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In the framework of Glauber optical limit approximation, considering the proton has an outer pion cloud of radius ∼ 0.87 f m and an inner core of radius ∼ 0.44 f m where the valence three quarks are confined, and including two-gluon exchange three-quark force, a good fit with the experimental data of p-p elastic scattering differential cross section up to q 2 ≈ 3 (GeV/c) 2 , total cross section and the ratio of real to imaginary parts of elastic scattering amplitude in the forward direction is obtained at laboratory momenta 200, 290, 500, 1070 and 1500 GeV/c. The radii of two-quark interaction r t and three-quark force r th are calculated. The quant energy representing the gluon E g is evaluated.

Inclined uniform magnetic field and mixed convention effects on micropolar non-Newtonian nanofluid Al2O3 flow with heat transfer are studied. The heat source, both viscous and ohmic dissipation and temperature micropolarity properties are considered. We transformed our system of non-linear partial differential equations into ordinary equations by using suitable similarity transformations. These equations are solved by making use of Rung–Kutta–Merson method in a shooting and matching technique. The numerical solutions of the tangential velocity, microtation velocity, temperature and nanoparticle concentration are obtained as functions of the physical parameters of the problem. Moreover, we discussed the effects of these parameters on the numerical solutions and depicted graphically. It is obvious that these parameters control the fluid flow. It is noticed that the tangential velocity magnifies with an increase in the value of Darcy number. Meanwhile, the value of the tangential velocity reduces with the elevation in the value of the magnetic field parameter. On the other hand, the elevation in the value of Brownian motion parameter leads to a reduction in the value of fluid temperature. Furthermore, increasing in the value of heat source parameter makes an enhancement in the value of nanoparticles concentration. The current study has many accomplishments in several scientific areas like medical industry, medicine, and others. Therefore, it represents the depiction of gas or liquid motion over a surface. When particles are moving from areas of high concentration to areas of low concentration.

An approach for the three-body force effect in the optical limit approximation is suggested. The differential cross sections of p−, p− and π − − d elastic scattering at 1.75 and 12.8 GeV/c for incident proton, 2 GeV/c for anti-proton and 9 GeV/c for pion are studied. The D-state and phase variation effects are considered. The experimental data is well described including the 2π -exchange three-body force. The three-body force effect, in this approach, plays a principal role over the complete range of momentum transfer square where the data is available.

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