Fermionic edge states and new physics

We investigate the properties of the Dirac operator on manifolds with boundaries in presence of the Atiyah-Patodi-Singer boundary condition. An exact counting of the number of edge states for boundaries with isometry of a sphere is given. We show that the problem with the above boundary condition can be mapped to one where the manifold is extended beyond the boundary and the boundary condition is replaced by a delta function potential of suitable strength. We also briefly highlight how the problem of the self-adjointness of the operators in the presence of moving boundaries can be simplified by suitable transformations which render the boundary fixed and modify the Hamiltonian and the boundary condition to reflect the effect of moving boundary.Comment: 24 pages, 3 figures. Title changed, additional material in the Introduction section, the Application section and in the Discussion section highlighting some recent work on singular potentials, several references added. Conclusions remain unchanged. Version matches the version to appear in PR

Communication Standards Adoption in Developing Economies: Issues and Options for India

Given the importance of communications in todays world, its spread in developing economies is critical for their development. Emergence of standards reduces market and technological uncertainty and lays the foundation for market creation and enhances the diffusion of communication technologies partly through the advantages associated with network and scale economies. Standardisation has also become important with the rise in cross-fertilisation between information technology (IT) and other technologies, especially in communications. Under these circumstances, strategic implications of IT standardisation are huge because standards can determine the growth potential of individual firms, affect the competitive advantage of nations and even development of technologies and their diffusion. Policies for standards adoption have been used world-wide to facilitate the diffusion of communications technologies, acquire a larger market share of the global telecom market, build technological capabilities. The paper reviews various approaches to communications standard adoption as well as the experiences of other countries. These approaches and experiences and the associated market and regulatory failures are evaluated in the context of the current Indian situation. This evaluation suggests that a standards neutral policy is desirable for India.

Tunable Band Gap in Graphene with a Non-Centrosymmetric Superlattice Potential

We show that, if graphene is subjected to the potential from an external superlattice, a band gap develops at the Dirac point provided the superlattice potential has broken inversion symmetry. As a numerical example, we calculate the band structure of graphene in the presence of an external potential due to periodically patterned gates arranged in a triangular graphene superlattice (TGS) with broken inversion symmetry, and find that a band gap is created at both the original and "second generation" Dirac point. The gap can be controlled, in principle, by changing the external potential and the lattice constant of the TGS.Comment: 6 figures, Phys. Rev. B 79, 20543

Resource utilization model for the algorithm to architecture mapping model

The analytical model for resource utilization and the variable node time and conditional node model for the enhanced ATAMM model for a real-time data flow architecture are presented in this research. The Algorithm To Architecture Mapping Model, ATAMM, is a Petri net based graph theoretic model developed at Old Dominion University, and is capable of modeling the execution of large-grained algorithms on a real-time data flow architecture. Using the resource utilization model, the resource envelope may be obtained directly from a given graph and, consequently, the maximum number of required resources may be evaluated. The node timing diagram for one iteration period may be obtained using the analytical resource envelope. The variable node time model, which describes the change in resource requirement for the execution of an algorithm under node time variation, is useful to expand the applicability of the ATAMM model to heterogeneous architectures. The model also describes a method of detecting the presence of resource limited mode and its subsequent prevention. Graphs with conditional nodes are shown to be reduced to equivalent graphs with time varying nodes and, subsequently, may be analyzed using the variable node time model to determine resource requirements. Case studies are performed on three graphs for the illustration of applicability of the analytical theories

Scaling laws in spherical shell dynamos with free-slip boundaries

Numerical simulations of convection driven rotating spherical shell dynamos have often been performed with rigid boundary conditions, as is appropriate for the metallic cores of terrestrial planets. Free-slip boundaries are more appropriate for dynamos in other astrophysical objects, such as gas-giants or stars. Using a set of 57 direct numerical simulations, we investigate the effect of free-slip boundary conditions on the scaling properties of heat flow, flow velocity and magnetic field strength and compare it with earlier results for rigid boundaries. We find that the nature of the mechanical boundary condition has only a minor influence on the scaling laws. We also find that although dipolar and multipolar dynamos exhibit approximately the same scaling exponents, there is an offset in the scaling pre-factors for velocity and magnetic field strength. We argue that the offset can be attributed to the differences in the zonal flow contribution between dipolar and multipolar dynamos.Comment: 10 pages, 9 figures, 1 table. To appear in ICARU

Novel black hole bound states and entropy

We solve for the spectrum of the Laplacian as a Hamiltonian on $\mathbb{R}^{2}-\mathbb{D}$ and in $\mathbb{R}^{3}-\mathbb{B}$. A self-adjointness analysis with $\partial\mathbb{D}$ and $\partial\mathbb{B}$ as the boundary for the two cases shows that a general class of boundary conditions for which the Hamiltonian operator is essentially self-adjoint are of the mixed (Robin) type. With this class of boundary conditions we obtain "bound state" solutions for the Schroedinger equation. Interestingly, these solutions are all localized near the boundary. We further show that the number of bound states is finite and is in fact proportional to the perimeter or area of the removed \emph{disc} or \emph{ball}. We then argue that similar considerations should hold for static black hole backgrounds with the horizon treated as the boundary.Comment: 13 pages, 3 figures, approximate formula for energy spectrum added at the end of section 2.1 along with additional minor changes to comply with the version accepted in PR

Formation of starspots in self-consistent global dynamo models: Polar spots on cool stars

Observations of cool stars reveal dark spot-like features on their surfaces. Compared to sunspots, starspots can be bigger or cover a larger fraction of the stellar surface. While sunspots appear only at low latitudes, starspots are also found in polar regions, in particular on rapidly rotating stars. Sunspots are believed to result from the eruption of magnetic flux-tubes rising from the deep interior of the Sun. The strong magnetic field locally reduces convective heat transport to the solar surface. Such flux-tube models have also been invoked to explain starspot properties. However, these models use several simplifications and so far the generation of either sunspots or starspots has not been demonstrated in a self-consistent simulation of stellar magnetic convection. Here we show that direct numerical simulations of a distributed dynamo operating in a density-stratified rotating spherical shell can spontaneously generate cool spots. Convection in the interior of the model produces a large scale magnetic field which interacts with near surface granular convection leading to strong concentrations of magnetic flux and formation of starspots. Prerequisites for the formation of sizeable high-latitude spots in the model are sufficiently strong density stratification and rapid rotation. Our model presents an alternate mechanism for starspot formation by distributed dynamo action.Comment: 14 pages; Important additions in version 2; To appear in A&

The Cluster Multipole Algorithm for Far-Field Computations

Computer simulations of N-body systems are beneficial to study the overall behavior of a number of physical systems in fields such as astrophysics, molecular dynamics, and computational fluid dynamics. A new approach for computer simulations of N-body systems is proposed in this research. The new algorithm is called the Cluster Multipole Algorithm (CMA). The goals of the new algorithm are to improve the applicability to non-point sources and to provide more control on the accuracy over current algorithms. The algorithm is targeted to applications that do not require rebuilding the data structure about the system every time step due to current limitations in the construction of the data structure. Examples of slowly changing systems can be found in molecular dynamics, capacitance, and computational fluid dynamics simulations. As the data structure development is improved, the new algorithm will be applicable to a wider range of applications. The CMA exhibits the flexibility of both Appel\u27s algorithm and the Fast Multipole Method (FMM) without sacrificing the order of computation (O(N)) for well structured clusters. The CMA provides more control on the accuracy of computations as compared to both the FMM and Appel\u27s algorithm resulting in enhanced performance. A set of requirements are imposed on the data structures which are applicable, to maintain O(N) computation. However, the algorithm is capable of handling a wide range of data structures beyond the FMM