Related papers: Physical pendulum model: Fractional differential e…

The fractional operators together with exponential quantum in coordinate and momentum space corresponding to the power of observables are introduced. Based on an exponential relation between energy and momentum, the fractional Schr\"odinger…

We theoretically investigate the optical rotational Doppler Effect using modal expansion method. We find that the frequency shift content is only determined by the surface of spinning object and the reduced Doppler shift is linear to the…

The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…

Inspired by the experimental results of Cuevas et al. (Physical Review Letters 102, 224101 (2009)), we consider theoretically the behavior of a chain of planar rigid pendulums suspended in a uniform gravitational field and subjected to a…

The main result of this work is to obtain the exponential decay of the solutions of a piezoelectric beam model with magnetic effect and delay term. The dampings are inserted into the equation of longitudinal displacement. The terms of…

The oscillation periods bounded by a simple pendulum and an oscillating rigid rod are illustrated using a multiple pendulum. Oscillation periods between these two limits are obtained. A theoretical approach using the Lagrangian formalism…

Analyzing the motion of a roller coaster allows for an instructive introduction of various theoretical concepts in a concrete and enjoyable context. We start by modeling the roller coaster train as a point particle. We then develop more…

We report on memory effects involved in the transient frictional response of a contact interface between a silicone rubber and a spherical glass probe when it is perturbed by changes in the orientation of the driving motion or by velocity…

We discuss a classical anisotropic oscillator and the Foucault pendulum as examples illustrating non-conservation of action variables in integrable classical mechanical systems with adiabatically slow evolution. We also emphasize the…

Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to…

Friction is a phenomenon that manifests across all spatial and temporal scales, from the molecular to the macroscopic scale. It describes the dissipation of energy from the motion of particles or abstract reaction coordinates and arises in…

We propose a new notion of Partial Inertial Manifold to study the long-time asymptotic behavior of dissipative differential equations. As shown on an example, such manifolds may exist in the cases when the classical Inertial manifold does…

Machine learning techniques have emerged as powerful tools to tackle various challenges. The integration of machine learning methods with Physics has led to innovative approaches in understanding, controlling, and simulating physical…

Particles in granular flows are often modeled as frictionless (smooth) inelastic spheres; however, there exist no frictionless grains, just as there are no elastic grains. Our molecular dynamics simulations reveal that friction is essential…

We consider a quantum mechanical system to model the effect of quantum fields on the evolution of the early universe. The system consists of an inverted oscillator bilinearly coupled to a set of harmonic oscillators. We point out that the…

Fractional-order dynamical systems are used to describe processes that exhibit long-term memory with power-law dependence. Notable examples include complex neurophysiological signals such as electroencephalogram (EEG) and blood-oxygen-level…

Models for piezoelectric beams and structures with piezoelectric patches generally ignore magnetic effects. This is because the magnetic energy has a relatively small effect on the overall dynamics. Piezoelectric beam models are known to be…

We developed a discrete two-dimensional model of a cantilever which incorporates the effects of inhomogeneity, the geometry of an attached particle, and the influence of external time-dependent forces. We provide a comparison between the…

Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases, both for aerial granular flows dominated by inertia, and for over-damped suspensions. Concomitantly, the…

In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their dynamics. The class of PDEs we focus on are reaction-diffusion equations but we also…