stability boundaries
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2021 ◽  
pp. 1-24
Author(s):  
Venkatesh Suriyanarayanan ◽  
Quentin Rendu ◽  
Mehdi Vahdati ◽  
Loic Salles

Abstract This paper presents the effect of manufacturing tolerance on performance and stability boundaries of a transonic fan using a RANS simulation. The effect of tip gap and stagger angle was analysed through a series of single passage and double passage simulation; based on which an optimal arrangement was proposed for random tip gap and random stagger angle in case of a whole annulus rotor. All simulations were carried out using NASA rotor 67 as a test case and AU3D an in-house CFD solver. Results illustrate that the stagger angle mainly affects efficiency and hence its circumferential variation must be as smooth as possible. Furthermore, the tip gap affects the stability boundaries, pressure ratio and efficiency. Hence its optimal configuration mandates that the blades be configured in a zigzag arrangement around the annulus i.e. larger tip gap between two smaller ones.


2021 ◽  
Vol 11 (11) ◽  
pp. 4833
Author(s):  
Afroja Akter ◽  
Md. Jahedul Islam ◽  
Javid Atai

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.


2021 ◽  
Author(s):  
Liangwei Zeng ◽  
Boris A. Malomed ◽  
Dumitru Mihalache ◽  
Yi Cai ◽  
Xiaowei Lu ◽  
...  

Abstract We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in the form of flat-floor “bubbles”, and topological excitations, in the form of dark solitons in 1D and vortices with winding number m in 2D. The ground and excited states are accurately approximated by the Thomas-Fermi expressions. The 1D and 2D bubbles, as well as vortices with m=1, are completely stable, while the dark solitons and vortices with m=2 have nontrivial stability boundaries in their existence areas. Unstable dark solitons are expelled to the periphery, while unstable double vortices split in rotating pairs of unitary ones. Displaced stable vortices precess around the central point.


2021 ◽  
Vol 1864 (1) ◽  
pp. 012062
Author(s):  
N.V. Kuznetsov ◽  
M.Y. Lobachev ◽  
M.V. Yuldashev ◽  
R.V. Yuldashev

2021 ◽  
pp. 107754632110004
Author(s):  
Naim Khader

The presented work examines the dynamic behavior of an asymmetric rotor with asymmetric flexible disk, contrary to previous works on the subject, where researchers examined the effect of either rigid disk asymmetry or disk flexibility at a time. Account for the asymmetry of flexible disk in rotors constitutes the new contribution in this work. The suggested mathematical model combines Lagrangian approach with Rayleigh–Ritz method to derive the governing equations of motion of the rotor. Account for asymmetry of the flexible disk results in complicated and lengthy expressions for the potential and kinetic energies of the rotor, required in the adopted Lagrangian approach. Using symbolic computation simplified the derivation of the governing equations of motion with constant coefficients in terms of rotating coordinate system. Solution of the resulting eigenvalue problem provided numerical results for rotors with symmetric and asymmetric flexible disks, required to assess the effect of disk flexibility and asymmetry on the resulting frequencies and stability boundaries of the examined rotor system.


2021 ◽  
Author(s):  
Susanne Marie Pettersson ◽  
Martin Nilsson Jacobi

Understanding ecosystem stability and functioning is a long-standing goal in theoretical ecology, with one of the main tools being dynamical modelling of species abundances. With the help of dynamical population models limits to stability and regions of various ecosystem dynamics have been extensively mapped in terms of diversity (number of species), types of interactions, interaction strengths, varying interaction networks (for example plant-pollinator, food-web) and varying structures of these networks. Although it is apparent that ecosystems reside in and are affected by a spatial environment, local differences (spatial heterogeneity) is often excluded from studies mapping stability boundaries under the assumption of an average and equal amount of interaction for all individuals of a species. Here we show that extending the classic dynamical Generalised-Lotka-Volterra model into a connected space the boundaries of stability change. When viewing the ecosystem as a spatially heterogeneous whole, limits previously marking the end of stability can now be crossed without any remarkable change in species abundances and without loss of stability. Thus limits previously thought to mark catastrophic transitions are not critical due to the possibility of spatial heterogeneity within the system. In addition, we show that too much spatial fragmentation of ecosystem habitats acts destabilising and leads back to the stability boundaries found in spatially homogeneous ecosystems with average interactions. Thus, we conclude that spatially heterogeneous but connected systems are the most robust. In terms of ecosystem management, the risk of collapse or irreversible changes is lower in spatially heterogeneous systems, which real ecosystems are, and we should expect local changes in populations well in advance of system collapse. Although, too much fragmentation of an ecosystem's available space can lead to a less robust system with higher risk of extinctions and collapse.


2021 ◽  
Vol 89 ◽  
pp. 208-224
Author(s):  
You-Qi Tang ◽  
Yuan Zhou ◽  
Shuang Liu ◽  
Shan-Ying Jiang

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