Admissible nonlinear perturbation of divergence equations

1983 ◽  
pp. 285-290
Author(s):  
Silviu Sburlan
Keyword(s):  
Nonlinear Perturbation ◽  
Divergence Equations

CASE STUDY OF THE CONVERGENCY OF NONLINEAR PERTURBATION SERIES: MORSE–FESHBACH NONLINEAR SERIES

1999 ◽  
Vol 14 (13) ◽  
pp. 2103-2115 ◽  
Author(s):  
BISWANATH RATH
Keyword(s):  
New York ◽  
Energy Levels ◽  
Perturbation Series ◽  
Nonlinear Perturbation ◽  
Theoretical Physics ◽  
The Matrix ◽  
Diagonalization Method ◽  
Matrix Diagonalization ◽  
Divergent Behavior

We study the divergent behavior of the Morse–Feshbach nonlinear perturbation series (MFNS) [P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953)] for producing convergent energy levels using the ground state of a quartic anharmonic oscillator (AHO) in the strong coupling limit. Numerical calculations have been done up to tenth order. Further comparison of the MFNS convergent result has been made with the matrix diagonalization method.

scholarly journals CP-violating transport theory for electroweak baryogenesis with thermal corrections

2021 ◽  
Vol 2021 (11) ◽  
pp. 042
Author(s):  
Kimmo Kainulainen
Keyword(s):  
Source Term ◽  
Transport Theory ◽  
Finite Width ◽  
Source Terms ◽  
Boltzmann Equations ◽  
Current Divergence ◽  
The One ◽  
Infrared Divergences ◽  
Correct Implementation ◽  
Divergence Equations

Abstract We derive CP-violating transport equations for fermions for electroweak baryogenesis from the CTP-formalism including thermal corrections at the one-loop level. We consider both the VEV-insertion approximation (VIA) and the semiclassical (SC) formalism. We show that the VIA-method is based on an assumption that leads to an ill-defined source term containing a pinch singularity, whose regularisation by thermal effects leads to ambiguities including spurious ultraviolet and infrared divergences. We then carefully review the derivation of the semiclassical formalism and extend it to include thermal corrections. We present the semiclassical Boltzmann equations for thermal WKB-quasiparticles with source terms up to the second order in gradients that contain both dispersive and finite width corrections. We also show that the SC-method reproduces the current divergence equations and that a correct implementation of the Fick's law captures the semiclassical source term even with conserved total current ∂μ j μ = 0. Our results show that the VIA-source term is not just ambiguous, but that it does not exist. Finally, we show that the collisional source terms reported earlier in the semiclassical literature are also spurious, and vanish in a consistent calculation.

On a convergent nonlinear perturbation theory without small denominators or secular terms

1976 ◽  
Vol 17 (1) ◽  
pp. 121-140 ◽  
Author(s):  
Charles R. Eminhizer ◽  
Robert H. G. Helleman ◽  
Elliott W. Montroll
Keyword(s):  
Perturbation Theory ◽  
Nonlinear Perturbation ◽  
Small Denominators ◽  
Secular Terms

A Study on the Instability of Disk-Shaped Gear

1999 ◽  
Author(s):  
Guangming Ren ◽  
Litang Yan
Keyword(s):  
Perturbation Method ◽  
Traveling Wave ◽  
Vibration Characteristics ◽  
Exciting Force ◽  
Nonlinear Perturbation ◽  
The Self ◽  
Experimental Investigations ◽  
Damping Force ◽  
Bevel Gears ◽  
Theory And Experiment

Abstract In this paper the theory and experiment concerning vibration instability of disk-shaped gear are presented. At first the self-exciting force of gear is searched and the works done by the exciting force and damping force are analyzed. Then the vibration instability of the disk-shaped plain gear is studied with multiple scale’s method of the nonlinear perturbation method. The vibration characteristics of a coupled pair of bevel gears are investigated experimentally. Both theoretical and experimental investigations show that there are actually self-exciting vibrations on the gear. Under certain conditions the forward traveling wave vibration of the driving gear and the backward traveling wave vibration of the driven gear can be instable.

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