Related papers: Analytical solutions for precipitation size distri…
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…
The approaches, based on the negative binomial model for the distribution of duration of the wet periods measured in days, are proposed to the definition of extreme precipitation. This model demonstrates excellent fit with real data and…
The theory of solute transfer and deposit growth in evaporating sessile drops on a plane substrate is presented. The main ideas and the principal equations are formulated. The problem is solved analytically for two important geometries:…
We explore the evolution of the aggregate size distribution in systems where aggregates grow by diffusive accretion of mass. Supersaturation is controlled in such a way that the overall aggregate volume grows linearly in time. Classical…
If the temperature of a cell containing two partially miscible liquids is changed very slowly, so that the miscibility is decreased, microscopic droplets nucleate, grow and migrate to the interface due to their buoyancy. The system may show…
This model considers reversible elementary acts of migration of point defects (interstitials and/or vacancies) across the precipitate-matrix interface and enables one to derive equations for the rates of emission and absorption of solute…
The equilibrium relative humidity values for a number of the most commonly used precipitants in biological macromolecule crystallisation have been measured using a new humidity control device. A simple argument in statistical mechanics…
Statistical systems with time-periodic spatially non-uniform forces are of immense importance in several areas of physics. In this paper, we provide an analytical expression of the time-periodic probability distribution function of…
In the area of supercritical wing design, a variety of principles, laws and rules have been summarized by scholars who perform theoretical and experimental analyses. The applicability of these rules is usually restricted by the airfoil…
This study presents a dynamic modeling approach for precipitation in electrolyte systems, focusing on the crystallization of an aromatic amine through continuous processes. A novel model, integrating equilibrium and crystallization…
We present solutions to the classical Liouville equation for ergodic and completely integrable systems - systems that are known to attain equilibrium. Ergodic systems are known to thermal equilibrate with a Maxwell-Boltzmann distribution…
To obtain further insight on possible power law generalizations of Boltzmann equilibrium concepts, a stochastic collision model is investigated. We consider the dynamics of a tracer particle of mass $M$, undergoing elastic collisions with…
Understanding and modeling snow particle dynamics in the atmosphere remains a significant challenge for atmospheric scientists, hydrologists, and glaciologists. Temporally and spatially varying rates of snow transport, deposition, and…
Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example spreading packets of particles. Mathematically, it concerns the exponential fall-of of the density of thin-tailed…
We investigate traffic flows using the kinetic Boltzmann equations with a Maxwell collision integral. This approach allows analytical determination of the transient behavior and the size distributions. The relaxation of the car and cluster…
Mathematical modelling of the evolution of the size-spectrum dynamics in aquatic ecosystems was discovered to be a powerful tool to have a deeper insight into impacts of human- and environmental driven changes on the marine ecosystem. In…
In this article, we carry out a study of long-term behavior of reaction-diffusion systems augmented with self- and cross-diffusion, using an augmented Gray-Scott system as a general example. The methodology remains generic, and is therefore…
We use an acoustic Lagrangian tracking technique, particularly adapted to measurements in open flows, and a versatile material particles generator (in the form of soap bubbles with adjustable size and density) to characterize Lagrangian…
Some fractional and anomalous diffusions are driven by equations involving fractional derivatives in both time and space. Such diffusions are processes with randomly varying times. In representing the solutions to those diffusions, the…
The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times and narrow distributed displacements with a non-zero mean, is a well studied model for anomalous diffusion. Using an analytical approach, we recently…