scholarly journals PERIOD REGION DISTRIBUTIONS OF MCMULLEN FAMILY M SETS

Fractals ◽  
2017 ◽  
Vol 25 (04) ◽  
pp. 1740012 ◽  
Author(s):  
ZHIXING LU ◽  
YUANYUAN SUN ◽  
XIAOPENG HU
Keyword(s):  
Dynamical System ◽  
System Theory ◽  
Critical Points ◽  
Experimental Results ◽  
Dynamical System Theory ◽  
Calculation Methods ◽  
Complex Dynamical System

In this study, the period-[Formula: see text] steady regions of McMullen family M sets are discussed. The calculation methods of the numbers of period-[Formula: see text] steady regions are presented and the center points and boundaries of period-1 are studied by complex dynamical system theory. In addition, the problem about the free critical points is discussed. The experimental results show that the free critical points do not influence the distributions of period-[Formula: see text] steady regions when [Formula: see text], which is proved theoretically.

Towards a More Holistic Approach to Quality Improvements in Aluminium Die Casting

2009 ◽  
Vol 618-619 ◽  
pp. 341-344
Author(s):  
Sandrine Zanna ◽  
Yakov Frayman ◽  
Bruce Gunn ◽  
Saeid Nahavandi
Keyword(s):  
Dynamical System ◽  
System Theory ◽  
Die Casting ◽  
Holistic Approach ◽  
Natural Process ◽  
Dynamical System Theory ◽  
Quality Improvements ◽  
System Perspective ◽  
Porosity Defects ◽  
Natural Equilibrium

This work evaluates the feasibility of using a holistic approach, based on dynamical system theory, to reduce porosity defects in high pressure aluminum die casting. Quality improvements, from a dynamical system perspective mean the ability to move the die casting process out of its natural equilibrium to a more beneficial state and the ability to maintain this new process state. This more beneficial state may be achieved in several ways. One way is to increase the amount of forcing to overcome natural process resistance. This forcing approach is represented by typical continuous intervention policy, with modifications in die/part design and/or process parameters. An alternative approach is to reduce the amount of natural process resistance, in particular the amount of process disturbance, allowing the process to move out of its natural equilibrium with much less forcing. This alternative uses the self-regulating ability of dynamical systems thus decreasing the amount of human intervention required. In this respect, the influence of vacuum on time on chattering at the first stage of the casting shot was identified as a good process candidate for testing using dynamical system theory. A significant reduction in porosity defects was achieved, which also set the process on a path of slow but consistent self-improvement.

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