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The model of random interlacements is a one-parameter family $\mathcal I^u,$ $u \ge 0,$ of random subsets of $\mathbb{Z}^d,$ which locally describes the trace of simple random walk on a $d$-dimensional torus run up to time $u$ times its…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
The slow viscous flow through a doubly-periodic array of cylinders does not have an analytical solution. However, as a reduced model for the flow within fibrous porous media, this solution is important for many real-world systems. We…
We introduce a new approach to connectivity-dependent properties of diluted systems, which is based on the transfer-matrix formulation of the percolation problem. It simultaneously incorporates the connective properties reflected in…
The Spiral Model (SM) corresponds to a new class of kinetically constrained models introduced in joint works with D.S. Fisher [8,9]. They provide the first example of finite dimensional models with an ideal glass-jamming transition. This is…
Finding conditions that support synchronization is a fertile and active area of research with applications across multiple disciplines. Here we present and analyze a scheme for synchronizing chaotic dynamical systems by transiently…
We examine transient axial creeping flow in the annular gap between a rigid cylinder and a concentric elastic tube. The gap is initially filled with a thin fluid layer. The study focuses on viscous-elastic time-scales for which the rate of…
In composite materials composed of soft polymer matrix and stiff, high-aspect-ratio particles, the composite undergoes a transition in mechanical strength when the inclusion phase surpasses a critical density. This phenomenon (rheological…
Viscoelastic flows through microscale porous arrays exhibit complex path-selection and switching phenomena. However, understanding this process is limited by a lack of studies linking between a single object and large arrays. Here, we…
The study of the Ising model from a percolation perspective has played a significant role in the modern theory of critical phenomena. We consider the celebrated square-lattice Ising model and construct percolation clusters by placing bonds,…
The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…
We prove that the Poisson-Boolean percolation on $\mathbb{R}^d$ undergoes a sharp phase transition in any dimension under the assumption that the radius distribution has a $5d-3$ finite moment (in particular we do not assume that the…
Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal the scaling behaviors of higher-order gaps in the largest…
Starting with a percolation model in $\Z^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$.…
We consider random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. In a companion paper, we have shown that if the random walk is pulled to the right by a positive bias $\lambda > 0$, then…
This experimental study reports on the behavior of a filament attached to the rear of a three- dimensional cylinder. The axis of the cylinder is placed normal to a uniform incoming flow and the filament is free to move in the cylinder wake.…
We study families of dependent site percolation models on the triangular lattice ${\mathbb T}$ and hexagonal lattice ${\mathbb H}$ that arise by applying certain cellular automata to independent percolation configurations. We analyze the…
Percolation in systems made up of randomly placed impermeable grains is often examined in the context of system spanning clusters of connected solids forming above a relatively low critical grain density $\rho_{c1}$ or networks of…
We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also…
The high-density plaquette percolation model in d dimensions contains a surface that is homeomorphic to the (d-1)-sphere and encloses the origin. This is proved by a path-counting argument in a dual model. When d=3, this permits an improved…