A fractal graph model of capillary type systems

Kozlov, Vladimir; Назаров, С. А.; Zavorokhin, G. L.

doi:10.1080/17476933.2017.1349117

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2017

2024

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Cited by 7 publications

(2 citation statements)

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“…For the periodic in time setting, it was studied in [20]. In [7], a linear stationary equation in an infinite fractal type graph is considered.…”

Section: Introduction and Main Definitionsmentioning

confidence: 99%

Numerical Study of the Equation on the Graph for the Steady State Non-Newtonian Flow in Thin Tube Structure

Kozulinas,

Panasenko,

Pileckas

et al. 2023

Mathematical Modelling and Analysis

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“…For the periodic in time setting, it was studied in [20]. In [7], a linear stationary equation in an infinite fractal type graph is considered.…”

Section: Introduction and Main Definitionsmentioning

confidence: 99%

Numerical Study of the Equation on the Graph for the Steady State Non-Newtonian Flow in Thin Tube Structure

Kozulinas,

Panasenko,

Pileckas

et al. 2023

Mathematical Modelling and Analysis

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“…Most of the nodes belong to the capillary system, the smallest blood vessels, which are peculiar to their functioning laws, cf. [11]. Arterial and venous systems have also a considerable large number of nodes.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model of an Arterial Bifurcation

Zavorokhin

2019

UMJ

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An asymptotic model of an arterial bifurcation is presented. We propose a simple approximate method of calculation of the pressure drop matrix. The entries of this matrix are included in the modified transmission conditions, which were introduced earlier by Kozlov and Nazarov, and which give better approximation of 3D flow by 1D flow near a bifurcation of an artery as compared to the classical Kirchhoff conditions. The present modeling takes into account the heuristic Murrey cubic law.

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