In undergraduate classrooms, while teaching chaos and fractals, it is taught as if there is no relation between these two. By using some non linear oscillators we demonstrate that there is a connection between chaos and fractals. By plotting the phase space diagrams of four nonlinear oscillators and using box counting method of finding the fractal dimension we established the chaotic nature of the nonlinear oscillators. The awareness that all chaotic systems are good fractals will add more insights to the concept of chaotic systems.
In 1968, Kittel published the zipper model for demonstrating the first order phase transition which is applicable to DNA like structures. This paper utilize this model to explain the behavior of many thermodynamic properties before, at and after phase transition to get a clear picture about what the changes are happening to the system during phase transition. Many textbooks say that entropy and volume show discontinuity at phase transition whereas Gibbs free energy is continuous. The zipper model shows that energy is also discontinuous as shown in the paper. Understanding the phase transition is still a difficult topic for the undergraduate students and hopefully this paper can help them to overcome this difficulty.
The micro canonical ensemble (MCE) represents an isolated system having fixed energy. The nature of energy in MCE is always a subject of discussion. In this paper we are distinguishing the energy possessed by the system and the energy offered by the system for measurement in MCE. This we hope will help the learners of statistical mechanics to have a more understanding of MCE.
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