Singular Perturbation Analysis of Speed Controlled Reciprocating Compressors

1989 ◽  
Vol 111 (2) ◽  
pp. 313-321 ◽  
Author(s):  
A. Liakopoulos ◽  
W. H. Boykin
Keyword(s):  
Steady State ◽  
Singular Perturbation ◽  
Transient Response ◽  
Analytical Solutions ◽  
Perturbation Analysis ◽  
System Parameters ◽  
Singular Perturbation Analysis ◽  
Frequency Domains ◽  
Perturbed Systems ◽  
Reaction Forces

A singular perturbation analysis of speed controlled reciprocating compressors is presented. For weakly perturbed systems, analytical solutions for the steady-state and transient response are given. For strongly perturbed systems numerical results in both time and frequency domains are presented. The analytical solutions are useful in calculating reaction forces and torques applied on inertially stabilized platforms, in designing feed forward compensators and in simplifying parameter identification procedures. Furthermore, they clearly exhibit the dependence of response to system parameters.

scholarly journals Singular perturbation analysis of the steady-state Poisson–Nernst–Planck system: Applications to ion channels

2008 ◽  
Vol 19 (5) ◽  
pp. 541-560 ◽  
Author(s):  
A. SINGER ◽  
D. GILLESPIE ◽  
J. NORBURY ◽  
R. S. EISENBERG
Keyword(s):  
Steady State ◽  
Ion Channels ◽  
Singular Perturbation ◽  
Perturbation Analysis ◽  
Characteristic Curve ◽  
Three Dimensions ◽  
Dimensional System ◽  
Biological Time ◽  
Singular Perturbation Analysis ◽  
Wide Range

Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst–Planck) equations called PNP in biophysics. We use singular perturbation techniques to analyse the steady-state PNP system for a channel with a general geometry and a piecewise constant permanent charge profile. We construct an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system. The asymptotical current–voltage (I–V) characteristic curve of the device (obtained by the singular perturbation analysis) is shown to be a very good approximation of the numerical I–V curve (obtained by solving the system numerically). The physical constraint of non-negative concentrations implies a unique solution, i.e., for each given applied potential there corresponds a unique electric current (relaxing this constraint yields non-physical multiple solutions for sufficiently large voltages).

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