Number of adaptive steps to a local fitness peak

We consider a population of genotype sequences evolving on a rugged fitness landscape with many local fitness peaks. The population walks uphill until it encounters a local fitness maximum. We find that the statistical properties of the walk length depend on whether the underlying fitness distribution has a finite mean. If the mean is finite, all the walk length cumulants grow with the sequence length but approach a constant otherwise. Experimental implications of our analytical results are also discussed

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

Relevance of inter-composite fermion interaction to the edge Tomonaga-Luttinger liquid

It is shown that Wen's effective theory correctly describes the Tomonaga-Luttinger liquid at the edge of a system of non-interacting composite fermions. However, the weak residual interaction between composite fermions appears to be a relevant perturbation. The filling factor dependence of the Tomonaga-Luttinger parameter is estimated for interacting composite fermions in a microscopic approach and satisfactory agreement with experiment is achieved. It is suggested that the electron field operator may not have a simple representation in the effective one dimensional theory.Comment: 5 pages; accepted in Phys. Rev. Let

Laser heterodyne system for obtaining height profiles of minor species in the atmosphere

An infrared laser heterodyne system for obtaining height profiles of minor constituents of the atmosphere was developed and erected. A brief discription of the system is given. The system consists of a tunable CO2 waveguide laser in the 9 to 11 micrometer band, that is used as a local oscillator and a heliostat that follows the sun and brings in solar radiation, that is mixed with the laser beam in a high speed liquid nitrogen cooled mercury cadmium telluride detector. The detected signal is analysed in a RF spectrum analyser that allows tracing absorption line profiles. Absorption lines of a number of minor constituents in the troposphere and stratosphere, such as O3, NH3, H2O, SO2, ClO, N2O, are in the 9 to 11 micrometer band and overlap with that of CO2 laser range. The experimental system has been made operational and trial observations taken. Current measurements are limited to ozone height profiles. Results are presented

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

Static and Dynamic Properties of Type-II Composite Fermion Wigner Crystals

The Wigner crystal of composite fermions is a strongly correlated state of complex emergent particles, and therefore its unambiguous detection would be of significant importance. Recent observation of optical resonances in the vicinity of filling factor {\nu} = 1/3 has been interpreted as evidence for a pinned Wigner crystal of composite fermions [Zhu et al., Phys. Rev. Lett. 105, 126803 (2010)]. We evaluate in a microscopic theory the shear modulus and the magnetophonon and magnetoplasmon dispersions of the composite fermion Wigner crystal in the vicinity of filling factors 1/3, 2/5, and 3/7. We determine the region of stability of the crystal phase, and also relate the frequency of its pinning mode to that of the corresponding electron crystal near integer fillings. These results are in good semiquantitative agreement with experiment, and therefore support the identification of the optical resonance as the pinning mode of the composite fermions Wigner crystal. Our calculations also bring out certain puzzling features, such as a relatively small melting temperature for the composite fermion Wigner crystal, and also suggest a higher asymmetry between Wigner crystals of composite fermion particles and holes than that observed experimentally.Comment: Composite Fermion Wigner Crystal; 14 pages, 9 figure

Decision Sheet and Learning Diary: New Tools for Improved Learning Through the Case Method

Of the three phases of learning through the case method, instructors have focused on the in-class phase in training of both teachers and participants. The other two phases, pre-class preparation and post class-reflection, have not received much attention leading to lack of exploitation of the full learning potential from the method. This paper shares continued efforts to conceptualize and develop two tools, decision sheet and learning diary, to strengthen the two phases. These were designed and tested in three executive development programmes. The results and our reflections suggest that the tools enhance the process of learning and the learning itself.