Related papers: Holder continuity of interfaces for scale-invarian…
We consider a discrete-time model for random interface growth which admits exact formulas and converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the…
A coarse grained description of a two phase fluid is used to study the steady state configuration of the interface separating the coexisting phases, and the motion of the contact line at which the interface intersects a solid boundary. The…
A Poisson line process is a random set of straight lines contained in the plane, as the image of the map $(x,v)\mapsto (x+vt)_{t\in\mathbb{R}}$, for each point $(x,v)$ of a Poisson process in the space-velocity plane. By associating a step…
We consider critical percolation on the triangular lattice in a bounded simply connected domain with boundary conditions that force an interface between two prescribed boundary points. We say the interface forms a "near-loop" when it comes…
Percolation in an information-theoretically secure graph is considered where both the legitimate and the eavesdropper nodes are distributed as Poisson point processes. For both the path-loss and the path-loss plus fading model, upper and…
General sufficient conditions are given for absolute continuity and convergence in variation of the distributions of the unctionals on a probability space, generated by a Poisson point measure. The phase space of the Poisson point measure…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance S above an unperturbed two-fluid interface. At low withdrawal rates, Q, the interface forms a steady state hump and only the upper…
The dynamics of compressible liquid-vapor flow depends sensitively on the microscale behavior at the phase boundary. We consider a sharp-interface approach, and propose a multiscale model to describe liquid-vapor flow accurately, without…
We study the pore-scale transport of a conservative scalar forming an advancing mixing front, which can be re-interpreted to predict instantaneous mixing-limited bimolecular reactions. We investigate this using a set of two-dimensional,…
Topological complexity is a homotopy invariant that measures the minimal number of continuous rules required for motion planning in a space. In this work, we introduce persistent analogs of topological complexity and its cohomological lower…
The sliding mode approach is recognized as an efficient tool for treating the chattering behavior in hybrid systems. However, the amplitude of chattering, by its nature, is proportional to magnitude of discontinuous control. A possible…
We derive an anomalous, sub-diffusive scaling limit for a one-dimensional version of the Mott random walk. The limiting process can be viewed heuristically as a one-dimensional diffusion with an absolutely continuous speed measure and a…
We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in…
We analyze the geometry of scaling limits of near-critical 2D percolation, i.e., for $p=p_c+\lambda\delta^{1/\nu}$, with $\nu=4/3$, as the lattice spacing $\delta \to 0$. Our proposed framework extends previous analyses for $p=p_c$, based…
We consider one-dimensional infinite chains of harmonic oscillators with random exchanges of momenta and long-range interaction potentials which have polynomial decay rate $|x|^{-\theta}, x \to \infty, \theta > 1$ where $x \in \mathbb{Z}$…
It is well-known that at the high Reynolds number, the linearized Navier-Stokes equations around the inviscid stable shear profile admit growing mode solutions due to the destabilizing effect of the viscosity. This phenomenon, called…
In this work we study the Poisson Boolean model of percolation in locally compact Polish metric spaces and we prove the invariance of subcritical and supercritical phases under mm-quasi-isometries. In other words, we prove that if the…
We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…
This paper is concerned with the incompressible limit problem for strong solutions of compressible two-phase flow models under periodic boundary conditions, where the Navier-Stokes equations are nonlinearly coupled with either Cahn-Hilliard…