Algebraic stability modes in rotational shear flow

2021 ◽  
Author(s):  
Tim Gebler ◽  
Dominik Plümacher ◽  
Judith Kahle ◽  
Martin Oberlack
Keyword(s):  
Eigenvalue Problem ◽  
Temporal Evolution ◽  
Normal Mode Analysis ◽  
Normal Modes ◽  
Base Flow ◽  
Mode Analysis ◽  
Infinite Domain ◽  
Mode Decomposition ◽  
Linearized Stability ◽  
Rotational Shear

Abstract We investigate the two-dimensional (2D) stability of rotational shear flows in an unbounded domain. The eigenvalue problem is formulated by using a novel algebraic mode decomposition distinct from the normal modes with temporal evolution $\exp(\omega t)$. Based on the work of \citeasnoun{NoldOberlack2013}, we show how these new modes can be constructed from the symmetries of the linearized stability equation. For the azimuthal base flow velocity $V(r)=r^{-1}$ an additional symmetry exists, such that a mode with algebraic temporal evolution $t^s$ is found. $s$ refers to an eigenvalue for the algebraic growth or decay of the kinetic energy of the perturbations. An eigenvalue problem for the viscous and inviscid stability using algebraic modes is formulated on an infinite domain with $r \to \infty$. An asymptotic analysis of the eigenfunctions shows that the flow is linearly stable under 2D perturbations. We find stable modes with the algebraic mode ansatz, which can not be obtained by a normal mode analysis. The stability results are in line with Rayleigh's inflection point theorem.

scholarly journals Thermosolutal Instability in Compressible Viscoelastic Dusty Fluid through Porous Medium

2013 ◽  
Vol 18 (1) ◽  
pp. 99-112 ◽  
Author(s):  
P. Kumar ◽  
H. Mohan
Keyword(s):  
Porous Medium ◽  
Viscoelastic Fluid ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Linearized Stability ◽  
Medium Permeability ◽  
The Stability ◽  
Solute Gradient

Thermosolutal instability in a compressible Walters B’ viscoelastic fluid with suspended particles through a porous medium is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the Walters B’ viscoelastic fluid behaves like a Newtonian fluid and it is found that suspended particles and medium permeability have a destabilizing effect whereas the stable solute gradient and compressibility have a stabilizing effect on the system. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient and viscoelasticity are found to introduce oscillatory modes in the system which are non-existent in their absence.

scholarly journals Normal Mode Analysis as a Routine Part of a Structural Investigation

Molecules ◽  
2019 ◽  
Vol 24 (18) ◽  
pp. 3293 ◽  
Author(s):  
Jacob A. Bauer ◽  
Jelena Pavlović ◽  
Vladena Bauerová-Hlinková
Keyword(s):  
Normal Mode ◽  
Structural Study ◽  
Computer Technology ◽  
Structural Investigation ◽  
Normal Mode Analysis ◽  
Computational Cost ◽  
Normal Modes ◽  
Mode Analysis ◽  
Computationally Expensive ◽  
The Web

Normal mode analysis (NMA) is a technique that can be used to describe the flexible states accessible to a protein about an equilibrium position. These states have been shown repeatedly to have functional significance. NMA is probably the least computationally expensive method for studying the dynamics of macromolecules, and advances in computer technology and algorithms for calculating normal modes over the last 20 years have made it nearly trivial for all but the largest systems. Despite this, it is still uncommon for NMA to be used as a component of the analysis of a structural study. In this review, we will describe NMA, outline its advantages and limitations, explain what can and cannot be learned from it, and address some criticisms and concerns that have been voiced about it. We will then review the most commonly used techniques for reducing the computational cost of this method and identify the web services making use of these methods. We will illustrate several of their possible uses with recent examples from the literature. We conclude by recommending that NMA become one of the standard tools employed in any structural study.

scholarly journals On a New Characterization of Some Class Nonlinear Eigenvalue Problem

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Lutfi Akin
Keyword(s):  
Asymptotic Behavior ◽  
Eigenvalue Problem ◽  
Nonlinear Eigenvalue Problem ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Electrical System ◽  
Eigenvalues And Eigenfunctions ◽  
Complete Study ◽  
Nonlinear Eigenvalue

A normal mode analysis of a vibrating mechanical or electrical system gives rise to an eigenvalue problem. Faber made a fairly complete study of the existence and asymptotic behavior of eigenvalues and eigenfunctions, Green’s function, and expansion properties. We will investigate a new characterization of some class nonlinear eigenvalue problem.

Complex Modal Analysis of a Nonmodally Damped Continuous Beam

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Xing Xing ◽  
Brian F. Feeny
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Normal Modes ◽  
Damping Coefficient ◽  
Mode Analysis ◽  
Element Analysis ◽  
Assumed Mode Method ◽  
State Variable ◽  
Complex Modes ◽  
Assumed Mode

This work represents an investigation of the complex modes of continuous vibration systems with nonmodal damping. As an example, a cantilevered beam with damping at the free end is studied. Assumed modes are applied to discretize the eigenvalue problem in state-variable form and then to obtain estimates of the true complex normal modes and frequencies. The finite element method (FEM) is also used to get the mass, stiffness, and damping matrices and further to solve a state-variable eigenvalue problem. A comparison between the complex modes and eigenvalues obtained from the assumed-mode analysis and the finite element analysis shows that the methods produce consistent results. The convergence behavior when using different assumed mode functions is investigated. The assumed-mode method is then used to study the effects of the end-damping coefficient on the estimated normal modes and modal damping. Most modes remain underdamped regardless of the end-damping coefficient. There is an optimal end-damping coefficient for vibration decay, which correlates with the maximum modal nonsynchronicity.

scholarly journals ProMode-Oligomer: Database of Normal Mode Analysis in Dihedral Angle Space for a Full-Atom System of Oligomeric Proteins

2012 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
Hiroshi Wako ◽  
Shigeru Endo
Keyword(s):  
Normal Mode ◽  
Protein Complexes ◽  
Normal Mode Analysis ◽  
Normal Modes ◽  
Point Of View ◽  
Mode Analysis ◽  
Dihedral Angles ◽  
Oligomeric Proteins ◽  
Displacement Vectors ◽  
Atom System

The database ProMode-Oligomer (http://promode.socs.waseda.ac.jp/promode_oligomer) was constructed by collecting normal-mode-analysis (NMA) results for oligomeric proteins including protein-protein complexes. As in the ProMode database developed earlier for monomers and individual subunits of oligomers (Bioinformatics vol. 20, pp. 2035–2043, 2004), NMA was performed for a full-atom system using dihedral angles as independent variables, and we released the results (fluctuations of atoms, fluctuations of dihedral angles, correlations between atomic fluctuations, etc.). The vibrating oligomer is visualized by animation in an interactive molecular viewer for each of the 20 lowest-frequency normal modes. In addition, displacement vectors of constituent atoms for each normal mode were decomposed into two characteristic motions in individual subunits, i.e., internal and external (deformation and rigid-body movements of the individual subunits, respectively), and then the mutual movements of the subunits and the movement of atoms around the interface regions were investigated. These results released in ProMode-Oligomer are useful for characterizing oligomeric proteins from a dynamic point of view. The analyses are illustrated with immunoglobulin light- and heavy-chain variable domains bound to lysozyme and to a 12-residue peptide.

Effect of Rotation and Magnetic Field on Thermal Stability of Ferromagnetic Fluid

2013 ◽  
Author(s):  
Amrish K. Aggarwal ◽  
Anushri Verma
Keyword(s):  
Magnetic Field ◽  
Thermal Stability ◽  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Free Boundaries ◽  
Linearized Stability ◽  
Ferromagnetic Fluid ◽  
Exchange Of Stability ◽  
Thermal Stability Of

In this paper, the effect of rotation and magnetic field on thermal stability of a layer of ferromagnetic fluid heated from below has been investigated. For a fluid layer between two free boundaries, an exact solution is obtained using a linearized stability theory and normal mode analysis. For the case of stationary convection, it is found that magnetic field and rotation have stabilizing effect on the thermal stability of the system. The principle of exchange of stability is not valid for the problem under consideration, whereas in the absence of rotation and magnetic field, it is valid.

Perturbed normal-mode analysis of induction times, relaxation times, and reaction rates in unimolecular reactions

1979 ◽  
Vol 57 (13) ◽  
pp. 1723-1730 ◽  
Author(s):  
Andrew W. Yau ◽  
Huw O. Pritchard
Keyword(s):  
Normal Mode ◽  
Transition Probabilities ◽  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Normal Modes ◽  
Reaction Rates ◽  
Mode Analysis ◽  
Decomposition Reactions ◽  
Induction Times ◽  
Network Relationship

A perturbed normal-mode analysis is presented of the induction (or incubation) time, the relaxation rate, and the reaction rate of a diluted unimolecular system. At high temperature, the unimolecular rate approaches the Lindemann behaviour and the low-pressure rate is related to the normal modes of relaxation of the reactive states in a simple manner. In a step-ladder model system, the network relationship between the normal modes and the microscopic transition probabilities leads to explicit theoretical correlations between the respective experimental quantities. Illustrative calculations of such correlations are presented for the decomposition reactions of N2O and CO2 diluted in Ar at shock wave temperatures, and are compared with experiment.

scholarly journals Skeletal animation for visualizing dynamic shapes of macromolecules

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yutaka Ueno ◽  
Shinya Muraoka ◽  
Tetsuo Sato
Keyword(s):  
Computer Graphics ◽  
Normal Mode Analysis ◽  
Normal Modes ◽  
Dynamics Simulation ◽  
Coarse Grained ◽  
Mode Analysis ◽  
Protein Molecules ◽  
Skeletal Animation ◽  
Detailed Computer ◽  
Animation Software

AbstractWe apply a skeletal animation technique developed for general computer graphics animation to display the dynamic shape of protein molecules. Polygon-based models for macromolecules such as atomic representations, surface models, and protein ribbon models are deformed by the motion of skeletal bones that provide coarse-grained descriptions of detailed computer graphics models. Using the animation software Blender, we developed methods to generate the skeletal bones for molecules. Our example of the superposition of normal modes demonstrates the thermal fluctuating motion obtained from normal mode analysis. The method is also applied to display the motions of protein molecules using trajectory coordinates of a molecular dynamics simulation. We found that a standard motion capture file was practical and useful for describing the motion of the molecule using available computer graphics tools.

scholarly journals Hall Effect on Thermal Instability of Viscoelastic Dusty Fluid in Porous Medium

2013 ◽  
Vol 18 (3) ◽  
pp. 871-886
Author(s):  
M. Singh ◽  
R.K. Gupta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Linearized Stability ◽  
Medium Permeability ◽  
Rayleigh Numbers ◽  
The Magnetic Field

Abstract The effect of Hall currents and suspended dusty particles on the hydromagnetic stability of a compressible, electrically conducting Rivlin-Ericksen elastico viscous fluid in a porous medium is considered. Following the linearized stability theory and normal mode analysis the dispersion relation is obtained. For the case of stationary convection, Hall currents and suspended particles are found to have destabilizing effects whereas compressibility and magnetic field have stabilizing effects on the system. The medium permeability, however, has stabilizing and destabilizing effects on thermal instability in contrast to its destabilizing effect in the absence of the magnetic field. The critical Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers are depicted graphically. The magnetic field, Hall currents and viscoelasticity parameter are found to introduce oscillatory modes in the systems, which did not exist in the absence of these parameters

Rotatory Thermosolutal Convection in a Couple-Stress Fluid

2009 ◽  
Vol 64 (7-8) ◽  
pp. 448-454
Author(s):  
Pardeep Kumar ◽  
Mahinder Singh
Keyword(s):  
Dispersion Relation ◽  
Couple Stress ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Thermosolutal Convection ◽  
Mode Analysis ◽  
Couple Stress Fluid ◽  
Stationary Convection ◽  
Linearized Stability ◽  
Solute Gradient

AbstractThe thermosolutal instability of couple-stress fluid in the presence of uniform vertical rotation is considered. Following the linearized stability theory and normal mode analysis, the dispersion is obtained. For the case of stationary convection, the stable solute gradient and rotation have stabilizing effects on the system, whereas the couple-stress has both stabilizing and destabilizing effects. The dispersion relation is also analyzed numerically. The stable solute gradient and the rotation introduce oscillatory modes in the system, which did not occur in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

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