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Saibal Mitra

Jun 2004
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  • Responses: 326


  • MSc, University of Utrecht, 1999
  • PhD (IP), University of Amstedam, 2004


  • Physics
  • Mathematics

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Waiting line problem

Speedy oil provides a single channel automobile oil change and lubrication service. Customers provide an arrive rate of 2.5 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability dist READ MORE »

Mathematics / Probability » 121398

Derive the formula for the multiplicity (entropy) of the two state paramagnet in the large N limit and when the number of excess spins relative to N is small.

For a single large two-state paramagnet, the multiplicity function is very sharply peaked about N/2.

(a) Use Stirling's approximation to estimate the height of the peak in the
multiplicity function.

(b) Derive a formula for the multiplicity function in the vicinity of the peak.


Physics / Heat & Thermodynamics / Heat Engines / Second Law of Thermodynamics / Entropy » 99091

Expansion coefficient and the Lennard-Jones potential.

Consider a classical particle moving in a one-dimensional potential well u(x). The particle is in thermal equilibrium with a reservoir at temperature T, so the probabilities of its various states are determined by Boltzmann statistics.

(a) Show that the average position of the particle is given READ MORE »

Physics / Nuclear / Radioactivity / Beta » 106342

Derive hooke's law and find the "elastic entropy".

Polymers, like rubber, are made of very long molecules that tangle into a configuration that has lots of S. A crude model of a rubber band contains N links, all of equal length L, which can only point either left or right (2 possible states). The total length of the band is thus the net displacemen READ MORE »

Physics / Heat & Thermodynamics / Internal Energy / System Work » 60267

Semi-infinite square well.

Consider the semi-infinite square well given by V(x)=-Vo

Physics / Quantum Physics / Photoelectric Effect / Wavefunction » 149762
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