A Unified Treatment of the Characters of SU(2) and SU(1,1)

The character problems of SU(2) and SU(1,1) are reexamined from the standpoint of a physicist by employing the Hilbert space method which is shown to yield a completely unified treatment for SU(2) and the discrete series of representations of SU(1,1). For both the groups the problem is reduced to the evaluation of an integral which is invariant under rotation for SU(2) and Lorentz transformation for SU(1,1). The integrals are accordingly evaluated by applying a rotation to a unit position vector in SU(2) and a Lorentz transformation to a unit SO(2,1) vector which is time-like for the elliptic elements and space-like for the hyperbolic elements in SU(1,1). The details of the procedure for the principal series of representations of SU(1,1) differ substantially from those of the discrete series.Comment: 31 pages, RevTeX, typos corrected. To be published in Journal of Mathematical Physic

Modified Bethe-Weizsacker mass formula with isotonic shift and new driplines

Nuclear masses are calculated using the modified Bethe-Weizsacker mass formula in which the isotonic shifts have been incorporated. The results are compared with the improved liquid drop model with isotonic shift. Mass excesses predicted by this method compares well with the microscopic-macroscopic model while being much more simple. The neutron and proton drip lines have been predicted using this modified Bethe-Weizsacker mass formula with isotonic shifts.Comment: 9 pages including 2 figure

Absorbing Phase Transition in a Four State Predator Prey Model in One Dimension

The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator, or occupied by a single prey, or by both. Along with the pairwise death of predators and growth of preys, we introduce an interaction where the predators can eat one of the neighboring prey and reproduce a new predator there instantly. The model shows a non-equilibrium phase transition into a unusual absorbing state where predators are absent and the lattice is fully occupied by preys. The critical exponents of the system are found to be different from that of the Directed Percolation universality class and they are robust against addition of explicit diffusion.Comment: 10 pages, 6 figures, to appear in JSTA

Symmetries and novel universal properties of turbulent hydrodynamics in a symmetric binary fluid mixture

We elucidate the universal properties of the nonequilibrium steady states (NESS) in a driven symmetric binary fluid mixture, an example of active advection, in its miscible phase. We use the symmetries of the equations of motion to establish the appropriate form of the structure functions which characterise the statistical properties of the NESS of a driven symmetric binary fluid mixture. We elucidate the universal properties described by the scaling exponents and the amplitude ratios. Our results suggest that these exponents and amplitude ratios vary continuously with the degree of crosscorrelations between the velocity and the gradient of the concentration fields. Furthermore, we demonstrate, in agreement with Celani et al, Phys. Rev. Lett., 89, 234502 (2002, that the conventional structure functions as used in passive scalar turbulence studies exhibit only simple scaling in the problem of symmetric binary fluid mixture even in the weak concentration limit. We also discuss possible experimental verifications of our results.Comment: To appear in JSTAT (letters) (2005

Influence of Quench Rates on the Properties of Rapidly Solidified FeNbCuSiB Alloy

FeNbCuSiB based materials were produced in the form of ribbons by rapid solidification techniques. The crystallization, magnetic, mechanical and corrosion behaviour were studied for the prepared materials as a function of quenching rate from liquid to the solid state. Higher quench rates produced a more amorphous structure exhibiting superior soft magnetic properties with improved corrosion resistance

Theory of the Normal/Superfluid interface in population imbalanced Fermi gases

We present a series of theoretical studies of the boundary between a superfluid and normal region in a partially polarized gas of strongly interacting fermions. We present mean-field estimates of the surface energy in this boundary as a function of temperature and scattering length. We discuss the structure of the domain wall, and use a previously introduced phenomonological model to study its influence on experimental observables. Our microscopic mean-field calculations are not consistent with the magnitude of the surface tension found from our phenomonological modelling of data from the Rice experiments. We conclude that one must search for novel mechanisms to explain the experiments.Comment: 15 pages, 9 figures (13 subfigures) -- v2: minor change

Two-dimensional random walk in a bounded domain

In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce regular patterns. Our numerical calculations suggest that the cumulative probability distribution function of the returning walkers along the base curve is a Devil's staircase, which can be explained from the mapping of these walks to a non-linear stochastic map. The non-trivial probability distribution function(PDF) is a universal feature of CCRW characterized by the fractal dimension d=1.75(0) of the PDF bounding curve.Comment: 4 pages, 7 eps figures, revtex

Neutron and proton drip lines using the modified Bethe-Weizsacker mass formula

Proton and neutron separation energies have been calculated using the extended Bethe-Weizsacker mass formula. This modified Bethe-Weizsacker mass formula describes minutely the positions of all the old and the new magic numbers. It accounts for the disappearance of some traditional magic numbers for neutrons and provides extra stability for some new neutron numbers. The neutron and proton drip lines have been predicted using this extended Bethe-Weizsacker mass formula. The implications of the proton drip line on the astrophysical rp-process and of the neutron drip line on the astrophysical r-process have been discussed.Comment: 5 pages, 2 figure

Statistical properties of driven Magnetohydrodynamic turbulence in three dimensions: Novel universality

We analyse the universal properties of nonequilibrium steady states of driven Magnetohydrodynamic (MHD) turbulence in three dimensions (3d). We elucidate the dependence of various phenomenologically important dimensionless constants on the symmetries of the two-point correlation functions. We, for the first time, also suggest the intriguing possibility of multiscaling universality class varying continuously with certain dimensionless parameters. The experimental and theoretical implications of our results are discussed.Comment: To appear in Europhys. Lett. (2004