Domain-wall creep driven by spin torque in nanoscale ferromagnetic cylinders

We have explored the mechanism of spin-torque-driven domain-wall (DW) depinning in cylindrical nanowires of nickel using noise in electrical resistance. We find that the spectral slope of noise is a sensitive probe to the DW kinetics that reveals a creeplike behavior of the DWs at the depinning threshold, and diffusive DW motion at higher spin-torque drive. Different regimes of DW kinetics were characterized by universal kinetic exponents.

A System-C based Micro architectural Exploration Framework for Latency, Power and Performance Trade-offs of On-Chip Interconnection

We describe a System-C based framework we are developing, to explore the impact of various architectural and microarchitectural level parameters of the on-chip interconnection network elements on its power and performance. The framework enables one to choose from a variety of architectural options like topology, routing policy, etc., as well as allows experimentation with various microarchitectural options for the individual links like length, wire width, pitch, pipelining, supply voltage and frequency. The framework also supports a flexible traffic generation and communication model. We provide preliminary results of using this framework to study the power, latency and throughput of a 4x4 multi-core processing array using mesh, torus and folded torus, for two different communication patterns of dense and sparse linear algebra. The traffic consists of both Request-Response messages (mimicing cache accesses)and One-Way messages. We find that the average latency can be reduced by increasing the pipeline depth, as it enables higher link frequencies. We also find that there exists an optimum degree of pipelining which minimizes energy-delay product.

Combinatorial Representations of Block Codes

We look at graphical descriptions of block codes known as trellises, which illustrate connections between algebra and graph theory, and can be used to develop powerful decoding algorithms. Trellis sizes for linear block codes are known to grow exponentially with the code parameters. Of considerable interest to coding theorists therefore, are more compact descriptions called tail-biting trellises which in some cases can be much smaller than any conventional trellis for the same code . We derive some interesting properties of tail-biting trellises and present a new decoding algorithm.

Classical screw theory: A fresh look using dual eigenvalue approach

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

On Pushing Multilingual Query Operators into Relational Engines

To effectively support today’s global economy, database systems need to manage data in multiple languages simultaneously. While current database systems do support the storage and management of multilingual data, they are not capable of querying across different natural languages. To address this lacuna, we have recently proposed two cross-lingual functionalities, LexEQUAL[13] and SemEQUAL[14], for matching multilingual names and concepts, respectively. In this paper, we investigate the native implementation of these multilingual functionalities as first-class operators on relational engines. Specifically, we propose a new multilingual storage datatype, and an associated algebra of the multilingual operators on this datatype. These components have been successfully implemented in the PostgreSQL database system, including integration of the algebra with the query optimizer and inclusion of a metric index in the access layer. Our experiments demonstrate that the performance of the native implementation is up to two orders-of-magnitude faster than the corresponding outsidethe- server implementation. Further, these multilingual additions do not adversely impact the existing functionality and performance. To the best of our knowledge, our prototype represents the first practical implementation of a crosslingual database query engine.

Ferromagnetic transition and specific heat of Pr(0.6)Sr(0.4)MnO(3)

The critical properties of orthorhombic Pr(0.6)Sr(0.4)MnO(3) single crystals were investigated by a series of static magnetization measurements along the three different crystallographic axes as well as by specific heat measurements. A careful range-of-fitting-analysis of the magnetization and susceptibility data obtained from the modified Arrott plots shows that Pr(0.6)Sr(0.4)MnO(3) has a very narrow critical regime. Nevertheless, the system belongs to the three-dimensional (3D) Heisenberg universality class with short-range exchange. The critical exponents obey Widom scaling and are in excellent agreement with the single scaling equation of state M(H,epsilon) = vertical bar epsilon vertical bar(beta) f(+/-)(H/vertical bar epsilon vertical bar((beta+gamma)); with f(+) for T > T(c) and f(-) for T < T(c). A detailed analysis of the specific heat that account for all relevant contributions allows us to extract and analyze the contribution related to the magnetic phase transition. The specific heat indicates the presence of a linear electronic term at low temperatures and a prominent contribution from crystal field excitations of Pr. A comparison with data from literature for PrMnO(3) shows that a Pr-Mn magnetic exchange is responsible for a sizable shift in the lowest lying excitation.

Dynamic Multiscaling in Two-Dimensional Fluid Turbulence

We obtain, by extensive direct numerical simulations, time-dependent and equal-time structure functions for the vorticity, in both quasi-Lagrangian and Eulerian frames, for the direct-cascade regime in two-dimensional fluid turbulence with air-drag-induced friction. We show that different ways of extracting time scales from these time-dependent structure functions lead to different dynamic-multiscaling exponents, which are related to equal-time multiscaling exponents by different classes of bridge relations; for a representative value of the friction we verify that, given our error bars, these bridge relations hold.

A simple numerical method for three-dimensional analysis of simple expansion chamber mufflers of rectangular as well as circular cross-section with a stationary medium

Three-dimensional effects are a primary source of discrepancy between the measured values of automotive muffler performance and those predicted by the plane wave theory at higher frequencies. The basically exact method of (truncated) eigenfunction expansions for simple expansion chambers involves very complicated algebra, and the numerical finite element method requires large computation time and core storage. A simple numerical method is presented in this paper. It makes use of compatibility conditions for acoustic pressure and particle velocity at a number of equally spaced points in the planes of the junctions (or area discontinuities) to generate the required number of algebraic equations for evaluation of the relative amplitudes of the various modes (eigenfunctions), the total number of which is proportional to the area ratio. The method is demonstrated for evaluation of the four-pole parameters of rigid-walled, simple expansion chambers of rectangular as well as circular cross-section for the case of a stationary medium. Computed values of transmission loss are compared with those computed by means of the plane wave theory, in order to highlight the onset (cutting-on) of various higher order modes and the effect thereof on transmission loss of the muffler. These are also compared with predictions of the finite element methods (FEM) and the exact methods involving eigenfunction expansions, in order to demonstrate the accuracy of the simple method presented here.

Design space exploration of systolic realization of QR factorization on a runtime reconfigurable platform

In the world of high performance computing huge efforts have been put to accelerate Numerical Linear Algebra (NLA) kernels like QR Decomposition (QRD) with the added advantage of reconfigurability and scalability. While popular custom hardware solution in form of systolic arrays can deliver high performance, they are not scalable, and hence not commercially viable. In this paper, we show how systolic solutions of QRD can be realized efficiently on REDEFINE, a scalable runtime reconfigurable hardware platform. We propose various enhancements to REDEFINE to meet the custom need of accelerating NLA kernels. We further do the design space exploration of the proposed solution for any arbitrary application of size n × n. We determine the right size of the sub-array in accordance with the optimal pipeline depth of the core execution units and the number of such units to be used per sub-array.

Distributed Function Computation over Fields and Rings via Linear Compression of Sources

The setting considered in this paper is one of distributed function computation. More specifically, there is a collection of N sources possessing correlated information and a destination that would like to acquire a specific linear combination of the N sources. We address both the case when the common alphabet of the sources is a finite field and the case when it is a finite, commutative principal ideal ring with identity. The goal is to minimize the total amount of information needed to be transmitted by the N sources while enabling reliable recovery at the destination of the linear combination sought. One means of achieving this goal is for each of the sources to compress all the information it possesses and transmit this to the receiver. The Slepian-Wolf theorem of information theory governs the minimum rate at which each source must transmit while enabling all data to be reliably recovered at the receiver. However, recovering all the data at the destination is often wasteful of resources since the destination is only interested in computing a specific linear combination. An alternative explored here is one in which each source is compressed using a common linear mapping and then transmitted to the destination which then proceeds to use linearity to directly recover the needed linear combination. The article is part review and presents in part, new results. The portion of the paper that deals with finite fields is previously known material, while that dealing with rings is mostly new.Attempting to find the best linear map that will enable function computation forces us to consider the linear compression of source. While in the finite field case, it is known that a source can be linearly compressed down to its entropy, it turns out that the same does not hold in the case of rings. An explanation for this curious interplay between algebra and information theory is also provided in this paper.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation eta and eta + d eta, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice.We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation η and η + dη, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary

Griffiths phase-like behavior and spin-phonon coupling in double perovskite Tb(2)NiMnO(6)

The Griffiths phase-like features and the spin-phonon coupling effects observed in Tb(2)NiMnO(6) are reported. The double perovskite compound crystallizes in monoclinic P2(1)/n space group and exhibits a magnetic phase transition at T(c) similar to 111 K as an abrupt change in magnetization. A negative deviation from ideal Curie-Weiss law exhibited by 1/chi(T) curves and less-than-unity susceptibility exponents from the power-law analysis of inverse susceptibility are reminiscent of Griffiths phase-like features. Arrott plots derived from magnetization isotherms support the inhomogeneous nature of magnetism in this material. The observed effects originate from antiferromagnetic interactions that arise from inherent disorder in the system. Raman scattering experiments display no magnetic-order-induced phonon renormalization below Tc in Tb(2)NiMnO(6), which is different from the results observed in other double perovskites and is correlated to the smaller size of the rare earth. The temperature evolution of full-width-at-half-maximum for the stretching mode at 645 cm(-1) presents an anomaly that coincides with the magnetic transition temperature and signals a close connection between magnetism and lattice in this material. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3671674]

Noncommutative vortices and instantons from generalized Bose operators

Generalized Bose operators correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the generalized Bose operator. When used in conjunction with the noncommutative ADHM construction, we find that these new instantons are in general not unitarily equivalent to the ones currently known in literature.

A computational procedure to generate difference equations from differential equations

In this paper we have developed methods to compute maps from differential equations. We take two examples. First is the case of the harmonic oscillator and the second is the case of Duffing's equation. First we convert these equations to a canonical form. This is slightly nontrivial for the Duffing's equation. Then we show a method to extend these differential equations. In the second case, symbolic algebra needs to be used. Once the extensions are accomplished, various maps are generated. The Poincare sections are seen as a special case of such generated maps. Other applications are also discussed.