Related papers: Clasical solids dynamics as 4D statics of elastic …
Mechanical and elastic properties of materials are among the most fundamental quantities for many engineering and industrial applications. Here, we present a formulation that is efficient and accurate for calculating the elastic and bending…
A full selfconsistent set of equations is deduced to describe the kinetics and dynamics of charged quasiparticles (electrons, holes etc.) with arbitrary dispersion law in crystalline solids subjected to time-varying deformations. The set…
From the mesoscopic point of view, a new concept of soft matching for mass points is proposed. Then a soft Lasso's approach to learn the soft dynamical equation for the physical mechanical relationship is proposed, too. Furthermore, a…
An explicit dynamical model for non relativistic quantum mechanics with an effective gravitational interaction is proposed, which, as being well defined, allows in principle for the evaluation of every physical quantity. Its non unitary…
Classical, Quantum and Relativistic mechanics elect time and space as fundamentals, extracting the measure of motion -velocity- from this static space-time platform. Conversely, the timelessness of Statistical mechanics computes the…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
For the first time a method is devised for non-iterative modeling of motion of a radiating, electrified pointlike mass that has an internal structure. New, supplementary kinetic constants of accelerated charged particles are defined, that…
A new microscopic derivation of the elastic constants of amorphous solids is presented within the framework of nonaffine lattice dynamics, which makes use of a perturbative form of the low-frequency eigenvectors of the dynamical matrix…
Using the contemporary thermodynamic equations of elastic solids leads to contradictions with the fundamental statements of thermodynamics. Two examples are presented to expose the inconsistencies. In example one the internal energy between…
We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…
In heterogeneous solids such as rocks and concrete, the speed of sound diminishes with the strain amplitude of a dynamic loading (softening). This decrease known as "slow dynamics" occurs at time scales larger than the period of the…
We consider a charged particle moving in the plane subject to electromagnetic potentials with non-vanishing radial limits. We analyse the classical and the quantum dynamics for large time in the case the angular part of the (limiting)…
We present a relativistic formalism inspired on the Minkowski four-vectors that also includes conservation laws such as the first law of thermodynamics. It remains close to the relativistic four-vector formalism developed for a single…
We present an overdamped continuum description of oriented active solids in which interactions respect the symmetries of space but do not obey the principle of action and reaction. Taking position and orientation as kinematic variables, we…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
A statistical theory of cholesteric liquid crystals composed of short rigid biaxial molecules is presented. It is derived in the thermodynamic limit at a small density and a small twist. The uniaxial (biaxial) cholesteric phase is regarded…
The existence of static self-gravitating Newtonian elastic balls is proved under general assumptions on the constitutive equations of the elastic material. The proof uses methods from the theory of finite-dimensional dynamical systems and…
Recent progress in approaches to determine the elastic constants of solids starting from the microscopic particle interactions is reviewed. On the theoretical side, density functional theory approaches are discussed and compared to more…
The formalism of classical particle dynamics is reinvestigated according to the basic requirement of causal consistency, and a new equation of particle dynamics, which is more general and more in line with classical mechanics experiments…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…