scholarly journals Numerical Method for the Stability Analysis of Ideal MHD Modes with a Wide Range of Toroidal Mode Numbers in Tokamaks

2007 ◽  
Vol 2 (0) ◽  
pp. 010-010 ◽  
Author(s):  
Nobuyuki AIBA ◽  
Shinji TOKUDA ◽  
Takaaki FUJITA ◽  
Takahisa OZEKI ◽  
Ming S. CHU ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Numerical Method ◽  
Toroidal Mode ◽  
Wide Range ◽  
Ideal Mhd ◽  
The Stability

scholarly journals A General Numerical Method for Analyzing the Linear Stability of Stratified Parallel Shear Flows

2014 ◽  
Vol 31 (12) ◽  
pp. 2795-2808 ◽  
Author(s):  
Tim Rees ◽  
Adam Monahan
Keyword(s):  
Stability Analysis ◽  
Numerical Method ◽  
Shear Flows ◽  
Numerical Solutions ◽  
Analytical Approximations ◽  
Onset Of Turbulence ◽  
Parallel Shear Flows ◽  
Critical Layers ◽  
The Stability ◽  
Stability Results

Abstract The stability analysis of stratified parallel shear flows is fundamental to investigations of the onset of turbulence in atmospheric and oceanic datasets. The stability analysis is performed by considering the behavior of small-amplitude waves, which is governed by the Taylor–Goldstein (TG) equation. The TG equation is a singular second-order eigenvalue problem, whose solutions, for all but the simplest background stratification and shear profiles, must be computed numerically. Accurate numerical solutions require that particular care be taken in the vicinity of critical layers resulting from the singular nature of the equation. Here a numerical method is presented for finding unstable modes of the TG equation, which calculates eigenvalues by combining numerical solutions with analytical approximations across critical layers. The accuracy of this method is assessed by comparison to the small number of stratification and shear profiles for which analytical solutions exist. New stability results from perturbations to some of these profiles are also obtained.

scholarly journals Failure Process and Stability Analysis of Rock Blocks in a Large Underground Excavation Based on a Numerical Method

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Shijie Chen ◽  
Ming Xiao ◽  
Juntao Chen
Keyword(s):  
Stability Analysis ◽  
Numerical Analysis ◽  
Numerical Method ◽  
Failure Process ◽  
Surrounding Rock ◽  
Underground Excavation ◽  
Analysis Method ◽  
Safety Factors ◽  
Geological Conditions ◽  
The Stability

A numerical analysis method for block failure is proposed that is based on continuum mechanics. First, a mesh model that includes marked blocks was established based on the grid-based block identification method. Then, expressions of the contact force under various contact states were derived based on the explicit contact force algorithm, and a contact simulation method between blocks and the surrounding rock was proposed. The safety factors of the blocks were calculated based on the strength reduction method. This numerical analysis method can simulate both the continuous deformation of the surrounding rock and the discontinuous failure processes of the blocks. A simple example of a sliding block was used to evaluate the accuracy and rationality of the numerical method. Finally, combined with a deep underground excavation project under complex geological conditions, the stability of the blocks and rock were analyzed. The results indicate that the key blocks are damaged after excavation, the potentially dangerous blocks loosen and undergo large deformations, and the cracks between the blocks and the rock gradually increase as the excavation proceeds. The safety factors of the blocks change during the excavation. The numerical results demonstrate the influence of the surrounding rock on the failure process and on the stability of the blocks, and an effective analysis method is provided for the stability analysis of blocks under complex geological conditions.

scholarly journals Solving Volterra Integrodifferential Equations via Diagonally Implicit Multistep Block Method

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Nur Auni Baharum ◽  
Zanariah Abdul Majid ◽  
Norazak Senu
Keyword(s):  
Stability Analysis ◽  
Numerical Solution ◽  
Numerical Method ◽  
Numerical Computation ◽  
Numerical Solutions ◽  
Numerical Results ◽  
Integrodifferential Equations ◽  
Block Method ◽  
The Stability ◽  
Predictor Corrector

The performance of the numerical computation based on the diagonally implicit multistep block method for solving Volterra integrodifferential equations (VIDE) of the second kind has been analyzed. The numerical solutions of VIDE will be computed at two points concurrently using the proposed numerical method and executed in the predictor-corrector (PECE) mode. The strategy to obtain the numerical solution of an integral part is discussed and the stability analysis of the diagonally implicit multistep block method was investigated. Numerical results showed the competence of diagonally implicit multistep block method when solving Volterra integrodifferential equations compared to the existing methods.

Influence of Coflow On Buoyant Plume Puffing

2021 ◽  
Author(s):  
Kuchimanchi K Bharadwaj ◽  
Debopam Das
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Density Ratio ◽  
Buoyant Plume ◽  
Frequency Increase ◽  
Buoyant Plumes ◽  
Air Stream ◽  
Wide Range ◽  
Dimensional Parameters ◽  
The Stability

Abstract The present study investigates the influence of an annular coflowing air stream on the puffing behaviour of a buoyant plume by employing the BiGlobal Linear Stability Analysis. An increase in the coflow is found to mitigate the puffing intensity and eventually stabilize the plumes. From the stability analysis, the critical coflow ratios, which represent the amount of coflow required to completely suppress the puffing, have been estimated for plumes spanning a wide range of non-dimensional parameters. The analysis shows that the critical coflow ratio largely depends on the two buoyancy parameters, the Froude number, and the density ratio whereas it remains marginally affected by the plume Reynolds number. Plumes with higher buoyancy require larger coflow for suppressing puffing. From the instability analysis, we have obtained a correlation law for critical coflow ratios in buoyant plumes. Also, it is found that the plume puffing frequency increases with an increase in the coflow. We attempt to ascertain the reasons for instability mitigation and frequency increase in the puffing plumes because of coflow.

scholarly journals Theoretical predictions of dynamic necking formability of ductile metallic sheets with evolving plastic anisotropy and tension-compression asymmetry

2021 ◽  
Author(s):  
Murlidhar Anil Kumar ◽  
Komi Espoir N'souglo ◽  
navab hosseini ◽  
Nicolas Jacques ◽  
Jose Rodriguez-Martinez
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Plastic Anisotropy ◽  
Theoretical Models ◽  
Unit Cell ◽  
Forming Limit ◽  
Plastic Behavior ◽  
Zone Model ◽  
Wide Range ◽  
The Stability

In this paper, we have investigated necking formability of anisotropic and tension-compression asymmetric metallic sheets subjected to in-plane loading paths ranging from plane strain tension to equibiaxial tension. For that purpose, we have used three different approaches: a linear stability analysis, a nonlinear two-zone model and unit-cell finite element calculations. We have considered three materials –AZ31-Mg alloy, high purity α-titanium and OFHC copper– whose mechanical behavior is described with an elastic-plastic constitutive model with yielding defined by the CPB06 criterion [10] which includes specific features to account for the evolution of plastic orthotropy and strength differential effect with accumulated plastic deformation [37]. From a methodological standpoint, the main novelty of this paper with respect to the recent work of N’souglo et al. [32] –which investigated materials with yielding described by the orthotropic criterion of Hill [19]– is the extension of both stability analysis and nonlinear two-zone model to consider anisotropic and tension-compression asymmetric materials with distortional hardening. The results obtained with the stability analysis and the nonlinear two-zone model show reasonable qualitative and quantitative agreement with forming limit diagrams calculated with the finite element simulations, for the three materials considered, and for a wide range of loading rates varying from quasi-static loading up to 40000 s−1, which makes apparent the capacity of the theoretical models to capture the mechanisms which control necking formability of metallic materials with complex plastic behavior. Special mention deserves the nonlinear two-zone model, as it does not need prior calibration –unlike the stability analysis– and it yields accurate predictions that rarely deviate more than 10% from the results obtained with the unit-cell calculations

Stability Analysis of QFT Controllers Designed for Hydraulic Actuators Using Takagi-Sugeno Fuzzy Modeling Approach

2013 ◽  
Author(s):  
Masoumeh Esfandiari ◽  
Nariman Sepehri
Keyword(s):  
Stability Analysis ◽  
Linear Models ◽  
Fuzzy Model ◽  
Hydraulic Actuators ◽  
Local Linear ◽  
Guaranteed Stability ◽  
Wide Range ◽  
Position Controller ◽  
The Stability ◽  
Takagi Sugeno

Although, robust controllers that have been designed for hydraulic actuators based on quantitative feedback theory (QFT) have shown satisfactory performance, their stability is limited to certain set of inputs-outputs. This paper explores, for the first time, the stability of a QFT controller using stability theorem of Takagi-Sugeno (T-S) fuzzy systems. To do this, first the hydraulic closed-loop system is represented by a T-S fuzzy model that is formed through a nonlinear combination of some local linear models. Next, the stability of the resulting T-S fuzzy system is analyzed simply by stability analysis of its local linear models. This approach is used to study the stability of a QFT position controller previously developed for hydraulic actuators. Results show guaranteed stability of the QFT controller over a wide range of operation and in the presence of parametric uncertainties.

Stability Analysis of Some Novel Cytoplasmic Male Sterile Sources of Sunflower and Their Hybrids

Helia ◽  
2018 ◽  
Vol 41 (69) ◽  
pp. 153-200 ◽  
Author(s):  
Vikrant Tyagi ◽  
S. K. Dhillon ◽  
Prashant Kaushik
Keyword(s):  
Stability Analysis ◽  
Environment Interaction ◽  
Spring Season ◽  
Male Sterile ◽  
Cross Combination ◽  
Yield And Quality ◽  
Genotype Environment Interaction ◽  
Standard Procedures ◽  
Wide Range ◽  
The Stability

AbstractGenetic makeup along with environmental stimuli affect the expression of a trait in plants. Drought tolerance in addition to stability of characters over a wide range of environmental conditions is not well studied in sunflower. Therefore, here we have performed a stability analysis study of sunflower genotypes. The experimental material comprised of 19 lines of sunflower comprising 9 alloplasmic cms lines from different wild sources along with one common maintainer from petiolaris source, 4 cms lines and one maintainer from cultivated source (cytoplasm from H. petiolaris), 4 restorer lines and 60 F1 hybrids (developed in line x tester design). The experiment was conducted over two years i. e. spring season 2011 and spring season 2012 over the two environments one normal irrigated and another water stress environment at Punjab Agricultural University, Ludhiana, India. The data were recorded for different morphophysiology, yield and quality trais and analysis as per standard procedures. The genotype×environment interaction was further partitioned into linear and non-linear components according to Eberhart and Russel model. Eleven sunflower hybrids were found to be stable across the environments for seed yield. While, sufficient variability was also recorded for the oil content with the highest oil percentage in the cross combination ARG-2A×P100R (34.61). Overall, this study provides useful information regarding the stability of newly developed and cytoplasmically diverse sunflower hybrids under north Indian conditions.

scholarly journals Mean flow stability analysis of oscillating jet experiments

2014 ◽  
Vol 757 ◽  
pp. 1-32 ◽  
Author(s):  
Kilian Oberleithner ◽  
Lothar Rukes ◽  
Julio Soria
Keyword(s):  
Stability Analysis ◽  
Wave Model ◽  
Flow Stability ◽  
Mean Flow ◽  
Axisymmetric Mode ◽  
Wide Range ◽  
Flow Oscillations ◽  
The Mean ◽  
Wave Models ◽  
The Stability

AbstractLinear stability analysis (LSA) is applied to the mean flow of an oscillating round jet with the aim of investigating the robustness and accuracy of mean flow stability wave models. The jet’s axisymmetric mode is excited at the nozzle lip through a sinusoidal modulation of the flow rate at amplitudes ranging from 0.1 % to 100 %. The instantaneous flow field is measured via particle image velocimetry (PIV) and decomposed into a mean and periodic part utilizing proper orthogonal decomposition (POD). Local LSA is applied to the measured mean flow adopting a weakly non-parallel flow approach. The resulting global perturbation field is carefully compared with the measurements in terms of spatial growth rate, phase velocity, and phase and amplitude distribution. It is shown that the stability wave model accurately predicts the excited flow oscillations during their entire growth phase and during a large part of their decay phase. The stability wave model applies over a wide range of forcing amplitudes, showing no pronounced sensitivity to the strength of nonlinear saturation. The upstream displacement of the neutral point and the successive reduction of gain with increasing forcing amplitude is very well captured by the stability wave model. At very strong forcing ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{>}40\, \%$), the flow becomes essentially stable to the axisymmetric mode. For these extreme cases, the prediction deteriorates from the measurements due to an interaction of the forced wave with the geometric confinement of the nozzle. Moreover, the model fails far downstream in a region where energy is transferred from the oscillation back to the mean flow. This study supports previously conducted mean flow stability analysis of self-excited flow oscillations in the cylinder wake and in the vortex breakdown bubble and extends the methodology to externally forced convectively unstable flows. The high accuracy of mean flow stability wave models as demonstrated here is of great importance for the analysis of coherent structures in turbulent shear flows.

scholarly journals Stability of a Viable Non-Minimal Bounce

Universe ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 62
Author(s):  
Debottam Nandi
Keyword(s):  
Fixed Point ◽  
Stability Analysis ◽  
Early Universe ◽  
Stable Solution ◽  
Barotropic Fluid ◽  
Stable Attractor ◽  
Attractor Solution ◽  
Wide Range ◽  
The Stability ◽  
The Universe

The main difficulties in constructing a viable early Universe bouncing model are: to bypass the observational and theoretical no-go theorem, to construct a stable non-singular bouncing phase, and perhaps, the major concern of it is to construct a stable attractor solution which can evade the Belinsky–Khalatnikov–Lifshitz (BKL) instability as well. In this article, in the homogeneous and isotropic background, we extensively study the stability analysis of the recently proposed viable non-minimal bouncing theory in the presence of an additional barotropic fluid and show that, the bouncing solution remains stable and can evade BKL instability for a wide range of the model parameter. We provide the expressions that explain the behavior of the Universe in the vicinity of the required fixed point i.e., the bouncing solution and compare our results with the minimal theory and show that ekpyrosis is the most stable solution in any scenario.

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