K. M. Udayanandan

During the development of physics, we can see that the Equipartition Theorem (EPT) has been redefined many times. In this paper, we start with the description of the historical development of the theorem along with the various definitions given by different scientists. Then we found the expressions for classical, quantum, and discrete energy system...

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...

Many natural phenomena we find in our surroundings, are fractals. Studying and learning about fractals in classrooms is always a challenge for both teachers and students. We here show that the sound of musical instruments can be used as a good resource in the laboratory to study fractals. Measurement of fractal dimension which indicates how much fr...

Many consider physics to be a highly mathematical oriented subject to study. To break this opinion and also to generate a deep interest in physics, a course on ‘Physics of Music’ can be introduced at any level of a curriculum. We present a simple and practical way of introducing this topic even for school level students. Teachers, along with studen...

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...

Rhythmic drums are given great importance in religious festivals and art forms in India. A variety of drums were invented and used in different parts of India. The well-developed rhythmic sound patterns produced by the drums make people dance to the sound with great enjoyment. Thrissur Pooram in Kerala is an example to show the importance, attracti...

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...

Bose–Einstein condensations (BEC) for an ideal Bose gas and an imperfect Bose gas are presented using cluster expansion method by using a new generating function obtained by Ushcats. The saturation density is calculated from the known values of virial coefficients for both ideal and uniform hard-sphere imperfect Bose gas. The values of saturation d...

Physics teachers always face great difficulties in introducing the many component nature of tensors to students. This article is intended to help the instructors with some convincing examples of more than 3 component physical quantities. We will also show that tensor nature of many physical quantities are both medium and interacting physical quanti...

In this paper we revisit the vibrational modes of a circular membrane with different boundary conditions. This we hope will serve as an exercise to get more insight into the study of percussion instruments. The displacement for various modes are found for two initial velocities and two initial displacements. The first three modes are plotted for bo...

The Ising model which was introduced to explain ferromagnetism in physics provides a general background to build realistic models of social interactions. Here we use the thermodynamic study of a financial market using Ising model in which agents have three opinions (buy, sell or hold).

In this paper we studied about a simple market using statistical ensembles and obtained the equation of state for a market in micro canoni-cal, canonical and grand canonical formalism.

Many of the drums played all over the world are circular in shape. There are many practical reasons for the instrument makers to choose a circular shape for the drums. Apart from practical side, there are some scientific bases for the circular shape of drums. This paper investigates the physics behind the circular shape of the drums. La mayoría de...

The equation of state for a collection of ideal bosons in both the low-density and high-density regions is found using the method of cluster expansion with a new generating function. The importance of the radius of convergence in the cluster expansion and its connection to the Bose–Einstein condensation phenomenon are studied. The radius of converg...

The equation of state of an ideal collection of bosons in the low-density and high-density regime are found using the method of cluster expansion with Mayer’s generating function. The saturation density and the other thermodynamic properties are calculated by the application of Mayer’s convergence of the partition function. By calculating the value...

The spin-half Ising model has been used with remarkable success in describing magnetism and phase transition in magnetic materials. Likewise, the lattice gas model, which uses the spin-1 Ising model, was employed to investigate the phase transition in liquid-gas systems. In all the earlier lattice gas models, the kinetic energy of atoms occupying t...

Entropy of mixing leading to Gibbs paradox is studied for different physical systems with and without potentials. The effect of potentials on the mixing and non mixing character of physical systems is discussed. We hope this article will encourage students to search for new problems which will help them understand statistical mechanics better.

We usually study or teach physics in the three dimensional or four dimensional space in classrooms. But now a days there is a growing interest among researchers [1-11] in multidimensional physics. In this article, we make a study of the Blackbody Radiation(BBR), Bose Einstein Condensation(BEC) and Pauli para magnetism in different dimensions. The r...

The equation of state (EOS) of quark-gluon plasma (QGP) using the Cornell potential based on Mayer's cluster expansion is presented. The string constant and the strong coupling constant for QGP are calculated. The EOS developed could describe the lattice EOS for pure gauge, two-flavor and three-flavor QGP qualitatively.

We develop statistical mechanics and thermodynamics of Bose and Fermi systems in relativistic harmonic oscillator (RHO) confining potential, which is applicable in quark gluon plasma (QGP), astrophysics, Bose–Einstein condensation (BEC) etc. Detailed study of QGP system is carried out and compared with lattice results. Furthermore, as an applicatio...

Three parallel connected pendulums and three mutually connected pendulums are not properly distinguished in many of the text books. Here we in this article is trying to distinguish them based on normal frequencies and phase differences.

Boltzmann Correction Factor (BCF) ! N is used in Micro Canonical Ensemble (MCE) and Canonical Ensemble (CE) as a dividing term to reduce the over counting of the states while finding the number of states and partition function. For Grand Canonical Ensemble the indistinguishability was taken into account while deriving the Partition Function (PF) an...