Adaptive wavelet collocation for the solution of steady-state equations

1995 ◽  
Author(s):  
Silvia Bertoluzza
Keyword(s):  
Steady State ◽  
State Equations ◽  
Adaptive Wavelet

Validation of a new method for determination of free fatty acid turnover

1987 ◽  
Vol 252 (3) ◽  
pp. E431-E438 ◽  
Author(s):  
J. M. Miles ◽  
M. G. Ellman ◽  
K. L. McClean ◽  
M. D. Jensen
Keyword(s):  
Steady State ◽  
Fatty Acid ◽  
Free Fatty Acid ◽  
Clearance Rate ◽  
Experimental Period ◽  
Metabolic Clearance ◽  
Metabolic Clearance Rate ◽  
State Equations ◽  
Tracer Methods

The accuracy of tracer methods for estimating free fatty acid (FFA) rate of appearance (Ra), either under steady-state conditions or under non-steady-state conditions, has not been previously investigated. In the present study, endogenous lipolysis (traced with 14C palmitate) was suppressed in six mongrel dogs with a high-carbohydrate meal 10 h before the experiment, together with infusions of glucose, propranolol, and nicotinic acid during the experimental period. Both steady-state and non-steady-state equations were used to determine oleate Ra ([3H]oleate) before, during, and after a stepwise infusion of an oleic acid emulsion. Palmitate Ra did not change during the experiment. Steady-state equations gave the best estimates of oleate inflow approximately 93% of the known oleate infusion rate overall, while errors in tracer estimates of inflow were obtained when non-steady-state equations were used. The metabolic clearance rate of oleate was inversely related to plasma concentration (P less than 0.01). In conclusion, accurate estimates of FFA inflow were obtained when steady-state equations were used, even under conditions of abrupt and recent changes in Ra. Non-steady-state equations, in contrast, may provide erroneous estimates of inflow. The decrease in metabolic clearance rate during exogenous infusion of oleate suggests that FFA transport may follow second-order kinetics.

The basic equations for a supplemented GSMP and its applications to queues

1988 ◽  
Vol 25 (03) ◽  
pp. 565-578 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Genji Yamazaki
Keyword(s):  
Stochastic Process ◽  
Steady State ◽  
Queueing Networks ◽  
General Setting ◽  
Main Concern ◽  
Stationary Condition ◽  
State Equations ◽  
Semi Markov Process ◽  
Basic Equations ◽  
Stieltjes Transforms

A supplemented GSMP (generalized semi-Markov process) is a useful stochastic process for discussing fairly general queues including queueing networks. Although much work has been done on its insensitivity property, there are only a few papers on its general properties. This paper considers a supplemented GSMP in a general setting. Our main concern is with a system of Laplace–Stieltjes transforms of the steady state equations called the basic equations. The basic equations are derived directly under the stationary condition. It is shown that these basic equations with some other conditions characterize the stationary distribution. We mention how to get a solution to the basic equations when the solution is partially known or inferred. Their applications to queues are discussed.

KINETIC EQUATIONS FOR ENZYME REACTIONS IN THE PRESENCE OF POWERFUL INHIBITORS

1959 ◽  
Vol 37 (8) ◽  
pp. 1268-1271 ◽  
Author(s):  
Richard M. Krupka ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Kinetic Equations ◽  
Competitive Inhibitor ◽  
Graphical Analysis ◽  
Rate Data ◽  
State Equations ◽  
Enzyme Reactions ◽  
Simple Addition

Steady-state equations are worked out for the case of a competitive inhibitor that is present in concentrations comparable with that of the enzyme; allowance is made for the inhibitor attached to the enzyme. Two cases are considered: in case 1 the enzyme and inhibitor form a simple addition complex, while in case 2 a molecule is split off. Methods of graphical analysis of rate data are described.

Hopf Bifurcation in the Double-Glazing Problem With Conducting Boundaries

1987 ◽  
Vol 109 (4) ◽  
pp. 894-898 ◽  
Author(s):  
K. H. Winters
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Gravity Waves ◽  
Traveling Waves ◽  
Critical Rayleigh Number ◽  
Boussinesq Approximation ◽  
Time Dependent ◽  
Oscillatory Convection ◽  
Extended System ◽  
State Equations

Oscillatory convection has been observed in recent experiments in a square, air-filled cavity with differentially heated sidewalls and conducting horizontal surfaces. We show that the onset of the oscillatory convection occurs at a Hopf bifurcation in the steady-state equations for free convection in the Boussinesq approximation. The location of the bifurcation point is found by solving an extended system of steady-state equations. The predicted critical Rayleigh number and frequency at the onset of oscillations are in excellent agreement with the values measured recently and with those of a time-dependent simulation. Four other Hopf bifurcation points are found near the critical point and their presence supports a conjectured resonance between traveling waves in the boundary layers and interior gravity waves in the stratified core.

The influence of pH and inhibitors on the kinetics of enzyme reactions involving two intermediates

1967 ◽  
Vol 45 (5) ◽  
pp. 539-546 ◽  
Author(s):  
Harvey Kaplan ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Ph Dependence ◽  
Free Enzyme ◽  
State Equations ◽  
Enzyme Reactions ◽  
Substrate Complex ◽  
Rate Determining Step ◽  
Enzyme Substrate ◽  
Special Cases ◽  
Influence Of Ph

General steady-state equations are worked out for enzyme reactions which occur according to the scheme [Formula: see text]Equations showing the pH dependence of the kinetic parameters are developed in a form which distinguishes between essential and nonessential ionizing groups. The pK dependence of [Formula: see text], the second-order constant extrapolated to zero substrate constant, gives pK values for groups which ionize on the free enzyme, but reveals such a pK only if the corresponding group is also involved in the breakdown of the Michaelis complex. General steady-state equations are also developed for the case in which an inhibitor can combine with the free enzyme, the enzyme–substrate complex, and also a second intermediate (e.g. an acyl enzyme). The equations are given in a form that is convenient for analyzing the experimental results, and a number of special cases are considered. It is shown how the type of inhibition depends not only on the nature of the inhibitor but also on that of the substrate, an important factor being the rate-determining step of the reaction. Examples of the various kinds of behavior are given.

Combined cycle dynamics

2003 ◽  
Vol 217 (3) ◽  
pp. 247-258 ◽  
Author(s):  
F. M. Mansour ◽  
A. M. Abdul Aziz ◽  
S. M. Abdel-Ghany ◽  
H. M. El-shaer
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Combined Cycle ◽  
Stable Operation ◽  
Algebraic Equations ◽  
State Equations ◽  
Combined Cycle Plant ◽  
Fast Settling ◽  
Operational Data ◽  
Good Agreement

A mathematical model describing the dynamic behaviour of each major component of the combined cycle is presented. The formulae are deduced from continuity, momentum, energy, and state equations. Partial differential equations (PDEs) are discretized to algebraic equations by using the implicit backward-central finite difference scheme and then solved by iteration. Explicit-Euler's integration method is applied to other differential equations (DEs). A multi-element control system is implemented to investigate its effect on the combined cycle's dynamic response. The simulation results are compared with the design and steady-state operational data of the unit number 4 in Cairo South Combined Cycle Power Plant, showing good agreement. The dynamic results prove the effectiveness of the multi-element control strategy to control the combined cycle plant with fast settling time, neglected steady-state error, and moderate overshoot or undershoot while assuring a stable operation under sudden changes of load.

Simulation of Unsteady Turbomachinery Flows Using an Implicitly Coupled Nonlinear Harmonic Balance Method

2011 ◽  
Author(s):  
Jonathan M. Weiss ◽  
Venkataramanan Subramanian ◽  
Kenneth C. Hall
Keyword(s):  
Steady State ◽  
Harmonic Balance ◽  
Time Derivative ◽  
Computational Cost ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Computationally Efficient ◽  
State Equations ◽  
Approximate Factorization ◽  
Efficient Manner

A nonlinear harmonic balance method for the simulation of turbomachinery flows is presented. The method is based on representing an unsteady, time periodic flow by a Fourier series in time and then solving a set of mathematically steady-state equations to obtain the Fourier coefficients. The steady-state solutions are stored at discrete time levels distributed throughout one period of unsteadiness and are coupled via the physical time derivative and at periodic boundaries. Implicit coupling between time levels is achieved in a computationally efficient manner through approximate factorization of the linear system that results from the discretized equations. Unsteady, rotor-stator interactions are performed to validate the implementation. Results based on the harmonic balance method are compared against those obtained using a full unsteady, time-accurate calculation using moving meshes. The implicitly coupled nonlinear harmonic balance method is shown to produce a solution of reasonable accuracy compared to the full unsteady approach but with significantly less computational cost.

scholarly journals The Geometry of Power Systems Steady-State Equations– Part II: a Power Surface Study

2020 ◽  
pp. 47-53
Author(s):  
B. Ayuev ◽  
V. Davydov ◽  
P. Erokhin ◽  
V. Neuymin ◽  
A. Pazderin
Keyword(s):  
Steady State ◽  
Power Systems ◽  
Transmission Loss ◽  
Normal Vector ◽  
State Equations ◽  
Marginal State ◽  
Normal Vectors ◽  
System States ◽  
Steady State Solutions ◽  
System Power

Steady-state equations play an essential part in the theory of power systems and the practice of computations. These equations are directly or mediately used almost in all areas of the theory of power system states, constituting its basis. This two-part study deals with a geometrical interpretation of steady-state solutions in a power space. Part I has proposed considering the power system's steady states in terms of power surface. Part II is devoted to an analytical study of the power surface through its normal vectors. An interrelationship between the entries of the normal vector is obtained through incremental transmission loss coefficients. Analysis of the normal vector has revealed that in marginal states, its entry of the slack bus active power equals zero, and the incremental transmission loss coefficient of the slack bus equals one. Therefore, any attempts of the slack bus to maintain the system power balance in the marginal state are fully compensated by associated losses. In real-world power systems, a change in the slack bus location in the marginal state makes this steady state non-marginal. Only in the lossless power systems, the marginal states do not depend on a slack bus location.

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