Related papers: Physical pendulum model: Fractional differential e…
The object of this laboratory work: to explore dependence mass point oscillatory motion parameters in the following cases: - without resistance (free oscillations); - the resistance force is proportional to the velocity vector; - the…
The dynamics and the transition to the centrifugal regime are studied analytically and numerically for particles in rotating drum. The importance of the particle-wall friction coefficient is demonstrated by studying first the motion of one…
When granular systems are modeled by frictionless hard spheres, particle-particle collisions are considered as instantaneous events. This implies that while the velocities change according to the collision rule, the positions of the…
We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics." The presence of…
Because the local concentration of vacancies in any material is bounded, their motion must be accompanied by nonlinear effects. Here we look for such effects in a simple model for electric field driven vacancy motion in memristors, solving…
A model system inspired by recent experiments on the dynamics of a folded protein under the influence of a sinusoidal force is investigated and found to replicate many of the response characteristics of such a system. The essence of the…
Fractional equations appear in the description of the dynamics of various physical systems. For Lagrangian systems, the embedding theory developped by Cresson ["Fractional embedding of differential operators and Lagrangian systems", J.…
This work aims to raise awareness among engineering students from different disciplines on the importance of feedback control. The proposal consists in comparing the performance of different control strategies in a laboratory session,…
We demonstrate that an effect other than anharmonicity can severely distort the spectroscopic signatures of quantum mechanical systems. This is done through an analytic calculation of the spectroscopic response of a simple system, a charged…
Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
Most field theories for active matter neglect effects of memory and inertia. However, recent experiments have found inertial delay to be important for the motion of self-propelled particles. A major challenge in the theoretical description…
In this paper, we present a theory of six classes of vibrators with variable-order fractional forces of inertia, damping, and restoration. The novelty and contributions of the present theory are reflected in six aspects. 1) Equivalent…
We introduce a classical fractional particle model in $\mathbb{R}^{n}$, extending the Newtonian particle concept with the incorporation of the fractional Laplacian. A comprehensive discussion on kinetic properties, including linear momentum…
A Swinging Atwood Machine (SAM) is built and some experimental results concerning its dynamic behaviour are presented. Experiments clearly show that pulleys play a role in the motion of the pendulum, since they can rotate and have…
Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes,…
Two low-dimensional magnetohydrodynamic models containing three velocity and three magnetic modes are described. One of them (nonhelical model) has zero kinetic and current helicity, while the other model (helical) has nonzero kinetic and…
Computational studies of the thermodynamic properties of materials at the mesoscopic and macroscopic scales -- involving lengths and times of at least $\mu$m and $\mu$s, respectively -- rely on a coarse-graining approximation such that only…
Dynamical stabilization processes (homeostasis) are ubiquitous in nature, but energetic resources needed for their existence were not studied systematically. Here we undertake such a study using the famous model of Kapitza's pendulum, which…
A spherical robot has many practical advantages as the entire electronics are protected within a hull and can be carried easily by any Unmanned Aerial Vehicle (UAV). However, its use is limited due to finding mounts for sensors. Pendulum…