New methods of flow visualization near absolute zero have opened the way to directly compare quantum turbulence (in superfluid helium) to classical turbulence (in ordinary fluids such as air or water) and explore analogies and differences. We present results of numerical simulations in which we examine the statistics of the superfluid acceleration in thermal counterflow. We find that, unlike th...

1 Initial Value Problem We are given a right hand side function f(t, y) with f : [t0, T ]×Rn → Rn and an initial value y0 ∈ Rn. We want to find a function y(t) with y : [t0, T ] → Rn such that y′(t) exists, is continuous and satisfies the initial value problem y′(t) = f (t, y(t)) , y(t0) = y0. (1) We assume that f(t, y) satisfies a Lipschitz condition with respect to y (at least for y with |y −...

Our purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be constructed by means of the solutions of linear differential equations. We give several families of differential systems which illustrate how the integrability of the system passes through the solutions of a linear diff...

Abstract We extend the Eruguin result exposed in the paper ”Construction of the whole set of ordinary differential equations with a given integral curve” published in 1952 and construct a differential system in R which admits a given set of the partial integrals, in particular we study the case when theses functions are polynomials. We construct a non-Darboux integrable planar polynomial system...

Most physical processes are modeled by differential equations. First order ordinary differential equations, also known as dynamical systems, arise in a wide range of applications, including population dynamics, mechanical systems, planetary motion, ecology, chemical diffusion, etc., etc. See [19, 72,ODES] for additional material and applications. The goal of this chapter is to study and solve i...

The dynamics of supercooled water in aqueous solutions of the single amino acid L-lysine has been studied by broadband dielectric spectroscopy. The chosen biological system is unique in the sense that the water content is high enough to fully dissolve the amino acid, but low enough to avoid crystallisation to ice at any temperature. This is not possible to achieve for proteins or other larger b...

In this paper, we propose a new receptor-based model for pattern formation and regulation in a fresh-water polyp, namely hydra. The model is defined in the form of a system of reaction-diffusion equations with zero-flux boundary conditions coupled with a system of ordinary differential equations. The production of diffusible biochemical molecules has a hysteretic dependence on the density of th...

Cement kiln dust produced in a local cement production plant in Saudi Arabia, along with fly ash resulting from combustion of heavy fuel oil in a local power generation plant were utilized as waste materials blended with ordinary Portland cement at various ratios. These blends were tested for their water requirements for normal consistency, initial setting times, and compression and tensile str...

nano materials have been widely used in laboratory and industrial scales in order to improve various properties of concrete and concrete mixture. the mainstream practice of the researches in this field is to add metallic nano-particles into the concrete mixture. the present research focuses on adding micro-nano air bubbles (mnab) into water before mixing it with aggregate and cement mixtures. i...

spatiality assessment of groundwater pollution is very important to determine water quality condition, pollution sources and management decisions. in this case, gis and geostatistics methods can be useful tools. spatiality of groundwater quality parameters, in relation with various land uses, can be very extremely. therefore water samples from 52 wells in the kurdan area were analyzed in this s...