scholarly journals On the Extremum Properties of Thermodynamic Steady State in Non-Linear Systems

10.5772/21871 ◽  
2011 ◽  
Author(s):  
Gy. Vincze ◽  
A. Szasz
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Non Linear ◽  
Non Linear Systems

Effects of Suspension Design on the Attitudes of a Car during Braking and Acceleration

1973 ◽  
Vol 187 (1) ◽  
pp. 787-794
Author(s):  
J. R. Ellis
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Degrees Of Freedom ◽  
Coupled Systems ◽  
Two Degrees Of Freedom ◽  
Simulation Techniques ◽  
Non Linear ◽  
Non Linear Systems ◽  
Effort Distribution

Two degrees of freedom models of a car are employed to demonstrate the effects of the suspension derivative ∂ x/∂ z on the pitch and bounce attitudes during braking or accelerating. The work equation is employed to show that brake effort distribution between the axles has a significant effect on the attitudes when anti-dive suspension characteristics are utilized. The steady-state positions in both pitch and bounce are developed for linear systems of typical suspensions that may be either standard or coupled systems. Non-linear systems are considered using simulation techniques. A description of some simulation circuits is contained in an appendix.

A method of calculation of steady state oscillations in autonomous non-linear systems

1990 ◽  
Vol 136 (1) ◽  
pp. 35-44 ◽  
Author(s):  
S.S. Qiu ◽  
I.M. Filanovsky
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Method Of Calculation ◽  
Non Linear ◽  
Non Linear Systems

scholarly journals Dynamic Catalysis Fundamentals: I. Fast calculation of limit cycles in dynamic catalysis

2021 ◽  
Author(s):  
Brandon Foley ◽  
Neil Razdan
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Closed Form ◽  
Linear Systems ◽  
Computational Cost ◽  
Kinetic Equations ◽  
Reaction Rates ◽  
Closed Form Solutions ◽  
Non Linear ◽  
Non Linear Systems

Dynamic catalysis—the forced oscillation of catalytic reaction coordinate potential energy surfaces (PES)—has recently emerged as a promising method for the acceleration of heterogeneously-catalyzed reactions. Theoretical study of enhancement of rates and supra-equilibrium product yield via dynamic catalysis has, to-date, been severely limited by onerous computational demands of forward integration of stiff, coupled ordinary differential equations (ODEs) that are necessary to quantitatively describe periodic cycling between PESs. We establish a new approach that reduces, by ≳108×, the computational cost of finding the time-averaged rate at dynamic steady state (i.e. the limit cycle for linear and nonlinear systems of kinetic equations). Our developments are motivated by and conceived from physical and mathematical insight drawn from examination of a simple, didactic case study for which closed-form solutions of rate enhancement are derived in explicit terms of periods of oscillation and elementary step rate constants. Generalization of such closed-form solutions to more complex catalytic systems is achieved by introducing a periodic boundary condition requiring the dynamic steady state solution to have the same periodicity as the kinetic oscillations and solving the corresponding differential equations by linear algebra or Newton-Raphson-based approaches. The methodology is well-suited to extension to non-linear systems for which we detail the potential for multiple solutions or solutions with different periodicities. For linear and non-linear systems alike, the acute decrement in computational expense enables rapid optimization of oscillation waveforms and, consequently, accelerates understanding of the key catalyst properties that enable maximization of reaction rates, conversions, and selectivities during dynamic catalysis.

An artificial damping method for the determination of the steady state of harmonically excited non-linear systems

1988 ◽  
Vol 120 (3) ◽  
pp. 597-608 ◽  
Author(s):  
A.E. Kanarachos ◽  
C.N. Spentzas
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Artificial Damping ◽  
Non Linear ◽  
Non Linear Systems

A Harmonic Analysis for the Steady Analysis of Non-Linear Systems

2012 ◽  
Vol 433-440 ◽  
pp. 5536-5541
Author(s):  
Shan Chai ◽  
Can Chang Liu ◽  
Hong Yan Li
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Steady State Solution ◽  
Response Analysis ◽  
Time Interval ◽  
Harmonic Response ◽  
Non Linear ◽  
Non Linear Systems ◽  
Harmonic Response Analysis ◽  
Linear Differential

A numerical analysis is used to investigate the response of non-linear systems under aperiodic excitations based on the harmonic response analysis method. An idea of fine discretization is proposed to turn the aperiodic excitations into the superposition of a series of periodic excitations in a tiny time interval. The method of perturbation is employed to transform the non-linear governing equation into a series of linear differential equations. Harmonic response analysis can be applied in the solution of aperiodic steady response. The algebraic algorithm of direct steady-state analysis can improve computational efficiency. The defect that the steady-state solution can be gotten out until the free vibration attenuates is avoided. The examples show that the numerical results match well with the analytic data.

Time-averaged non-linear systems: steady-state analysis

1973 ◽  
Vol 17 (6) ◽  
pp. 1143-1152
Author(s):  
HANOCH UR ◽  
TSVI LISSACK
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Steady State Analysis ◽  
Non Linear ◽  
Non Linear Systems ◽  
State Analysis

A Galerkin method for the steady state analysis of harmonically excited non-linear systems

1992 ◽  
Vol 27 (6) ◽  
pp. 661-671 ◽  
Author(s):  
A.E Kanarachos ◽  
C.N Spentzas
Keyword(s):  
Steady State ◽  
Galerkin Method ◽  
Linear Systems ◽  
Steady State Analysis ◽  
Non Linear ◽  
Non Linear Systems ◽  
State Analysis
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