scholarly journals Mathematical modeling of the demographic dividend (DD) capture applied in economy.

2021 ◽  
Author(s):  
GUEYE cheikh ◽  
TOUMBOU Babacar ◽  
DIOUF Abdoulaye
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
System Modeling ◽  
Natural Mortality ◽  
Demographic Dividend ◽  
Mathematical Study ◽  
System Parameters ◽  
Ode System ◽  
Tools And Techniques

Abstract The purpose of this work is to develop tools and techniques for modeling the capture of the Demographic Dividend. We presented the ordinary differential equation (ODE) system modeling the variation of economically dependent and economically non dependent populations. The system uses natality, natural mortality, infant mortality, migration (incoming and outgoing), and transfers. The mathematical study of this ODE system shows the existence of an equilibrium point whose stability depends on a certain number of system parameters. Numerical simulations of the resulting model were performed using scenarios approach.

scholarly journals Small Symmetrical Deformation of Thin Torus with Circular Cross-Section

2021 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Cross Section ◽  
Circular Cross Section ◽  
Complex Form ◽  
Real Form ◽  
Element Analysis ◽  
Numerical Studies ◽  
Ode System ◽  
Symmetrical Deformation

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, a complex-form ordinary differential equation (ODE) for the small symmetrical deformation of an elastic torus is successfully transformed into the well-known Heun's ODE, whose exact solution is obtained in terms of Heun's functions. To overcome the computational difficulties of the complex-form ODE in dealing with boundary conditions, a real-form ODE system is proposed. A general code of numerical solution of the real-form ODE is written by using Maple. Some numerical studies are carried out and verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell.

ODE observers for DAE systems

2018 ◽  
Vol 36 (4) ◽  
pp. 1375-1393 ◽  
Author(s):  
Thomas Berger ◽  
Timo Reis
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Linear Time ◽  
Observer Design ◽  
Simple Criterion ◽  
Linear Time Invariant ◽  
Ode System ◽  
Dae Systems ◽  
Invariant Differential ◽  
Time Invariant

Abstract We consider linear time-invariant differential-algebraic systems which are not necessarily regular. The following question is addressed: when does an (asymptotic) observer which is realized by an ordinary differential equation (ODE) system exist? In our main result we characterize the existence of such observers by means of a simple criterion on the system matrices. To be specific, we show that an ODE observer exists if, and only if, the completely controllable part of the system is impulse observable. Extending the observer design from earlier works we provide a procedure for the construction of (asymptotic) ODE observers.

scholarly journals Mathematical modeling of transfer intensive of edges of spatial cracks on the fronts of longitudinal and shear waves by a ray method

2020 ◽  
pp. 164-181
Author(s):  
Мария Игоревна Быкова ◽  
Николай Дмитриевич Вервейко ◽  
Светлана Евгеньевна Крупенко ◽  
Александр Иванович Шашкин ◽  
Софья Александровна Шашкина
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Plastic Deformation ◽  
Longitudinal Shear ◽  
Shock Velocity ◽  
Ray Method ◽  
Longitudinal And Shear Waves ◽  
Change Intensity ◽  
Space Case

В ближайшей окрестности вершины плоской трещины, а в общем случае, вблизи передней кромки пространственной трещины, деформирование материала носит неупругий характер. В работе предложено лучевое моделирование высокоскоростного деформирования материала в δ-окрестности подвижной передней кромки трещины, используя динамическую упруговязкопластическую модель тела Бингама с условием пластичности Мизеса. Показано, что распространяющаяся передняя кромка трещины продольного сдвига лежит на поверхности сильного разрыва продольной скорости, бегущей со скоростью упругих продольных волн, а передняя кромка трещины отрыва и трещины поперечного сдвига лежит на поверхности сдвиговой волны, бегущей со скоростью волн сдвига. Введены интенсивности передних кромок трещин: скачок скорости сдвига поперек передней кромки трещины продольного сдвига, скачок поперечной скорости на передней кромке трещины отрыва, скачок касательной скорости к передней кромке трещины поперечного сдвига. Построены обыкновенные дифференциальные уравнения переноса интенсивностей передних кромок трещин вдоль лучей как ортогональных траекторий точек переднего фронта. Получены приближенные решения уравнений переноса интенсивностей передних кромок пространственных трещин в напряженный материал и приведены выражения для глубины проникания пространственных трещин. Показано изменение направления сдвига и отрыва в передних кромках соответствующих трещин в зависимости от напряженного состояния перед трещинами. Приведены графики численных расчетов переноса интенсивностей передних кромок трещин и глубины их проникания. In the near neighborhood of the top of the plane crack, and in General, in the space case, near the edge of the spatial crack, the deformations of the material have the inelastic character. In this article proposes the elasticviscoplastic model of the Bingham body with the condition of plasticity of Mises for modeling high velocity deformation material near of the top of crack. Shown that an edge of crack belong a surface of elastic wave: cracks of longitudinal shear belong of longitudinal wave and a crack of untiplane shear and avulsion belong a surface of shear wave. For intensity of the crack suggest a shock velocity on the curve of the edge of crack and made ordinary differential equation for transfer intensity of crack on the front of the wave. Shown that a distant of propagation edge of the crack depend from plastic deformation material on the front of the wave. In the process of propagation crack this direction of shear can change from a stresses in front of the wave. Three-D graphics show change intensity of the crack in a process of propagation from parameters.

scholarly journals METASTABILITY IN THE CLASSICAL, TRUNCATED BECKER–DÖRING EQUATIONS

2002 ◽  
Vol 45 (3) ◽  
pp. 701-716 ◽  
Author(s):  
Dugald B. Duncan ◽  
Rachel M. Dunwell
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Rate Constants ◽  
Cluster Size ◽  
Monomer Concentration ◽  
System Size ◽  
Linear Ordinary Differential Equation ◽  
Zero Eigenvalue ◽  
Ode System ◽  
Slow Evolution

AbstractWe show that in the classical (fixed-monomer-concentration) Becker–Döring equations truncated at finite cluster size, the slow evolution (metastability) of solutions can be explained in terms of the eigensystem of this linear ordinary differential equation (ODE) system. In particular, for a common choice of coagulation–fragmentation rate constants there is an extremely small non-zero eigenvalue which is isolated from the rest of the spectrum. We give estimates and bounds on the size of this eigenvalue, the gap between it and the second smallest, and the size of the largest eigenvalue. The bounds on the smallest eigenvalue are very sharp when the system size and/or monomer concentration are large enough.AMS 2000 Mathematics subject classification: Primary 34A30; 15A18; 65F15

scholarly journals Small Symmetrical Deformation of Thin Torus with Circular Cross-Section

2021 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Cross Section ◽  
Circular Cross Section ◽  
Complex Form ◽  
Real Form ◽  
Element Analysis ◽  
Numerical Studies ◽  
Ode System ◽  
Symmetrical Deformation

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, a complex-form ordinary differential equation (ODE) for the small symmetrical deformation of an elastic torus is successfully transformed into the well-known Heun's ODE, whose exact solution is obtained in terms of Heun's functions. To overcome the computational difficulties of the complex-form ODE in dealing with boundary conditions, a real-form ODE system is proposed. A general code of numerical solution of the real-form ODE is written by using Maple. Some numerical studies are carried out and verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell.

scholarly journals The Boundary Proportion Differential Control Method of Micro-Deformable Manipulator with Compensator Based on Partial Differential Equation Dynamic Model

Micromachines ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 799
Author(s):  
Xiangli Pei ◽  
Ying Tian ◽  
Minglu Zhang ◽  
Ruizhuo Shi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dynamic Model ◽  
Control Method ◽  
System Modeling ◽  
Working Environment ◽  
Partial Differential ◽  
External Interference ◽  
Differential Control ◽  
Differential Control Method

It is challenging to accurately judge the actual end position of the manipulator—regarded as a rigid body—due to the influence of micro-deformation. Its precise and efficient control is a crucial problem. To solve the problem, the Hamilton principle was used to establish the partial differential equation (PDE) dynamic model of the manipulator system based on the infinite dimension of the working environment interference and the manipulator space. Hence, it resolves the common overflow instability problem in the micro-deformable manipulator system modeling. Furthermore, an infinite-dimensional radial basis function neural network compensator suitable for the dynamic model was proposed to compensate for boundary and uncertain external interference. Based on this compensation method, a distributed boundary proportional differential control method was designed to improve control accuracy and speed. The effectiveness of the proposed model and method was verified by theoretical analysis, numerical simulation, and experimental verification. The results show that the proposed method can effectively improve the response speed while ensuring accuracy.

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