Frontiers in Physics (Feb 2020)
A Concise Review of Gradient Models in Mechanics and Physics
Abstract
The various mathematical models developed over the years to interpret the behavior of materials and corresponding processes they undergo were based on observations and experiments made at that time. Classical laws for solids (Hooke) and fluids (Navier–Stokes) form the basis of current technology. The discovery of new phenomena with the aid of newly developed experimental probes have led to various modifications of these laws, especially at small scales. The emergence of nanotechnology is ultimately connected with the design of novel tools for observation and measurements, as well as with the development of new methods and approaches for quantification and understanding. This paper first reviews the author's previously developed weakly non-local or gradient models for elasticity, diffusion, and plasticity. It then proposes a similar extension for fluids and electrodynamics. Finally, it suggests a gradient modification of Newton's law of gravity, with a possible connection to the strong force of elementary particle physics.
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