in this system is evidenced through a classical deflection function. The Fraunhöfer oscillations observed in the elastic angular distributions can be explained due to interference between the near- and far-side amplitudes. We have found that the hyperbolic trajectory effect on the eikonal model is important when the absorptive potential is weak and the real potential is strong.