Asymptotic Analysis of the Curved-Pipe Flow with a Pressure-Dependent Viscosity Satisfying Barus Law

Curved-pipe flows have been the subject of many theoretical investigations due to their importance in various applications. The goal of this paper is to study the flow of incompressible fluid with a pressure-dependent viscosity through a curved pipe with an arbitrary central curve and constant circular cross section. The viscosity-pressure dependence is described by the well-known Barus law extensively used by the engineers. We introduce the small parameter ε (representing the ratio of the pipe’s thickness and its length) into the problem and perform asymptotic analysis with respect to ε. The main idea is to rewrite the governing problem using the appropriate transformation and then to compute the asymptotic solution using curvilinear coordinates and two-scale asymptotic expansion. Applying the inverse transformation, we derive the asymptotic approximation of the flow clearly showing the influence of pipe’s distortion and viscosity-pressure dependence on the effective flow

A stochastic model for population growth

U ovome radu bavimo se izvodom jednostavnog stohastičkog modela koji opisuje rast populacije. Za razliku od klasičnih determinističkih modela, u takvom modelu veličinu populacije tretiramo kao diskretnu slučajnu varijablu. Kao rezultat, dobivamo model opisan sustavom linearnih običnih diferencijalnih jednadžbi prvog reda za pripadnu funkciju gustoće kojeg je moguće eksplicitno riješiti.In this paper, we derive a simple stochastic model describing population growth. As opposed to classical deterministic models, in such model the size of population is considered to be a discrete random variable. As a result, we obtain the model described by the system of linear first-order ODEs satisfied by the corresponding probability mass function which can be explicitly solved

Heat flow through a thin cooled pipe filled with micropolar fluid

In this paper, a non-isothermal flow of a micropolar fluid in a thin pipe with circular cross-section is considered. The fluid in the pipe is cooled by the exterior medium and the heat exchange on the lateral part of the boundary is described by Newton’s cooling condition. Assuming that the hydrodynamic part of the system is provided, we seek for the micropolar effects on the heat flow using the standard perturbation technique. Different asymptotic models are deduced depending on the magnitude of the Reynolds number with respect to the pipe thickness. The critical case is identified and the explicit approximation for the fluid temperature is built improving the known result for the classical Newtonian flow as well. The obtained results are illustrated by some numerical simulations.Grant Agency of the Czech RepublicCroatian Science FoundationMinisterio de Economía y CompetitividadJunta de Andalucí

Effects of rough boundary and nonzero boundary conditions on the lubrication process with micropolar fluid

The lubrication theory is mostly concerned with the behavior of a lubricant flowing through a narrow gap. Motivated by the experimental findings from the tribology literature, we take the lubricant to be micropolar fluid and study its behavior in a thin domain with rough boundary. Instead of considering (commonly used) simple zero boundary condition, we impose physically relevant (nonzero) boundary condition for microrotation and perform asymptotic analysis of the corresponding 3D boundary value problem. We formally derive a simplified mathematical model acknowledging the roughness-induced effects and the effects of the nonzero boundary conditions on the macroscopic flow. Using the obtained asymptotic model, we study numerically the influence of the specific rugosity profile on the performance of a linear slider bearing. The numerical results clearly indicate that the use of the rough surfaces may contribute to enhance the mechanical performance of such device.Croatian Science FoundationUniversity of ZagrebMinisterio de Economía y CompetitividadJunta de Andalucí

A mathematical model for unemployment

U ovome radu prezentiramo matematički model koji opisuje problem nezaposlenosti pomoću sustava običnih diferencijalnih jednadžbi.In this paper we present a mathematical model for unemployment described by a system of ordinary differential equations

A mathematical model for unemployment

U ovome radu prezentiramo matematički model koji opisuje problem nezaposlenosti pomoću sustava običnih diferencijalnih jednadžbi.In this paper we present a mathematical model for unemployment described by a system of ordinary differential equations

Matematičko modeliranje konflikta - Richardsonov model

U ovom radu prezentiramo matematički model koji opisuje mogući konflikt između dviju država/saveza s pomoću jednostavnog sustava običnih diferencijalnih jednadžbi. Koristeći se osnovnim pojmovima i rezultatima teorije stabilnosti, analiziramo izvedeni model i diskutiramo njegovu valjanost na temelju stvarnih događanja uoči Prvog svjetskog rata. http://e.math.hr/math_e_article/br16/matijasevic_pazani