Related papers: Dynamics in fractal spaces
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…
Stochastic thermodynamics is a framework for describing non-equilibrium processes at the level of fluctuating trajectories, where the state of a system evolves as a stochastic time series, allowing thermodynamic quantities such as work,…
The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is…
The theoretical understanding of active matter, which is driven out of equilibrium by directed motion, is still fragmental and model oriented. Stochastic thermodynamics, on the other hand, is a comprehensive theoretical framework for driven…
Collisionless suspensions of inertial particles (finite-size impurities) are studied in 2D and 3D spatially smooth flows. Tools borrowed from the study of random dynamical systems are used to identify and to characterise in full generality…
Stochastic growth processes give rise to diverse intricate structures everywhere and across all scales in nature. Despite the seemingly unrelated complex phenomena at their origin, the Laplacian growth theory has succeeded in unifying their…
Fractons are exotic quasiparticles whose mobility in space is restricted by symmetries. In potential real-world realisations, fractons are likely lodged to a physical material rather than absolute space. Motivated by this, we propose and…
We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable…
Fracture processes in heterogeneous materials comprise a large number of disordered spatial degrees of freedom, representing the dynamical state of a sample over the entire domain of interest. This complexity is usually modeled directly,…
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of…
This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the…
A quantum fractal is a wavefunction with a real and an imaginary part continuous everywhere, but differentiable nowhere. This lack of differentiability has been used as an argument to deny the general validity of Bohmian mechanics (and…
In this paper, it is presented the well known aspect of non linearity of internal human body structures. Similarity on the basis of the Fractional Brownian Motion from the static ones, as the geometrical fractals like the Intestine and…
The long time dynamics of large particles trapped in two inhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different…
When an ensemble of particles interact hydrodynamically, they generically display large-scale transient structures such as swirls in sedimenting particles [1], or colloidal strings in sheared suspensions [2]. Understanding these…
We study active run-and-tumble particles with an additional two-state internal variable characterizing their motile or non-motile state. Motile particles change irreversibly into non-motile ones upon collision with a non-motile particle.…
It is shown that preferential concentrations of inertial (finite-size) particle suspensions in turbulent flows follow from the dissipative nature of their dynamics. In phase space, particle trajectories converge toward a dynamical fractal…
We investigate numerically the dynamics and statistics of inertial particles transported by stratified turbulence, in the case of particle density intermediate in the average density profile of the fluid. In these conditions, particles tend…
We study the dynamics of inertial particles in turbulence using datasets obtained from both direct numerical simulations and laboratory experiments of turbulent swirling flows. By analyzing time series of particle velocity increments at…
We introduce a framework to identify Fluctuation Relations for vector-valued observables in physical systems evolving through a stochastic dynamics. These relations arise from the particular structure of a suitable entropic functional and…