Synchronization framework for modeling transition to thermoacoustic instability in laminar combustors

We, herein, present a new model based on the framework of synchronization to describe a thermoacoustic system and capture the multiple bifurcations that such a system undergoes. Instead of applying flame describing function to depict the unsteady heat release rate as the flame's response to acoustic perturbation, the new model considers the acoustic field and the unsteady heat release rate as a pair of nonlinearly coupled damped oscillators. By varying the coupling strength, multiple dynamical behaviors, including limit cycle oscillation, quasi-periodic oscillation, strange nonchaos, and chaos can be captured. Furthermore, the model was able to qualitatively replicate the different behaviors of a laminar thermoacoustic system observed in experiments by Kabiraj et al.~[Chaos 22, 023129 (2012)]. By analyzing the temporal variation of the phase difference between heat release rate oscillations and pressure oscillations under different dynamical states, we show that the characteristics of the dynamical states depend on the nature of synchronization between the two signals, which is consistent with previous experimental findings.Comment: 18 pages, 7 figure

Some Aspects on the Utility of Distance Measures in Comparing Two MROC Curves

Receiver Operating Characteristic (ROC) curve is a widely used and accepted tool to assess the performance of a classifier or procedure. Apart from this, comparing the procedures or ROC curves is also of interest. A multivariate extension of ROC (MROC) curve that considers a linear combination of several markers for classification was proposed by Sameera, Vishnu Vardhan and Sarma [13]. In the present paper, some inferential procedures are given to compare two MROC curves by means of distance measures based on scores of MROC curve and summary measures such as mean vectors and dispersion matrices. Real and Simulated data sets are used to demonstrate the above proposed inferential aspects

Statistical mechanics of confined quantum particles

We develop statistical mechanics and thermodynamics of Bose and Fermi systems in relativistic harmonic oscillator (RHO) confining potential, which may be applicable in quark gluon plasma (QGP), astrophysics, Bose-Einstein condensation (BEC), condensed matter physics etc. Detailed study of QGP system is carried out and compared with lattice results. Further, as an application, our equation of state (EoS) of QGP is used to study compact stars like quark star.Comment: 9 pages, 2 figures, articl