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.

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.

Non-equilibrium Thermodynamics of Fast Traveling Waves in a Catalytic Fixed Bed. Emergence of Near-equilibrium Spatiotemporal Dissipative Structure

2018 ◽  
Vol 43 (3) ◽  
pp. 221-235
Author(s):  
Alexander P. Gerasev
Keyword(s):  
Mathematical Model ◽  
Wave Propagation ◽  
Traveling Wave ◽  
Dissipative Structure ◽  
Fixed Bed ◽  
Dissipative Structures ◽  
Catalytic Reactors ◽  
Linear Ordinary Differential Equations ◽  
Physical And Chemical ◽  
Non Equilibrium

AbstractThis work presents the results of the mathematical modeling of the fast traveling wave propagation phenomenon in the fixed-bed catalytic reactors according to a simple (basic) mathematical model with a reversible reaction. Qualitative and quantitative research is used to study the behavior of separatrices’ trajectories of the system’s non-linear ordinary differential equations. Special attention has been paid to the non-equilibrium thermodynamic methods. The entropy balance equation is constructed and analyzed under the assumption of the simple mathematical model of physical and chemical processes. The influence of key physical and chemical parameters on the fast traveling wave properties is studied. The phenomenon of fast traveling wave propagation in the fixed-bed catalytic reactors provides a vivid example of a spatiotemporal dissipative structure in active heterogeneous medium. These dissipative structures are shown to exist near the thermodynamic equilibrium.

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.

Traveling wave solutions in the mathematical model of blood coagulation

2016 ◽  
Vol 96 (16) ◽  
pp. 2891-2905 ◽  
Author(s):  
T. Galochkina ◽  
H. Ouzzane ◽  
A. Bouchnita ◽  
V. Volpert
Keyword(s):  
Mathematical Model ◽  
Blood Coagulation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
The Mathematical Model

scholarly journals TRAVELING WAVES FOR IN-SITU COMBUSTION IN POROUS MEDIA

2020 ◽  
Vol 5 (6) ◽  
Author(s):  
Tatiana Danelon De Assis ◽  
Mariane Dos Santos Bispo ◽  
Jessica Yvonne Santa Cruz Cárdenas ◽  
Giulia Carvalho Fritis ◽  
Angel Enrique Ramírez Gutiérrez ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Oil Recovery ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Necessary Conditions ◽  
Combustion Process ◽  
Traveling Wave Solution ◽  
In Situ Combustion ◽  
Theoretical Results

This work presents a mathematical model describing the in-situ combustion process, which can be used in enhanced oil recovery. The hyperbolic part of the system was solved as a Riemann Problem. Necessary conditions for the existence of a traveling wave solution were verified. Furthermore, theoretical results are verified by using numerical simulations.

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