Estimation of Toxic Gases’ Density Increment in the Integral Mathematical Model of Initial Fire Stage in Buildings

2021 ◽  
Vol 9 (2) ◽  
pp. 31-36
Author(s):  
Yu. Fedorov ◽  
V. Pavlidis ◽  
V. Urban ◽  
E. Yakovleva
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Initial Instant ◽  
Toxic Gases

In the framework of an integral mathematical model of initial fire stage in a building the differential equation for toxic gases’ volume-averaged density has been considered. Representations for toxic gases’ density increment in the vicinity of initial instant have been found, and estimates for this increment have been given.

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

A MATHEMATICAL MODEL OF ANEURYSM OF CIRCLE OF WILLIS

1995 ◽  
Vol 03 (03) ◽  
pp. 653-659 ◽  
Author(s):  
J. J. NIETO ◽  
A. TORRES
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Ordinary Differential Equation ◽  
Blood Flow ◽  
Nonlinear Analysis ◽  
Existence Of Solutions ◽  
Circle Of Willis ◽  
Second Order ◽  
Qualitative Properties

We introduce a new mathematical model of aneurysm of the circle of Willis. It is an ordinary differential equation of second order that regulates the velocity of blood flow inside the aneurysm. By using some recent methods of nonlinear analysis, we prove the existence of solutions with some qualitative properties that give information on the causes of rupture of the aneurysm.

Mathematical Modeling of the λ Switch

2010 ◽  
pp. 573-603
Author(s):  
Dmitriy Laschov ◽  
Michael Margaliot
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Mathematical Model ◽  
Gene Regulation ◽  
Equilibrium Points ◽  
Domain Of Attraction ◽  
Verbal Description ◽  
Quantitative Understanding ◽  
Living Organisms ◽  
Scientific Challenge

Gene regulation plays a central role in the development and functioning of living organisms. Developing a deeper qualitative and quantitative understanding of gene regulation is an important scientific challenge. The Lambda switch is commonly used as a paradigm of gene regulation. Verbal descriptions of the structure and functioning of the Lambda switch have appeared in biological textbooks. We apply fuzzy modeling to transform one such verbal description into a well-defined mathematical model. The resulting model is a piecewise-quadratic, second-order differential equation. It demonstrates functional fidelity with known results while being simple enough to allow a rather detailed analysis. Properties such as the number, location, and domain of attraction of equilibrium points can be studied analytically. Furthermore, the model provides a rigorous explanation for the so-called stability puzzle of the Lambda switch.

scholarly journals Bifurcation phenomena and statistical regularities in dynamics of forced impacting oscillator

2019 ◽  
Vol 98 (3) ◽  
pp. 1795-1806 ◽  
Author(s):  
Sergii Skurativskyi ◽  
Grzegorz Kudra ◽  
Krzysztof Witkowski ◽  
Jan Awrejcewicz
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Physical Model ◽  
Dry Friction ◽  
Stepper Motor ◽  
Nonlinear Phenomenon ◽  
Hertz Contact ◽  
Bifurcation Phenomena ◽  
Statistical Regularities ◽  
The Mathematical Model

Abstract The paper is devoted to the study of harmonically forced impacting oscillator. The physical model for oscillator is a cart on a guide connected to the support with springs and excited by the stepper motor. The support also is provided with limiter of motion. The mathematical model for this system is defined with the second-order piecewise smooth differential equation. Model’s nonlinearity is connected with the incorporation of dry friction and generalized Hertz contact law. Analyzing the classical Poincare sections and inter-impact sequences obtained experimentally and numerically, the bifurcations and statistical properties of periodic, multi-periodic, and chaotic regimes were examined. The development of impact-adding regime as a new nonlinear phenomenon when the forcing frequency varies was observed.

scholarly journals Chemotherapeutic Effects on Hematopoiesis: A Mathematical Model

1998 ◽  
Vol 1 (3) ◽  
pp. 209-221 ◽  
Author(s):  
John Carl Panetta
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Cell Cycle ◽  
Growth Factors ◽  
Blood Cell ◽  
Blood Cells ◽  
Blood Stream ◽  
Hematopoietic Growth Factors ◽  
Cell Production ◽  
Delay Differential

Blood cell production is one of the major limiting effects of cell-cycle-specific chemotherapy. By studying the effects of the drugs on a mathematical model of hematopoiesis, a better understanding of how to prevent over-reduction of circulating blood may be investigated.In this model we will use a delay-differential equation developed by Mackey and Glass (1977) to show acceptable chemotherapeutic deses (i.e. survival of the circulating blood cells) as a function of: the period which the drugs are administered; the strength of the dose; and the delay from initiation of blood cell production to its release into the blood stream. We then make qualitative comparisons to know effects of cell-cycle-specific chemotherapy on circulating blood cell elements. Finally, we also consider how the effects of hematopoietic growth factors alter the outcome of the therapy.

Digital/analog simulation of electromechanical devices on a graphics terminal

SIMULATION ◽  
1972 ◽  
Vol 18 (3) ◽  
pp. 99-104
Author(s):  
Satya P. Sharma ◽  
C.D. Roe
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
System Modeling ◽  
Continuous System ◽  
Equation Model ◽  
Measuring System ◽  
Differential Equation Model ◽  
Analog Simulation ◽  
Optical Displacement ◽  
Electromechanical Devices

Computer simulation of electromechanical devices by exercising a suitable mathematical model has advantages in studying the effects of parameter changes. As a specific example, an electromechan ical relay has been chosen for simulation in this investigation. A differential equation model of the relay 1 is developed and simulated on an IBM 1130/2250 graphics terminal using the 1130 Continuous System Modeling Program (CSMP). An optical displacement measuring system was used to measure the armature travel as a function of time while the relay was functioning. These mea sured characteristics were compared with the analogous characteristics of the simulated relay to evaluate the validity and accuracy of the mathematical model. It is concluded that the differential equation model is an adequate appro ximation provided the lumped parameters of the magnetic circuit are appropriately chosen. The influence on the dynamic response of the relay as various relay parameters are changed can easily be predicted from the simulated model in this study.

Numerical Simulation of Orientation Distribution on Fibers Suspensions in Planar Extensional Field

2013 ◽  
Vol 395-396 ◽  
pp. 1174-1178
Author(s):  
Pei Fang Luo ◽  
Zan Huang
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Fiber Orientation ◽  
Extensional Flow ◽  
Orientation Distribution ◽  
Specific Form ◽  
Fiber Orientation Distribution ◽  
Planar Extensional Flow

A mathematical model of evolution process is adopted to simulate orientation distribution of fibers suspensions in planar extensional flow, i.e., specific form of Fokker-Plank partial differential equation and Jeffery equation. The analytical solution of differential equation on forecast fiber orientation distribution is deduced.

A model of a fishery with fish stock involving delay equations

2009 ◽  
Vol 367 (1908) ◽  
pp. 4907-4922 ◽  
Author(s):  
P. Auger ◽  
Arnaud Ducrot
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Delay Differential Equation ◽  
Bifurcation Analysis ◽  
Infinite Delay ◽  
Steady States ◽  
Delay Equations ◽  
Fish Stock ◽  
Delay Differential

The aim of this paper is to provide a new mathematical model for a fishery by including a stock variable for the resource. This model takes the form of an infinite delay differential equation. It is mathematically studied and a bifurcation analysis of the steady states is fulfilled. Depending on the different parameters of the problem, we show that Hopf bifurcation may occur leading to oscillating behaviours of the system. The mathematical results are finally discussed.

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