Related papers: The falling raindrop, revisited
The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More…
A modification of the classical primitive equations of the atmosphere is considered in order to take into account important phase transition phenomena due to air saturation and condensation. We provide a mathematical formulation of the…
We study mixed finite element methods for the linearized rotating shallow water equations with linear drag and forcing terms. By means of a strong energy estimate for an equivalent second-order formulation for the linearized momentum, we…
Plant differently colored points in the plane, then let random points ("Poisson rain") fall, and give each new point the color of the nearest existing point. Previous investigation and simulations strongly suggest that the colored regions…
Raindrop removal is a challenging task in image processing. Removing raindrops while relying solely on a single image further increases the difficulty of the task. Common approaches include the detection of raindrop regions in the image,…
In this paper, we apply the random walk model in designing a raindrop algorithm to find the global optimal solution of a non-linear programming problem. The raindrop algorithm does not require the information of the first or second order…
A mathematical model describing the erosion or leaching of a solid material by a flowing fluid in a column is developed. This involves an advection-diffusion equation coupled to a linear kinetic reaction describing the mass transfer between…
We investigate the scattering response of parity-time (PT) symmetric structures. We show that, due to the local flow of energy between gain and loss regions, such systems can deflect light in unusual ways, as a function of the gain/loss…
The waterdrops on windshields during driving can cause severe visual obstructions, which may lead to car accidents. Meanwhile, the waterdrops can also degrade the performance of a computer vision system in autonomous driving. To address…
We derive the modified L\"uscher equation in the presence of the long-range force caused by the exchange of a light particle. It is shown that the use of this equation enables one to circumvent the problems related to the strong…
This paper addresses the problem of single image de-raining, that is, the task of recovering clean and rain-free background scenes from a single image obscured by a rainy artifact. Although recent advances adopt real-world time-lapse data…
Precipitation data collected at sub-hourly resolution represents specific challenges for missing data recovery by being largely stochastic in nature and highly unbalanced in the duration of rain vs non-rain. Here we present a two-step…
Optical flow estimation in the rainy scenes is challenging due to background degradation introduced by rain streaks and rain accumulation effects in the scene. Rain accumulation effect refers to poor visibility of remote objects due to the…
Motion of chemically driven droplets is analyzed by applying a solvability condition of perturbed hydrodynamic equations affected by the adsorbate concentration. Conditions for traveling bifurcation analogous to a similar transition in…
We study a particle model for a simple system of partial differential equations describing, in dimension $d\geq 2$, a two component mixture where light particles move in a medium of absorbing, fixed obstacles; the system consists in a…
The equations governing the motion of a three-dimensional liquid drop moving freely in an unbounded liquid reservoir under the influence of a gravitational force are investigated. Provided the (constant) densities in the two liquids are…
In this paper we consider dissipative hydrodynamic equations for systems with continuous broken symmetries. We first present the case of superfluidity, in which the symmetry U(1) is broken and then generalize to the chiral symmetry $SU(2)_L…
Raindrops adhered to a glass window or camera lens can severely hamper the visibility of a background scene and degrade an image considerably. In this paper, we address the problem by visually removing raindrops, and thus transforming a…
We investigate the dripping of liquids around solid surfaces in the regime of inertial flows, a situation commonly encountered with the so-called "teapot effect". We demonstrate that surface wettability is an unexpected key factor in…
We demonstrate how, from the point of view of energy flow through an open system, rain is analogous to many other relaxational processes in Nature such as earthquakes. By identifying rain events as the basic entities of the phenomenon, we…