To this end, we start with the introduction for the first time of the notion of entropy in thermodynamics by R. At the same time, we will incorporate some mathematical foundations of such old and new ideas until the appearance of Shannon entropy. In this paper, we are reviewing the origins of the notion of entropy and studying some developing of it leading to modern notions of entropies. Such systems are interesting from theoretical point of view in Topological Dynamics and appear frequently in applied sciences such as Electronics and Control Theory. For example, X can be non-compact or f can be discontinuous (only in a finite number of points and with bounded jumps on the values of f or even non-bounded jumps). In modern applications, other conditions on X and f have been considered. Among them, one of the most popular is that of topological entropy. During years, a long list of results have appeared to precise and understand what is the complexity of the systems. “A promising CoFeNi 2V 0.5Mo 0.Discrete dynamical systems are given by the pair ( X,f) where X is a compact metric space and f: X→ X is a continuous map.“Irradiation effects of medium-entropy alloy NiCoCr with and without pre-indentation”.“Radiation-induced segregation on defect clusters in single-phase concentrated solid-solution alloys”.“Effect of alloying elements on defect evolution in Ni-20X binary alloys”.“Enhancing radiation tolerance by controlling defect mobility and migration pathways in multicomponent single-phase alloys”.The following are some examples for additional reading: Wang’s group and collaborators have published dozens of research papers on the related subject in recent years. The research was supported by the US Department of Energy via the Energy Frontier Research Center (EFRC) on Energy Dissipation to Defect Dissipation. Kai Sun in Michigan Center for Material Characterization (MC2). Li Jiang, a research fellow in Wang’s group at NERS and the first author of the paper, made the main discovery using TEM with the help of Dr. Yanwen Zhang and William Weber, both of Oak Ridge National Laboratory and University of Tennessee – Knoxville, processed the material.ĭr. Professor Liang Qi’s group at the U-M Department of Materials Science and Engineering ran the computer simulation that helped to explain their experimental result. The paper is the result of a collaboration between Wang’s group and several others. The paper on this research, titled, “High‐Entropy Alloys: Irradiation‐Induced Extremes Create Hierarchical Face‐/Body‐Centered‐Cubic Phases in Nanostructured High Entropy Alloys,” was recently published in the high-impact journal Advanced Materials with a highlighted frontispiece. Through further testing on physical and chemical properties, Wang expects to eventually use this type of material in advanced nuclear reactors or other advanced devices that require the combination of properties from both fcc and bcc materials. “Bread, meats, or vegetables alone might not be as ideal or tasty as a sandwich with all the ingredients sandwiched (laminated) together.” The team set out to understand the behavior of HEA under extreme conditions, such as in advanced nuclear reactors, as part of a project to find an optimized radiation-tolerant material. The layering structure found by the research team, led by NERS Professor Lumin Wang, a professor of nuclear engineering and radiological sciences and materials science and engineering, should make the material stronger, more ductile and more radiation resistant. They recently discovered the formation of nano-scale laminating, or alternating layers, of two different crystals: face-centered-cubic (fcc) and body-centered cubic (bcc) in an ion irradiated HEA that had some preexisting stacking faults. A research team from the U-M Department of Nuclear Engineering and Radiological Sciences (NERS) has used ion beams and transmission electron microscopy (TEM) to study the radiation tolerance of single phase high entropy alloys (HEA).
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