scholarly journals General connection between time-local and time-nonlocal perturbation expansions

2021 ◽  
Vol 104 (15) ◽  
Author(s):  
K. Nestmann ◽  
M. R. Wegewijs
Keyword(s):  
Perturbation Expansions ◽  
General Connection

Orientation relationships of carlsbergite in schreibersite and kamacite in the north Chile iron meteorite

2006 ◽  
Vol 70 (4) ◽  
pp. 373-382 ◽  
Author(s):  
G. Nolze ◽  
G. Wagner ◽  
R. Saliwan Neumann ◽  
R. Skála ◽  
V. Geist
Keyword(s):  
Electron Backscatter Diffraction ◽  
Metallic Matrix ◽  
Iron Meteorite ◽  
Orientation Relationships ◽  
Orientation Relation ◽  
Crystalline Materials ◽  
The North ◽  
Transmission Electron ◽  
Backscatter Diffraction ◽  
General Connection

AbstractThe crystallographic orientation of carlsbergite (CrN) in the north Chile meteorite (hexahedrite) was investigated using electron backscatter diffraction and transmission electron microscopy. These studies examined the CrN crystals in the rhabdites (idiomorphic schreibersite) and in kamacite. It was found that the CrN crystals embedded in rhabdite show a number of different orientation relationships with the host crystals. These orientations can be explained based on the lattice dimensions of both coexisting crystalline materials. It was also found that both carlsbergite and kamacite are characterized by a high dislocation density (≥ l09 cm-2) while rhabdite is free of dislocations. It is supposed that in spite of the deformed metallic matrix, a general connection between the orientation relation of all the phases involved exists.

scholarly journals Adjoint-based parametric sensitivity analysis for swirling M-flames

2018 ◽  
Vol 859 ◽  
pp. 516-542 ◽  
Author(s):  
Calum S. Skene ◽  
Peter J. Schmid
Keyword(s):  
Sensitivity Analysis ◽  
Frequency Response ◽  
Stokes Equations ◽  
Numerical Study ◽  
Computational Cost ◽  
Base Flow ◽  
Sensitivity Analyses ◽  
Perturbation Expansions ◽  
Mean Flow ◽  
Adjoint Solutions

A linear numerical study is conducted to quantify the effect of swirl on the response behaviour of premixed lean flames to general harmonic excitation in the inlet, upstream of combustion. This study considers axisymmetric M-flames and is based on the linearised compressible Navier–Stokes equations augmented by a simple one-step irreversible chemical reaction. Optimal frequency response gains for both axisymmetric and non-axisymmetric perturbations are computed via a direct–adjoint methodology and singular value decompositions. The high-dimensional parameter space, containing perturbation and base-flow parameters, is explored by taking advantage of generic sensitivity information gained from the adjoint solutions. This information is then tailored to specific parametric sensitivities by first-order perturbation expansions of the singular triplets about the respective parameters. Valuable flow information, at a negligible computational cost, is gained by simple weighted scalar products between direct and adjoint solutions. We find that for non-swirling flows, a mode with azimuthal wavenumber $m=2$ is the most efficiently driven structure. The structural mechanism underlying the optimal gains is shown to be the Orr mechanism for $m=0$ and a blend of Orr and other mechanisms, such as lift-up, for other azimuthal wavenumbers. Further to this, velocity and pressure perturbations are shown to make up the optimal input and output showing that the thermoacoustic mechanism is crucial in large energy amplifications. For $m=0$ these velocity perturbations are mainly longitudinal, but for higher wavenumbers azimuthal velocity fluctuations become prominent, especially in the non-swirling case. Sensitivity analyses are carried out with respect to the Mach number, Reynolds number and swirl number, and the accuracy of parametric gradients of the frequency response curve is assessed. The sensitivity analysis reveals that increases in Reynolds and Mach numbers yield higher gains, through a decrease in temperature diffusion. A rise in mean-flow swirl is shown to diminish the gain, with increased damping for higher azimuthal wavenumbers. This leads to a reordering of the most effectively amplified mode, with the axisymmetric ($m=0$) mode becoming the dominant structure at moderate swirl numbers.

scholarly journals ANALYTICITY OF PERTURBATION EXPANSIONS

1961 ◽  
Vol 17 (1) ◽  
pp. 1
Author(s):  
T. S. CHANG
Keyword(s):  
Perturbation Expansions

scholarly journals On naturality of some construction of connections

2020 ◽  
Vol 74 (1) ◽  
pp. 57
Author(s):  
Jan Kurek ◽  
Włodzimierz Mikulski
Keyword(s):  
Linear Connection ◽  
Bundle Functor ◽  
Fibred Manifold ◽  
Natural Transformations ◽  
General Connection

Let \(F\) be a bundle functor on the category of all fibred manifolds and fibred maps. Let \(\Gamma\) be a general connection in a fibred manifold \(\mathrm{pr}:Y\to M\) and \(\nabla\) be a classical linear connection on \(M\). We prove that the  well-known general connection \(\mathcal{F}(\Gamma,\nabla)\) in \(FY\to M\) is canonical with respect to fibred maps and with respect to natural transformations of bundle functors.

Analysis of Combined Forced and Free Flow in a Vertical Channel With Viscous Dissipation and Isothermal-Isoflux Boundary Conditions

1999 ◽  
Vol 121 (2) ◽  
pp. 349-356 ◽  
Author(s):  
A. Barletta
Keyword(s):  
Boundary Conditions ◽  
Parallel Plate ◽  
Vertical Channel ◽  
Uniform Heat Flux ◽  
Viscous Heating ◽  
Perturbation Expansions ◽  
Nusselt Numbers ◽  
Buoyancy Parameter ◽  
Laminar Mixed Convection ◽  
Friction Factors

Fully developed and laminar mixed convection in a parallel-plate vertical channel is investigated in the case of non-negligible viscous heating. The channel walls are subjected to asymmetric boundary conditions: One wall experiences a constant and uniform heat flux, while the other is kept at a uniform and constant temperature. The velocity field and the temperature field are evaluated analytically by means of perturbation expansions with respect to a buoyancy parameter, i.e., the ratio between the Grashof number and the Reynolds number. The Nusselt numbers and the friction factors are obtained as functions of the buoyancy parameter.

scholarly journals X. Theory of the Earth; or an Investigation of the Laws observable in the Composition, Dissolution, and Restoration of Land upon the Globe.

1788 ◽  
Vol 1 (2) ◽  
pp. 209-304 ◽  
Author(s):  
James Hutton
Keyword(s):  
Terrestrial System ◽  
The Earth ◽  
General Connection

When we trace the parts of which this terrestrial system is composed, and when we view the general connection of those several parts, the whole presents a machine of a peculiar construction by which it is adapted to a certain end. We perceive a fabric, erected in wisdom, to obtain a purpose worthy of the power that is apparent in the production of it.

RESONANCE RISK AND MODE SHAPE MANAGEMENT IN THE FREQUENCY DOMAIN TO PREVENT SQUEAK AND RATTLE

2021 ◽  
pp. 1-30
Author(s):  
Mohsen Bayani ◽  
Casper Wickman ◽  
Aswin Dhananjai Krishnaswamy ◽  
Chidambaram Sathappan ◽  
Rikard Söderberg
Keyword(s):  
Frequency Domain ◽  
Mode Shape ◽  
Autonomous Driving ◽  
System Response ◽  
Shape Similarity ◽  
Passenger Cars ◽  
Baseline Design ◽  
Loop Design ◽  
The Time Domain ◽  
General Connection

Abstract Avoiding quality problems in passenger cars, such as squeak and rattle (S&R), has been a remarkable cost-saving consideration. The introduction of electric engines and less engaged drivers due to autonomous driving is expected to further stress the need for quieter cabins. However, the complexity of the virtual evaluation of S&R events has obstructed the practical treatment of these quality issues in the pre-design-freeze phases of product development. In this study, new quantified frequency-domain metrics are proposed to measure the risk for the generation of S&R in subsystem assemblies. The proposed metrics measure the resonance risk and the mode shape similarity in the critical interfaces for S&R. The calculations are done based on the system response in the frequency domain. Compared to the time-domain evaluation methods, the knowledge about the system excitation levels is not essential and the calculations are more time-efficient. The proposed metrics can be used in closed-loop design optimisation processes to involve S&R attributes in the pre-design-freeze attribute trade-off activities besides other attributes. In this work, these metrics were used in a two-stage optimisation problem to optimise the connection configuration in two industrial cases. As compared to the baseline design, the risk for S&R was reduced by improving the system behaviour in terms of resonance risk and mode shape similarity. This was achieved by applying some adjustments to the location of the fasteners while maintaining the same general connection configuration concept.

Perturbation Expansions

1982 ◽  
pp. 52-84
Author(s):  
F. Langouche ◽  
D. Roekaerts ◽  
E. Tirapegui
Keyword(s):  
Perturbation Expansions
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