Classical Physics
In geometric algebra, the rotation of a vector is described using rotors. Rotors are phasors where the imaginary number has been replaced by a oriented plane element of unit area called a unit bivector. The algebra in three dimensional…
Numerical simulation of evolution of a cluster of a finite number of gravitating bodies interacting only by their intrinsic gravity has been carried out. The goal of the study was to reveal the main characteristic phases of the spatial…
We explore the stability of floating objects through mathematical modeling and experimentation. Our models are based on standard ideas of center of gravity, center of buoyancy, and Archimedes' Principle. We investigate a variety of floating…
The block medium is modeled by a discrete-periodic spatial lattice of masses connected by elastic springs and viscous dampers. To describe the viscoelastic behavior of the interblock layers, a rheological model of internal friction with two…
Exploring the dynamical response of mechanical metamaterials has gathered increasing attention in the last decades, enabling the design of microstructures exotically interacting with elastic waves (focusing, channeling, band-gaps, negative…
The special theory of relativity has fundamentally changed our views of space and time. The relativity of simultaneity in particular, and the theory of relativity as a whole, still presents significant difficulty for beginners in the…
This work shows how two simple derivations of the centripetal acceleration are fundamentally related to seminal works of Huygens and Newton. A different, more physically motivated derivation is then given.
A coordinate system is proposed for the purposes of analysis of far-field radiation from a localized source at the origin. The proposed coordinates exhibit no singularities over the far-field hemi-sphere, making them a good choice for…
In this work, we study the localization of flexural waves in highly symmetric clusters of scatterers. It is shown that when the scatterers are placed regularly in the perimeter of a circumference the quality factor of the resonances…
Waveguiding in general and acoustic waveguiding in particular are possible at the condition of having a transverse "discontinuity" or modulation of the refractive index. We propose here a radically different approach that relies on imposing…
Metasurfaces provide unique capability in guiding surface waves and controlling their polarization and dispersion properties. One way to do that is by analyzing their equifrequency contours. Equifrequency contours are the 2D projection of…
Three hundred years ago, Antonio Stradivari enjoyed the golden period of the violin making in the human history. Luthiers and researchers endeavor to study his legendary legacy. Unfortunately, a consensus that the present progress has…
Elastic waves scattering off a periodic single and double array of thin cylindrical defects is considered for isotropic materials. An analytical expression for the scattering matrix is obtained by means of the Lippmann-Schwinger formalism…
The boundary-value problem for the perturbation of an electric potential by a homogeneous anisotropic dielectric sphere in vacuum was formulated. The total potential in the exterior region was expanded in series of radial polynomials and…
An explicit compatibility condition formula is presented for the Eulerian left Cauchy-Green deformation tensor field. It is shown to be the appropriate finite-strain counterpart of Saint-Venant's compatibility condition. The difference…
The appearance of the time derivative of the acceleration in the equation of motion (EOM) of an electric charge is studied. It is shown that when an electric charge is accelerated, a stress force exists in the curved electric field of the…
We consider the electrodynamics of electric charges and currents in vacuum and then generalise our results to the description of a dielectric and magnetic material medium : first in spatial algebra (SA) and then in space-time algebra (STA).…
We present a unified framework for the study of wave propagation in homogeneous linear thermo-visco-elastic (TVE) continua, starting from conservation laws. In free-space such media admit two thermo-compressional modes and a shear mode. We…
The Maxwell equations and the constitutive relations describe the classical propagation of electromagnetic waves in continuous matter. Here, we investigate the effects stemming from extended constitutive relations on the propagation of…
We propose a method for the description and simulation of the nonlinear dynamics of slender structures modeled as Cosserat rods. It is based on interpreting the strains and the generalized velocities of the cross sections as basic variables…