scholarly journals ANALYTICITY OF PERTURBATION EXPANSIONS

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

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.

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.

Perturbation Expansions

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

ARE GLUONS MASSIVE?

1994 ◽  
Vol 09 (18) ◽  
pp. 3283-3306 ◽  
Author(s):  
J.H. FIELD
Keyword(s):  
Experimental Determination ◽  
Perturbative Qcd ◽  
Renormalization Scheme ◽  
Perturbation Expansions

The mass of the gluon is determined using asymptotic perturbative QCD in the [Formula: see text] renormalization scheme. The experimental determination of the couplant ās(2), which occurs in the perturbation expansions for [Formula: see text] and [Formula: see text] together with an estimate of the on-shell couplant, αs=0.096±0.016 [or αs(0)=0.30±0.05], yields the results [Formula: see text] if typical current (constituent) masses are assigned to the quarks.

A general derivation of the Hall conductivity on the noncommutative plane

2011 ◽  
Vol 89 (7) ◽  
pp. 769-772 ◽  
Author(s):  
Yue Jiang ◽  
Mai-Lin Liang ◽  
Ya-Bin Zhang
Keyword(s):  
Algebraic Approach ◽  
Hall Conductivity ◽  
Perturbation Expansions ◽  
General Derivation ◽  
Noncommutative Plane

By algebraic approach, Hall conductivity on the noncommutative plane is derived exactly. The calculations are carried out in noncommutative phase spaces without any representations or perturbation expansions of the coordinate and momentum operators.

A CONVERGENT PERTURBATION METHOD FOR THE HOLSTEIN MODEL AND ITS APPLICATION TO THE DOUBLE EXCHANGE SYSTEM

2001 ◽  
Vol 15 (19n20) ◽  
pp. 2647-2663 ◽  
Author(s):  
A. N. DAS ◽  
JAYITA CHATTERJEE ◽  
M. MITRA
Keyword(s):  
Coupling Strength ◽  
Analytical Method ◽  
Entire Range ◽  
Magnetic Transition ◽  
Double Exchange ◽  
Perturbation Expansions ◽  
Entire Region ◽  
Exchange System ◽  
Holstein Model ◽  
Large Polaron

We look for an analytical method which can describe the Holstein model over the entire region of electron–phonon (e–ph) coupling strength. Considering a toy model of two sites the perturbation expansions are developed for the Holstein Hamiltonian using different standard phonon bases. It is found that the modified Lang Firsov phonon basis shows satisfactory convergence for almost the entire range of e–ph coupling from the antiadiabatic limit to the intermediate range of hopping. This method is used to study the magnetic transition and the small to large polaron crossover in a double exchange model with e–ph interaction. Implications of the results in the context of manganites are discussed.

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