Classical Physics
Pendulum-like dynamics is a universal motif across many areas of physics, underlying systems ranging from classical nonlinear oscillators to superconducting qubits and cold-atom tunneling platforms. Here we present an exact frequency-domain…
Extremal materials are a specific class of Cauchy materials whose elasticity tensor has one or more zero eigenvalues. Each zero eigenvalue corresponds to a soft mode requiring zero strain energy, while non-zero eigenvalues correspond to…
The relationship between balance laws and the Principle of Virtual Work as well as the structure of contact interactions in continua remain foundational issues in Mechanics. In this work, we revisit these issues within the distributional…
Noting that there is very little literature on the topic, a first analytical approach is proposed in this work for estimating the viscosity-like parameter of three-phase viscoplastic materials. In a first part, the conditions of application…
An outline is given of how Jackson may have obtained the inhomogeneous wave equations for the auxiliary functions $\Psi$ and $\bf V$ in his influential 2002 AJP paper on the transformation from the Lorenz gauge to other electromagnetic…
Despite their apparent simplicity, coupled oscillators exhibit surprisingly complex phenomena. Two notable examples are Berry phase (a geometric or topological aspect of the oscillators' memory) and non-Hermiticity (the often…
We present the variational action principle for initial value problems in classical, conservative-force point particle mechanics. We rigorously derive this formulation by taking the classical limit of the Schwinger-Keldysh expression for…
According to the atomic principle an elementary particle has no excited states and under any interaction, if it is not annihilated, its internal structure cannot be modified. The intrinsic properties are the mass $m$ and the absolute value…
For a gas confined in a container, particle-wall interactions produce modifications to the partition function involving the average surface density of gas particles. While such correlations have a vanishing effect in the thermodynamic…
It is demonstrated that energy conservation allows for a straight derivation of Newtonian mechanics without an apriori definition of the concept of work. Furthermore it is shown that energy must be depicted as a function of position and…
In this note, we analyze the relationships that should govern the use of thermodynamics in fluid mechanics in a way that we believe is understandable to mathematicians. We also aim to better define the reasons why mechanics and…
The radiation-reaction problem of standard Lorentz electrodynamics with point charges is pathological, standing in contrast to Bopp--Land\'e--Thomas--Podolsky (BLTP) electrodynamics where it is in fact well-defined and calculable, as…
Approximate formulas are derived to describe energy loss in a harmonic oscillator that experiences three distinct damping mechanisms: constant-magnitude (Coulomb), velocity-proportional (Stokes), and velocity-squared (Newton), using…
Interesting phenomena occur when an eccentric rigid body rolls on an inclined or horizontal plane. For example, a variety of motions between rolling and sliding are exhibited until suddenly a jump occurs. We provide a detailed theoretical…
This text is the support for the course of Modeling of Solids, of the Master of Mechanics of the University Paris-Saclay - Curriculum MMM: Mathematical Methods for Mechanics, held at Versailles. The course is the continuation of the course…
In an interesting recent paper [1] (A. Acharya, Stress of a spatially uniform dislocation density field, J. Elasticity 137 (2019), 151--155), Acharya proved that the stress produced by a spatially uniform dislocation density field in a body…
Previously we derived the leading term asymptotic solution of temperature distribution in skin heating by an electromagnetic beam at an arbitrary incident angle. The asymptotic analysis is based on that the penetration depth of the beam…
First-order phase transitions are commonly associated with a discontinuous behavior of some of the thermodynamic variables and the presence of a latent heat. In the present study it is shown that this is not necessarily the case. Using…
This study presents an advanced sharp-interface immersed boundary method (IBM) integrated with the blastFOAM library on the OpenFOAM platform for high-speed compressible flow simulations. The developed solver extends the existing IBM…
The four-spacecraft formation is essential for measurements of various physical fields. The use of this formation on substantially elliptical heliocentric Kepler orbits allows measuring gradients of gravitation field in Solar system. The…