Mechanics in the Eighteenth Century

This article focuses on mechanics in the eighteenth century. The publication in 1687 of Isaac Newton’s Mathematical Principles of Natural Philosophy has long been regarded as the event that ushered in the modern period in mathematical physics. The success and scope of the Principia heralded the arrival of mechanics as the model for the mathematical investigation of nature. This subject would be at the cutting edge of science for the next two centuries. This article first provides an overview of the fundamental principles and theorems of mechanics, including the principles of inertia and relativity, before discussing the dynamics of rigid bodies. It also considers the formulation of mechanics by Jean-Baptiste le Rond d’Alembert and Joseph-Louis Lagrange, the statics and dynamics of elastic bodies, and the mechanics of fluids. Finally, it describes major developments in celestial mechanics.

Simulation of electromagnetic scattering with stationary or accelerating targets

The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be modeled in this context since they turn out to be explicit solutions. From the numerical viewpoint, the interaction of these waves with a material body is examined. Computations are carried out via a parallel high-order finite-differences code. Due to the presence of a gradient of pressure in the model equations, waves hitting the obstacle may impart acceleration to it. Some explicative 2D dynamical configurations are then studied, enabling the simulation of photon-particle iterations through classical arguments.

Micro-Mechanics of Contact Erosion

In the present paper a simulation framework is presented coupling the mechanics of fluids and solids to study the contact erosion phenomenon. The fluid is represented by the Lattice Boltzmann Method (LBM) and the soil particles are modeled using the Discrete Element Method (DEM). The coupling law considers accurately the momentum transfer between both phases. A soil composed of particles of two distinct sizes is simulated by the DEM and then hydraulically loaded with an LBM fluid. It is observed how the hydraulic gradient compromises the stability of the soil by pushing the smaller particles into the voids between the largest ones. The hydraulic gradient is more pronounced in the areas occupied by the smallest particles due to a reduced constriction size, which at the same time increases the buoyancy acting on them. At the mixing zone, where both particles sizes coexist, the fluid transfers its momentum to the small particles, increasing the erosion rate in the process. The results offer new insights into the erosion and suffusion processes, which could be used to better predict and design structures on hydraulically loaded soils.