scholarly journals Optimization and Stability of Heat Engines: The Role of Entropy Evolution

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 865 ◽  
Author(s):  
Julian Gonzalez-Ayala ◽  
Moises Santillán ◽  
Maria Santos ◽  
Antonio Calvo Hernández ◽  
José Mateos Roco
Keyword(s):  
Local Stability ◽  
Production Efficiency ◽  
Basin Of Attraction ◽  
Heat Engine ◽  
Time Constraints ◽  
Thermal Gradients ◽  
Heat Engines ◽  
Low Dissipation ◽  
The Basin Of Attraction

Local stability of maximum power and maximum compromise (Omega) operation regimes dynamic evolution for a low-dissipation heat engine is analyzed. The thermodynamic behavior of trajectories to the stationary state, after perturbing the operation regime, display a trade-off between stability, entropy production, efficiency and power output. This allows considering stability and optimization as connected pieces of a single phenomenon. Trajectories inside the basin of attraction display the smallest entropy drops. Additionally, it was found that time constraints, related with irreversible and endoreversible behaviors, influence the thermodynamic evolution of relaxation trajectories. The behavior of the evolution in terms of the symmetries of the model and the applied thermal gradients was analyzed.

On-Off Intermittency and Riddled Basins of Attraction in a Coupled Map System

1998 ◽  
Vol 01 (02n03) ◽  
pp. 161-180 ◽  
Author(s):  
J. Laugesen ◽  
E. Mosekilde ◽  
Yu. L. Maistrenko ◽  
V. L. Maistrenko
Keyword(s):  
Periodic Orbits ◽  
Basin Of Attraction ◽  
Basins Of Attraction ◽  
Chaotic State ◽  
One Dimensional ◽  
Type Iii ◽  
Different Types ◽  
One Dimensional Maps ◽  
The Basin Of Attraction

The paper examines the appearance of on-off intermittency and riddled basins of attraction in a system of two coupled one-dimensional maps, each displaying type-III intermittency. The bifurcation curves for the transverse destablilization of low periodic orbits embeded in the synchronized chaotic state are obtained. Different types of riddling bifurcation are discussed, and we show how the existence of an absorbing area inside the basin of attraction can account for the distinction between local and global riddling as well as for the distinction between hysteric and non-hysteric blowout. We also discuss the role of the so-called mixed absorbing area that exists immediately after a soft riddling bifurcation. Finally, we study the on-off intermittency that is observed after a non-hysteric blowout bifurcaton.

THE EFFECT OF DAMPING ON THE STEADY STATE AND BASIN BIFURCATION PATTERNS OF A NONLINEAR MECHANICAL OSCILLATOR

1992 ◽  
Vol 02 (01) ◽  
pp. 81-91 ◽  
Author(s):  
MOHAMED S. SOLIMAN ◽  
J.M.T. THOMPSON
Keyword(s):  
Steady State ◽  
Basin Of Attraction ◽  
Period Doubling ◽  
Qualitative And Quantitative ◽  
Periodically Driven ◽  
Resonance Response ◽  
Nonlinear Mechanical ◽  
Damped Oscillator ◽  
The Basin Of Attraction

This paper examines the role of damping on both the steady state and basin behavior of a periodically driven damped oscillator with the ability to escape from a potential well. We examine the effect of damping on both the qualitative and quantitative resonance response of the system. Particular attention is paid to how the damping scales the main steady state bifurcations; saddle-nodes, period-doubling flips, cascades to chaos, boundary crises, etc. We also investigate how the damping level effects the main homoclinic and heteroclinic basin bifurcations that may result in a rapid erosion and stratification of the basin of attraction and hence a loss of engineering integrity of the system.

ROLES OF CHAOTIC SADDLE AND BASIN OF ATTRACTION IN BIFURCATION AND CRISIS ANALYSIS

2011 ◽  
Vol 21 (03) ◽  
pp. 903-915 ◽  
Author(s):  
YING ZHANG ◽  
BRUNO ROSSETTO ◽  
WEI XU ◽  
XIAOLE YUE ◽  
TONG FANG
Keyword(s):  
Simple Model ◽  
Dynamical Behavior ◽  
Basin Of Attraction ◽  
Transient Chaos ◽  
Invariant Property ◽  
The Basin Of Attraction ◽  
Chaotic Saddle

This paper is devoted to the dynamical behavior of a parametrically driven double-well Duffing (PDWD) system. Despite the invariant property of symmetry, this simple model exhibits a large diversity of patterns which can be observed in different situations. The transitions between symmetric forms of system responses often lead to bifurcation or crisis and complicated behaviors, such as the coexistence of different kinds of attractors. The bifurcations and crises are discussed, especially those inside the main periodic window. In particular, the role of chaotic saddles and their intrinsic links with the basin of attraction and transient chaos is studied.

CHAOS AND CHAOTIC TRANSIENTS IN A FORCED MODEL OF THE ECONOMIC LONG WAVE: THE ROLE OF HOMOCLINIC BIFURCATION TO INFINITY

1995 ◽  
Vol 05 (03) ◽  
pp. 741-749 ◽  
Author(s):  
JEPPE STURIS ◽  
MORTEN BRØNS
Keyword(s):  
Limit Cycle ◽  
Basin Of Attraction ◽  
Homoclinic Bifurcation ◽  
Periodic Forcing ◽  
Stable And Unstable Manifolds ◽  
Long Wave ◽  
Unstable Manifolds ◽  
Chaotic Transients ◽  
The Basin Of Attraction

When an autonomous system of ordinary differential equations exhibits limit cycle behavior but is close in parameter space to a homoclinic bifurcation to infinity in which the limit cycle blows up to infinite amplitude and disappears, periodic forcing of the system may result in the appearance of both chaos and chaotic transients. In this paper, we use numerical techniques to map out Arnol’d tongues of a forced model of the economic long wave and illustrate how the system becomes chaotic and also exhibits chaotic transients for certain parameter combinations. Based on linearizations at infinity, we argue that infinity acts like a saddle with stable and unstable manifolds. By numerical computation, we show that chaotic transients occur when the manifolds intersect. Depending on parameters, two types of bifurcations have been identified: A chaotic attractor blows up to infinite size and disappears or the boundary of the basin of attraction of a periodic solution becomes fractal.

scholarly journals Optimization and Efficiency Studies of Heat Engines: A Review

2020 ◽  
Vol 07 (03) ◽  
pp. 37-58
Author(s):  
Preety Aneja ◽  
Keyword(s):  
Objective Function ◽  
Power Efficiency ◽  
Heat Engine ◽  
Maximum Power ◽  
Maximum Efficiency ◽  
Heat Engines ◽  
Low Dissipation ◽  
Optimization Efficiency ◽  
Efficient Power ◽  
Operating Regimes

This review aims to study the various theoretical and numerical investigations in the optimization of heat engines. The main focus is to discuss the procedures to derive the efficiency of heat engines under different operating regimes (or optimization criteria) for different models of heat engines such as endreversible models, stochastic models, low-dissipation models, quantum models etc. Both maximum power and maximum efficiency operational regimes are desirable but not economical, so to meet the thermo-ecological considerations, some other compromise-based criteria have been proposed such as Ω criterion (ecological criterion) and efficient power criterion. Thus, heat engines can be optimized to work at an efficiency which may not be the maximum (Carnot) efficiency. The optimization efficiency obtained under each criterion shows a striking universal behaviour in the near-equilibrium regime. We also discussed a multi-parameter combined objective function of heat engines. The optimization efficiency derived from the multi-parameter combined objective function includes a variety of optimization efficiencies, such as the efficiency at the maximum power, efficiency at the maximum efficiency-power state, efficiency at the maximum criterion, and Carnot efficiency. Thus, a comparison of optimization of heat engines under different criteria enables to choose the suitable one for the best performance of heat engine under different conditions.

Local stability analysis of a low-dissipation cyclic refrigerator

2021 ◽  
Author(s):  
Kai Li ◽  
Jie Lin ◽  
Jian-Hui Wang
Keyword(s):  
Steady State ◽  
Local Stability ◽  
Figure Of Merit ◽  
Coefficient Of Performance ◽  
Stable Steady State ◽  
Local Stability Analysis ◽  
Low Dissipation ◽  
Internal Dissipation ◽  
The Stability

Abstract We study the local stability near the maximum figure of merit for the low-dissipation cyclic refrigerator, where the irreversible dissipation occurs not only in the thermal contacts but also the adiabatic strokes. We find that the bounds of the coefficient of performance at maximum figure of merit or maximum cooling rate in presence of internal dissipation are identical to corresponding those in absence of internal dissipation. Using two different scenarios, we prove the existence of a single stable steady state for the refrigerator, and clarify the role of internal dissipation on the stability of thermodynamic steady state, showing that the speed of system evolution to the steady state decreases due to internal dissipation.

scholarly journals Link between optimization and local stability of a low-dissipation heat engine: Dynamic and energetic behaviors

2018 ◽  
Vol 98 (3) ◽  
Author(s):  
J. Gonzalez-Ayala ◽  
M. Santillán ◽  
I. Reyes-Ramírez ◽  
A. Calvo-Hernández
Keyword(s):  
Local Stability ◽  
Heat Engine ◽  
Low Dissipation ◽  
Engine Dynamic
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