Related papers: The falling raindrop, revisited
Ball lightning is an impressive natural electromagnetic phenomenon occurring in atmosphere under suitable circumstances. Its origin, composition and stability issues are a matter of debate, due to presence of many evidences still…
We derive the equations of motion for all the irreducible moments of the single-particle distribution function. We find that these moment equations of motion are highly coupled, with the dynamics of lower-rank moments always being coupled…
We show that rain events are analogous to a variety of nonequilibrium relaxation processes in Nature such as earthquakes and avalanches. Analysis of high-resolution rain data reveals that power laws describe the number of rain events versus…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
In these lectures I give an introduction to the time-dependent approach to inverse scattering, that has been developed recently. The aim of this approach is to solve various inverse scattering problems with time-dependent methods that…
It is well known that mode coupling theory (MCT) leads to a two step power-law time decay in dense simple fluids. We show that much of the mathematical machinery used in the MCT analysis can be taken over to the analysis of the systematic…
Using direct numerical simulations, the fragmentation of falling liquid droplets in a quiescent media is studied. Three simulations with different Eotvos numbers were performed. An adaptive volume of fluid(VOF) method based on octree…
Pressure-solution is a chemo-mechanical process, involving dissolution at grain/asperity contacts and precipitation away from them. It induces a compaction in time of rocks and sediments. The present study investigates numerically the…
We investigate the 3D structure and drying dynamics of complex mixtures of emulsion droplets and colloidal particles, using confocal microscopy. Air invades and rapidly collapses large emulsion droplets, forcing their contents into the…
We consider large random matrices $X$ with centered, independent entries but possibly different variances. We compute the normalized trace of $f(X) g(X^*)$ for $f,g$ functions analytic on the spectrum of $X$. We use these results to compute…
The moist shallow water equations offer a promising route for advancing understanding of the coupling of physical parametrisations and dynamics in numerical atmospheric models, an issue known as 'physics-dynamics coupling'. Without moist…
We address the spherical accretion of generic fluids onto black holes. We show that, if the black hole metric satisfies certain conditions, in the presence of a test fluid it is possible to derive a fully relativistic prescription for the…
Pendant drops suspended on the underside of a wet substrate are known to accumulate fluid from the surrounding thin liquid film, a process that often results in dripping. The growth of such drops is hastened by their ability to translate…
The theory of the effect of external fluctuation force on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using classical…
In this paper we deal with the classical problem of random cover times. We investigate the distribution of the time it takes for a Poisson process of cylinders to cover a set $A \subset \mathbb{R}^d.$ This Poisson process of cylinders is…
We consider a variational model of electrified liquid drops, involving competition between surface tension and charge repulsion. Since the natural model happens to be ill-posed, we show that by adding to the perimeter a Willmore-type…
Sessile droplets exposed to an incipient condition lead to an inevitable loss of mass, which is critical in many practical applications. By considering an arbitrarily configured two-dimensional array of droplets, here we provide a simple…
Existing deep learning-based image deraining methods have achieved promising performance for synthetic rainy images, typically rely on the pairs of sharp images and simulated rainy counterparts. However, these methods suffer from…
We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we prove existence of a unique solution to this equation with…
Mutually uncorrelated random discrete events, manifesting a common basic process, are examined often in terms of their occurrence rate as a function of one or more of their distinguishing attributes, such as measurements of photon spectrum…