Related papers: The falling raindrop, revisited
We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker-Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power…
We investigate two common numerical techniques for integrating reversible moist processes in atmospheric flows in the context of solving the fully compressible Euler equations. The first is a one-step, coupled technique based on using…
We consider the Riemann problem of the dilute approximation equations with spatiotemporally dependent volume fractions from the full model of suspension, in which the particles settle to the solid substrate and the clear liquid film flows…
We establish a recursive representation that fully decouples jumps from a large class of multivariate inhomogeneous stochastic differential equations with jumps of general time-state dependent unbounded intensity, not of L\'evy-driven type…
Heavy rainfall distributional modeling is essential in any impact studies linked to the water cycle, e.g.\ flood risks. Still, statistical analyses that both take into account the temporal and multivariate nature of extreme rainfall are…
This letter proposes a simple method of transferring rain structures of a given exemplar rain image into a target image. Given the exemplar rain image and its corresponding masked rain image, rain patches including rain structures are…
In the field of differential equations, particularly fluid dynamics, many researchers have shown an interest in the behavior of time periodic solutions. In this paper, we study isentropic gas flow in a bounded interval and apply a time…
A moisture process with dynamics that switch after hitting a threshold gives rise to a rainfall process. This rainfall process is characterized by its random holding times for dry and wet periods. On average, the holding times for the wet…
Firstly, we get the completely bouncing criteria Cr for droplet on moving substrate. The bouncing without splashing condition is $\mathrm{Cr}>1$. Then, we mainly research the effect of wind field for droplet, and get the completely bouncing…
The role of external forces in systems exhibiting anomalous diffusion is discussed on the basis of the describing Langevin equations. Since there exist different possibilities to include the effect of an external field the concept of {\it…
The dynamics of a subdiffusive continuous time random walker in an inhomogeneous environment is analyzed. In each microscopic jump, a random time is drawn from a waiting time probability density function (WT-PDF) that decays as a power law:…
Turbulence in growth of rain droplets and rain formation is studied under an approximating particle system representing aggregation at the level of individuals, depending on their volume and distance in space, of the Smoluchowski…
The classical Prats' problem of flow instability in a horizontal porous channel saturated by a fluid subject to a buoyancy force is reconsidered. In the original formulation, the driving buoyancy force results from thermal diffusion. This…
Mathematical modeling of fluid flow in a porous medium is usually described by a continuity equation and a chosen constitutive law. The latter, depending on the problem at hand, may be a nonlinear relation between the fluid's pressure…
The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are:…
Rainfall is an important component of the climate system and its statistical properties are vital for prediction purposes. In this study, we have developed a statistical method for constructing the distribution of annual precipitation. The…
This paper discusses the evolution of the droplet size distribution for a liquid-in-gas aerosol contained in a Rayleigh-B\'enard cell. It introduces a non-collisional model for broadening the droplet size distribution, termed 'convective…
The coefficients of different combinations of terms of the liquid drop model have been determined by a least square fitting procedure to the experimental atomic masses. The nuclear masses can also be reproduced using a Coulomb radius taking…
Dust-gas mixtures are the simplest example of a two fluid mixture. We show that when simulating such mixtures with particles or with particles coupled to grids a problem arises due to the need to resolve a very small length scale when the…
In this paper we investigate the porous medium equation with a fractional temporal derivative. We justify that the resulting equation emerges when we consider the waiting-time (or trapping) phenomenon that can happen in the medium. Our…