The effect of laser polarization and focusing is theoretically studied on the final energy gain of a particle in the Auto-resonant acceleration scheme using a finite duration laser pulse with Gaussian shaped temporal envelope. The exact expressions for dynamical variables viz. position, momentum, and energy are obtained by analytically solving the relativistic equation of motion describing particle dynamics in the combined field of an elliptically polarized finite duration pulse and homogeneous static axial magnetic field. From the solutions, it is shown that for a given set of laser parameters viz. intensity and pulse length along with static magnetic field, the energy gain by a positively charged particle is maximum for a right circularly polarized laser pulse. Further, a new scheme is proposed for particle acceleration by subjecting it to the combined field of a focused finite duration laser pulse and static axial magnetic field. In this scheme, the particle is initially accelerated by the focused laser field, which drives the non-resonant particle to second stage of acceleration by cyclotron Auto-resonance. The new scheme is found to be efficient over two individual schemes, i.e., auto-resonant acceleration and direct acceleration by focused laser field, as significant particle acceleration can be achieved at one order lesser values of static axial magnetic field and laser intensity.

The effects of radiation reaction force on laser driven auto-resonant particle acceleration scheme are studied using Landau-Lifshitz equation of motion. These studies are carried out for both linear as well as circularly polarized laser fields in the presence of static axial magnetic field. From the parametric study, a radiation reaction dominated region has been identified in which the particle dynamics is greatly effected by this force. In the radiation reaction dominated region the two significant effects on particle dynamics are seen viz., (1) saturation in energy gain by the initially resonant particle, (2) net energy gain by a initially non-resonant particle which is caused due to resonance broadening. It has been further shown that with the optimum choice of parameters this scheme can be efficiently used to produce electrons with energies in the range of hundreds of TeV. The quantum corrections to the Landu-Lifshitz equation of motion have also been taken into account. The difference in the energy gain estimates of the particle by the quantum corrected and classical Landu-Lifshitz equation are found to be insignificant for the present day as well as upcoming laser facilities.

Dynamics of a charged particle is studied in the field of a relativistically intense linearly polarized finite duration laser pulse in the presence of a static axial magnetic field. For a finite duration laser pulse whose temporal shape is defined by Gaussian profile, exact analytical expressions are derived for the particle trajectory, momentum, and energy as function of laser phase. From the solutions, it is shown that, unlike for the monochromatic plane wave case, resonant phase locking time between the particle and laser pulse is finite. The net energy transferred to the particle does not increase monotonically but tends to saturate. It is further shown that appropriate tuning of cyclotron frequency of the particle with the characteristic frequency in the pulse spectrum can lead to the generation of accelerated particles with variable energies in MeV-TeV range.

In the present work, the effect of personal behavior induced preventive measures is studied on the spread of epidemics over scale free networks that are characterized by the differential rate of disease transmission. The role of personal behavior induced preventive measures is parameterized in terms of variable λ, which modulates the number of concurrent contacts a node makes with the fraction of its neighboring nodes. The dynamics of the disease is described by a non-linear Susceptible Infected Susceptible model based upon the discrete time Markov Chain method. The network mean field approach is generalized to account for the effect of non-linear coupling between the aforementioned factors on the collective dynamics of nodes. The upper bound estimates of the disease outbreak threshold obtained from the mean field theory are found to be in good agreement with the corresponding non-linear stochastic model. From the results of parametric study, it is shown that the epidemic size has inverse dependence on the preventive measures (λ). It has also been shown that the increase in the average degree of the nodes lowers the time of spread and enhances the size of epidemics.

A non-linear stochastic model is presented to study the effect of time variation of transmission rates on the co-evolution of epidemics and its corresponding awareness over a two layered multiplex network. In the model, the infection transmission rate of a given node in the epidemic layer depends upon its awareness probability in the awareness layer. Similarly, the infection information transmission rate of a node in the awareness layer depends upon its infection probability in the epidemic layer. The spread of disease resulting from physical contacts is described in terms of a SIS (Susceptible Infected Susceptible) process over the epidemic layer and the spread of information about the disease outbreak is described in terms of an UAU (Unaware Aware Unaware) process over the virtual interaction mediated awareness layer. The time variation of the transmission rates and the resulting co-evolution of these mutually competing processes is studied in terms of a network topology dependent parameter (α). Using a second order linear theory it is shown that in the continuous time limit, the co-evolution of these processes can be described in terms of damped and driven harmonic oscillator equations. From the results of a Monte-Carlo simulation, it is shown that for a suitable choice of the parameter(α), the two processes can either exhibit sustained oscillatory or damped dynamics. The damped dynamics corresponds to the endemic state. Further, for the case of an endemic state it is shown that inclusion of the awareness layer significantly lowers the disease transmission rate and reduces the size of the epidemic. The endemic state infection probability of a given node corresponding to the damped dynamics is found to have a dependence upon both the transmission rates as well as on the absolute intra-layer and relative inter-layer degrees of the individual nodes.