arXiv subjects
Publications and source records attributed to Anindya Kumar Biswas.
We study twenty four written natural languages. We draw in the log scale, number of words starting with a letter vs rank of the letter, both normalised. We find that all the graphs are of the similar type. The graphs are tantalisingly closer to the curves of reduced magnetisation vs reduced temperature for magnetic materials. We make a weak conjecture that a curve of magnetisation underlies a written natural language.
In this note, we would like to find the laws of electrodynamics in simple economic systems. In this direction, we identify the chief economic variables and parameters, scalar and vector, which are amenable to be put directly into the crouch of the laws of electrodynamics, namely Maxwell's equations. Moreover, we obtain Phillp's curve, recession and Black-Scholes formula, as sample applications.
A simple text book problem in mechanics\cite{klep}, describes a massive horizontal bar placed on two oppositely rotating rollers, kept at a fixed center to center distance. Subsequent motion is to be found out in presence of kinetic frictions at the point of contacts of the two rollers\cite{demo}. Introducing bulk rolling friction effects, through the contact planes and considering viscoelastic rollers, we find that the inverse of the square of the oscillation frequency of the bar has a linear relationship with the center to center distance. The gradient and intercept of the linear relation together with observations about two consecutive positions of the bar, determine the rolling friction coefficient of the viscoelastic materials of the two rollers fully.
A small sphere placed on the top of a big static frictionless sphere, slips until it leaves the surface at an angle $θ_{l}=\cos^{-1}{2/3}$. On the other extreme, if the surface of the big sphere has coefficient of static friction, $μ_s\to\infty$, the small sphere starts rolling and continues to do so until it leaves the surface at an angle $θ_{l} =\cos^{-1}{10/17}$. In the case where, $0\leqμ_s<\infty$, we get a simple phase diagram. The three phases are pure rolling, rolling with slipping and detached state. One phase line separates pure rolling from rolling with slipping. This diagram is obtained when stopping angles for pure rolling are plotted against static friction coefficients $μ_s$. Study in this article is restricted to the case when the mobile sphere starts at the top of the static sphere with infinitesimal kinetic energy.
We took three lawn tennis balls arbitrarily. One was moderately old, one was old and another was new. Fabricating a conveyor belt set-up we have measured rolling friction coefficients, $μ_{r}$, of the three balls as a function of their angular velocities, $ω_{ball}$. In all the three cases, plotting the results and using linear fits, we have obtained relations of the form $μ_{r}= k_{rol} ω_{ball}$ and have deduced the proportionality constant $k_{rol}$. Moreover, core of a lawn tennis ball is made of vulcanised India-rubber. Using the known values of Young modulus and shear viscosity of vulcanised India-rubbers in the theoretical formula for $k_{rol}$, we estimate $k_{rol}$s for the cores made of vulcanised India-rubbers, assuming Trouton ratio as three. The experimental results for the balls and the semi-theoretical estimates for the cores, of $k_{rol}$, are of the same order of magnitudes.