A shallow-layer model for granular flows is completed with a closure relation for the macroscopic bed friction or basal roughness obtained from micro-scale discrete particle simulations of steady flows. We systematically vary the bed friction by changing the contact friction coefficient between basal and flowing particles, while the base remains geometrically rough. By simulating steady uniform...

In the framework of the classical Maxwell-Lorentz electrodynamics the energy conservation law is reconsidered.

Using the Spencer-Goldschmidt version of the Cartan-Kähler theorem, we give conditions for (local) existence of conservation laws for analytical quasi-linear systems of two independent variables. This result is applied to characterize the recursion operator (in the sense of Magri) of completely integrable systems. Introduction A conservation law for a (1-1) tensor field h on a manifold M is a 1...

Under certain conditions usually fulfilled in classical mechanics, the principle of conservation of linear momentum and the Newton’s third law are equivalent. However, the demonstration of such fact is usually incomplete in textbooks. We shall show here that to demonstrate the equivalence, we require the explicit use of the principle of superposition contained in the Newton’s second law. On the...

A recently developed micrometer-scale spatially offset Raman spectroscopy (μ-SORS) method provides a new analytical capability for investigating non-destructively the chemical composition of sub-surface, micrometer-scale thickness, diffusely scattering layers at depths beyond the reach of conventional confocal Raman microscopy. Here, we demonstrate experimentally, for the first time, the capabi...