Related papers: Classical Liquids in Fractal Dimension
We apply connectedness percolation theory to fractal liquids of hard particles, and make use of a Percus-Yevick liquid state theory combined with a geometric connectivity criterion. We find that in fractal dimensions the percolation…
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension $d$ ($1 \leq d \leq 3$) are developed as heuristic interpolations from the knowledge of…
The fractal dimension of a liquid column is a crucial parameter in several models describing the main features of the primary break-up occurring at the interface of a liquid phase surrounded by the gas-flow. In this work, the deformation of…
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…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
The paper deals with the fundamental problem of a modeling of the physical, in particular, thermal hydraulic processes, in various media of fractal structure of the natural, technological and technical systems and devices. The examples of a…
The complex behavior of liquid ${}^4$He and liquid ${}^3$He in nanoporous media is determined by influence of randomly distributed geometrical confinement as well as by significant contribution from the atoms near walls. In the present…
Using liquid integral equation theory, we calculate the pair correlations of particles that interact via a smooth repulsive pair potential in d = 4 spatial dimensions. We discuss the performance of different closures for the…
Using a generalization of vector calculus for the case of non-integer dimensional space we consider a Poiseuille flow of an incompressible viscous fractal fluid in the pipe. Fractal fluid is described as a continuum in non-integer…
The formulation of the mean-field, infinite-dimensional solution of hard sphere glasses is a significant milestone for theoretical physics. How relevant this description might be for understanding low-dimensional glass-forming liquids,…
Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the…
Fracton emerges from strongly interacting many-body systems whose excitations, referred to as sub-dimensional particles, have restricted mobility or kinetic motions. These entities have garnered significant interest due to their…
We use fractional integrals to generalize the description of hydrodynamic accretion in fractal media. The fractional continuous medium model allows the generalization of the equations of balance of mass density and momentum density. These…
Anomalous short- and long-time self-diffusion of non-overlapping fractal particles on a percolation cluster with spreading dimension $1.67(2)$ is studied by dynamic Monte Carlo simulations. As reported in Phys. Rev. Lett. 115, 097801…
The interstellar medium seems to have an underlying fractal structure which can be characterized through its fractal dimension. However, interstellar clouds are observed as projected two-dimensional images, and the projection of a…
We obtain analytic expressions for the time correlation functions of a liquid of spherical particles, exact in the limit of high dimensions $d$. The derivation is long but straightforward: a dynamic virial expansion for which only the first…
Perfect fractals are mathematical objects that, because they are generated by recursive processes, have self-similarity and infinite complexity. In particular, they also have a fractional dimension. Although several proposals for the study…
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical…
We review some of the exactly solvable one dimensional continuum fluid models of equilibrium classical statistical mechanics under the unified setting of functional integration in one dimension. We make some further developments and remarks…
An accurate modeling of reactive flows in fractured porous media is a key ingredient to obtain reliable numerical simulations of several industrial and environmental applications. For some values of the physical parameters we can observe…