scholarly journals Evaluation of melt-water premixture formation due to Rayleigh-Taylor instabilities

2021 ◽  
Vol 2088 (1) ◽  
pp. 012029
Author(s):  
V I Melikhov ◽  
O I Melikhov ◽  
D V Finoshkina
Keyword(s):  
Water Layer ◽  
Water Mixture ◽  
Water Steam ◽  
Melt Water ◽  
Circular Frequency ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
Theoretical Results ◽  
Steam Bubble ◽  
System Water

Abstract A linear analysis of the stability of the three-layer stratified hydrodynamic system “water (top) – steam – melt (bottom)” has been performed. Kinematic and dynamic conditions on the “water – steam” and “steam – melt” interfaces are formulated, and on their basis a dispersion equation is obtained that relates the circular frequency of perturbations to the wavenumber. Analysis of this equation made it possible to determine the region of instability of this system and to find the wavenumber of the most fastly growing harmonics. The results obtained were used to estimate the size of bubbles formed at the interface between steam and water due to the development of the Rayleigh-Taylor instability. The obtained theoretical results are consistent with experimental observations in such systems. The heights of the melt splashes into water due to the collapse of the formed steam bubble were estimated. The obtained estimations demonstrate possibilities of the formation of melt-water mixture region during the spreading of the melt under a water layer, in which a strong steam explosion can occur.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

scholarly journals Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Hongwei Luo ◽  
Jiangang Zhang ◽  
Wenju Du ◽  
Jiarong Lu ◽  
Xinlei An
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Points ◽  
Bifurcation Theorem ◽  
Center Manifold Theorem ◽  
Governing System ◽  
Normal Form Method ◽  
The Stability ◽  
System Frequency ◽  
Realistic Significance ◽  
Theoretical Results

A PI hydroturbine governing system with saturation and double delays is generated in small perturbation. The nonlinear dynamic behavior of the system is investigated. More precisely, at first, we analyze the stability and Hopf bifurcation of the PI hydroturbine governing system with double delays under the four different cases. Corresponding stability theorem and Hopf bifurcation theorem of the system are obtained at equilibrium points. And then the stability of periodic solution and the direction of the Hopf bifurcation are illustrated by using the normal form method and center manifold theorem. We find out that the stability and direction of the Hopf bifurcation are determined by three parameters. The results have great realistic significance to guarantee the power system frequency stability and improve the stability of the hydropower system. At last, some numerical examples are given to verify the correctness of the theoretical results.

scholarly journals Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hai Zhang ◽  
Daiyong Wu ◽  
Jinde Cao
Keyword(s):  
Asymptotic Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Stability Criteria ◽  
Differential Systems ◽  
Discrete Delays ◽  
Transcendental Equations ◽  
The Stability ◽  
Theoretical Results

We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

An extended optimal velocity difference model in a cooperative driving system

2015 ◽  
Vol 26 (05) ◽  
pp. 1550054
Author(s):  
Jinliang Cao ◽  
Zhongke Shi ◽  
Jie Zhou
Keyword(s):  
Traffic Flow ◽  
Linear Stability Theory ◽  
Difference Model ◽  
Optimal Velocity ◽  
Driving System ◽  
Cooperative Driving ◽  
Proposed Model ◽  
De Vries ◽  
The Stability ◽  
Theoretical Results

An extended optimal velocity (OV) difference model is proposed in a cooperative driving system by considering multiple OV differences. The stability condition of the proposed model is obtained by applying the linear stability theory. The results show that the increase in number of cars that precede and their OV differences lead to the more stable traffic flow. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions, respectively. To verify these theoretical results, the numerical simulation is carried out. The theoretical and numerical results show that the stabilization of traffic flow is enhanced by considering multiple OV differences. The traffic jams can be suppressed by taking more information of cars ahead.

scholarly journals Suitability of base liquid in a nanofluid-laden solar flat-plate collector with emphasize on bioglycol

2018 ◽  
Vol 225 ◽  
pp. 04014
Author(s):  
Seyed Reza Shamshirgaran ◽  
Hussain H. Al-Kayiem ◽  
Morteza K. Assadi ◽  
K.V. Sharma
Keyword(s):  
Ethylene Glycol ◽  
Flat Plate ◽  
Propylene Glycol ◽  
Energetic Efficiency ◽  
Water Mixture ◽  
Safe Product ◽  
The Stability ◽  
Flat Plate Collector ◽  
Matlab Programming ◽  
Base Liquid

Ethylene glycol and propylene glycol are commonly used as thermal liquids in solar flat-plate collectors (FPCs). They are utilized as base liquid as well as for improving the stability of nanofluids in FPCs. The objective of the present paper is to introduce a renewable-derived bio glycol for use as base liquid in FPCs. The effect of base ratio (BR) of different glycol products on the performance of a conventional FPC and a nanofluidladen FPC is investigated in this paper to determine its suitability. MATLAB programming was employed for modeling the performance of the FPC operating with copper and cerium oxide nanomaterials. The results show that 20:80 bio glycol/water mixture is capable of enhancing the FPC’s energetic efficiency up to 72.1% which is higher than with either ethylene glycol and propylene glycol. The energy efficiency of a glycol-based nanofluid-filled FPC decreases with the base ratio of all three glycol products. Since bio glycol is a non-toxic and safe product, it can be utilized as a safe and environmentally-friend antifreeze and base liquid in nanofluid-filled FPCs.

scholarly journals Rayleigh-Taylor instability of two superposed magnetized viscous fluids with suspended dust particles

2010 ◽  
Vol 14 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Praveen Sharma ◽  
Ram Prajapati ◽  
Rajendra Chhajlani
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Relaxation Frequency ◽  
Taylor Instability ◽  
Dust Particles ◽  
Stable Configuration ◽  
Rayleigh Taylor Instability ◽  
Suspended Dust ◽  
The Stability

The linear Rayleigh-Taylor instability of two superposed incompressible magnetized fluids is investigated incorporating the effects of suspended dust particles and viscosity. The basic magnetohydrodynamic set of equations have been constructed and linearized. The dispersion relation for 2-D and 3-D perturbations is obtained by applying the appropriate boundary conditions. The condition of Rayleigh-Taylor instability is investigated for potentially stable and unstable modes, which depends upon magnetic field, viscosity and suspended dust particles. The stability of the system is discussed by applying the Routh-Hurwitz criterion. It is found that the Alfven mode comes into the dispersion relation for perturbations in x, y-directions and in only x-direction, while it does not come into y-directional perturbation. The stable configuration is found to remain stable even in the presence of suspended dust particles. Numerical calculations have been performed to see the effects of various parameters on the growth rate of Rayleigh-Taylor instability. It is found that magnetic field and relaxation frequency of suspended dust particles both have destabilizing influence on the growth rate of Rayleigh-Taylor instability. The effects of kinematic viscosity and mass concentration of dust particles are found to have stabilized the growth rate of linear Rayleigh-Taylor instability.

scholarly journals Effect of Horizontal and Vertical Magnetic Fields on Rayleigh?Taylor Instability

1968 ◽  
Vol 21 (6) ◽  
pp. 923 ◽  
Author(s):  
RC Sharma ◽  
KM Srivastava
Keyword(s):  
Magnetic Fields ◽  
General Equation ◽  
Taylor Instability ◽  
Combined Effect ◽  
Physical Situation ◽  
Stable Case ◽  
Unstable Case ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
Superposed Fluids

A general equation studying the combined effect of horizontal and vertical magnetic fields on the stability of two superposed fluids has been obtained. The unstable and stable cases at the interface (z = 0) between two uniform fluids, with both the possibilities of real and complex n, have been. separately dealt with. Some new results are obtained. In the unstable case with real n, the perturbations are damped or unstable according as 2(k'-k~L2)_(<X2-<Xl)k is> or < 0 under the physical situation (35). In the stable case, the perturbations are stable or unstable according as 2(k2_k~L2)+(<Xl-<X2)k is > or < 0 under the same physical situation (35). The perturbations become unstable if HIlIH 1- (= L) is large. Both the cases are also discussed with imaginary n.

scholarly journals Research Results of the Potato Digger Technological Process

2018 ◽  
Vol 12 (5) ◽  
pp. 14-19 ◽  
Author(s):  
V. M. Alakin ◽  
G. S. Nikitin
Keyword(s):  
Design Parameters ◽  
Operating Speed ◽  
Working Process ◽  
Projectile Motion ◽  
Operating Process ◽  
Cutoff Angle ◽  
The Stability ◽  
Theoretical Results ◽  
Optimum Working

A potato digger equipped with a four­bladed beater operating in connection with rotary separating surface has low material and energy consumption, higher separating efficiency, as well as lower degree of tuber damaging. The potato digger design should include a four­bladed intake­and­feed beater to prevent potato heap transportation faults in front of the first section. (Research purpose) Increasing the technological and economic efficiency of a potato digging­and­ separating unit through the determination of the optimum values of the design parameters and operating process of the intake­and­feed beater. (Materials and methods) the authors have made an overview of general principles of ensuring the stability of the potato heap movement provided by the four­bladed intake­and­feed beater. The dependency of the minimum beater speed on the operating speed of the potato digger has been found to exclude a probability of its overloading. The methodology of calculating the potato heap velocity and the cutoff angle between the material and the beater blades has been worked out by analyzing potato heap lifting to the upper points of the working units of the rotary separator’s first section. Operating speed of the beater has been determined through the differential equation for the speed of a potato heap moving along the blade surface. (Results and discussion) Preliminary potato heap speed and cutoff angle have been found through the equation of dynamics describing the projectile motion of an object thrown at an angle. The operating values of the angles are dependent on the potato digger working speed and can be selected from the triangle of speeds. The authors have determined the dependence of the optimal beater speed on the working speed of a potato digger. Its value should exceed the minimum speed of the beater. (Conclusions) Theoretical results allow proposing the best design features and optimum working process parameters of a four­bladed beater receiving a potato heap, transporting it and lifting on the rotary separating surface.

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