Related papers: Classical Liquids in Fractal Dimension
The structural properties of single component fluids of hard hyperspheres in odd space dimensionalities $d$ are studied with an analytical approximation method that generalizes the Rational Function Approximation earlier introduced in the…
We develop a replicated liquid theory for structural glasses which exhibit spatial variation of physical quantities along one axis, say $z$-axis. The theory becomes exact with infinite transverse dimension $d-1 \to \infty$. It provides an…
Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to…
The atomic-level structures of liquids and glasses are amorphous, lacking long-range order. We characterize the atomic structures by integrating radial distribution functions (RDF) from molecular dynamics (MD) simulations for several…
Motivated by the recent appearance of the trillium lattice in the search for materials hosting spin liquids, we study the ground state of the classical Heisenberg model on its linegraph, the trilline lattice. We find that this network…
When strained beyond the linear regime, soft colloidal glasses yield to steady-state plastic flow in a way that is similar to the deformation of conventional amorphous solids. Due to the much larger size of the colloidal particles with…
Using Monte Carlo simulations we study the distributions of the 3-block mass $N_3$ in 4d, 5d, and 6d percolation systems. Because the probability of creating large 3-blocks in these dimensions is very small, we use a ``go with the winners''…
Two-dimensional polar liquid crystals have been discovered recently in monolayers of anisotropic molecules. Here, we provide a systematic theoretical description of liquid-crystalline phases for polar particles in two spatial dimensions.…
The main goal of this paper has a double purpose. On the one hand, we propose a new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting…
We establish pointwise and distributional fractal tube formulas for a large class of relative fractal drums in Euclidean spaces of arbitrary dimensions. A relative fractal drum (or RFD, in short) is an ordered pair $(A,\Omega)$ of subsets…
We view a complex liquid as a network of bonds connecting each particle to its nearest neighbors; the dynamics of this network is a chain of discrete events signaling particles rearrangements. Within this picture, we studied a…
The shapes of cooperatively rearranging regions in glassy liquids change from being compact at low temperatures to fractal or ``stringy'' as the dynamical crossover temperature from activated to collisional transport is approached from…
Using classical density functional theory (DFT) in a modified mean-field approximation we investigate the fluid phase behavior of quasi-two dimensional dipolar fluids confined to a plane. The particles carry three-dimensional dipole moments…
We investigate the discretization of Darcy flow through fractured porous media on general meshes. We consider a hybrid dimensional model, invoking a complex network of planar fractures. The model accounts for matrix-fracture interactions…
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…
We consider the practicalities of defining, simulating, and characterizing "Liquids" from a pedagogical standpoint based on atomistic computer simulations. For simplicity and clarity we study two-dimensional systems throughout. In addition…
A fractal approach to numerical analysis of electromagnetic space-time crystals, created by three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency, is presented. Finite models of electromagnetic…
We study the fractal dimension of the contour of the liquid-gas interface in a spray. Our images include both, the linking region and the break-up region and are obtained with a high-resolution shadowgraph technique; this means that the…
We consider the concept of fractons as particles or quasiparticles which obey a specific fractal statistics in connection with a one-dimensional Luttinger liquid theory. We obtain a dual statistics parameter ${\tilde{\nu}}=\nu+1$ which is…
We construct a non-perturbative fully analytical approximation for the thermodynamics and the structure of nonadditive hard-sphere fluid mixtures. The method essentially lies in a heuristic extension of the Percus-Yevick solution for…