Related papers: Scale- and Structure-Dependent Fractal Dimensions …
The air entrainment due to the turbulence in a free surface boundary layer shear flow created by a horizontally moving vertical surface-piercing wall is studied through experiments and direct numerical simulations. In the experiments, a…
Many natural and engineering systems involve the mixing of two fluid streams, in which the effects of density and viscosity gradients play important roles in determining flow stability. We perform linear stability calculations for a jet…
Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) have been employed to investigate the dynamics of finite-size spherical particles, slightly heavier than the carrier fluid, in a horizontal turbulent square duct flow.…
The breakup dynamics of a capillary bridge on a hydrophobic stripe between two hydrophilic stripes is studied experimentally and numerically using direct numerical simulations. The capillary bridge is formed from an evaporating water…
We study the structures of ultra-relativistic jets injected into the intracluster medium (ICM) and the associated flow dynamics, such as shocks, velocity shear, and turbulence, through three-dimensional relativistic hydrodynamic (RHD)…
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored…
The Interstellar Medium seems to have an underlying fractal structure, which can be characterized through its fractal dimension (Df). However, several factors may affect the determination of Df, such as distortions due to projection, low…
We propose diagrams representing the equilibrium morphologies of two immiscible liquid droplets brought into contact. We study the dependence of the shape of the droplets on the surface tensions and ratio of volumes. We study theoretically…
The phase behavior of liquids confined in a slit geometry does not reveal a crossover from a three to a two-dimensional behavior as the gap size decreases. Indeed, the prototypical two-dimensional hexatic phase only occurs in liquids…
Fractal-like structures of varying complexity are common in nature, and measure-based dimensions (Minkowski, Hausdorff) supply their basic geometric characterization. However, at the level of fundamental dynamics, which is quantum,…
We review understanding of kinetics of fluid phase separation in various space dimensions. Morphological differences, percolating or disconnected, based on overall composition in a binary liquid or density in a vapor-liquid system, have…
The breakup of water droplets when exposed to high-speed gas flows is investigated using both high-magnification shadowgraphy experiments as well as fully three-dimensional numerical simulations, which account for viscous as well as…
Fractal dimensions can be used to characterize the clustering and lacunarities in density distributions. We use generalized fractal dimensions to study the neutral hydrogen distribution (HI) during the epoch of reionization. Using a…
Fractal structures naturally emerge in quantum systems whose initial states exhibit spatial discontinuities, a phenomenon first identified by Berry in the paradigmatic case of a particle confined in an infinite potential well. While…
Partially motivated by the desire to better understand the connectivity phase transition in fractal percolation, we introduce and study a class of continuum fractal percolation models in dimension d greater than or equal to 2. These include…
As a fluid object breaks, it often leaves behind satellite fragments. Here we show that satellite formation can follow universal dynamics, leading to robust satellite sizes. Specifically, we consider the breakup of a slowly stretched fluid…
Aqueous foams and a wide range of related systems are believed to coarsen by gas diffusion between neighboring domains into a statistically self-similar scaling state, after the decay of initial transients, such that dimensionless size and…
The conformation and scaling properties of self-avoiding fluid vesicles with zero extrinsic bending rigidity subject to an internal pressure increment $\Delta p>0$ are studied using Monte Carlo methods and scaling arguments. With increasing…
We study dimensional properties of visible parts of fractal percolation in the plane. Provided that the dimension of the fractal percolation is at least 1, we show that, conditioned on non-extinction, almost surely all visible parts from…
Fractal dimensions have been used as a quantitative measure for structure of eigenstates of quantum many-body systems, useful for comparison to random matrix theory predictions or to distinguish many-body localized systems from chaotic…