n-compartment mathematical model for the uptake and distribution of inhaled inert gases in the human body: an analytical solution

1983 ◽  
Vol 21 (2) ◽  
pp. 128-133 ◽  
Author(s):  
E. Palazzi ◽  
M. Rovatti ◽  
M. del Borghi ◽  
A. Peloso ◽  
J. Zattoni
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Human Body ◽  
Inert Gases

Tissue necrosis and passage of fluid due to cold stress from the thermally damaged human body peripherals: A mathematical model

2015 ◽  
Vol 04 (02) ◽  
pp. 1550012
Author(s):  
M. A. Khanday ◽  
Fida Hussain ◽  
Khalid Nazir
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Heat Equation ◽  
Cold Stress ◽  
Human Body ◽  
Human Subjects ◽  
Diffusion Equations ◽  
Tissue Necrosis ◽  
Cold Temperatures ◽  
Element Technique

The development of cold injury takes place in the human subjects by means of crystallization of tissues in the exposed regions at severe cold temperatures. The process together with the evaluation of the passage of fluid discharge from the necrotic regions with respect to various degrees of frostbites has been carried out by using variational finite element technique. The model is based on the Pennes' bio-heat equation and mass diffusion equations together with suitable initial and boundary conditions. The results are analyzed in relation with atmospheric temperatures and other parameters of the tissue medium.

MATHEMATICAL MODEL OF TWO-DIMENSIONAL LAYERED PRESSURE FLOW IN THE AUGER CHANNEL

2018 ◽  
Author(s):  
А.В. ГУКАСЯН ◽  
В.С. КОСАЧЕВ ◽  
Е.П. КОШЕВОЙ
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Cross Section ◽  
Dynamic Pressure ◽  
Two Dimensional ◽  
Flow Dynamic ◽  
Pressure Flow ◽  
Rectangular Channels ◽  
Wide Range ◽  
Pressure Characteristics

Получено аналитическое решение двумерного слоистого напорного течения в канале шнека, позволяющее моделировать расходно-напорные характеристики прямоугольных каналов шнековых прессов с учетом гидравлического сопротивления формующих устройств и рассчитывать расходно-напорные характеристики экструдеров в широком диапазоне геометрии витков как в поперечном сечении, так и по длине канала. Obtained the analytical solution of two-dimensional layered pressure flow in the screw channel, allow to simulate the flow-dynamic pressure characteristics of rectangular channels screw presses taking into account the hydraulic resistance of the forming device and calculate the mass flow-dynamic pressure characteristics of the extruders in a wide range of the geometry of the coils, as in its cross section and along the length of the channel.

scholarly journals A Multiphase Flow in the Antroduodenal Portion of the Gastrointestinal Tract: A Mathematical Model

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
P. V. Trusov ◽  
N. V. Zaitseva ◽  
M. R. Kamaltdinov
Keyword(s):  
Mathematical Model ◽  
Gastrointestinal Tract ◽  
Multiphase Flow ◽  
Human Body ◽  
Digestive System ◽  
System Model ◽  
Food Density ◽  
Secretory Function ◽  
Functional Disorders ◽  
Food Particles

A group of authors has developed a multilevel mathematical model that focuses on functional disorders in a human body associated with various chemical, physical, social, and other factors. At this point, the researchers have come up with structure, basic definitions and concepts of a mathematical model at the “macrolevel” that allow describing processes in a human body as a whole. Currently we are working at the “mesolevel” of organs and systems. Due to complexity of the tasks, this paper deals with only one meso-fragment of a digestive system model. It describes some aspects related to modeling multiphase flow in the antroduodenal portion of the gastrointestinal tract. Biochemical reactions, dissolution of food particles, and motor, secretory, and absorbing functions of the tract are taken into consideration. The paper outlines some results concerning influence of secretory function disorders on food dissolution rate and tract contents acidity. The effect which food density has on inflow of food masses from a stomach to a bowel is analyzed. We assume that the future development of the model will include digestive enzymes and related reactions of lipolysis, proteolysis, and carbohydrates breakdown.

Analytical Buckling Loads of Columns Weakened Simultaneously with Transverse Cracks and Partial Delamination

2019 ◽  
Vol 19 (03) ◽  
pp. 1950027 ◽  
Author(s):  
Igor Planinc ◽  
Simon Schnabl
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Parametric Study ◽  
Transverse Crack ◽  
Transverse Cracks ◽  
Buckling Loads ◽  
Crack Location ◽  
Benchmark Solution ◽  
First Time

This paper focuses on development of a new mathematical model and its analytical solution for buckling analysis of elastic columns weakened simultaneously with transverse open cracks and partial longitudinal delamination. Consequently, the analytical solution for buckling loads is derived for the first time. The critical buckling loads are calculated using the proposed analytical model. A parametric study is performed to investigate the effects of transverse crack location and magnitude, length and degree of partial longitudinal delamination, and different boundary conditions on critical buckling loads of weakened columns. It is shown that the critical buckling loads of weakened columns can be greatly affected by all the analyzed parameters. Finally, the presented results can be used as a benchmark solution.

The New Methodology of Working Load Classification in Engineering Operations

2013 ◽  
Vol 664 ◽  
pp. 1186-1190
Author(s):  
Maria Kapustova
Keyword(s):  
Mathematical Model ◽  
Working Conditions ◽  
Human Body ◽  
Complex Loading ◽  
Summary Effect ◽  
Moment Load ◽  
Forging Press ◽  
Negative Factors

Working conditions in engineering operations are often characterized by a complex of negative factors, which at every moment load the human body during the active work with various intensity. Determination of the intensity of the workload is important for creation of workplace comfort, which is closely connected to workers’ contentment. The contribution presents a description and application of a mathematical model for determination of the workers´ complex loading at forging press workplace. It's a new and human way of evaluating work comfort, which can take into account the summary effect of all the negative factors at the workplace.

scholarly journals A Mathematical Model of Epidemics—A Tutorial for Students

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1174 ◽  
Author(s):  
Yutaka Okabe ◽  
Akira Shudo
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Sir Model ◽  
Exact Analytical Solutions ◽  
The Mathematical Model ◽  
Epidemic Diseases

This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. Additionally, we treat the generalization of the SIR model including births and natural deaths.

Dynamics of Submerged Expandable Tubes in Borehole Wells

2005 ◽  
Author(s):  
Ali Karrech ◽  
Abdennour Seibi ◽  
Tasneem Pervez ◽  
Karam Sab
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Elastic Limit ◽  
Petroleum Industry ◽  
Differential Pressure ◽  
Pressure Waves ◽  
Expansion Process ◽  
Fluid System ◽  
New Development ◽  
Potential Failure

Solid Expandable Tubular Technology (SETT) is a new development in the petroleum industry. It consists in accomplishing hydraulic expansion of a submerged tube by propelling a mandrel through it using a differential pressure. The progress of the mandrel deforms the tube beyond its elastic limit. Towards the end of the expansion process, the mandrel pops out of the tube resulting in displacement, stress and pressure waves. A mathematical model is developed to describe the dynamics of the tube-fluid system due to the pop-out phenomenon. The model takes into consideration the effects of the coupling between fluids and structure as well as the inherent system damping on the response. Through a specific field case, the model provides an analytical solution describing the wave propagating in the tube-fluid system and identifies the potential failure locations.

scholarly journals C2 Continuous Blending of Time-Dependent Parametric Surfaces

2019 ◽  
Vol 19 (4) ◽  
Author(s):  
Xiangyu You ◽  
Feng Tian ◽  
Wen Tang
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
High Efficiency ◽  
Approximate Analytical Solution ◽  
Time Dependent ◽  
Order Partial Differential Equation ◽  
Parametric Surfaces ◽  
Boundary Constraints ◽  
Surface Blending ◽  
C2 Continuity

Surface blending is widely applied in mechanical engineering. Creating a smooth transition surface of C2 continuity between time-dependent parametric surfaces that change their positions and shapes with time is an important and unsolved topic in surface blending. In order to address this issue, this paper develops a new approach to unify both time-dependent and time-independent surface blending with C2 continuity. It proposes a new surface blending mathematical model consisting of a vector-valued sixth-order partial differential equation and blending boundary constraints and investigates a simple and efficient approximate analytical solution of the mathematical model. A number of examples are presented to demonstrate the effectiveness and applications. The proposed approach has the advantages of (1) unifying time-independent and time-dependent surface blending, (2) always maintaining C2 continuity at trimlines when parametric surfaces change their positions and shapes with time, (3) providing effective shape control handles to achieve the expected shapes of blending surfaces but still exactly satisfy the given blending boundary constraints, and (4) quickly generating C2 continuous blending surfaces from the approximate analytical solution with easiness, good accuracy, and high efficiency.

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