Eigenvalue spectrum for single particle in a spheroidal cavity: A Semiclassical approach

Following the semiclassical formalism of Strutinsky et al., we have obtained the complete eigenvalue spectrum for a particle enclosed in an infinitely high spheroidal cavity. Our spheroidal trace formula also reproduces the results of a spherical billiard in the limit $\eta\to1.0$. Inclusion of repetition of each family of the orbits with reference to the largest one significantly improves the eigenvalues of sphere and an exact comparison with the quantum mechanical results is observed upto the second decimal place for $kR_{0}\geq{7}$. The contributions of the equatorial, the planar (in the axis of symmetry plane) and the non-planar(3-Dimensional) orbits are obtained from the same trace formula by using the appropriate conditions. The resulting eigenvalues compare very well with the quantum mechanical eigenvalues at normal deformation. It is interesting that the partial sum of equatorial orbits leads to eigenvalues with maximum angular momentum projection, while the summing of planar orbits leads to eigenvalues with $L_z=0$ except for L=1. The remaining quantum mechanical eigenvalues are observed to arise from the 3-dimensional(3D) orbits. Very few spurious eigenvalues arise in these partial sums. This result establishes the important role of 3D orbits even at normal deformations.Comment: 17 pages, 7 ps figure

Nonuniversal exponents in sandpiles with stochastic particle number transfer

We study fixed density sandpiles in which the number of particles transferred to a neighbor on relaxing an active site is determined stochastically by a parameter $p$. Using an argument, the critical density at which an active-absorbing transition occurs is found exactly. We study the critical behavior numerically and find that the exponents associated with both static and time-dependent quantities vary continuously with $p$.Comment: Some parts rewritten, results unchanged. To appear in Europhys. Let

Two-Proton Radioactivity with 2p halo in light mass nuclei A==18−-34

Two-proton radioactivity with 2p halo is reported theoretically in light mass nuclei A $=$ 18-34. We predict $^{19}$Mg, $^{22}$Si, $^{26}$S, $^{30}$Ar and $^{34}$Ca as promising candidates of ground state 2p-radioactivity with S$_{2p}$ $$ 0. Observation of extended tail of spatial charge density distribution, larger charge radius and study of proton single particle states, Fermi energy and the wave functions indicate 2p halo like structure which supports direct 2p emission. The Coulomb and centrifugal barriers in experimentally identified 2p unbound $^{22}$Si show a quasi-bound state that ensures enough life time for such experimental probes. Our predictions are in good accord with experimental and other theoretical data available so far.Comment: 5 Pages, 5 figure

Adaptation dynamics of the quasispecies model

We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local peaks separated by low fitness valleys. We mainly focus on the Eigen's model that describes the deterministic dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population forms a {\it quasispecies} which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on rugged fitness landscape follow a punctuated (or step-like) pattern in which a population jumps from a low fitness peak to a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum of the fitness landscape. We calculate exactly several properties of this dynamical process within a simplified version of the quasispecies model.Comment: Proceedings of Statphys conference at IIT Guwahati, to be published in Praman

Study of Low Energy Spin Rotons in the Fractional Quantum Hall Effect

Motivated by the discovery of extremely low energy collective modes in the fractional quantum Hall effect (Kang, Pinczuk {\em et al.}), with energies below the Zeeman energy, we study theoretically the spin reversed excitations for fractional quantum Hall states at $\nu=2/5$ and 3/7 and find qualitatively different behavior than for $\nu=1/3$. We find that a low-energy, charge-neutral "spin roton," associated with spin reversed excitations that involve a change in the composite-fermion Landau level index, has energy in reasonable agreement with experiment.Comment: Postscript figures included. Accepted in Phys. Rev. B (Rapid Communication

Synchronization in Networks of Identical Systems via Pinning: Application to Distributed Secondary Control of Microgrids

Motivated by the need for fast synchronized operation of power microgrids, we analyze the problem of single and multiple pinning in networked systems. We derive lower and upper bounds on the algebraic connectivity of the network with respect to the reference signal. These bounds are utilized to devise a suboptimal algorithm with polynomial complexity to find a suitable set of nodes to pin the network effectively and efficiently. The results are applied to secondary voltage pinning control design for a microgrid in islanded operation mode. Comparisons with existing single and multiple pinning strategies clearly demonstrates the efficacy of the obtained results.Comment: 11 pages, 9 figures, submitted to Transactions on Control Systems Technolog

Extreme value distributions for weakly correlated fitnesses in block model

We study the limit distribution of the largest fitness for two models of weakly correlated and identically distributed random fitnesses. The correlated fitness is given by a linear combination of a fixed number of independent random variables drawn from a common parent distribution. We find that for certain class of parent distributions, the extreme value distribution for correlated random variables can be related either to one of the known limit laws for independent variables or the parent distribution itself. For other cases, new limiting distributions appear. The conditions under which these results hold are identified.Comment: Expanded, added reference