Finite-size effects on the cluster expansions for quantum gases in restricted geometries

We have analytically obtained 1-particle density matrices for ideal Bose and Fermi gases in both the 3-D box geometries and the harmonically trapped geometries for the entire range of temperature. We have obtained quantum cluster expansions of the grand free energies in closed forms for the same systems in the restricted geometries. We have proposed a theorem (with a proof) about the generic form of the quantum cluster integral. We also have considered short ranged interactions in our analyses for the quasi 1-D cases of Bose and Fermi gases in the box geometries. Our theoretical results are exact, and are directly useful for understanding finite-size effects on quantum cluster expansion of Bose and Fermi gases in the restricted geometries. Our results would be relevant in the context of experimental study of spatial correlations in ultra-cold systems of dilute Bose and Fermi gases of alkali atoms (i) in 3-D magneto-optical box traps with quasi-uniform potential around the center [1], and (ii) in 3-D harmonic traps [2, 3].Comment: 12 pages, 6 figure

Analysis of DevR regulated genes in Mycobacterium tuberculosis

The DevRS two component system of Mycobacterium tuberculosis is responsible for its dormancy in host and becomes operative under hypoxic condition. It is experimentally known that phosphorylated DevR controls the expression of several downstream genes in a complex manner. In the present work we propose a theoretical model to show role of binding sites in DevR mediated gene expression. Individual and collective role of binding sites in regulating DevR mediated gene expression has been shown via modeling. Objective of the present work is two fold. First, to describe qualitatively the temporal dynamics of wild type genes and their known mutants. Based on these results we propose that DevR controlled gene expression follows a specific pattern which is efficient in describing other DevR mediated gene expression. Second, to analyze behavior of the system from information theoretical point of view. Using the tools of information theory we have calculated molecular efficiency of the system and have shown that it is close to the maximum limit of isothermal efficiency.Comment: Title changed in this submission. 33 pages, 16 figures, 2 table