Quantum phase analysis of 1D superconducting quantum dot lattice using extended Bose-Hubbard model

We have obtained the quantum phase diagram of a one-dimensional superconducting quantum dot lattice using the extended Bose-Hubbard model for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from the Mott insulating phase to the superconducting phase for integer band fillings of Cooper pairs. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, besides the charge density wave and superconducting phases for half-integer band fillings. We also predict that extended range interactions are necessary to obtain the correct phase boundary of a one-dimensional interacting Cooper system. We have used the density matrix renormalization group method and Abelian bosonization to study our system.

An algebraic formulation of static isotropy and design of statically isotropic 6-6 Stewart platform manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulators is identified analytically. We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration. (C) 2008 Elsevier Ltd. All rights reserved.

Single-resolution and multiresolution extended-Kalman-filter-based reconstruction approaches to optical refraction tomography

The problem of reconstruction of a refractive-index distribution (RID) in optical refraction tomography (ORT) with optical path-length difference (OPD) data is solved using two adaptive-estimation-based extended-Kalman-filter (EKF) approaches. First, a basic single-resolution EKF (SR-EKF) is applied to a state variable model describing the tomographic process, to estimate the RID of an optically transparent refracting object from noisy OPD data. The initialization of the biases and covariances corresponding to the state and measurement noise is discussed. The state and measurement noise biases and covariances are adaptively estimated. An EKF is then applied to the wavelet-transformed state variable model to yield a wavelet-based multiresolution EKF (MR-EKF) solution approach. To numerically validate the adaptive EKF approaches, we evaluate them with benchmark studies of standard stationary cases, where comparative results with commonly used efficient deterministic approaches can be obtained. Detailed reconstruction studies for the SR-EKF and two versions of the MR-EKF (with Haar and Daubechies-4 wavelets) compare well with those obtained from a typically used variant of the (deterministic) algebraic reconstruction technique, the average correction per projection method, thus establishing the capability of the EKF for ORT. To the best of our knowledge, the present work contains unique reconstruction studies encompassing the use of EKF for ORT in single-resolution and multiresolution formulations, and also in the use of adaptive estimation of the EKF's noise covariances. (C) 2010 Optical Society of America

Quench dynamics and defect production in the Kitaev and extended Kitaev models

We study quench dynamics and defect production in the Kitaev and the extended Kitaev models. For the Kitaev model in one dimension, we show that in the limit of slow quench rate, the defect density n∼1/√τ, where 1/τ is the quench rate. We also compute the defect correlation function by providing an exact calculation of all independent nonzero spin correlation functions of the model. In two dimensions, where the quench dynamics takes the system across a critical line, we elaborate on the results of earlier work [K. Sengupta, D. Sen, and S. Mondal, Phys. Rev. Lett. 100, 077204 (2008)] to discuss the unconventional scaling of the defect density with the quench rate. In this context, we outline a general proof that for a d-dimensional quantum model, where the quench takes the system through a d−m dimensional gapless (critical) surface characterized by correlation length exponent ν and dynamical critical exponent z, the defect density n∼1/τmν/(zν+1). We also discuss the variation of the shape and spatial extent of the defect correlation function with both the rate of quench and the model parameters and compute the entropy generated during such a quenching process. Finally, we study the defect scaling law, entropy generation and defect correlation function of the two-dimensional extended Kitaev model.

A combined extended and helical backbone for Boc-(Ala-Leu-Ac(7)c-)(2)-OMe

The structure of the peptide Boc-Ala-Leu-Ac(7)c-Ala-Leu-Ac(7)c-OMe (Ac(7)c,1-aminocycloheptane-1-carboxylic acid) is described in crystals. The presence of two Ac(7)c residues was expected to stabilize a 3(10)-helical fold. Contrary to expectation the structural analysis revealed an unfolded amino terminus, with Ala(1) adopting an extended beta-conformation (phi = -93degrees,psi = 112degrees). Residues 2-5 form a 3(10)-helix, stabilized by three successive intramolecular hydrogen bonds. Notably, two NH groups Ala(1) and Ac(7)c(3) do not form any hydrogen bonds in the crystal. Peptide assembly appears to be dominated by packing of the cycloheptane rings that stack against one another within the molecule and also throughout the crystal in columns.

STBC's from representation of extended Clifford Algebras

A set of sufficient conditions to construct lambda-real symbol Maximum Likelihood (ML) decodable STBCs have recently been provided by Karmakar et al. STBCs satisfying these sufficient conditions were named as Clifford Unitary Weight (CUW) codes. In this paper, the maximal rate (as measured in complex symbols per channel use) of CUW codes for lambda = 2(a), a is an element of N is obtained using tools from representation theory. Two algebraic constructions of codes achieving this maximal rate are also provided. One of the constructions is obtained using linear representation of finite groups whereas the other construction is based on the concept of right module algebra over non-commutative rings. To the knowledge of the authors, this is the first paper in which matrices over non-commutative rings is used to construct STBCs. An algebraic explanation is provided for the 'ABBA' construction first proposed by Tirkkonen et al and the tensor product construction proposed by Karmakar et al. Furthermore, it is established that the 4 transmit antenna STBC originally proposed by Tirkkonen et al based on the ABBA construction is actually a single complex symbol ML decodable code if the design variables are permuted and signal sets of appropriate dimensions are chosen.

An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates

A three-dimensional linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates. The solution is exact and involves determining a triply infinite sequence of eigenvalues from a doubly infinite set of closed form transcendental equations. As no restrictions are placed on the thickness variation of stresses or displacements, this formulation yields a triply infinite spectrum of frequencies, instead of only one doubly infinite spectrum by thin plate theory and three doubly infinite spectra by Mindlin's thick plate theory. Further, the present analysis yields symmetric thickness modes which neither of the approximate theories can identify. Some numerical results from the two approximate theories are compared with those from the present solution and some important conclusions regarding the effect of the assumptions made in the approximate theories are drawn. The thickness variations of stresses and displacements are also discussed. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for three-ply laminates, and are used to assess the accuracy of thin plate theory predictions for laminates. Extension to general lateral surface conditions and forced vibrations is indicated.

Extended self-similarity works for the Burgers equation and why

Extended self-similarity (ESS), a procedure that remarkably extends the range of scaling for structure functions in Navier-Stokes turbulence and thus allows improved determination of intermittency exponents, has never been fully explained. We show that ESS applies to Burgers turbulence at high Reynolds numbers and we give the theoretical explanation of the numerically observed improved scaling at both the IR and UV end, in total a gain of about three quarters of a decade: there is a reduction of subdominant contributions to scaling when going from the standard structure function representation to the ESS representation. We conjecture that a similar situation holds for three-dimensional incompressible turbulence and suggest ways of capturing subdominant contributions to scaling.

An extended verifiable secret redistribution protocol for archival systems

Existing protocols for archival systems make use of verifiability of shares in conjunction with a proactive secret sharing scheme to achieve high availability and long term confidentiality, besides data integrity. In this paper, we extend an existing protocol (Wong et al. [9]) to take care of more realistic situations. For example, it is assumed in the protocol of Wong et al. that the recipients of the secret shares are all trustworthy; we relax this by requiring that only a majority is trustworthy.

Hole pairing within an extended Anderson impurity model applicable to the high-Tc cuprates

We calculate the binding energy of a hole pair within the extended Anderson Hamiltonian for the high-Tc cuprates including a Cu impurity and an oxygen-derived band. The results indicate that stable hole pairs can be formed for intra-atomic and interatomic Coulomb repulsion strengths larger than 6 and 3.5 eV, respectively. It is also shown that the total hybridization strength between the Cu 3d and oxygen p band should be less than 2.5 eV. The hole pairing takes place primarily within the oxygen-derived p band. The range of parameter values for which hole pairing occurs is also consistent with the earlier photoemission results from these cuprates.

A self-consistent formulation for analysis and generation of non-uniform DNA structure

A fully self-consistent formulation is described here for the analysis and generation of base-pairs in non-uniform DNA structures, in terms of various local parameters. It is shown that the internal "wedge parameters" are mathematically related to the parameters describing the base-pair orientation with respect to an external helix axis. Hence any one set of three translation and three rotation parameters are necessary and sufficient to completely describe the relative orientation of the base-pairs comprising a step (or doublet). A general procedure is outlined for obtaining an average or global helix axis from the local helix axes for each step. A graphical representation of the local helix axes in the form of a polar plot is also shown and its application for estimating the curvature of oligonucleotide structures is illustrated, with examples of both A and B type structures.

A series of transition metal-azido extended complexes with various anionic and neutral co-ligands: synthesis, structure and their distinct magnetic behavior

The crystal structures and magnetic properties of five new transition metal-azido complexes with two anionic [pyrazine-2-carboxylate (pyzc) and p-aminobenzoate (paba)] and two neutral [pyrazine (pyz) and pyridine (py)] coligands are reported All five complexes were synthesized bysolvothermal methods The complex [Co-2(pyzc)(2)(N-3)(2)(H2O)(2)](n) (1) is 1D and exhibit canted antiferromagnetism, while the 3D complex [MnNa(pyzc)(N-3)(2)(H2O)(2)](n) (2) has a complicated structure and is weakly ferromagnetic in nature [Mn-2(paba)(2)(N-3)(2)(H2O)(2)](n) (3). is a 2D sheet and the Mn-II ions are found to be antiferromagnetically coupled The isostructural 2D complexes [Cu-3(pyz)(2)(N-3)(6)](n) (4) and [Cu-3(py)(2)(N-3)(6)](n) (5) resemble remarkably in their magnetic properties exhibiting moderately strong ferromagnetism. Density functional theory calculations (B3LYP functional) have been performed to provide a qualitative theoretical interpietation of the overall magnetic behavior shown by these complexes.

Extended colored Petri net: An efficient tool for analyzing concurrent systems

This paper proposes a novel and simple definition of general colored Petri nets. This definition is coherent with that of (uncolored) Petri nets, preserves the reflexivity of the original net and is extended to represent inhibitors. Also suggested are systematic and formal merging rules to obtain a well-formed structure of the extended colored Petri net by folding a given uncolored net. Finally, we present a technique to compute colored invariants by selecting colored RP-subnets. On the average, the proposed technique performs better than the existing ones. The analysis procedure is explained through an illustrative example of a three-level interrupt-priority-handler scheme.

An algebraic formulation of static isotropy and design of statically isotropic 6–6 Stewart platform manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulators is identified analytically. We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration.

Path-integral derivation of the superconformal anomaly for the Wess-Zumino model

Fujikawa's method of evaluating the anomalies is extended to the on-shell supersymmetric (SUSY) theories. The supercurrent and the superconformal current anomalies are evaluated for the Wess-Zumino model using the background-field formulation and heat-kernel regularization. We find that the regularized Jacobians for SUSY and superconformal transformations are finite. The results can be expressed in a form such that there is no supercurrent anomaly but a finite nonzero superconformal anomaly, in agreement with similar results obtained using other methods.