Quantum phases of dimerized and frustrated Heisenberg spin chains with s=1/2, 1 and 3/2: an entanglement entropy and fidelity study

We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one-dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction J(2)) and dimerization (delta). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the J(2)-delta plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.

Projecting low and extensive dimensional chaos from spatio-temporal dynamics

We review the spatio-temporal dynamical features of the Ananthakrishna model for the Portevin-Le Chatelier effect, a kind of plastic instability observed under constant strain rate deformation conditions. We then establish a qualitative correspondence between the spatio-temporal structures that evolve continuously in the instability domain and the nature of the irregularity of the scalar stress signal. Rest of the study is on quantifying the dynamical information contained in the stress signals about the spatio-temporal dynamics of the model. We show that at low applied strain rates, there is a one-to-one correspondence with the randomly nucleated isolated bursts of mobile dislocation density and the stress drops. We then show that the model equations are spatio-temporally chaotic by demonstrating the number of positive Lyapunov exponents and Lyapunov dimension scale with the system size at low and high strain rates. Using a modified algorithm for calculating correlation dimension density, we show that the stress-strain signals at low applied strain rates corresponding to spatially uncorrelated dislocation bands exhibit features of low dimensional chaos. This is made quantitative by demonstrating that the model equations can be approximately reduced to space independent model equations for the average dislocation densities, which is known to be low-dimensionally chaotic. However, the scaling regime for the correlation dimension shrinks with increasing applied strain rate due to increasing propensity for propagation of the dislocation bands. The stress signals in the partially propagating to fully propagating bands turn to have features of extensive chaos.

Codes for solving three dimensional linear elastostatic problems using constant boundary elements while ignoring body forces

Three codes, that can solve three dimensional linear elastostatic problems using constant boundary elements while ignoring body forces, are provided here. The file 'bemconst.m' contains a MATLAB code for solving three dimensional linear elastostatic problems using constant boundary elements while ignoring body forces. The file 'bemconst.f90' is a Fortran translation of the MATLAB code contained in the file 'bemconst.m'. The file 'bemconstp.f90' is a parallelized version of the Fortran code contained in the file 'bemconst.f90'. The file 'inbem96.txt' is the input file for the Fortran codes contained in the files 'bemconst.f90' and 'bemconstp.f90'. Author hereby declares that the present codes are the original works of the author. Further, author hereby declares that any of the present codes, in full or in part, is not a translation or a copy of any of the existing codes written by someone else. Author's institution (Indian Institute of Science) has informed the author in writing that the institution is not interested in claiming any copyright on the present codes. Author is hereby distributing the present codes under the MIT License; full text of the license is included in each of the files that contain the codes.

New Structural Topologies in a Series of 3d Metal Complexes with Isomeric Phenylenediacetates and 1,3,5-Tris(1-imidazolyl)benzene Ligand: Syntheses, Structures, and Magnetic and Luminescence Properties

In this article we present the syntheses, characterizations, magnetic and luminescence properties of five 3d-metal complexes, Co(tib)(1,2-phda)](n)center dot(H2O)(n) (1), Co-3(tib)(2)(1,3-phda)(3)(H2O)](n)center dot(H2O)(2n) (2), Co-5(tib)(3)(1,4-phda)(5)(H2O)(3)](n)center dot(H2O)(7n) (3), Zn-3(tib)(2)(1,3-phda)(3)](n)center dot(H2O)(4n) (4), and Mn(tib)(2)(H2O)(2)](n)center dot(1,4-phdaH)(2n)center dot(H2O)(4n) (5), obtained from the use of isomeric phenylenediacetates (phda) and the neutral 1,3,5-tris(1-imidazolyl)benzene (tib) ligand. Single crystal X-ray structures showed that 1 constitutes 3,5-connected 2-nodal nets with a double-layered two-dimensional (2D) structure, while 2 forms an interpenetrated 2D network (3,4-connected 3-nodal net). Complex 3 has a complicated three-dimensional structure with 10-nodal 3,4,5-connected nets. Complex 4, although it resembles 2 in stoichiometry and basic building structures, forms a very different overall 2D assembly. In complex 5 the dicarboxylic acid, upon losing only one of the acidic protons, does not take part in coordination; instead it forms a complicated hydrogen bonding network with water molecules. Magnetic susceptibility measurements over a wide range of temperatures revealed that the metal ions exchange very poorly through the tib ligand, but for the Co(II) complexes the effects of nonquenched orbital contributions are prominent. The 3d(10) metal complex 4 showed strong luminescence with lambda(max) = 415 nm (lambda(ex) = 360 nm).

Differential evolution based 3-D guidance law for a realistic interceptor model

This paper presents a novel, soft computing based solution to a complex optimal control or dynamic optimization problem that requires the solution to be available in real-time. The complexities in this problem of optimal guidance of interceptors launched with high initial heading errors include the more involved physics of a three dimensional missile-target engagement, and those posed by the assumption of a realistic dynamic model such as time-varying missile speed, thrust, drag and mass, besides gravity, and upper bound on the lateral acceleration. The classic, pure proportional navigation law is augmented with a polynomial function of the heading error, and the values of the coefficients of the polynomial are determined using differential evolution (DE). The performance of the proposed DE enhanced guidance law is compared against the existing conventional laws in the literature, on the criteria of time and energy optimality, peak lateral acceleration demanded, terminal speed and robustness to unanticipated target maneuvers, to illustrate the superiority of the proposed law. (C) 2013 Elsevier B. V. All rights reserved.

Rare-earth carboxylates, Ln(2)(III)(mu(3)-OH)(C4H4O5)(2)(C4H2O4)]center dot 2H(2)O Ln = Ce, Pr and Nd]: synthesis, structure and properties

A new series of inorganic-organic hybrid framework compounds, Ln(2)(mu(3)-OH)(C4H4O5)(2)(C4H2O4)]center dot 2H(2)O, (Ln = Ce, Pr and Nd), have been prepared employing a hydrothermal method. Malic acid and fumaric acid form part of the structure. The malate units connect the lanthanide centers forming Ln-O-Ln two-dimensional layers, which are cross-linked by the fumarate units forming the three-dimensional structure. Extra framework water molecules form a dimer and occupy the channels. The water molecules can be reversibly adsorbed. The dehydrated structure did not show any differences in framework structure/ connectivity. The presence of lattice water provides a pathway for proton conductivity. Optical studies suggest an up-conversion behavior involving more than one photon for a neodymium compound.

Edge states of a three-dimensional topological insulator

We use the bulk Hamiltonian for a three-dimensional topological insulator such as Bi-2 Se-3 to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based on a lattice discretization of the bulk Hamiltonian. We find that the application of a potential barrier along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering and conductance across the edge is studied as a function of the edge potential. We show that a magnetic field in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states.

Stepwise Crystallization: Illustrative Examples of the Use of Metalloligands Cu-6(mna)(6)](6-) and (Ag-6(Hmna)(2)(mna)(4)](4-) (H(2)mna=2-Mercapto Nicotinic Acid) in the Formation of Heterometallic Two- and Three-Dimensional Assemblies with brucite, pcu, and sql Topologies

Three new inorganic coordination polymers, {Mn(H2O)(6)]-Mn-2(H2O)(6)](Cu-6(mna)(6)]center dot 6H(2)O}, 1, {Mn-4(OH)(2)(H2O)(10)] (Cu-6(mna)6]center dot 8H(2)O}, 2, and {Mn-2(H2O)(5)]Ag-6(Hmna)(2)(mna)(4)]center dot 20H(2)O}, 3, have been synthesized at room temperature through a sequential crystallization route. In addition, we have also prepared and characterized the molecular precursor Cu-6(Hmna)(6)]. Compounds 1 and 3 have a two-dimensional structure, whereas 2 has a three-dimensional structure. The formation of 2 has been achieved by minor modification in the synthetic composition, suggesting the subtle relationship between the reactant composition and the structure. The hexanudear copper and silver duster cores have Cu center dot center dot center dot Cu and Ag center dot center dot center dot Ag distances close to the sum of the van der Waals radii of Cu1+ and Ag1+, respectively. The connectivity between Cu-6(mna)(6)](6-) cluster units and Mn2+ ions gives rise to a brucite related layer in 1 and a pcu-net in 2. The Ag-6(Hmna)(2)(mna)(4)](4-) cluster in 3, on the other hand, forms a sql-net with Mn2+. Compound 1 exhibits an interesting and reversible hydrochromic behavior, changing from pale yellow to red, on heating at 70 degrees C or treatment under a vacuum. Electron paramagnetic resonance studies indicate no change in the valence states, suggesting the color change could be due to changes in the coordination environment only. The magnetic studies indicate weak antiferromagnetic behavior. Proton conductivity studies indicate moderate proton migrations in 1 and 3. The present study dearly establishes sequential crystallization as an important pathway for the synthesis of heterometallic coordination polymers.

Stabilization of Co-3 - Oxoclusters in a pcu Net: Synthesis, Structure, Solvent Exchange (Single Crystal to Single Crystal) and Magnetic Studies

The solvothermal reaction of CoCl(2)4H(2)O and 4,4-sulfonyldibenzoic acid (H(2)SDBA) resulted in the formation of a three-dimensional coordination polymer Co-3(C14H8O6S)(3)(DMA)(2)(MeOH)].DMA (Ia) consisting of trinuclear Co-3 oxo-cluster units. The Co-3 trimeric units are connected by SDBA(2-) anions leading to a three dimensional structure with a pcu topology. The terminal methanol molecules could be exchanged in a single crystal to single crystal (SCSC) fashion by other similar solvent molecules (ethanol, acetonitrile, water, ethyleneglycol). Magnetic studies on the parent compound, Ia, indicate antiferromagnetic interactions between the central metal atoms.

Monopoles, Dirac operator, and index theory for fuzzy SU(3) / (U(1) x U(1))

The intersection of the ten-dimensional fuzzy conifold Y-F(10) with S-F(5) x S-F(5) is the compact eight-dimensional fuzzy space X-F(8). We show that X-F(8) is (the analogue of) a principal U(1) x U(1) bundle over fuzzy SU(3) / U(1) x U(1)) ( M-F(6)). We construct M-F(6) using the Gell-Mann matrices by adapting Schwinger's construction. The space M-F(6) is of relevance in higher dimensional quantum Hall effect and matrix models of D-branes. Further we show that the sections of the monopole bundle can be expressed in the basis of SU(3) eigenvectors. We construct the Dirac operator on M-F(6) from the Ginsparg-Wilson algebra on this space. Finally, we show that the index of the Dirac operator correctly reproduces the known results in the continuum.

Dielectric elastomers: Asymptotically-correct three-dimensional displacement field

Asymptotically-accurate dimensional reduction from three to two dimensions and recovery of 3-D displacement field of non-prestretched dielectric hyperelastic membranes are carried out using the Variational Asymptotic Method (VAM) with moderate strains and very small ratio of the membrane thickness to its shortest wavelength of the deformation along the plate reference surface chosen as the small parameters for asymptotic expansion. Present work incorporates large deformations (displacements and rotations), material nonlinearity (hyperelasticity), and electrical effects. It begins with 3-D nonlinear electroelastic energy and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a 2-D nonlinear plate analysis. Major contribution of this paper is a comprehensive nonlinear through-the-thickness analysis which provides a 2-D energy asymptotically equivalent of the 3-D energy, a 2-D constitutive relation between the 2-D generalized strain and stress tensors for the plate analysis and a set of recovery relations to express the 3-D displacement field. Analytical expressions are derived for warping functions and stiffness coefficients. This is the first attempt to integrate an analytical work on asymptotically-accurate nonlinear electro-elastic constitutive relation for compressible dielectric hyperelastic model with a generalized finite element analysis of plates to provide 3-D displacement fields using VAM. A unified software package `VAMNLM' (Variational Asymptotic Method applied to Non-Linear Material models) was developed to carry out 1-D non-linear analysis (analytical), 2-D non-linear finite element analysis and 3-D recovery analysis. The applicability of the current theory is demonstrated through an actuation test case, for which distribution of 3-D displacements are provided. (C) 2014 Elsevier Ltd. All rights reserved.

High Proton Mobility, Solvent Induced Single Crystal to Single Crystal Structural Transformation, and Related Studies on a Family of Compounds Formed from Mn-3 Oxo-Clusters

The reaction between 4,4'-sulfonyldibenzoic acid (H(2)SDBA) and manganese under mild conditions resulted in the isolation of two new three-dimensional compounds, Mn-4(C14H8O6S)(4)(DMA)(2)]center dot 3DMA, I, and Mn-3(C14H8O6S)(3)(DMA)(2)(MeOH)]center dot DMA, IIa. Both structures have Mn-3 trimer oxo cluster units. While the Mn-3 oxoclusters are connected through octahedral manganese forming one-dimensional Mn-O-Mn chains in I, the Mn-3 units are isolated in IIa. The SDBA units connect the Mn-O-Mn chains and the Mn-3 clusters giving rise to the three-dimensional structure. Both compounds have coordinated and free solvent molecules. In IIa, two different solvent molecules are coordinated, of which one solvent can be reversibly exchanged by a variety of other similar solvents via a solvent-mediated single crystal to single crystal (SCSC) transformation. The free lattice DMA solvent molecules in I can be exchanged by water molecules resulting in hydrophilic channels. Proton conductivity studies on I reveals a high proton mobility with conductivity values of similar to 0.87 x 10(-3) Omega(-1) cm(-1) at 34 degrees C and 98% RH, which is comparable to some of the good proton conductivity values observed in inorganic coordination polymers. We have also shown structural transformation of I to IIa through a possible dissolution and recrystallization pathway. In addition, both I and IIa appear to transform to two other manganese compounds H3O]Mn-3(mu(3)-OH)(C14H8O6S)(3)(H2O)](DMF)(5) and H3O](2)Mn-7(mu 3-OH)(4)(C14H8O6S)(6)(H2O)(4)](H2O)(2)(DMF)(8) under suitable reaction conditions. We have partially substituted Co in place of Mn in the Mn-3 trimer clusters forming CoMn2(C14H8O6S)(3)(DMA)(2)(EtOH)]center dot DMA, III, a structure that is closely related to IIa. All the compounds reveal antiferromagnetic behavior. On heating, the cobalt substituted phase (compound III) forms a CoMn2O4 spinel phase with particle sizes in the nanometer range.

Spatial filter based light-sheet laser interference technique for three-dimensional nanolithography

We propose a laser interference technique for the fabrication of 3D nano-structures. This is possible with the introduction of specialized spatial filter in a 2 pi cylindrical lens system (consists of two opposing cylindrical lens sharing a common geometrical focus). The spatial filter at the back-aperture of a cylindrical lens gives rise to multiple light-sheet patterns. Two such interfering counter-propagating light-sheet pattern result in periodic 3D nano-pillar structure. This technique overcomes the existing slow point-by-point scanning, and has the ability to pattern selectively over a large volume. The proposed technique allows large-scale fabrication of periodic structures. Computational study shows a field-of-view (patterning volume) of approximately 12: 2mm(3) with the pillar-size of 80 nm and inter-pillar separation of 180 nm. Applications are in nano-waveguides, 3D nano-electronics, photonic crystals, and optical microscopy. (C) 2015 AIP Publishing LLC.

Two-dimensional homogeneous isotropic fluid turbulence with polymer additives

We carry out an extensive and high-resolution direct numerical simulation of homogeneous, isotropic turbulence in two-dimensional fluid films with air-drag-induced friction and with polymer additives. Our study reveals that the polymers (a) reduce the total fluid energy, enstrophy, and palinstrophy; (b) modify the fluid energy spectrum in both inverse-and forward-cascade regimes; (c) reduce small-scale intermittency; (d) suppress regions of high vorticity and strain rate; and (e) stretch in strain-dominated regions. We compare our results with earlier experimental studies and propose new experiments.

VAM Applied to Dimensional Reduction of Nonlinear Multifunctional Film-fabric Laminates

This work aims at asymptotically accurate dimensional reduction of non-linear multi-functional film-fabric laminates having specific application in design of envelopes for High Altitude Airships (HAA). The film-fabric laminate for airship envelope consists of a woven fabric core coated with thin films on each face. These films provide UV protection and Helium leakage prevention, while the core provides required structural strength. This problem is both geometrically and materially non-linear. To incorporate the geometric non-linearity, generalized warping functions are used and finite deformations are allowed. The material non-linearity is handled by using hyper-elastic material models for each layer. The development begins with three-dimensional (3-D) nonlinear elasticity and mathematically splits the analysis into a one-dimensional through-the-thickness analysis and a two-dimensional (2-D) plate analysis. The through-the-thickness analysis provides the 2-D constitutive law which is then given as an input to the 2-D reference surface analysis. The dimensional reduction is carried out using Variational Asymptotic Method (VAM) for moderate strains and very small thickness-to-wavelength ratio. It features the identification and utilization of additional small parameters such as ratio of thicknesses and stiffness coefficients of core and films. Closed form analytical expressions for warping functions and 2-D constitutive law of the film-fabric laminate are obtained.