Related papers: The falling raindrop, revisited
We consider the initial-value problem of abstract wave equations with weak dissipation. We show that under conditions on the dissipation coefficient and its derivative the solutions to the abstract dissipative equation are closely related…
We present a three-dimensional model, based on cohesive spherical particles, of rain-induced landslides. The rainwater infiltration into the soil follow the either the fractional or the fractal diffusion equations. We solve analytically the…
A potential scattering theory from deterministic and random $\mathcal{PT}$ collections of particles with gain and loss is introduced and the forms of their structure and pair-structure factors are elucidated. An example relating to light…
We present a comprehensive experimental and theoretical investigation of the evaporation dynamics of freely levitated water droplets in an upward airstream under varying temperature and relative humidity conditions, using a custom-designed…
Outdoor videos sometimes contain unexpected rain streaks due to the rainy weather, which bring negative effects on subsequent computer vision applications, e.g., video surveillance, object recognition and tracking, etc. In this paper, we…
In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the…
We present a mean-field model that describes droplet growth due to condensation and collisions and droplet loss due to fallout. The model allows for an effective numerical simulation. We study how the rain initiation time depends on…
As a simplified model for subsurface flows elliptic equations may be utilized. Insufficient measurements or uncertainty in those are commonly modeled by a random coefficient, which then accounts for the uncertain permeability of a given…
We give a sufficient condition for blow up of positive mild solutions to an initial value problem for a nonautonomous weakly coupled system with distinct fractional diffusions. The proof is based on the study of blow up of a particular…
Charged water drops are more widespread than commonly acknowledged. For example, raindrops typically carry charges of order Q ~ 1 pC, while routine pipetting in the laboratory produces drops with Q ~ 50 pC. Here, we show that such modest…
The problem of reconstructing the time dependence of the dynamic pressure of a plasma jet impinging on one end of a solid rod based on the measured displacement of the opposite end has been solved. This solution allows for a reduction in…
A falling liquid drop, after impact on a rigid substrate, deforms and spreads, owing to the normal reaction force. Subsequently, if the substrate is non-wetting, the drop retracts and then jumps off. As we show here, not only is the impact…
Differentially rotating, "advection-dominated" accretion flows are considered in which the heat generated by viscous dissipation is retained in the fluid. The equations of time-dependent quasi-spherical accretion are solved in a simplified…
Dynamics of a dry-rebounding drop was studied experimentally, numerically, and theoretically. Experimental results were reproduced by our computational fluid dynamics simulations, from which time series of kinetic energy, potential energy,…
From the mesoscopic point of view, a new concept of soft matching for mass points is proposed. Then a soft Lasso's approach to learn the soft dynamical equation for the physical mechanical relationship is proposed, too. Furthermore, a…
We consider a second order linear evolution equation with a dissipative term multiplied by a time-dependent coefficient. Our aim is to design the coefficient in such a way that all solutions decay in time as fast as possible. We discover…
We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…
Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it…
Small mass uniqueness in the anisotropic atomic liquid drop model for all values of the parameters is obtained and the critical mass conjecture is investigated.
Employing a kinetic framework, we calculate all transport coefficients for relativistic dissipative (second-order) hydrodynamics for arbitrary particle masses in the 14-moment approximation. Taking the non-relativistic limit, it is shown…