Related papers: The falling raindrop, revisited
A hypothesis proposed in the paper (Entropy 2017, 19, 345) on the deductive formulation of a physical theory based on explicitly- and universally-introduced basic concepts is further developed. An entropic measure of time with a number of…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…
We study the asymptotic behaviour of scaling solutions with a dissipative fluid and we show that, contrary to recent claims, the existence of stable accelerating attractor solution which solves the `energy' coincidence problem depends…
The fascinating and anomalous behaviour of a chain that instead of falling straight down under gravity, first rises and then falls, acquiring a steady shape in space that resembles a fountain's sprinkle, has recently attracted both popular…
Originating from the mathematical modelling of rainfall infiltration, we derive the solution of an initial-boundary value problem of a linear evolution partial differential equation, by using the Fokas method. We present numerical examples…
We propose the symmetry reduction method of partial differential equations to the system of differential equations with fewer number of independent variables. We also obtain generalized sufficient conditions for the solution found by…
We analyse the probability densities of daily rainfall amounts at a variety of locations on the Earth. The observed distributions of the amount of rainfall fit well to a q-exponential distribution with exponent q close to q=1.3. We discuss…
It is shown, for the self-consistent system of scalar, electro-magnetic and gravitational fields in general relativity, that the equations of motion admit a special kind of solutions with spherical or cylindrical symmetry. For these…
The time evolution equation of motion and shape are derived for a self-propelled droplet driven by a chemical reaction. The coupling between the chemical reaction and motion makes an inhomogeneous concentration distribution as well as a…
We consider daily rainfall observations at 32 stations in the province of North Holland (the Netherlands) during 30 years. Let $T$ be the total rainfall in this area on one day. An important question is: what is the amount of rainfall $T$…
At large scales and for sufficiently early times, dark matter is described as a pressureless perfect fluid---dust---non-interacting with Standard Model fields. These features are captured by a simple model with two scalars: a Lagrange…
The discrete periodic lattice of masses and springs with line and point defects is considered. The dispersion equations for propagative, guided and localised waves are obtained. The detailed analysis of example with three masses is…
Climate models robustly imply that some significant change in precipitation patterns will occur. Models consistently project that the intensity of individual precipitation events increases by approximately 6-7%/K, following the increase in…
We address the challenge of single-image de-raining, a task that involves recovering rain-free background information from a single rain image. While recent advancements have utilized real-world time-lapse data for training, enabling the…
Exact solutions are obtained for the steady flow of a power-law fluid between parallel plates with partial slip conditions and uniform cross flow. The problem is properly formulated and similarities are exploited. The exact solutions are…
In this paper we propose a two-dimensional (2D) computational model, based on a molecular dynamics (MD) approach, for deep landslides triggered by rainfall. Our model is based on interacting particles or grains and describes the behavior of…
The method of variational completion allows one to transform an (in principle, arbitrary) system of partial differential equations -- based on an intuitive ``educated guess'' -- into the Euler-Lagrange one attached to a Lagrangian, by…
Techniques are developed for decoupling dissipative differential equations. The approach considered is based upon obtaining a sufficient gap in the time dependent linear portion of the equation that corresponds to the linear variational…
We are concerned with a time periodic supersonic flow through a bounded interval. This motion is described by the compressible Euler equation with a time periodic outer force. Our goal in this paper is to prove the existence of a time…