Related papers: Dynamical covering sets in self-similar sets
We investigate the dynamics of model microswimmers under confinement, in cylindrical geometries, by means of three dimensional direct numerical calculations with fully resolved hydrodynamics. Such swimmers are known to show collective…
We develop a new mathematical model for describing a dynamical system at limited resolution (or finite scale), and we give precise meaning to the notion of a dynamical system having some property at all resolutions coarser than a given…
Existing models for droplet impact prescribe the spreading contact time and effective spreading velocity from asymptotic arguments, which prevents a self-consistent prediction of the maximum spreading ratio across regimes. Here, the total…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
Colloidal building blocks with re-configurable shapes and dynamic interactions can exhibit unusual self-assembly behaviors and pathways. In this work, we consider the phase behavior of colloids coated with surface-mobile polymer brushes…
We consider the rate of volume growth of large Carnot-Carath\'eodory metric balls on a class of unbounded model hypersurfaces in $\mathbb{C}^2$. When the hypersurface has a uniform global structure, we show that a metric ball of radius…
The mechanical properties of cells, which influence the properties of the tissue they belong to, are controlled by various mechanisms. Bi et al. theoretically demonstrated that density-independent rigidity transition occurs in…
The dynamics of the expansion of a Lennard-Jones system, initially confined at high density and subsequently expanding freely in the vacuum, is confronted to an expanding statistical ensemble, derived in the diluted quasi-ideal Boltzmann…
Saturated random sequential adsorption packings built of two-dimensional ellipses, spherocylinders, rectangles, and dimers placed on a one-dimensional line are studied to check analytical prediction concerning packing growth kinetics [A.…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
In this paper we define distance expanding random dynamical systems. We develop the appropriate thermodynamic formalism of such systems. We obtain in particular the existence and uniqueness of invariant Gibbs states, the appropriate…
We are interested in situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result shows that this equality holds for any subset of a self-similar set corresponding to a…
Isomorphs are curves in the thermodynamic phase diagram of invariant excess entropy, structure, and dynamics, while pseudoisomorphs are curves of invariant structure and dynamics, but not of the excess entropy. The latter curves have been…
Accurate measurement of dynamic contact angles in aqueous environments is essential for evaluating surface wettability. However, conventional captive bubble methods often suffer from limitations such as bubble instability and interference…
An approximate analytical scheme of the dynamical mean field theory (DMFT) is developed for the description of the electron (ion) lattice systems with Hubbard correlations within the asymmetric Hubbard model where the chemical potentials…
Smoothed Dissipative Particle Dynamics (SDPD) is a mesoscopic method which allows to select the level of resolution at which a fluid is simulated. In this work, we study the consistency of the resulting thermodynamic properties as a…
In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approximation. This result shows that for a family of limsup sets,…
Following a recent work by Yoshino, we study the aging dynamics of a directed polymer in random media, in 1+1 dimensions. Through temperature quench, and temperature cycling numerical experiments similar to the experiments on real spin…
In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these…
Building on work of Ruelle and Putnam in the Smale space case, Thomsen defined the homoclinic and heteroclinic $C^\ast$-algebras for an expansive dynamical system. In this paper we define a class of expansive dynamical systems, called…