We present a summary of the rotating Lepton model (RLM) of composite particles which is a Bohr-type model using gravity rather than electrostatic attraction as the centripetal force and examines the formation of hadrons via the rotational motion of three gravitating relativistic neutrinos. Model solution via the use of Special or General relativity and of the de Broglie wavelength equation shows that the three neutrinos can get confined in circular orbits of fm radii with velocities extremely close to the speed of light. The computed Lorentz factor 𝛾(= (1 − v 2 ∕c 2 ) −1∕2 ) is ∼ 7.16 ⋅ 10 9 which, via energy conversation, implies that the mass of the composite particle (e.g., of a neutron) is a factor of 𝛾 larger than the rest mass of the three rotating neutrinos (∼0.14 eV/c 2 ), and equal (within 1%) with the experimental neutron mass value (∼ 939 MeV/c 2 ). The computed rotational radius (0.63 fm) is also in quantitative agreement with the experimental value. The application of the RLM to compute the masses of heavier composite particles, such as hadrons, bosons and mesons is then briefly oulined, together with its use to compute the masses of neutrinos from hadron masses and to relate the Strong and Weak nuclear forces with relativistic gravity.

An account of non-singular solutions of gradient elasticity (GradEla) models for dislocations, along with clarifications of certain issues raised on previously published results, is given. Then, an extension to fractional GradEla solutions is pursued and certain preliminary results on this emerging topic are listed.

An introductory discussion on a (weakly non-local) gradient generalization of some one-dimensional elastic and viscoelastic models, and their fractional extension is provided. Emphasis is placed on the possible implications of micro- and nano- engineering problems, including small-scale structural mechanics and composite materials, as well as collagen biomechanics and nanomaterials.

Motivated by the special theory of gradient elasticity (GradEla), a proposal is advanced for extending it to construct gradient models for interatomic potentials, commonly used in atomistic simulations. Our focus is on London's quantum mechanical potential which is an analytical expression valid until a certain characteristic distance where "attractive" molecular interactions change character and become "repulsive" and cannot be described by the classical form of London's potential. It turns out that the suggested internal length gradient (ILG) generalization of London's potential generates both an "attractive" and a "repulsive" branch, and by adjusting the corresponding gradient parameters, the behavior of the empirical Lennard-Jones potentials is theoretically captured.

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