Effect of Finite Thickness Flexible Boundary Upon the Stability of a Poiseuille Flow

1990 ◽  
Vol 57 (4) ◽  
pp. 1056-1060 ◽  
Author(s):  
Mauro Pierucci ◽  
Pedro G. Morales
Keyword(s):  
Poiseuille Flow ◽  
Finite Thickness ◽  
Stress Distributions ◽  
Stability Equation ◽  
Stability Behavior ◽  
Different Types ◽  
Improved Stability ◽  
Numerical Instabilities ◽  
The Stability ◽  
Sommerfeld Equation

The stability behavior, the stress, and velocity distributions for a plane Poiseuille flow bounded by a finite thickness elastic layer is studied. The analysis is performed by utilizing the coupled relationships between the Orr-Sommerfeld stability equation for the fluid and the Navier equations for the solid. The numerical instabilities experienced in the solution of the Orr-Sommerfeld equation have been overcome with the use of Davey’s orthonormalization technique. This study focuses only on the Tollimen-Schlichting instabilities. This mode is the most unstable of the three different types of instabilities. The results show that certain combinations of parameters can lead to improved stability conditions. Under these conditions the normal and shear stress distributions may behave completely different in certain regions of the fluid.

scholarly journals Calculation of the Orr-Sommerfeld stability equation for the plane Poiseuille flow

2019 ◽  
Vol 2 (5) ◽  
pp. 122-129
Author(s):  
Ngoc Anh Trinh ◽  
Dong Vuong Lap Tran
Keyword(s):  
Poiseuille Flow ◽  
Decimal Point ◽  
Plane Poiseuille Flow ◽  
Chebyshev Collocation Method ◽  
Stability Equation ◽  
Chebyshev Collocation ◽  
Unstable Eigenvalue ◽  
Collocation Points ◽  
The Stability ◽  
Sommerfeld Equation

The stability of plane Poiseuille flow depends on eigenvalues and solutions which are generated by solving Orr-Sommerfeld equation with input parameters including real wavenumber and Reynolds number . In the reseach of this paper, the Orr-Sommerfeld equation for the plane Poiseuille flow was solved numerically by improving the Chebyshev collocation method so that the solution of the Orr-Sommerfeld equation could be approximated even and odd polynomial by relying on results of proposition 3.1 that is proved in detail in section 2. The results obtained by this method were more economical than the modified Chebyshev collocation if the comparison could be done in the same accuracy, the same collocation points to find the most unstable eigenvalue. Specifically, the present method needs 49 nodes and only takes 0.0011s to create eigenvalue while the modified Chebyshev collocation also uses 49 nodes but takes 0.0045s to generate eigenvalue with the same accuracy to eight digits after the decimal point in the comparison with , see [4], exact to eleven digits after the decimal point.

Influence of viscosity temperature dependence on the spectral characteristics of the thermoviscous liquids flow stability equation

2019 ◽  
Vol 14 (1) ◽  
pp. 52-58 ◽  
Author(s):  
A.D. Nizamova ◽  
V.N. Kireev ◽  
S.F. Urmancheev
Keyword(s):  
Reynolds Number ◽  
Spectral Characteristics ◽  
Wave Number ◽  
Critical Parameters ◽  
Fluid Viscosity ◽  
Flat Channel ◽  
Stability Equation ◽  
The Stability ◽  
Thermoviscous Fluid ◽  
Sommerfeld Equation

The flow of a viscous model fluid in a flat channel with a non-uniform temperature field is considered. The problem of the stability of a thermoviscous fluid is solved on the basis of the derived generalized Orr-Sommerfeld equation by the spectral decomposition method in Chebyshev polynomials. The effect of taking into account the linear and exponential dependences of the fluid viscosity on temperature on the spectral characteristics of the hydrodynamic stability equation for an incompressible fluid in a flat channel with given different wall temperatures is investigated. Analytically obtained profiles of the flow rate of a thermovisible fluid. The spectral pictures of the eigenvalues of the generalized Orr-Sommerfeld equation are constructed. It is shown that the structure of the spectra largely depends on the properties of the liquid, which are determined by the viscosity functional dependence index. It has been established that for small values of the thermoviscosity parameter the spectrum compares the spectrum for isothermal fluid flow, however, as it increases, the number of eigenvalues and their density increase, that is, there are more points at which the problem has a nontrivial solution. The stability of the flow of a thermoviscous fluid depends on the presence of an eigenvalue with a positive imaginary part among the entire set of eigenvalues found with fixed Reynolds number and wavenumber parameters. It is shown that with a fixed Reynolds number and a wave number with an increase in the thermoviscosity parameter, the flow becomes unstable. The spectral characteristics determine the structure of the eigenfunctions and the critical parameters of the flow of a thermally viscous fluid. The eigenfunctions constructed in the subsequent works show the behavior of transverse-velocity perturbations, their possible growth or decay over time.

scholarly journals Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemes

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abdel-Haleem Abdel-Aty ◽  
Mostafa M. A. Khater ◽  
Dumitru Baleanu ◽  
E. M. Khalil ◽  
Jamel Bouslimi ◽  
...  
Keyword(s):  
Nervous System ◽  
Expansion Method ◽  
B Spline ◽  
Stability Behavior ◽  
Nerve Impulses ◽  
Dynamical Behaviors ◽  
Different Types ◽  
Nagumo Equation ◽  
The Stability

Abstract The dynamical attitude of the transmission for the nerve impulses of a nervous system, which is mathematically formulated by the Atangana–Baleanu (AB) time-fractional FitzHugh–Nagumo (FN) equation, is computationally and numerically investigated via two distinct schemes. These schemes are the improved Riccati expansion method and B-spline schemes. Additionally, the stability behavior of the analytical evaluated solutions is illustrated based on the characteristics of the Hamiltonian to explain the applicability of them in the model’s applications. Also, the physical and dynamical behaviors of the gained solutions are clarified by sketching them in three different types of plots. The practical side and power of applied methods are shown to explain their ability to use on many other nonlinear evaluation equations.

scholarly journals Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1935 ◽  
Author(s):  
Mohammad Malikan ◽  
Victor A. Eremeyev ◽  
Krzysztof Kamil Żur
Keyword(s):  
Material Properties ◽  
Gradient Elasticity ◽  
Small Scale ◽  
Stability Equation ◽  
Strain Gradients ◽  
Size Dependent ◽  
Different Types ◽  
Dependent Property ◽  
The Stability ◽  
Transverse Deflection

We investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. Similar to flexoelectricity, the flexomagneticity is a size-dependent property. Therefore, its effect is more pronounced at small scales. We merge the stability equation with a nonlocal model of the strain gradient elasticity. The Navier sinusoidal transverse deflection is employed to attain the critical buckling load. Furthermore, different types of axial symmetric and asymmetric porosity distributions are studied. It was revealed that regardless of the high magnetic field, one can realize the flexomagnetic effect at a small scale. We demonstrate as well that for the larger thicknesses a difference between responses of piezomagnetic and piezo-flexomagnetic nanobeams would not be significant.

Accurate solution of the Orr–Sommerfeld stability equation

1971 ◽  
Vol 50 (4) ◽  
pp. 689-703 ◽  
Author(s):  
Steven A. Orszag
Keyword(s):  
Reynolds Number ◽  
Chebyshev Polynomials ◽  
Critical Reynolds Number ◽  
Great Accuracy ◽  
Accurate Solution ◽  
Plane Poiseuille Flow ◽  
Stability Equation ◽  
Orthogonal Functions ◽  
The Stability ◽  
Sommerfeld Equation

The Orr-Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the QR matrix eigenvalue algorithm. It is shown that results of great accuracy are obtained very economically. The method is applied to the stability of plane Poiseuille flow; it is found that the critical Reynolds number is 5772·22. It is explained why expansions in Chebyshev polynomials are better suited to the solution of hydrodynamic stability problems than expansions in other, seemingly more relevant, sets of orthogonal functions.

Effects of Self-Stress Distributions on Stability of Tensegrity Structures

2017 ◽  
Vol 17 (03) ◽  
pp. 1750029 ◽  
Author(s):  
B. Shekastehband ◽  
N. Pourmand
Keyword(s):  
Stress Distribution ◽  
Dominant Role ◽  
Stress Distributions ◽  
Stability Behavior ◽  
Collapse Mechanisms ◽  
Tensegrity Systems ◽  
Load Carrying ◽  
Key Factor ◽  
The Stability ◽  
Selection Of

Tensegrity systems are composed of any given set of cables connected to a set of struts in which the cables connectivity must be able to stabilize the configuration. Self-stresses contribute to the rigidity and stability of the system. Therefore, self-stress distribution has a dominant effect on the stability behavior of these systems. In this study, the stability behavior of plane double-layer tensegrity systems considering different distributions of self-stresses is evaluated. Based on the results obtained, collapse mechanisms, load carrying capacities, stiffness of the systems and slackening of the cables are affected by self-stress distribution. Therefore, self-stress design is a key factor that plays a dominant role on the stability behavior of tensegrity systems. These results can lead to the suggestion of some guidelines on the selection of self-stress distribution for the design of tensegrity systems against instability.

Investigation on the Sedimentation Behavior of the α-Al2O3 Aqueous Suspension by the Combination of Two Dispersants

2011 ◽  
Vol 474-476 ◽  
pp. 687-692
Author(s):  
Fei Zhou Li ◽  
Yu Qiang Han ◽  
Bian Guo
Keyword(s):  
Zeta Potential ◽  
Ph Value ◽  
Aqueous Suspension ◽  
Sintered Sample ◽  
Dispersion Effect ◽  
Arabic Gum ◽  
Stability Behavior ◽  
Sedimentation Behavior ◽  
Different Types ◽  
The Stability

The effect of three different types dispersants on the stability behavior of alumina aqueous suspension were investigated by through sedimentation experiment , Zeta potential ,and residual porosity of sintered sample. The results showed that the optimal content and optimal sedimentation pH value of the three different types dispersants were 1.0% and aging at pH9 for PAA-NH4, 0.8% and nearly independent of pH value for Arabic gum , 0.4, 0.2 and aging at pH9 for PAA-NH4 and Arabic gum，respectively. The dispersion effect of the three different type dispersants was PAA-NH4and Arabic gum> PAA-NH4 > Arabic gum. Studies have shown that the combination of PAA-NH4 and Arabic gum has a better effect than one of them on the stability of suspension. Compared with single dispersant, the sedimentation volumes of the two dispersants dispersing suspension is reduced 3%, the dosage of dispersants is reduced 26.7%.

ASSESSMENT OF PINE CROPS GROWTH IN BAIMAK FORESTRY

2020 ◽  
Vol 37 (3) ◽  
pp. 83-90
Author(s):  
T.Z. Mutallapov ◽  
Keyword(s):  
Scots Pine ◽  
Forest Ecosystem ◽  
Distribution Curve ◽  
Comparative Assessment ◽  
Tree Distribution ◽  
Entire Structure ◽  
Structure Changes ◽  
Large Trees ◽  
Different Types ◽  
The Stability

The article presents the results of evaluating the growth of Scots pine in the Baymak forest area. The analysis of forestry and taxation indicators of Scots pine crops on the studied sample areas is carried out, and a comparative assessment of the growth of forest crops growing in different types of forest is given. Increased competition in plantings leads to the natural decline of stunted trees, which is the result of differentiation in the stand. As a result, its structure changes, the number of large trees increases, and, accordingly, the stability of the forest ecosystem increases. In this regard, the appearance of the tree distribution curve by thickness levels also changes. It becomes more "flat", and its competitive load is more evenly distributed over the entire structure of the stand, and competition is weakened.

A Survey on Computational Methods for Essential Proteins and Genes Prediction

2019 ◽  
Vol 14 (3) ◽  
pp. 211-225 ◽  
Author(s):  
Ming Fang ◽  
Xiujuan Lei ◽  
Ling Guo
Keyword(s):  
Computational Methods ◽  
Drug Targets ◽  
Disease Genes ◽  
Essential Proteins ◽  
Experimental Identification ◽  
Cellular Life ◽  
Different Types ◽  
The Stability ◽  
Human Disease Genes ◽  
Biology Research

Background: Essential proteins play important roles in the survival or reproduction of an organism and support the stability of the system. Essential proteins are the minimum set of proteins absolutely required to maintain a living cell. The identification of essential proteins is a very important topic not only for a better comprehension of the minimal requirements for cellular life, but also for a more efficient discovery of the human disease genes and drug targets. Traditionally, as the experimental identification of essential proteins is complex, it usually requires great time and expense. With the cumulation of high-throughput experimental data, many computational methods that make useful complements to experimental methods have been proposed to identify essential proteins. In addition, the ability to rapidly and precisely identify essential proteins is of great significance for discovering disease genes and drug design, and has great potential for applications in basic and synthetic biology research. Objective: The aim of this paper is to provide a review on the identification of essential proteins and genes focusing on the current developments of different types of computational methods, point out some progress and limitations of existing methods, and the challenges and directions for further research are discussed.

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