Related papers: Classical Liquids in Fractal Dimension
We address the crystallization of monodisperse hard spheres in terms of the properties of finite- size crystalline clusters. By means of large scale event-driven Molecular Dynamics simulations, we study systems at different packing…
Mixtures of hard hyperspheres in odd space dimensionalities are studied with an analytical approximation method. This technique is based on the so-called Rational Function Approximation and provides a procedure for evaluating equations of…
We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
Phase field crystal (PFC) models constitute central tools for a microscopic understanding of the dynamics of complex systems in soft matter physics. They have found widespread application in the modeling of the uniaxial orientational…
Atmospheric flows exhibit cantorian fractal space-time fluctuations signifying long-range spatiotemporal correlations. A recently developed cell dynamical system model shows that such non-local connections are intrinsic to quantum-like…
We present a complete numerical analysis for a general discretization of a coupled flow-mechanics model in fractured porous media, considering single-phase flows and including frictionless contact at matrix-fracture interfaces, as well as…
Spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal…
The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially fractal geometry in Euclidean spaces. We survey these developments, with emphasis on connections…
In this paper we introduce a numerical scheme for fluid-structure interaction problems in two or three space dimensions: A flexible elastic plate is interacting with a viscous, compressible barotropic fluid. Hence the physical domain of…
We present a systematic characterization of the fractal conduction pathways governing ionic transport in a non-crystalline solid below the glass-transition temperature. Using classical molecular dynamics simulations of lithium metasilicate,…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
We present a direct numerical simulation method for investigating the dynamics of dispersed particles in a compressible solvent fluid. The validity of the simulation is examined by calculating the velocity relaxation of an impulsively…
We introduce new classes of hydrodynamic theories inspired by the recently discovered fracton phases of quantum matter. Fracton phases are characterized by elementary excitations (fractons) with restricted mobility. The hydrodynamic…
We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the…
Fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems. Here, we focus on lattice multifractals which exhibit complex exponents associated with…
We introduce a three-dimensional model for jamming and glasses, and prove that the fraction of frozen particles is discontinuous at the directed-percolation critical density. In agreement with the accepted scenario for jamming- and…
Clouds in observations are fractals: they show self-similarity across scales ranging from one to 1000 km. This includes individual storms and large-scale cloud structures typical of organised convection. It is not known whether global…
This work presents a detailed analytical and geometrical investigation of the (2+1)-dimensional Boiti-Leon-Pempinelli system, a nonlinear dispersive model arising in the context of fluid and plasma dynamics. By employing a projective…
Central place systems have been demonstrated to possess self-similar patterns in both the theoretical and empirical perspectives. A central place fractal can be treated as a monofractal with a single scaling process. However, in the real…