Yang–Mills on Quantum Heisenberg Manifolds

In the noncommutative geometry program of Connes, there are two variations of the concept of the Yang–Mills action functional. We show that for the quantum Heisenberg manifolds for generic parameter values they agree.     

Optical transfer function of an imaging system aperture masked by a retarder

Modifications of the imaging characteristics of an imaging system and a consequent increase in relative resolution in the spatial frequency range of interest have assumed significance in view of the growing applications of microscope imagery. The present study shows that a diffraction limited imaging system zonally masked by an oblique retarder is much more versatile in the sense that the imaging characteristics can be controlled in real time by virtue of the higher degrees of freedom available to the user. It has been shown that the optical transfer function (OTF) of the system varies periodically with the orientation ϑ of the analyzer at the output. Interestingly, it follows that the optical characteristics of the proposed imaging system can be expressed in terms of three OTF components which combined together gives rise to the overall system OTF. By proper choice of the polarization parameters involved it also possible to isolate these components or to select a convenient combination of these components. Finally, simulated results show that subtraction of two images produced by the proposed retarder masked lens yields OTFs that are difficult to obtain otherwise.     

Topics in Noncommutative Geometry Inspired Physics

In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories and noncommutative gravity.     

Dilaton Dark Energy Model in f(R), f(T) and Ho?ava-Lifshitz Gravities

In this work, we have considered dilaton dark energy model in Weyl-scaled induced gravitational theory in presence of barotropic fluid. It is to be noted that the dilaton field behaves as a quintessence. Here we have discussed the role of dilaton dark energy in modified gravity theories, namely f(R),f(T) and Hořava-Lifshitz gravities and analyzed the behavior of the dilaton field and the corresponding potential in respect to these modified gravity theories instead of Einstein’s gravity. In f(R) and f(T) gravities, we have considered some particular forms of f(R) and f(T) and we have shown that the potentials always increase with the dilaton fields. But in Hořava-Lifshitz gravity, it has been seen that the potential always decreases as dilation field increases.     

X-ray diffraction and Mössbauer spectroscopy studies of cementite dissolution in cold-drawn pearlitic steel

Cementite dissolution in cold-drawn pearlitic steel (0.8 wt.% carbon) wires has been studied by quantitative X-ray diffraction (XRD) and Mössbauer spectroscopy up to drawing strain 1.4. Quantification of cementite-phase fraction by Rietveld analysis has confirmed more than 50% dissolution of cementite phase at drawing strain 1.4. It is found that the lattice parameter of the ferrite phase determined by Rietveld refinement procedure remains nearly unchanged even after cementite dissolution. This confirms that the carbon atoms released after cementite dissolution do not dissolve in the ferrite lattice as Fe-C interstitial solid solution. Detailed analysis of broadening of XRD line profiles for the ferrite phase shows high density of dislocations (～10¹⁵/m²) in the ferrite matrix at drawing strain 1.4. The results suggest a dominant role of ?1?1?1? screw dislocations in the cementite dissolution process. Post-deformation heat treatment leads to partial annihilation of dislocations and restoration of cementite phase. Based on these experimental observations, further supplemented by TEM studies, we have suggested an alternative thermodynamic mechanism of the dissolution process.