Shock Waves in Mathematical Models of the Aorta

1970 ◽  
Vol 37 (1) ◽  
pp. 34-37 ◽  
Author(s):  
George Rudinger
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Shock Waves ◽  
Method Of Characteristics ◽  
Wave Form ◽  
Shock Formation ◽  
Rapid Flow ◽  
Latex Tube ◽  
Flow Changes ◽  
The Mathematical Model

If the nonlinear equations for nonsteady blood flow are solved by the method of characteristics, shock discontinuities may develop as a result of omitting from the mathematical model some aspect of the system that becomes significant at rapid flow changes. As an illustration, the flow from the heart into the aorta at the beginning of systole is analyzed. An equation is derived which yields shock formation distances between a few centimeters and several meters depending on the elastic properties of the aorta. Since knowledge of the actual wave form would be useful for computer programming, a few exploratory experiments were performed with an unrestrained latex tube. They indicated wave transitions extending over several tube diameters, but maximum steepening of the wave has not yet been achieved.

MATHEMATICAL MODELING OF BLOOD FLOW IN A POROUS VESSEL HAVING DOUBLE STENOSES IN THE PRESENCE OF AN EXTERNAL MAGNETIC FIELD

2011 ◽  
Vol 04 (02) ◽  
pp. 207-225 ◽  
Author(s):  
J. C. MISRA ◽  
A. SINHA ◽  
G. C. SHIT
Keyword(s):  
Mathematical Modeling ◽  
Magnetic Field ◽  
Mathematical Model ◽  
Blood Flow ◽  
Shear Stress ◽  
External Magnetic Field ◽  
Volumetric Flow Rate ◽  
Hematocrit Level ◽  
Flow Through ◽  
The Mathematical Model

In this paper, a mathematical model has been developed for studying blood flow through a porous vessel with a pair of stenoses under the action of an externally applied magnetic field. Blood flowing through the artery is considered to be Newtonian. This model is consistent with the principles of ferro-hydrodynamics and magnetohydrodynamics. Expressions for the velocity profile, volumetric flow rate, wall shear stress and pressure gradient have been derived analytically under the purview of the model. The above said quantities are computed for a specific set of values of the different parameters involved in the model analysis. This serves as an illustration of the validity of the mathematical model developed here. The results estimated on the basis of the computation are presented graphically. The obtained results for different values of the parameters involved in the problem under consideration, show that the flow is appreciably influenced by the presence of magnetic field and the rise in the hematocrit level.

scholarly journals Coupling Model of Energy Flow and Material Flow in SKS Lead Smelting

2014 ◽  
Vol 8 (1) ◽  
pp. 131-135
Author(s):  
Hongcai Wang ◽  
Zhangming Shi ◽  
Liufang Lin ◽  
Bo Chen
Keyword(s):  
Mathematical Model ◽  
Material Flow ◽  
Energy Flow ◽  
Optimization Problems ◽  
Coupling Model ◽  
Flow Angle ◽  
Energy Saving Potential ◽  
Lead Smelting ◽  
Flow Changes ◽  
The Mathematical Model

This paper studied the coupling model of material flow and energy flow in the production process of lead smelting enterprises, and established the mathematical model for material flow and energy flow to resolve optimization problems. From the point of energy flow, the paper analyzed three kinds of energy flow changes which have an effect on the enterprise products. Through calculation and analysis, it has been found that there is 38.42% energy-saving potential in this enterprise. Separately from the material flow and energy flow angle, the paper put forward five aspects suggestions to reduce the energy consumption of the enterprise products.

scholarly journals MATHEMATICAL MODELLING OF IMMUNE PROCESSES AND ITS APPLICATION

2020 ◽  
Vol 13 (5) ◽  
pp. 5-18
Author(s):  
N. I. ARALOVA ◽  
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Blood Flow ◽  
Blood Circulation ◽  
Moving Objects ◽  
Scientific School ◽  
Blood Flows ◽  
Theory Of Optimal Control ◽  
Complex Mathematical Model ◽  
The Mathematical Model

The aim of the study was to develop a mathematical model to research hypoxic states in case of simulation of an organism infectious lesions. The model is based on the methods of mathematical modeling and the theory of optimal control of moving objects. The processes of organism damage are simulated with the mathematical model of immune response developed by G.I. Marchuk and the members of his scientific school, adapted to current conditions. This model is based on Burnet’s clone selection theory of the determining role of antigen. Simulation results using the model are presented. The dependencies of infectious courses on the volumetric velocity of systemic blood flow is analyzed on the complex mathematical model of immune response, respiratory and blood circulation systems. The immune system is shown to be rather sensitive to the changes in blood flow via capillaries. Thus, the organ blood flows can be used as parameters for the model by which the respiratory, immune response, and blood circulation systems interact and interplay.

scholarly journals Mathematical modelling of the crossover bypass operation in postthrombotic disease

1998 ◽  
Vol 79 (1) ◽  
pp. 38-40
Author(s):  
I. M. Ignatiev ◽  
Yu. Ya. Petrushenko
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Mathematical Modelling ◽  
Bypass Operation ◽  
Optimum Conditions ◽  
Valve Function ◽  
Crossover Bypass ◽  
The Mathematical Model

The mathematical model of the crossover femoro-femoral autovenous bypass operation using in the treatment of unilateral occlusions of iliac veins is created. The optimum conditions of crossover bypass functions on the basis of hydrodynamic laws are determined. The most important factors providing the success of the bypass operation are the sufficient diameter of a bypass and the gradient of pressure at its ends. The dependence between them is inversely proportional and its correlation can be fixed by experiments. The conservation ef valve function, of the crossover bypass has a relative meaning because a reverse blood flow is not hemodynamically meaningful even in the absence of valves.

A MATHEMATICAL MODEL OF BLOOD FLOW IN AN INTRACRANIAL ANEURYSM: ANALYTICAL AND NUMERICAL STUDY

2006 ◽  
Vol 06 (02) ◽  
pp. 137-151 ◽  
Author(s):  
SVETOSLAV NIKOLOV ◽  
STOYAN STOYTCHEV
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Numerical Study ◽  
Flow Stability ◽  
Wall Material ◽  
Pulsatile Pressure ◽  
Non Linear ◽  
Flow Through ◽  
Model Equations ◽  
The Mathematical Model

An aneurysm is a local enlargement of the vessel lumen due to the weakening of the wall material. We propose a mathematical model of the pulsatile blood flow through the system consisting of the cerebral artery and an aneurysm. The mathematical model is based on mass and energy conservation laws. It comprises non-linear rheological properties of the aneurysm and artery, and inertial and resistant properties of the blood flow. The model equations are analyzed by the methods of non-linear dynamics and they are solved numerically. Special attention is paid to the flow stability as a function of the aneurysmal and arterial material properties, the mean and oscillating arterial pressure, and the frequency of heart pulsations. The results of the work can be summarized as follows: (i) the model equations are stable at normal physiological conditions and developed aneurysms, (ii) with decreasing of the aneurysmal compliance, the aneurysmal volume pulsations increase and a limit point of flow stability is approached, (iii) the increased amplitude of the pulsatile pressure and the heart frequency cannot lead to flow instabilities.

Investigation of Blood-Flow Changes During Cognitive Task Activation using CASL

2004 ◽  
Vol 35 (03) ◽  
Author(s):  
T Mildner ◽  
S Zysset ◽  
R Trampel ◽  
W Driesel ◽  
HE Möller
Keyword(s):  
Blood Flow ◽  
Cognitive Task ◽  
Flow Changes ◽  
Task Activation

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

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