Search on a fractal lattice using a quantum random walk

The spatial search problem on regular lattice structures in integer number of dimensions d >= 2 has been studied extensively, using both coined and coinless quantum walks. The relativistic Dirac operator has been a crucial ingredient in these studies. Here, we investigate the spatial search problem on fractals of noninteger dimensions. Although the Dirac operator cannot be defined on a fractal, we construct the quantum walk on a fractal using the flip-flop operator that incorporates a Klein-Gordon mode. We find that the scaling behavior of the spatial search is determined by the spectral (and not the fractal) dimension. Our numerical results have been obtained on the well-known Sierpinski gaskets in two and three dimensions.

Catalytic Asymmetric Direct Vinylogous Michael Addition of Deconjugated Butenolides to Maleimides for the Construction of Quaternary Stereogenic Centers

Competition under control: A practical and efficient direct asymmetric vinylogous Michael reaction of deconjugated butenolides has been developed (see scheme). The products of this reaction, highly functionalized chiral succinimides, are obtained in excellent yield with high diastereoselectivity (up to d.r.=18:1) and outstanding enantioselectivity (up to e.r.=99.5:0.5).

Mechanistic Aspects for the Formation of Copper Dimer Bridged by Phosphonic Acid and Extending Its Dimensionality by Organic and Inorganic Linkers: Synthesis, Structural Characterization, Magnetic Properties, and Theoretical Studies

Six new copper metal complexes with formulas Cu(H2O)(2,2'-bpy) (H2L)](2) center dot H4L center dot 4 H2O (1), {Cu(H2O)(2,2'-bpy)-(H3L)}(2)(H2L)]center dot 2H(2)O (2), Cu(H2O)(1,10-phen)(H2L)](2)center dot 6H(2)O (3), Cu(2,2'-bpy)(H2L)](n)center dot nH(2)O (4), Cu(1,10-phen)(H2L)](n)center dot 3nH(2)O (5), and {Cu(2,2'-bpy)(MoO3)}(2)(L)](n)center dot 2nH(2)O (6) have been synthesized starting from p-xylylenediphosphonic acid (H4L) and 2,2'-bipyridine (2,2'-bpy) or 1,10-phenanthroline (1,10-phen) as secondary linkers and characterized by single crystal X-ray diffraction analysis, IR spectroscopy, and thermogravimetric (TG) analysis. All the complexes were synthesized by hydrothermal methods. A dinuclear motif (Cu-dimer) bridged by phosphonic acid represents a new class of simple building unit (SBU) in the construction of coordination architectures in metal phosphonate chemistry. The initial pH of the reaction mixture induced by the secondary linker plays an important role in the formation of the molecular phosphonates 1, 2, and 3. Temperature dependent hydrothermal synthesis of the compounds 1, 2, and 3 reveals the mechanism of the self assembly of the compounds based on the solubility of the phosphonic acid H4L. Two-dimensional coordination polymers 4, 5, and 6, which are formed by increasing the pH of the reaction mixture, comprise Cu-dimers as nodes, organic (H2L) and inorganic (Mo4O12) ligands as linkers. The void space-areas, created by the (4,4) connected nets in compounds 4 and 5, are occupied by lattice water molecules. Thus compounds 4 and 5 have the potential to accommodate guest species/molecules. Variable temperature magnetic studies of the compounds 3, 4, 5, and 6 reveal the antiferromagnetic interactions between the two Cu(II) ions in the eight membered ring, observed in their crystal structures. A density functional theory (DFT) calculation correlates the conformation of the Cu-dimer ring with the magnitude of the exchange parameter based on the torsion angle of the conformation.

Activation of Lattice Oxygen of TiO2 by Pd2+ Ion: Correlation of Low-Temperature CO and Hydrocarbon Oxidation with Structure of Ti1-xPdxO2-x (x=0.01-0.03)

Lattice oxygen of TiO2 is activated by the substitution of Pd ion in its lattice. Ti1-xPdxO2-x (x = 0.01-0.03) have been synthesized by solution combustion method crystallizing in anatase TiO2 structure. Pd is in +2 oxidation state and Ti is in +4 oxidation state in the catalyst. Pd is more ionic in TiO2 lattice compared to Pd in PdO. Oxygen storage capacity defined by ``amount of oxygen that is used reversibly to oxidize CO'' is as high as 5100 mu mol/g of Ti0.97Pd0.03O1.97. Oxygen is extracted by CO to CO2 in absence of feed oxygen even at room temperature which is more than 20 times compared to pure TiO2. Rate of CO oxidation is 2.75 mu mol g(-1) s(-1) at 60 degrees C over Ti0.97Pd0.03O1.97 and C2H2 gets oxidized to CO2 and H2O at room temperature. Catalyst is not poisoned on long time operation of the reactor. Such high catalytic activity is due to activated lattice oxygen created by the substitution of Pd ion as seen from first-principles density functional theory (DFT) calculations with 96 atom supercells of Ti32O64, Ti31Pd1O63, Ti30Pd2O62, and Ti29Pd3O61. The compounds crystallize in anatase TiO2 structure with Pd2+ ion in nearly square planar geometry and TiO6 octahedra are distorted by the creation of weakly bound oxygens. Structural analysis of Ti31Pd1O63 which is close to 3% Pd ion substituted TiO2 shows that oxygens associated with both Ti and Pd ions in the lattice show bond valence sum of 1.87, a low value characteristic of weak oxygen in the lattice compared to oxygens with valence 2 and above in the same lattice. Exact positions of activated oxygens have been identified in the lattice from DFT calculations.

Correlation between enhanced lattice polarizability and high piezoelectric response in BiScO3-PbTiO3

Piezoelectric and ex situ electric-field induced structural studies were carried out on closely spaced compositions in the morphotropic phase boundary region of (1 - x) PbTiO3-(x)BiScO3. While the common approach of zero field structural analysis failed to provide a unique relationship between the anomalous piezoresponse of x = 0.3725 and structural factor(s), ex situ study of electric-field induced structural changes revealed that the composition exhibiting the highest piezoelectric response is the one which also exhibits significantly enhanced polarizability of the lattices of both coexisting (monoclinic and tetragonal) phases. The enhanced lattice polarizability manifests as a significant fraction of the monoclinic phase transforming irreversibly to the tetragonal phase after electric poling. DOI: 10.1103/PhysRevB.87.064106

An approach toward the synthesis of PPAP natural product garsubellin A: construction of the tricyclic core

In a study directed toward the bioactive natural product garsubellin A, an expedient route to the bicyclo 3.3.1]nonan-9-one bearing tricyclic core, with a bridgehead anchored tetrahydrofuran ring, is delineated. The approach emanating from commercially available dimedone involved a DIBAL-H mediated retro aldol/re-aldol cyclization cascade and a PCC mediated oxidative cyclization as the key steps. (C) 2013 Elsevier Ltd. All rights reserved.

Chapman-Enskog analysis for finite-volume formulation of lattice Boltzmann equation

The classical Chapman-Enskog expansion is performed for the recently proposed finite-volume formulation of lattice Boltzmann equation (LBE) method D.V. Patil, K.N. Lakshmisha, Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys. 228 (2009) 5262-5279]. First, a modified partial differential equation is derived from a numerical approximation of the discrete Boltzmann equation. Then, the multi-scale, small parameter expansion is followed to recover the continuity and the Navier-Stokes (NS) equations with additional error terms. The expression for apparent value of the kinematic viscosity is derived for finite-volume formulation under certain assumptions. The attenuation of a shear wave, Taylor-Green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation.

Cl-35 NQR frequency and spin lattice relaxation time in 3,4-dichlorophenol as a function of pressure and temperature

The pressure dependences of Cl-35 nuclear quadrupole resonance (NQR) frequency, temperature and pressure variation of spin lattice relaxation time (T-1) were investigated in 3,4-dichlorophenol. T-1 was measured in the temperature range 77-300 K. Furthermore, the NQR frequency and T-1 for these compounds were measured as a function of pressure up to 5 kbar at 300 K. The temperature dependence of the average torsional lifetimes of the molecules and the transition probabilities W-1 and W-2 for the Delta m = +/- 1 and Delta m = +/- 2 transitions were also obtained. A nonlinear variation of NQR frequency with pressure has been observed and the pressure coefficients were observed to be positive. A thermodynamic analysis of the data was carried out to determine the constant volume temperature coefficients of the NQR frequency. An attempt is made to compare the torsional frequencies evaluated from NQR data with those obtained by IR spectra. On selecting the appropriate mode from IR spectra, a good agreement with torsional frequency obtained from NQR data is observed. The previously mentioned approach is a good illustration of the supplementary nature of the data from IR studies, in relation to NQR studies of compounds in solid state.

Compositional hierarchical monitoring automaton construction for LTL

In this paper we give a compositional (or inductive) construction of monitoring automata for LTL formulas. Our construction is similar in spirit to the compositional construction of Kesten and Pnueli [5]. We introduce the notion of hierarchical Büchi automata and phrase our constructions in the framework of these automata. We give detailed constructions for all the principal LTL operators including past operators, along with proofs of correctness of the constructions.

Construction of Block Orthogonal STBCs and Reducing Their Sphere Decoding Complexity

Construction of high rate Space Time Block Codes (STBCs) with low decoding complexity has been studied widely using techniques such as sphere decoding and non Maximum-Likelihood (ML) decoders such as the QR decomposition decoder with M paths (QRDM decoder). Recently Ren et al., presented a new class of STBCs known as the block orthogonal STBCs (BOSTBCs), which could be exploited by the QRDM decoders to achieve significant decoding complexity reduction without performance loss. The block orthogonal property of the codes constructed was however only shown via simulations. In this paper, we give analytical proofs for the block orthogonal structure of various existing codes in literature including the codes constructed in the paper by Ren et al. We show that codes formed as the sum of Clifford Unitary Weight Designs (CUWDs) or Coordinate Interleaved Orthogonal Designs (CIODs) exhibit block orthogonal structure. We also provide new construction of block orthogonal codes from Cyclic Division Algebras (CDAs) and Crossed-Product Algebras (CPAs). In addition, we show how the block orthogonal property of the STBCs can be exploited to reduce the decoding complexity of a sphere decoder using a depth first search approach. Simulation results of the decoding complexity show a 30% reduction in the number of floating point operations (FLOPS) of BOSTBCs as compared to STBCs without the block orthogonal structure.

Fractional Hilbert transform extensions and associated analytic signal construction

The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations. (C) 2013 Elsevier B.V. All rights reserved.

Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

We develop a strong-coupling (t << U) expansion technique for calculating the density profile for bosonic atoms trapped in an optical lattice with an overall harmonic trap at finite temperature and finite on-site interaction in the presence of superfluid regions. Our results match well with quantum Monte Carlo simulations at finite temperature. We also show that the superfluid order parameter never vanishes in the trap due to the proximity effect. Our calculations for the scaled density in the vacuum-to-superfluid transition agree well with the experimental data for appropriate temperatures. We present calculations for the entropy per particle as a function of temperature which can be used to calibrate the temperature in experiments. We also discuss issues connected with the demonstration of universal quantum critical scaling in the experiments.

Design and construction of geocell foundation to support the embankment on settled red mud

This paper presents the case history of the construction of a 3 m high embankment on the geocell foundation over the soft settled red mud. Red mud is a waste product from the Bayer process of Aluminum industry. Geotechnical problems of the site, the design of the geocell foundation based on experimental investigation and the construction sequences of the geocell foundations in the field are discussed in the paper. Based on the experimental studies, an analytical model was also developed to estimate the load carrying capacity of the soft clay bed reinforced with geocell and combination of geocell and geogrid. The results of the experimental and analytical studies revealed that the use of combination of geocell and the geogrid is always beneficial than using the geocell alone. Hence, the combination of geocell and geogrid was recommended to stabilize the embankment base. The reported embankment is located in Lanjigharh (Orissa) in India. Construction of the embankment on the geocell foundation has already been completed. The constructed embankmenthas already sustained two monsoon rains without any cracks and seepage. (C) 2013 Elsevier Ltd. All rights reserved.

Regenerating codes: A reformulated storage-bandwidth trade-off and a new construction

In this paper, the storage-repair-bandwidth (SRB) trade-off curve of regenerating codes is reformulated to yield a tradeoff between two global parameters of practical relevance, namely information rate and repair rate. The new information-repair-rate (IRR) tradeoff provides a different and insightful perspective on regenerating codes. For example, it provides a new motivation for seeking to investigate constructions corresponding to the interior of the SRB tradeoff. Interestingly, each point on the SRB tradeoff corresponds to a curve in the IRR tradeoff setup. We characterize completely, functional repair under the IRR framework, while for exact repair, an achievable region is presented. In the second part of this paper, a rate-half regenerating code for the minimum storage regenerating point is constructed that draws upon the theory of invariant subspaces. While the parameters of this rate-half code are the same as those of the MISER code, the construction itself is quite different.

Atomic Structure of Quantum Gold Nanowires: Quantification of the Lattice Strain

Theoretical studies exist to compute the atomic arrangement in gold nanowires and the influence on their electronic behavior with decreasing diameter. Experimental studies, e.g., by transmission electron microscopy, on chemically synthesized ultrafine wires are however lacking owing to the unavailability of suitable protocols for sample preparation and the stability of the wires under electron beam irradiation. In this work, we present an atomic scale structural investigation on quantum single crystalline gold nanowires of 2 nm diameter, chemically prepared on a carbon film grid. Using low dose aberration-corrected high resolution (S)TEM, we observe an inhomogeneous strain distribution in the crystal, largely concentrated at the twin boundaries and the surface along with the presence of facets and surface steps leading to a noncircular cross section of the wires. These structural aspects are critical inputs needed to determine their unique electronic character and their potential as a suitable catalyst material. Furthermore, electron-beam-induced structural changes at the atomic scale, having implications on their mechanical behavior and their suitability as interconnects, are discussed.