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

Matrix Model of QCD: Edge Localized Glue Balls and Phase Transitions

In a matrix model of pure $SU(2)$ Yang-Mills theory, boundaries emerge in the space of $\textrm{Mat}_{3}(\mathbb{R})$ and the Hamiltonian requires boundary conditions. We show the existence of edge localized glueball states which can have negative energies. These edge levels can be lifted to positive energies if the gluons acquire a London-like mass. This suggests a new phase of QCD with an incompressible bulk.Comment: 18 pages, 5 figures, minor reviso

Effective grain surface area in the formation of molecular hydrogen in interstellar clouds

In the interstellar clouds, molecular hydrogens are formed from atomic hydrogen on grain surfaces. An atomic hydrogen hops around till it finds another one with which it combines. This necessarily implies that the average recombination time, or equivalently, the effective grain surface area depends on the relative numbers of atomic hydrogen influx rate and the number of sites on the grain. Our aim is to discover this dependency. We perform a numerical simulation to study the recombination of hydrogen on grain surfaces in a variety of cloud conditions. We use a square lattice (with a periodic boundary condition) of various sizes on two types of grains, namely, amorphous carbon and olivine. We find that the steady state results of our simulation match very well with those obtained from a simpler analytical consideration provided the `effective' grain surface area is written as $\sim S^{\alpha}$, where, $S$ is the actual physical grain area and $\alpha$ is a function of the flux of atomic hydrogen which is determined from our simulation. We carry out the simulation for various astrophysically relevant accretion rates. For high accretion rates, small grains tend to become partly saturated with $H$ and $H_2$ and the subsequent accretion will be partly inhibited. For very low accretion rates, the number of sites to be swept before a molecular hydrogen can form is too large compared to the actual number of sites on the grain, implying that $\alpha$ is greater than unity.Comment: 8 pages, 5 figures in eps forma

Large-Signal Simulation of 94 GHz Pulsed Silicon DDR IMPATTs Including the Temperature Transient Effect

In this paper large-signal modeling and simulation has been carried to study the frequency chirping due to temperature transients and the large-signal power and efficiency of pulsed silicon Double-Drift Region (DDR) Impact Avalanche Transit Time (IMPATT) device operating at 94 GHz. A large-signal simulation method based on non-sinusoidal voltage excitation incorporating the transient thermal effect has been developed by the authors. Results show that the device is capable of delivering a peak pulsed power output of 17.5 W with 12.8% efficiency when the voltage modulation is 60%. The maximum junction temperature rise is 350.2 K for a peak pulsed bias current of 6.79 A with 100 ns pulsewidth and 0.5 percent duty cycle; whereas the chirp bandwidth is 8.3 GHz

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

Fluctuation Cumulant Behavior for the Field-Pulse Induced Magnetisation-Reversal Transition in Ising Models

The universality class of the dynamic magnetisation-reversal transition, induced by a competing field pulse, in an Ising model on a square lattice, below its static ordering temperature, is studied here using Monte Carlo simulations. Fourth order cumulant of the order parameter distribution is studied for different system sizes around the phase boundary region. The crossing point of the cumulant (for different system sizes) gives the transition point and the value of the cumulant at the transition point indicates the universality class of the transition. The cumulant value at the crossing point for low temperature and pulse width range is observed to be significantly less than that for the static transition in the same two-dimensional Ising model. The finite size scaling behaviour in this range also indicates a higher correlation length exponent value. For higher temperature and pulse width range, the transition seems to fall in a mean-field like universality class.Comment: 5 pages, 8 eps figures, thoroughly revised manuscript with new figures, accepted in Phys. Rev. E (2003

Dynamic Phase Transition in a Time-Dependent Ginzburg-Landau Model in an Oscillating Field

The Ginzburg-Landau model below its critical temperature in a temporally oscillating external field is studied both theoretically and numerically. As the frequency or the amplitude of the external force is changed, a nonequilibrium phase transition is observed. This transition separates spatially uniform, symmetry-restoring oscillations from symmetry-breaking oscillations. Near the transition a perturbation theory is developed, and a switching phenomenon is found in the symmetry-broken phase. Our results confirm the equivalence of the present transition to that found in Monte Carlo simulations of kinetic Ising systems in oscillating fields, demonstrating that the nonequilibrium phase transition in both cases belongs to the universality class of the equilibrium Ising model in zero field. This conclusion is in agreement with symmetry arguments [G. Grinstein, C. Jayaprakash, and Y. He, Phys. Rev. Lett. 55, 2527 (1985)] and recent numerical results [G. Korniss, C.J. White, P. A. Rikvold, and M. A. Novotny, Phys. Rev. E (submitted)]. Furthermore, a theoretical result for the structure function of the local magnetization with thermal noise, based on the Ornstein-Zernike approximation, agrees well with numerical results in one dimension.Comment: 16 pp. RevTex, 9 embedded ps figure