Sensitivity of Process Design to Phase Equilibrium—A New Perturbation Method Based Upon the Margules Equation

2013 ◽  
Vol 59 (4) ◽  
pp. 1006-1015 ◽  
Author(s):  
Paul M. Mathias
Keyword(s):  
Phase Equilibrium ◽  
Perturbation Method ◽  
Process Design ◽  
New Perturbation ◽  
Margules Equation

A perturbation method and the limit-point case of even order symmetric differential expressions

1983 ◽  
Vol 94 (1-2) ◽  
pp. 121-135 ◽  
Author(s):  
Bernhard Mergler ◽  
Bernd Schultze
Keyword(s):  
Perturbation Method ◽  
Fourth Order ◽  
Limit Point ◽  
Perturbation Theorem ◽  
Order Case ◽  
Even Order ◽  
Limit Point Case ◽  
New Perturbation ◽  
Bounded Perturbations

SynopsisWe give a new perturbation theorem for symmetric differential expressions (relatively bounded perturbations, with relative bound 1) and prove with this theorem a new limit-point criterion generalizing earlier results of Schultze. We also obtain some new results in the fourth-order case.

A new perturbation method for determining the broadband complex permeability of magnetic thin films

2008 ◽  
Vol 320 (5) ◽  
pp. 750-753 ◽  
Author(s):  
Jianjun Jiang ◽  
Gang Du ◽  
Yun Yao ◽  
Cheng Liu ◽  
Lin Yuan ◽  
...  
Keyword(s):  
Thin Films ◽  
Perturbation Method ◽  
Magnetic Thin Films ◽  
Complex Permeability ◽  
New Perturbation

A perturbation method for the Vlasov–Poisson system

1998 ◽  
Vol 60 (1) ◽  
pp. 181-192 ◽  
Author(s):  
JONAS LUNDBERG ◽  
TOR FLÅ
Keyword(s):  
Perturbation Method ◽  
Particle Distribution ◽  
Distribution Functions ◽  
Poisson System ◽  
Nonlinear Wave Propagation ◽  
Starting Point ◽  
Self Consistent ◽  
Good Starting Point ◽  
New Perturbation ◽  
Lie Transformations

A perturbation method for the Vlasov–Poisson system is presented. It is self-consistent and entirely based on Lie transformations, which are considered as active transformations, generating the dynamics of the particle distribution function in the space of distribution functions. The main result is a set of three equations that forms a good starting point for a wide variety of problems concerning nonlinear wave propagation. Besides being efficient, the new perturbation method is systematic and therefore also suited for the use of computer algebra.

Dispersion Correction for Acoustic Multipole Logging on Guided Waves in Transversely Isotropic Medium

2014 ◽  
Vol 687-691 ◽  
pp. 732-735
Author(s):  
Li Zhang ◽  
H.X. Chen ◽  
M.X. Hao ◽  
X. Gao
Keyword(s):  
Perturbation Method ◽  
Isotropic Medium ◽  
Dispersion Characteristic ◽  
Guided Waves ◽  
Principal Axis ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
New Perturbation ◽  
Perturbation Solutions

A new and effective analytical perturbation method is presented for the multipole acoustic logging in a transversely isotropic medium (TIM) whose symmetric principal axis is parallel to the borehole axis although the exact solutions could be found. In this paper, the new perturbation method is adopted to simulate the dispersion characteristic in a borehole surrounded by a TIM for the first time. The TIM is regarded as a reference unperturbed isotropic state added to the perturbations, and three perturbation quantities about moduli deviated from the isotropic medium are introduced. By selecting a group of displacement potentials and a cylindrical coordinate system oriented along the borehole axis, the zero-, first-order and second-order perturbation solutions of the multipole acoustic field are derived for the weak transversely isotropic elastic solid which has its symmetric principal axis parallel to the borehole axis. The acoustic fields inside and outside the borehole excited by a multipole source are investigated. The dispersion characteristics in the borehole are numerically simulated by the perturbation method in the range of the second perturbation solutions. It is found that the dispersion characteristic by the perturbation method inside the borehole excited by monopole, dipole sources and quadrupole source are similar to obtained by the exact solution.

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