scholarly journals The stability of a rising droplet: an inertialess non-modal growth mechanism

2015 ◽  
Vol 786 ◽  
Author(s):  
Giacomo Gallino ◽  
Lailai Zhu ◽  
François Gallaire
Keyword(s):  
Stability Analysis ◽  
Stokes Equations ◽  
Basin Of Attraction ◽  
Boundary Integral ◽  
Shape Evolution ◽  
Transient Growth ◽  
Critical Amplitude ◽  
Perturbation Amplitude ◽  
The Stability ◽  
The Basin Of Attraction

Prior modal stability analysis (Kojimaet al.,Phys. Fluids, vol. 27, 1984, pp. 19–32) predicted that a rising or sedimenting droplet in a viscous fluid is stable in the presence of surface tension no matter how small, in contrast to experimental and numerical results. By performing a non-modal stability analysis, we demonstrate the potential for transient growth of the interfacial energy of a rising droplet in the limit of inertialess Stokes equations. The predicted critical capillary numbers for transient growth agree well with those for unstable shape evolution of droplets found in the direct numerical simulations of Koh & Leal (Phys. Fluids, vol. 1, 1989, pp. 1309–1313). Boundary integral simulations are used to delineate the critical amplitude of the most destabilizing perturbations. The critical amplitude is negatively correlated with the linear optimal energy growth, implying that the transient growth is responsible for reducing the necessary perturbation amplitude required to escape the basin of attraction of the spherical solution.

Passive Dynamic Biped Walking—Part II: Stability Analysis of the Passive Dynamic Gait

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
Derek Koop ◽  
Christine Q. Wu
Keyword(s):  
Angular Momentum ◽  
Stability Analysis ◽  
Lyapunov Exponents ◽  
Basin Of Attraction ◽  
Dynamic Walking ◽  
Novel Method ◽  
The Stability ◽  
Dynamic Gait ◽  
Excellent Tool ◽  
The Basin Of Attraction

Passive dynamic walking is an excellent tool for evaluating biped stability measures, due to its simplicity, but an understanding of the stability, in the classical definition, is required. The focus of this paper is on analyzing the stability of the passive dynamic gait. The stability of the passive walking model, validated in Part I, was analyzed with Lyapunov exponents, and the geometry of the basin of attraction was determined. A novel method was created to determine the 2D projection of the basin of attraction of the model. Using the insights gained from the stability analysis, the relation between the angular momentum and the stability of gait was examined. The angular momentum of the passive walker was not found to correlate to the stability of the gait.

Basin of Attraction of the Simplest Walking Model

2001 ◽  
Author(s):  
A. L. Schwab ◽  
M. Wisse
Keyword(s):  
Equations Of Motion ◽  
Basin Of Attraction ◽  
Mapping Method ◽  
Walking Robots ◽  
Natural Energy ◽  
Walking Motion ◽  
The Stability ◽  
The Basin Of Attraction ◽  
General Method ◽  
Small Disturbances

Abstract Passive dynamic walking is an important development for walking robots, supplying natural, energy-efficient motions. In practice, the cyclic gait of passive dynamic prototypes appears to be stable, only for small disturbances. Therefore, in this paper we research the basin of attraction of the cyclic walking motion for the simplest walking model. Furthermore, we present a general method for deriving the equations of motion and impact equations for the analysis of multibody systems, as in walking models. Application of the cell mapping method shows the basin of attraction to be a small, thin area. It is shown that the basin of attraction is not directly related to the stability of the cyclic motion.

2D and 3D Stability of Cavity Flows in High Mach Number Regimes

2019 ◽  
Author(s):  
Parshwanath S. Doshi ◽  
Rajesh Ranjan ◽  
Datta V. Gaitonde
Keyword(s):  
Stability Analysis ◽  
Mach Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Cavity Flows ◽  
Flame Holder ◽  
High Mach Number ◽  
Eddy Simulation ◽  
High Mach ◽  
The Stability

Abstract The stability characteristics of an open cavity flow at very high Mach number are examined with BiGlobal stability analysis based on the eigenvalues of the linearized Navier-Stokes equations. During linearization, all possible first-order terms are retained without any approximation, with particular emphasis on extracting the effects of compressibility on the flowfield. The method leverages sparse linear algebra and the implicitly restarted shift-invert Arnoldi algorithm to extract eigenvalues of practical physical consequence. The stability dynamics of cavity flows at four Mach numbers between 1.4 and 4 are considered at a Reynolds number of 502. The basic states are obtained through Large Eddy Simulation (LES). Frequency results from the stability analysis show good agreement when compared to the theoretical values using Rossiter’s formula. An examination of the stability modes reveals that the shear layer is increasingly decoupled from the cavity as the Mach number is increased. Additionally, the outer lobes of the Rossiter modes are observed to get stretched and tilted in the direction of the freestream. Future efforts will extend the present analysis to examine current and potential cavity flame holder configurations, which often have downstream walls inclined to the vertical.

Finding Method and Analysis of Hidden Chaotic Attractors for Plasma Chaotic System From Physical and Mechanistic Perspectives

2020 ◽  
Vol 30 (05) ◽  
pp. 2050072 ◽  
Author(s):  
Yingjuan Yang ◽  
Guoyuan Qi ◽  
Jianbing Hu ◽  
Philippe Faradja
Keyword(s):  
Chaotic Attractor ◽  
Equilibrium Points ◽  
Basin Of Attraction ◽  
The Self ◽  
Numerical Continuation ◽  
Chaotic Attractors ◽  
Phase Portrait Analysis ◽  
The Stability ◽  
Two Parameters ◽  
The Basin Of Attraction

A method for finding hidden chaotic attractors in the plasma system is presented. Using the Routh–Hurwitz criterion, the stability distribution associated with two parameters is identified to find the region around the equilibrium points of the stable nodes, stable focus-nodes, saddles and saddle-foci for the purpose of investigating hidden chaos. A physical interpretation is provided of the stability distribution for each type of equilibrium point. The basin of attraction and parameter region of hidden chaos are identified by excluding the self-excited chaotic attractors of all equilibrium points. Homotopy and numerical continuation are also employed to check whether the basin of chaotic attraction intersects with the neighborhood of a saddle equilibrium. Bifurcation analysis, phase portrait analysis, and basins of different dynamical attraction are used as tools to distinguish visually the self-excited chaotic attractor and hidden chaotic attractor. The Casimir power reflects the error power between the dissipative energy and the energy supplied by the whistler field. It explains physically, analytically, and numerically the conditions that generate the different dynamics, such as sinks, periodic orbits, and chaos.

scholarly journals Basins of Attraction for Various Steffensen-Type Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Alicia Cordero ◽  
Fazlollah Soleymani ◽  
Juan R. Torregrosa ◽  
Stanford Shateyi
Keyword(s):  
Computer Algebra System ◽  
Dynamical Behavior ◽  
Basin Of Attraction ◽  
Basins Of Attraction ◽  
Numerical Tests ◽  
Derivative Free ◽  
Iteration Functions ◽  
The Stability ◽  
Programming Package ◽  
The Basin Of Attraction

The dynamical behavior of different Steffensen-type methods is analyzed. We check the chaotic behaviors alongside the convergence radii (understood as the wideness of the basin of attraction) needed by Steffensen-type methods, that is, derivative-free iteration functions, to converge to a root and compare the results using different numerical tests. We will conclude that the convergence radii (and the stability) of Steffensen-type methods are improved by increasing the convergence order. The computer programming package MATHEMATICAprovides a powerful but easy environment for all aspects of numerics. This paper puts on show one of the application of this computer algebra system in finding fixed points of iteration functions.

scholarly journals Stability Analysis of Symmetrical Rotors Partially Filled with a Viscous Incompressible Fluid

2001 ◽  
Vol 7 (5) ◽  
pp. 301-310 ◽  
Author(s):  
Zhu Changsheng
Keyword(s):  
Stability Analysis ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Damping Ratio ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Navier Stokes Equations ◽  
Rotor Systems ◽  
The Stability

On the basis of the linearized fluid forces acting on the rotor obtained directly by using the two-dimensional Navier-Stokes equations, the stability of symmetrical rotors with a cylindrical chamber partially filled with a viscous incompressible fluid is investigated in this paper. The effects of the parameters of rotor system, such as external damping ratio, fluid fill ratio, Reynolds number and mass ratio, on the unstable regions are analyzed. It is shown that for the stability analysis of fluid filled rotor systems with external damping, the effect of the fluid viscosity on the stability should be considered. When the fluid viscosity is included, the adding external damping will make the system more stable and two unstable regions may exist even if rotors are isotropic in some casIs.

Analysis of the dripping–jetting transition in compound capillary jets

2010 ◽  
Vol 649 ◽  
pp. 523-536 ◽  
Author(s):  
M. A. HERRADA ◽  
J. M. MONTANERO ◽  
C. FERRERA ◽  
A. M. GAÑÁN-CALVO
Keyword(s):  
Stability Analysis ◽  
Convective Instability ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Core ◽  
Outer Interface ◽  
Spatio Temporal ◽  
Capillary Jets ◽  
The Stability

We examine the behaviour of a compound capillary jet from the spatio-temporal linear stability analysis of the Navier–Stokes equations. We map the jetting–dripping transition in the parameter space by calculating the Weber numbers for which the convective/absolute instability transition occurs. If the remaining dimensionless parameters are set, there are two critical Weber numbers that verify Brigg's pinch criterion. The region of absolute (convective) instability corresponds to Weber numbers smaller (larger) than the highest value of those two Weber numbers. The stability map is affected significantly by the presence of the outer interface, especially for compound jets with highly viscous cores, in which the outer interface may play an important role even though it is located very far from the core. Full numerical simulations of the Navier–Stokes equations confirm the predictions of the stability analysis.

Some New Dissipative Chaotic Systems with Cyclic Symmetry

2018 ◽  
Vol 28 (13) ◽  
pp. 1850164 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Shirin Panahi ◽  
Anitha Karthikeyan ◽  
Ahmed Alsaedi ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Cyclic Symmetry ◽  
Circuit Implementation ◽  
New Chaotic System ◽  
The Basin Of Attraction

Designing new chaotic system with specific features is an interesting field in nonlinear dynamics. In this paper, some new chaotic systems with cyclic symmetry are proposed. In order to understand the overall behavior of such systems, the dynamical analyses such as stability analysis, bifurcation and Lyapunov exponent analysis are done. The accurate examination of bifurcation plot represents that these systems are multistable which makes them more interesting. Also, the basin of attraction of these systems is investigated to detect the type of attractors of these systems which are self-excited. Finally, the circuit implementation is carried out to show their feasibility.

Stability Analysis for Complex Rotational Flow

2021 ◽  
Vol 16 ◽  
pp. 62-72
Author(s):  
Ivan V. Kazachkov
Keyword(s):  
Stability Analysis ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Rotational Flow ◽  
Complex Flow ◽  
Navier Stokes Equations ◽  
Coriolis Forces ◽  
Cylindrical Coordinate ◽  
The Stability ◽  
Varying Mass

Based on the earlier developed mathematical model of the complex flow due to the double rotations in two perpendicular directions, the stability analysis is performed in the paper. The Navier-Stokes equations are derived in the coordinate system rotating around the two perpendicular different axes, the vertical one of them is arranged on some distance from the other axis of rotation, the horizontal axis is directed along the tangential line to the circle of the vertical rotation. The two centrifugal and Coriolis forces create the unique features in high oscillating flow, with localities of the stretched liquid, due to their action varying by the circumferential cylindrical coordinate in the channel flow. Stability analysis for the complex rotational flow under double rotations creating strongly varying mass forces and stretching of the liquid is considered at first

Viscous flow between two moving parallel disks: exact solutions and stability analysis

2002 ◽  
Vol 464 ◽  
pp. 209-215 ◽  
Author(s):  
S. N. ARISTOV ◽  
I. M. GITMAN
Keyword(s):  
Exact Solution ◽  
Stability Analysis ◽  
Incompressible Liquid ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Viscous Incompressible Liquid ◽  
Navier Stokes Equations ◽  
Parallel Disks ◽  
Different Types ◽  
The Stability

The motion of a viscous incompressible liquid between two parallel disks, moving towards each other or in opposite directions, is considered. The description of possible conditions of motion is based on the exact solution of the Navier–Stokes equations. Both stationary and transient cases have been considered. The stability of the motion is analysed for different initial perturbations. Different types of stability were found according to whether the disks moved towards or away from each other.

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