Related papers: Correlated Percolation
The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centres of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters,…
The theory of an induced energy polarized vacuum provides an alternative to the standard cosmological model. The theory has previously been shown to lead to the Baryonic Tully-Fisher Relationship [1], to agree with the observed rotation…
Taylor diffusion (or dispersion) refers to a phenomenon discovered experimentally by Taylor in the 1950s where a solute dropped into a pipe with a background shear flow experiences diffusion at a rate proportional to $1/\nu$, which is much…
When an ensemble of particles interact hydrodynamically, they generically display large-scale transient structures such as swirls in sedimenting particles [1], or colloidal strings in sheared suspensions [2]. Understanding these…
We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative…
The continuum random cluster model is a Gibbs modification of the standard boolean model of intensity $z > 0$ and law of radii $Q$. The formal unormalized density is given by $q^{N_{cc}}$ where $q$ is a fixed parameter and $N_{cc}$ is the…
'A basic and basically unsolved problem in fluid dynamics is to determine the evolution of rising bubbles and falling drops of one miscible liquid in another' [1]. Here, we address this important literature gap and present the first theory…
Breath figures are the complex patterns that form when water vapor condenses into liquid droplets on a surface. The primary question concerning breath figures is how the condensing vapor is allocated between the growth of existing droplets…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behaviour at criticality. Our…
We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the…
A new type of a levitating droplet clusters composed of often transforming small aggregates of water droplets is described for the first time. Unlike earlier observed droplet clusters controlled by aerodynamic forces, which formed either an…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
When a cold atomic gas is illuminated by a quasi-resonant laser beam, light-induced dipole-dipole correlations make the scattering of light a cooperative process. Once a fluid description is adopted for the atoms, many scattering properties…
A liquid droplet is fragmented by a sudden pressurized-gas blow, and the resulting droplets, adhered to the window of a flatbed scanner, are counted and sized by computerized means. The use of a scanner plus image recognition software…
This letter presents a scaling theory of the coalescence of two viscous spherical droplets. An initial value problem was formulated and analytically solved for the evolution of the radius of a liquid neck formed upon droplet coalescence.…
Droplet coalescence is essential in a host of biological and industrial processes, involving complex systems as diverse as cellular aggregates, colloidal suspensions, and polymeric liquids. Classical solutions for the time evolution of…
Fluids made of two-dimensional hard particles with polygonal shapes may stabilize symmetries which do not result directly from the particle shape. This is due to the formation of clusters in the fluid. Entropy alone can drive these effects,…
Phase separation is a fairly common physical phenomenon with examples including the formation of water droplets from humid air (fog, rain), the separation of a crystalline structure from an isotropic material such as a liquid or even the…