The vortex dynamics and the specific heat of a type II superconducting system with quasi-periodic geometry is studied theoretically for different values of interaction parameters using the numerical simulation technique, where the vortex-vortex inter
action potential is considered in the form of the modified Bessels function of first kind. The dynamics of the system is analysed by phase space trajectories of the vortex for both high and low values as well as for both high and low mismatch of vortex-vortex and vortex-pinning interaction parameters. The specific heat variation with temperature is analysed statistically for different values of interaction parameters. It is observed that for low values and lower mismatch of interaction parameters, the system is highly chaotic and shows a bifurcation pattern similar to Hopf bifurcation. The specific heat also shows a highly divergent character in this situation. However for high values and higher mismatch, the superconducting system tends to be a very regular one. The trajectory of the vortices will also be very stable in this situation. Similar situations are also observed respectively for low and high values of the quasi-periodic parameter.
We have investigated some features of the density and arrival time distributions of Cherenkov photons in extensive air showers using the CORSIKA simulation package. The main thrust of this study is to see the effect of hadronic interaction models on
the production pattern of Cherenkov photons with respect to distance from the shower core. Such studies are very important in ground based $gamma$-ray astronomy for an effective rejection of huge cosmic ray background, where the atmospheric Cherenkov technique is being used extensively within the energy range of some hundred GeV to few TeV. We have found that for all primary particles, the density distribution patterns of Cherenkov photons follow the negative exponential function with different coefficients and slopes depending on the type of primary particle, its energy and the type of interaction model combinations. Whereas the arrival time distribution patterns of Cherenkov photons follow the function of the form $t (r) = t_{0}e^{Gamma/r^{lambda}}$, with different values of the function parameters. There is no significant effect of hadronic interaction model combinations on the density and arrival time distributions for the $gamma$-ray primaries. However, for the hadronic showers, the effects of the model combinations are significant under different conditions.
We investigate the formation of caustics in Dirac-Born-Infeld type scalar field systems for generic classes of potentials, viz., massive rolling scalar with potential, $V(phi)=V_0e^{pm frac{1}{2} M^2 phi^2}$ and inverse power-law potentials with $V(p
hi)=V_0/phi^n,~0<n<2$. We find that in the case oftexttt{} exponentially decreasing rolling massive scalar field potential, there are multi-valued regions and regions of likely to be caustics in the field configuration. However there are no caustics in the case of exponentially increasing potential. We show that the formation of caustics is inevitable for the inverse power-law potentials under consideration in Minkowski space time whereas caustics do not form in this case in the FRW universe.
