Critical Slowing Down Along the Dynamic Phase Boundary in Ising Meanfield Dynamics

We studied the dynamical phase transition in kinetic Ising ferromagnets driven by oscillating magnetic field in meanfield approximation. The meanfield differential equation was solved by sixth order Runge-Kutta-Felberg method. The time averaged magnetisation plays the role of the dynamic order parameter. We studied the relaxation behaviour of the dynamic order parameter close to the transition temperature, which depends on the amplitude of the applied magnetic field. We observed the critical slowing down along the dynamic phase boundary. We proposed a power law divergence of the relaxation time and estimated the exponent. We also found its dependence on the field amplitude and compared the result with the exact value in limiting case.Comment: 6 pages Latex, 5 figure

Modelling and computer simulation of an insurance policy: A search for maximum profit

We have developed a model for a life insurance policy. In this model the net gain is calculated by computer simulation for a particular type of lifetime distribution function. We observed that the net gain becomes maximum for a particular value of upper age of last premium. This paper is dedicated to Professor Dietrich Stauffer on the occassion of his 60-th birthday.Comment: This paper is dedicated to Prof. D. Stauffer on the occassion of his 60th birthday. Int. J. Mod. Phys. C (2003) (in press

Dynamic Response of Ising System to a Pulsed Field

The dynamical response to a pulsed magnetic field has been studied here both using Monte Carlo simulation and by solving numerically the meanfield dynamical equation of motion for the Ising model. The ratio R_p of the response magnetisation half-width to the width of the external field pulse has been observed to diverge and pulse susceptibility \chi_p (ratio of the response magnetisation peak height and the pulse height) gives a peak near the order-disorder transition temperature T_c (for the unperturbed system). The Monte Carlo results for Ising system on square lattice show that R_p diverges at T_c, with the exponent $\nu z \cong 2.0$, while \chi_p shows a peak at $T_c^e$, which is a function of the field pulse width $\delta t$. A finite size (in time) scaling analysis shows that $T_c^e = T_c + C (\delta t)^{-1/x}$, with $x = \nu z \cong 2.0$. The meanfield results show that both the divergence of R and the peak in \chi_p occur at the meanfield transition temperature, while the peak height in $\chi_p \sim (\delta t)^y$, $y \cong 1$ for small values of $\delta t$. These results also compare well with an approximate analytical solution of the meanfield equation of motion.Comment: Revtex, Eight encapsulated postscript figures, submitted to Phys. Rev.

Nonequilibrium Phase Transition in the Kinetic Ising model: Critical Slowing Down and Specific-heat Singularity

The nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied both by Monte Carlo simulation and by solving numerically the mean field dynamic equation of motion for the average magnetisation. In both the cases, the Debye 'relaxation' behaviour of the dynamic order parameter has been observed and the 'relaxation time' is found to diverge near the dynamic transition point. The Debye relaxation of the dynamic order parameter and the power law divergence of the relaxation time have been obtained from a very approximate solution of the mean field dynamic equation. The temperature variation of appropiately defined 'specific-heat' is studied by Monte Carlo simulation near the transition point. The specific-heat has been observed to diverge near the dynamic transition point.Comment: Revtex, Five encapsulated postscript files, submitted to Phys. Rev.

Nonequilibrium phase transition in the kinetic Ising model: Is transition point the maximum lossy point ?

The nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied both by Monte Carlo simulation (in two dimension) and by solving the meanfield dynamical equation of motion for the average magnetization. The temperature variations of hysteretic loss (loop area) and the dynamic correlation have been studied near the transition point. The transition point has been identified as the minimum-correlation point. The hysteretic loss becomes maximum above the transition point. An analytical formulation has been developed to analyse the simulation results. A general relationship among hysteresis loop area, dynamic order parameter and dynamic correlation has also been developed.Comment: 8 pages Revtex and 4 Postscript figures; To appear in Phys. Rev.

Dynamic Magnetization-Reversal Transition in the Ising Model

We report the results of mean field and the Monte Carlo study of the dynamic magnetization-reversal transition in the Ising model, brought about by the application of an external field pulse applied in opposition to the existing order before the application of the pulse. The transition occurs at a temperature T below the static critical temperature T_c without any external field. The transition occurs when the system, perturbed by the external field pulse competing with the existing order, jumps from one minimum of free energy to the other after the withdrawal of the pulse. The parameters controlling the transition are the strength h_p and the duration Delta t of the pulse. In the mean field case, approximate analytical expression is obtained for the phase boundary which agrees well with that obtained numerically in the small Delta t and large T limit. The order parameter of the transition has been identified and is observed to vary continuously near the transition. The order parameter exponent beta was estimated both for the mean field (beta =1) and the Monte Carlo beta = 0.90 \pm 0.02 in two dimension) cases. The transition shows a "critical slowing-down" type behaviour near the phase boundary with diverging relaxation time. The divergence was found to be logarithmic in the mean field case and exponential in the Monte Carlo case. The finite size scaling technique was employed to estimate the correlation length exponent nu (= 1.5 \pm 0.3 in two dimension) in the Monte Carlo case.Comment: 13 pages, latex, 8 figure

Cofinite Graphs and their Profinite Completions

We generalize the idea of cofinite groups, due to B. Hartley. First we define cofinite spaces in general. Then, as a special situation, we study cofinite graphs and their uniform completions. The idea of constructing a cofinite graph starts with defining a uniform topological graph Gamma, in an appropriate fashion. We endow abstract graphs with uniformities corresponding to separating filter bases of equivalence relations with finitely many equivalence classes over Gamma. It is established that for any cofinite graph there exists a unique cofinite completion