Related papers: The falling raindrop, revisited
We consider the problem of shadowing for differential equations with grow-up. We introduce so-called nonuniform shadowing properties (in which size of the error depends on the point of the phase space) and prove for them analogs of…
An acoustic method is presented for analyzing the time of falling motion. A ball is dropped from a measured height. The dropping device makes a distinct sound a well-determined time (roughly 14 milliseconds) after release. The ball…
In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
Removing rain streaks from a single image continues to draw attentions today in outdoor vision systems. In this paper, we present an efficient method to remove rain streaks. First, the location map of rain pixels needs to be known as…
Two oppositely charged droplets of (say) water in e.g. oil or air will tend to drift together under the influence of their charges. As they make contact, one might expect them to coalesce and form one large droplet, and this indeed happens…
Rain drops form in clouds by collision of submillimetric droplets falling under gravity: larger drops fall faster than smaller ones and collect them on their path. The puzzling stability of fogs and non-precipitating warm clouds with…
Critical gravitational collapse and self similarity are used to probe the mass distribution of subsolar objects. We demonstrate that at very low mass the distribution is given by a power law, with an exponent opposite in sign to that…
This is the second paper in a series on light scattering from optically anisotropic scatterers embedded in an isotropic medium. The apparently complex T-matrix theory involving mixing of angular momentum components turns out to be an…
A spontaneous breakup of a liquid jet results in the formation of a chain of droplets, which is a daily observed phenomenon, such as in the raining process and under an open water-faucet. We here report inkjet printing experiments for the…
We present a model of coupling between a point wise particle and a compressible inviscid fluid following the Euler equations. The interaction between the fluid and the particle is achieved through a drag force. It writes as the product of a…
We revisit the problem of absorption by identical atoms with entanglement and symmetrization acting at once. We introduce the recoil of the atoms in the calculations and compare the results with those of distinguishable systems instead of…
The relativistic Maxwell-Boltzmann distribution for the system of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau $ is considered without the simplifying approximation $m^2\cong M^2$, where $M$ is…
We derive the special and general relativistic hydrodynamic equations of motion for ideal fluids from a variational principle. Our approach allows to find approximate solutions, whenever physically motivated trial functions can be used.…
We analyse under a simple approach the problem one must decide the best strategy to minimize the contact with rain when moving between two points through the rain. The available strategies: walk (low speed boost $<<$ $c$) or run…
We briefly report on our method [Fiore JPA 2017] of simplifying the equations of motion of charged particles in an electromagnetic field that is the sum of a plane travelling wave and a static part; it is based on changes of the dependent…
Although realizing wetting transitions of droplets spontaneously on solid rough surfaces is quite challenging, it is becoming a key research topic in many practical applications which require highly efficient removal of liquid. We report…
I lay out the problem of time facets as arising piecemeal from a number of aspects of background independence. Almost all of these already have simpler classical counterparts. This approach can be viewed as a facet by facet completion of…
For over a century, raindrop size distributions have been a subject of extensive scientific study, typically described by models including the Marshall-Palmer exponential equation, gamma, Weibull, lognormal, and other mathematical…
To trigger precipitation, water droplets in warm clouds need to attain a sufficient size. Theoretical estimates based on condensation and gravitational collisions alone fail to explain the observed timescales for the onset of precipitation…
The Richards' equation is a model for flow of water in unsaturated soils. The coefficients of this (nonlinear) partial differential equation describe the permeability of the medium. Insufficient or uncertain measurements are commonly…