Related papers: Equivalence between Geometric Frequency and Lagran…
Plane electromagnetic and gravitational waves interact with particles in such a way as to cause them to oscillate not only in the transverse direction but also along the direction of propagation. The electromagnetic case is usually shown by…
Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…
In this paper we construct periodic capillarity-gravity water waves with a piecewise constant vorticity distribution. They describe water waves traveling on superposed linearly sheared currents that have different vorticities. This is…
This paper introduces the trajectory divergence rate, a scalar field which locally gives the instantaneous attraction or repulsion of adjacent trajectories. This scalar field may be used to find highly attracting or repelling invariant…
A statistical mechanism is proposed for symmetrization of an extra space. The conditions and rate of attainment of a symmetric configuration and, as a consequence, the appearance of gauge invariance in low-energy physics is discussed. It is…
In the present manuscript, I examine an intriguing relation at the classical level between general relativity and a theory where matter couples uniquely multiplicatively to geometry in the Lagrangian density. Interestingly, the…
We present an innovative technique which allows the simultaneous measurement of the dielectric constant of a material at many frequencies, spanning a four orders of magnitude range chosen between 10 --2 Hz and 10 4 Hz. The sensitivity and…
First we discuss the definition of the instantaneous current in interacting particle systems, in particular in mass-energy systems and we point out its role in the derivation of the hydrodynamics. Later we present some geometrical…
Lagrangian averaging has been shown to be more effective than Eulerian mean in separating waves from slow dynamics in two-timescale flows. It also appears in many reduced models that capture the wave feedback on the slow flow. Its…
String vibration represents an active field of research in acoustics. Small-amplitude vibration is often assumed, leading to simplified physical models that can be simulated efficiently. However, the inclusion of nonlinear phenomena due to…
The nonlinear frequency shift is derived in a transparent asymptotic form for intense Langmuir waves in general collisionless plasma. The formula describes both fluid and kinetic effects simultaneously. The fluid nonlinearity is expressed,…
Extracting scientific understanding from particle-physics experiments requires solving diverse learning problems with high precision and good data efficiency. We propose the Lorentz Geometric Algebra Transformer (L-GATr), a new…
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…
This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with…
We discuss the emergence of time in quantum gravity, and ask whether time is always "something that flows"'. We first recall that this is indeed the case in both relativity and quantum mechanics, although in very different manners: time…
Lagrangian Descriptors (LDs) are scalar quantities able to reveal separatrices, manifolds of hyperbolic saddles, and chaotic seas of dynamical systems. A popular version of the LDs consists in computing the arc-length of trajectories over a…
In this paper we discuss some properties of linear fractional dispersive waves. In particular, we compare the dispersion relations emerging from the kinematic wave equation and from the linearised Korteweg - de Vries equation with the…
In this mostly pedagogical tutorial article a brief introduction to modern geometrical treatment of fluid dynamics and electrodynamics is provided. The main technical tool is standard theory of differential forms. In fluid dynamics, the…
Reflectance and transmittance of graphene in the optical region are analyzed as a function of frequency, temperature, and carrier density. We show that the optical graphene properties are determined by the direct interband electron…
Typical applications of gravitational lensing use the properties of electromagnetic or gravitational waves to infer the geometry through which those waves propagate. Nevertheless, the optical fields themselves - as opposed to their…