A Numerical Method for Analyzing the Stability of Bi-Parametric Biological Systems

2016 ◽  
Author(s):  
Changbo Chen ◽  
Wenyuan Wu
Keyword(s):  
Numerical Method ◽  
Biological Systems ◽  
The Stability

An Efficient Galerkin BEM to Compute High Acoustic Eigenfrequencies

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Mario Durán ◽  
Jean-Claude Nédélec ◽  
Sebastián Ossandón
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
High Frequency ◽  
High Accuracy ◽  
Integral Representations ◽  
Stability And Convergence ◽  
Symmetric Matrices ◽  
Frequency Interval ◽  
Numerical Treatment ◽  
The Stability

An efficient numerical method, using integral equations, is developed to calculate precisely the acoustic eigenfrequencies and their associated eigenvectors, located in a given high frequency interval. It is currently known that the real symmetric matrices are well adapted to numerical treatment. However, we show that this is not the case when using integral representations to determine with high accuracy the spectrum of elliptic, and other related operators. Functions are evaluated only in the boundary of the domain, so very fine discretizations may be chosen to obtain high eigenfrequencies. We discuss the stability and convergence of the proposed method. Finally we show some examples.

scholarly journals Hydrodynamic Analysis for the Morphing Median Fins of Tuna during Yaw Motions

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Xiaohu Li
Keyword(s):  
Numerical Method ◽  
Hydrodynamic Forces ◽  
The Body ◽  
Robotic Fish ◽  
Hydrodynamic Performance ◽  
Hydrodynamic Analysis ◽  
Dorsal Fin ◽  
The Stability ◽  
Median Fins

Tuna can change the area and shape of the median fins, including the first dorsal, second dorsal, and anal fins. The morphing median fins have the ability of adjusting the hydrodynamic forces, thereby affecting the yaw mobility of tuna to a certain extent. In this paper, the hydrodynamic analysis of the median fins under different morphing states is carried out by the numerical method, so as to clarify the influence of the erected median fins on the yaw maneuvers. By comparing the two morphing states of erected and depressed, it can be concluded that the erected median fins can increase their own hydrodynamic forces during the yaw movement. However, the second dorsal and anal fins have limited influence on the yaw maneuverability, and they tend to maintain the stability of tuna. The first dorsal fin has more lift increment in the erection state, which can obviously affect the hydrodynamic performance of tuna. Moreover, as the median fins are erected, the hydrodynamic forces of the tuna’s body increase synchronously due to the interaction between the body and the median fins, which is also very beneficial to the yaw motion. This study indicates that tuna can use the morphing median fins to adjust its mobility and stability, which provides a new idea for the design of robotic fish.

Variable-step-size second-order-derivative multistep method for solving first-order ordinary differential equations in system simulation

2020 ◽  
Vol 11 (01) ◽  
pp. 2050001
Author(s):  
Lei Zhang ◽  
Chaofeng Zhang ◽  
Mengya Liu
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Multistep Method ◽  
Second Order ◽  
Order Derivative ◽  
Variable Step Size ◽  
Variable Order ◽  
Step Size ◽  
Variable Step ◽  
The Stability

According to the relationship between truncation error and step size of two implicit second-order-derivative multistep formulas based on Hermite interpolation polynomial, a variable-order and variable-step-size numerical method for solving differential equations is designed. The stability properties of the formulas are discussed and the stability regions are analyzed. The deduced methods are applied to a simulation problem. The results show that the numerical method can satisfy calculation accuracy, reduce the number of calculation steps and accelerate calculation speed.

Adhesion of lipid tubules in an assembly

1998 ◽  
Vol 9 (5) ◽  
pp. 485-506 ◽  
Author(s):  
RICCARDO ROSSO ◽  
EPIFIANO G. VIRGA
Keyword(s):  
Surface Tension ◽  
External Field ◽  
Equilibrium Problem ◽  
Biological Systems ◽  
Critical Value ◽  
Stability Diagram ◽  
Energy Functional ◽  
Highly Nonlinear ◽  
The Stability ◽  
Lipid Tubules

We study a unilateral equilibrium problem for the energy functional of a lipid tubule subject to an external field. These tubules, which constitute many biological systems, may form assemblies when they are brought in contact, and so made to adhere to one another along at interstices. The contact energy is taken to be proportional to the area of contact through a constant, which is called the adhesion potential. This competes against the external field in determining the stability of patterns with flat interstices. Though the equilibrium problem is highly nonlinear, we determine explicitly the stability diagram for the adhesion between tubules. We conclude that the higher the field, the lower the adhesion potential needed to make at interstices energetically favourable, though its critical value depends also on the surface tension of the interface between the tubules and the isotropic fluid around them.

scholarly journals A Harmonic-Based Method for Computing the Stability of Periodic Oscillations of Non-Linear Structural Systems

2010 ◽  
Author(s):  
O. Thomas ◽  
A. Lazarus ◽  
C. Touze´
Keyword(s):  
Numerical Method ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Computation Time ◽  
Fourier Series Expansion ◽  
Simple Strategy ◽  
The Stability ◽  
Linear Periodic System ◽  
Continuation Technique

In this paper, we present a validation on a practical example of a harmonic-based numerical method to determine the local stability of periodic solutions of dynamical systems. Based on Floquet theory and Fourier series expansion (Hill method), we propose a simple strategy to sort the relevant physical eigenvalues among the expanded numerical spectrum of the linear periodic system governing the perturbed solution. By mixing the Harmonic Balance Method and Asymptotic Numerical Method continuation technique with the developed Hill method, we obtain a purely-frequency based continuation tool able to compute the stability of the continued periodic solutions in a reduced computation time. This procedure is validated by considering an externally forced string and computing the complete bifurcation diagram with the stability of the periodic solutions. The particular coupled regimes are exhibited and found in excellent agreement with results of the literature, allowing a method validation.

scholarly journals Unconditional Stability of a Numerical Method for the Dual-Phase-Lag Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
M. A. Castro ◽  
J. A. Martín ◽  
F. Rodríguez
Keyword(s):  
Numerical Method ◽  
Numerical Solutions ◽  
Unconditional Stability ◽  
Bioheat Transfer ◽  
Phase Lag ◽  
Dual Phase ◽  
Stability Properties ◽  
The Stability ◽  
Transfer Problems ◽  
Uniformly Bounded

The stability properties of a numerical method for the dual-phase-lag (DPL) equation are analyzed. The DPL equation has been increasingly used to model micro- and nanoscale heat conduction in engineering and bioheat transfer problems. A discretization method for the DPL equation that could yield efficient numerical solutions of 3D problems has been previously proposed, but its stability properties were only suggested by numerical experiments. In this work, the amplification matrix of the method is analyzed, and it is shown that its powers are uniformly bounded. As a result, the unconditional stability of the method is established.

Investigation of Self-Recycling-Casing-Treatment (SRCT) Influence on Stability of High Pressure Ratio Centrifugal Compressor With a Volute

2011 ◽  
Author(s):  
Mingyang Yang ◽  
Ricardo Martinez-Botas ◽  
Yangjun Zhang ◽  
Xinqian Zheng ◽  
Takahiro Bamba ◽  
...  
Keyword(s):  
High Pressure ◽  
Numerical Method ◽  
Flow Rate ◽  
Centrifugal Compressor ◽  
Static Pressure ◽  
Pressure Ratio ◽  
Flow Distortion ◽  
Casing Treatment ◽  
High Pressure Ratio ◽  
The Stability

Large feasible operation range is a challenge for high pressure ratio centrifugal compressor of turbocharger in vehicle engine. Self-Recycling-Casing-Treatment (SRCT) is a widely used flow control method to enlarge the range for this kind of compressor. This paper investigates the influence of symmetrical/asymmetrical SRCT (ASRCT) on the stability of a high pressure ratio centrifugal compressor by experimental testing and numerical simulation. Firstly, the performance of the compressor with/without SRCT is tested is measured investigate the influence of flow distortion on the stability of compressor as well as the numerical method validation. Then detailed flow field investigation is conducted by experimental measurement and the numerical method to unveil the reasons for stability enhancement by symmetrical/asymmetrical SRCT. Results show that static pressure distortion at impeller outlet caused by the volute can make passages be confronted with flow distortion less stable than others because of their larger positive slope of T-S pressure ratio performance at small flow rate. SRCT can depress the flow distortion and reduce the slope by non-uniform recycling flow rate at impeller inlet. Moreover, ASRCT can redistribute the recycling flow in circumferential direction according to the asymmetric geometries. When the largest recycling flow rate is imposed on the passage near the distorted static pressure, the slope will be the most effectively reduced. Therefore, the stability is effectively enhanced by the optimized recycling flow device.

On the stability of viscous flow between rotating cylinders Part 2. Numerical analysis

1964 ◽  
Vol 20 (1) ◽  
pp. 95-101 ◽  
Author(s):  
D. L. Harris ◽  
W. H. Reid
Keyword(s):  
Numerical Analysis ◽  
Eigenvalue Problem ◽  
Viscous Flow ◽  
Numerical Method ◽  
Couette Flow ◽  
Stream Function ◽  
Oscillatory Behaviour ◽  
Rotating Cylinders ◽  
The Stability

A simple numerical method is presented for solving the eigenvalue problem which governs the stability of Couette flow. The method is particularly useful in obtaining the eigenfunctions associated with the various modes of instability. When the cylinders rotate in opposite directions, these eigenfunctions exhibit an exponentially damped oscillatory behaviour for sufficiently large values of − μ, where μ = Ω2/Ω1. In terms of the stream function which describes the motion in planes through the axis of the cylinders, this means that weak, viscously driven cells appear in the outer layes of the fluid which, according to Rayleigh's criterion, are dynamically stable. For μ = − 3, for example, four cells are present, the amplitudes of which are in the ratios 1·0:0·0172:0·013:0·00125.

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