About one highly singular mathematical model of the fourth order with derivatives on the measure

2015 ◽  
Vol 3 (9) ◽  
pp. 298-301
Author(s):  
F. Golovaneva ◽  
S. Shabrov
Keyword(s):  
Mathematical Model ◽  
Fourth Order

Dynamics of the Head-Neck Complex in Response to the Trunk Horizontal Vibration: Modeling and Identification

2003 ◽  
Vol 125 (4) ◽  
pp. 533-539 ◽  
Author(s):  
Mohammad A. Fard ◽  
Tadashi Ishihara ◽  
Hikaru Inooka
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Fourth Order ◽  
Optimization Method ◽  
Horizontal Vibration ◽  
Domain Identification ◽  
Viscoelastic Parameters ◽  
Resonance Frequencies ◽  
Fourth Order Model ◽  
Head Neck

Although many studies exist concerning the influence of seat vibration on the head in the seated human body, the dynamic response of the head-neck complex (HNC) to the trunk vibration has not been well investigated. Little quantitative knowledge exists about viscoelastic parameters of the neck. In this study, the dynamics of the HNC is identified when it is exposed to the trunk horizontal (fore-and-aft) vibration. The frequency response functions between the HNC angular velocity and the trunk horizontal acceleration, corresponding to four volunteers, are obtained in the frequency range of 0.5 Hz to 10 Hz. A fourth-order mathematical model, derived by considering a double-inverted-pendulum model for the HNC, is designed to simulate the dynamic response of the HNC to the trunk horizontal vibration. The frequency domain identification method is used to determine the coefficients of the mathematical model of the HNC. Good agreement has been obtained between experimental and simulation results. This indicates that the system, similar to the designed fourth-order model, has mainly two resonance frequencies. The viscoelastic parameters of the neck, including the spring and damping coefficients, are then obtained by use of the optimization method.

scholarly journals Colpitts Chaotic Oscillator Coupling with a Generalized Memristor

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Ling Lu ◽  
Changdi Li ◽  
Zicheng Zhao ◽  
Bocheng Bao ◽  
Quan Xu
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Fourth Order ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Nonlinear Phenomena ◽  
Unique Equilibrium ◽  
First Order ◽  
The Mathematical Model ◽  
Order Parallel

By introducing a generalized memristor into a fourth-order Colpitts chaotic oscillator, a new memristive Colpitts chaotic oscillator is proposed in this paper. The generalized memristor is equivalent to a diode bridge cascaded with a first-order parallel RC filter. Chaotic attractors of the oscillator are numerically revealed from the mathematical model and experimentally captured from the physical circuit. The dynamics of the memristive Colpitts chaotic oscillator is investigated both theoretically and numerically, from which it can be found that the oscillator has a unique equilibrium point and displays complex nonlinear phenomena.

Numerical Modeling and Experimental Testing of a Solar Grill

1993 ◽  
Vol 115 (1) ◽  
pp. 5-10 ◽  
Author(s):  
Ibrahim Olwi ◽  
Adel Khalifa
Keyword(s):  
Mathematical Model ◽  
Numerical Modeling ◽  
Fourth Order ◽  
Heat Balance ◽  
Experimental Testing ◽  
Balance Equations ◽  
Runge Kutta

A detailed study of a solar cooker used for meat grilling was performed. Experiments were undertaken to test the effects of several parameters on the cooker performance. A mathematical model for the solar grill was developed. Heat balance equations were solved using the fourth-order Runge-Kutta technique. It was concluded that an air-tight oven with double glazing and maximum meat charge will give the best performance and highest efficiency for the solar grill.

Dynamics of two gas bubbles in liquid in an ultrasonic traveling wave

2017 ◽  
Vol 12 (1) ◽  
pp. 33-39 ◽  
Author(s):  
A.A. Aganin ◽  
A.I. Davletshin
Keyword(s):  
Mathematical Model ◽  
Ultrasonic Wave ◽  
Fourth Order ◽  
Traveling Wave ◽  
Hydrodynamic Interaction ◽  
Air Bubbles ◽  
Liquid Viscosity ◽  
Initial Distance ◽  
Running Wave ◽  
Spatial Displacements

The influence of the liquid viscosity and compressibility on the dynamics of two air bubbles (with equilibrium radii of 5 μm) in water at room conditions under the action of a plane ultrasonic wave traveling along the line of the bubble centers (the wavelength is 5000 μm, the amplitude is 0.3 bar) is studied. The initial distance between the centers of the bubbles is six bubble radii. A mathematical model is used, which is fourth-order accurate in terms of the ratio of the radius of the bubbles to the distance between them. It is shown that the spatial displacements of the bubbles are determined mainly by their hydrodynamic interaction. The influence of the liquid viscosity and compressibility is generally significant, and the viscosity affects much more. Without account of the liquid viscosity and compressibility, the bubbles collide with each other after the action of 4.5 running-wave lengths. With taking into account the liquid compressibility, the bubbles under the same action remain remote at a distance on the order of their equilibrium radii, while with additionally allowing for the liquid viscosity, their spacing is kept close to the initial one.

Application of Adomian Decomposition Method on a Mathematical Model of Malaria

2020 ◽  
pp. 417-435
Author(s):  
Adesoye Idowu Abioye ◽  
Olumuyiwa James Peter ◽  
Ayotunde Abayomi Ayoade ◽  
Ohigweren Airenoni Uwaheren ◽  
Mohammed Olanrewaju Ibrahim
Keyword(s):  
Mathematical Model ◽  
Fourth Order ◽  
Decomposition Method ◽  
Deterministic Model ◽  
Adomian Decomposition Method ◽  
Model Solution ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Adomian Decomposition ◽  
Malaria Model

In this paper, we consider a deterministic model of malaria transmission. Adomian decomposition method (ADM) is used to calculate an approximation to the solution of the non-linear couple of differential equations governing the model. Classical fourth-order Runge-Kutta method implemented in Maple18 confirms the validity of the ADM in solving the problem. Graphical results show that ADM agrees with R-K 4. In order words, these produced the same behaviour, validating ADM's efficiency and accuracy of ADM in finding the malaria model solution.

scholarly journals Analysis of singularity planar multi-linkage mechanism of fourth order

2020 ◽  
pp. 17-21
Author(s):  
E. S. Gebel ◽  
Keyword(s):  
Mathematical Model ◽  
Angular Velocity ◽  
Fourth Order ◽  
Duty Cycle ◽  
Closed Loop ◽  
Linkage Mechanism ◽  
Equilibrium Equations ◽  
Singularity Problem ◽  
Critical Position ◽  
The Mathematical Model

The planar multi-linkage mechanism of the fourth order, the output rocker of which implements an approximate stopping in one critical position is described in the article. The mechanism consists of three dyads passing through their limit positions in a single duty cycle. That is why the singularity problem is relevant for such mechanisms and should be studied to avoid jamming of links or the appearance of uncontrolled movements. The mathematical model is based on the theory of screws and contains the closed-loop equilibrium equations obtained for the investigated mechanism. Based on the obtained results of the geometry and singularity analyses, it is shown that there are eight different positions in which some joints stop momentarily and then their angular velocity direction changes

scholarly journals Some Numerical Methods and Comparisons for Solving Mathematical Model of Surface Decontamination by Disinfectant Solution

MATEMATIKA ◽  
2018 ◽  
Vol 34 (2) ◽  
pp. 271-291
Author(s):  
Chai Jin Sian ◽  
Yeak Su Hoe ◽  
Ali H. M. Murid
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Fourth Order ◽  
Difference Method ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Disinfectant Solution ◽  
Surface Decontamination ◽  
Runge Kutta

A mathematical model is considered to determine the effectiveness of disinfectant solution for surface decontamination. The decontamination process involved the diffusion of bacteria into disinfectant solution and the reaction of the disinfectant killing effect. The mathematical model is a reaction-diffusion type. Finite difference method and method of lines with fourth-order Runge-Kutta method are utilized to solve the model numerically. To obtain stable solutions, von Neumann stability analysis is employed to evaluate the stability of finite difference method. For stiff problem, Dormand-Prince method is applied as the estimated error of fourth-order Runge-Kutta method. MATLAB programming is selected for the computation of numerical solutions. From the results obtained, fourth-order Runge-Kutta method has a larger stability region and better accuracy of solutions compared to finite difference method when solving the disinfectant solution model. Moreover, a numerical simulation is carried out to investigate the effect of different thickness of disinfectant solution on bacteria reduction. Results show that thick disinfectant solution is able to reduce the dimensionless bacteria concentration more effectively

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