Synthesis, Structures, and Magnetic Behavior of a Series of Copper(II) Azide Polymers of Cu-4 Building Clusters and Isolation of a New Hemiaminal Ether as the Metal Complex

Four new neutral copper azido polymers, Cu-4(N-3)(8)(L-1)(2)](n) (1), Cu-4(N-3)(8)(L-2)(2)](n) (2), Cu-4(N-3)(8)(L-3)(2)](n) (3), and Cu-9(N-3)(18)(L-4)(4)](n) (4) L1-4 are formed in situ by reacting pyridine-2-carboxaldehyde with 22-(methylamino)ethyl]pyridine (mapy, L-1), N,N-dimethylethylenediamine (N,N-dmen, L-2), N,N-diethylethylenediamine (N,N-deen, L-3), and N,N,2,2-tetramethylpropanediamine (N,N,2,2-tmpn, L-4)], have been synthesized by using 0.5 mol equiv of the chelating tridentate ligands with Cu-(NO3)(2)center dot 3H(2)O and an excess of NaN3. Single-crystal X-ray structures show that the basic unit of these complexes, especially 1-3, contains very similar Cu-4(II) building blocks. The overall structure of 3 is two-dimensional, while the other three complexes are one-dimensional in nature. Complex 1 represents a unique example containing hemiaminal ether arrested by copper(R). Complexes 1 and 2 have a rare bridging azido pathway: both end-on and end-to-end bridging azides between a pair of Cu-II centers. Cryomagnetic susceptibility measurements over a wide range of temperature exhibit dominant ferromagnetic behavior in all four complexes. Density functional theory calculations (B3LYP functional) have been performed on complexes 1-3 to provide a qualitative theoretical interpretation of their overall ferromagnetic behavior.

Understanding the building-up process of three dimensional open-framework metal phosphates: Acid degradation of the 3D structures to lower dimensional structures

Acid degradation of 3D zinc phosphates primarily yields a one-dimensional ladder compound, an observation that is significant considering that the latter forms 3D structures on heating in water.

Limit Laws for Coverage in Backbone-Sensor Networks

We study the coverage in sensor networks having two types of nodes, sensor and backbone nodes. Each sensor is capable of transmitting information over relatively small distances. The backbone nodes collect information from the sensors. This information is processed and communicated over an ad-hoc network formed by the backbone nodes,which are capable of transmitting over much larger distances. We consider two modes of deployment of sensors, one a Poisson-Poisson cluster model and the other a dependently-thinned Poisson point process. We deduce limit laws for functionals of vacancy in both models using properties of association for random measures.

Universality of scaling laws in correlation between velocity and shear stress in turbulent boundary layers

In this study, we analyse simultaneous measurements (at 50 Hz) of velocity at several heights and shear stress at the surface made during the Utah field campaign for the presence of ranges of scales, where distinct scale-to-scale interactions between velocity and shear stress can be identified. We find that our results are similar to those obtained in a previous study [Venugopal et al., 2003] (contrary to the claim in V2003, that the scaling relations might be dependent on Reynolds number) where wind tunnel measurements of velocity and shear stress were analysed. We use a wavelet-based scale-to-scale cross-correlation to detect three ranges of scales of interaction between velocity and shear stress, namely, (a) inertial subrange, where the correlation is negligible; (b) energy production range, where the correlation follows a logarithmic law; and (c) for scales larger than the boundary layer height, the correlation reaches a plateau.

Two new 1D chains of Ni(2)Na(2) heterometallic double half-cubane building units: Synthesis, structures and variable temperature magnetic study

An equimolar mixture of Ni(NO(3))(2)center dot 6H(2)O and pyridine-2-aldehyde with two equivalents of NaN(3) in methanol in the presence of NaOMe resulted in the formation of light green precipitate which upon crystallization from dimethylformamide (DMF) yielded light green single crystals [{Ni(2)Na(2)(pic)(4)(N(3))(2)(H(2)O)(2)(MeOH)}center dot MeOH center dot 3H(2)O](n) (1) and [{Ni(2)Na(2)(pic)(4)(N(3))(2)(H(2)O)(4)}center dot 2DMF center dot H(2)O](n) (2) (pic = pyridine-2-carboxylate) at room temperature and high temperature (100 degrees C), respectively. Variable temperature magnetic studies revealed the existence of overall ferromagnetic behaviour with J approximate to + 10 cm(-1) and D approximate to -2 to -7 cm(-1) for 1 and 2, respectively. Negative D values as well as variation of D upon slight distortion of structure by varying reaction temperature were observed. The X-band Electron Paramagnetic Resonance (EPR) spectra of both 2 and 3 were recorded below 50 K. The structural distortion was also implicated from the EPR spectra. Density Functional Theory (DFT) calculations on both complexes were performed in two different ways to corroborate the magnetic results. Considering only Ni(2)(II) dimeric unit, results were J = + 20.65 cm(-1) and D = -3.16 cm(-1) for 1, and J = +24.56 cm(-1) and D = -4.67 cm(-1) for 2. However, considering Ni(2)(II)Na(2)(I) cubane as magnetic core the results were J = +16.35 cm(-1) (1), +19.54 cm(-1) (2); D = -3.05 cm(-1) (1), -4.25 cm(-1) (2).

Quenching across quantum critical points in periodic systems: Dependence of scaling laws on periodicity

We study the quenching dynamics of a many-body system in one dimension described by a Hamiltonian that has spatial periodicity. Specifically, we consider a spin-1/2 chain with equal xx and yy couplings and subject to a periodically varying magnetic field in the (z) over cap direction or, equivalently, a tight-binding model of spinless fermions with a periodic local chemical potential, having period 2q, where q is a positive integer. For a linear quench of the strength of the magnetic field (or chemical potential) at a rate 1/tau across a quantum critical point, we find that the density of defects thereby produced scales as 1/tau(q/(q+1)), deviating from the 1/root tau scaling that is ubiquitous in a range of systems. We analyze this behavior by mapping the low-energy physics of the system to a set of fermionic two-level systems labeled by the lattice momentum k undergoing a nonlinear quench as well as by performing numerical simulations. We also show that if the magnetic field is a superposition of different periods, the power law depends only on the smallest period for very large values of tau, although it may exhibit a crossover at intermediate values of tau. Finally, for the case where a zz coupling is also present in the spin chain, or equivalently, where interactions are present in the fermionic system, we argue that the power associated with the scaling law depends on a combination of q and the interaction strength.

Fatigue crack growth due to overloads in plain concrete using scaling laws

Scaling laws are represented in power law form and can be utilized to extract the characteristic properties of a new phenomenon with the help of self-similar solutions. In this work, an attempt has been made to propose a scaling law analytically, for plain concrete when subjected to variable amplitude loading. Due to the application of overload on concrete structures, acceleration in the crack growth process takes place. A closed form expression has been developed to capture the acceleration in crack growth rate in conjunction with the principles of dimensional analysis and self-similarity. The proposed model accounts for parameters such as, the tensile strength, fracture toughness, overload effect and the structural size. Knowing the governed and the governing parameters of the physical problem and by using the concepts of self-similarity, a relationship is obtained between the different parameters involved. The predicted results are compared with experimental crack growth data for variable amplitude loading and are found to capture the overload effect with sufficient accuracy. Through a sensitivity analysis, fracture toughness is found to be the most dominant parameter in accelerating the crack length due to application of overload.

Dendrimer building toolkit: Model building and characterization of various dendrimer architectures

We have developed a graphical user interface based dendrimer builder toolkit (DBT) which can be used to generate the dendrimer configuration of desired generation for various dendrimer architectures. The validation of structures generated by this tool was carried out by studying the structural properties of two well known classes of dendrimers: ethylenediamine cored poly(amidoamine) (PAMAM) dendrimer, diaminobutyl cored poly(propylene imine) (PPI) dendrimer. Using full atomistic molecular dynamics (MD) simulation we have calculated the radius of gyration, shape tensor and monomer density distribution for PAMAM and PPI dendrimer at neutral and high pH. A good agreement between the available simulation and experimental (small angle X-ray and neutron scattering; SAXS, SANS) results and calculated radius of gyration was observed. With this validation we have used DBT to build another new class of nitrogen cored poly(propyl ether imine) dendrimer and study it's structural features using all atomistic MD simulation. DBT is a versatile tool and can be easily used to generate other dendrimer structures with different chemistry and topology. The use of general amber force field to describe the intra-molecular interactions allows us to integrate this tool easily with the widely used molecular dynamics software AMBER. This makes our tool a very useful utility which can help to facilitate the study of dendrimer interaction with nucleic acids, protein and lipid bilayer for various biological applications. © 2012 Wiley Periodicals, Inc.

Dendrimer building toolkit: Model building and characterization of various dendrimer architectures

We have developed a graphical user interface based dendrimer builder toolkit (DBT) which can be used to generate the dendrimer configuration of desired generation for various dendrimer architectures. The validation of structures generated by this tool was carried out by studying the structural properties of two well known classes of dendrimers: ethylenediamine cored poly(amidoamine) (PAMAM) dendrimer, diaminobutyl cored poly(propylene imine) (PPI) dendrimer. Using full atomistic molecular dynamics (MD) simulation we have calculated the radius of gyration, shape tensor and monomer density distribution for PAMAM and PPI dendrimer at neutral and high pH. A good agreement between the available simulation and experimental (small angle X-ray and neutron scattering; SAXS, SANS) results and calculated radius of gyration was observed. With this validation we have used DBT to build another new class of nitrogen cored poly(propyl ether imine) dendrimer and study it's structural features using all atomistic MD simulation. DBT is a versatile tool and can be easily used to generate other dendrimer structures with different chemistry and topology. The use of general amber force field to describe the intra-molecular interactions allows us to integrate this tool easily with the widely used molecular dynamics software AMBER. This makes our tool a very useful utility which can help to facilitate the study of dendrimer interaction with nucleic acids, protein and lipid bilayer for various biological applications. (c) 2012 Wiley Periodicals, Inc.

Directional Diffusion Regulator (DDR) for some numerical solvers of hyperbolic conservation laws

A computational tool called ``Directional Diffusion Regulator (DDR)'' is proposed to bring forth real multidimensional physics into the upwind discretization in some numerical schemes of hyperbolic conservation laws. The direction based regulator when used with dimension splitting solvers, is set to moderate the excess multidimensional diffusion and hence cause genuine multidimensional upwinding like effect. The basic idea of this regulator driven method is to retain a full upwind scheme across local discontinuities, with the upwind bias decreasing smoothly to a minimum in the farthest direction. The discontinuous solutions are quantified as gradients and the regulator parameter across a typical finite volume interface or a finite difference interpolation point is formulated based on fractional local maximum gradient in any of the weak solution flow variables (say density, pressure, temperature, Mach number or even wave velocity etc.). DDR is applied to both the non-convective as well as whole unsplit dissipative flux terms of some numerical schemes, mainly of Local Lax-Friedrichs, to solve some benchmark problems describing inviscid compressible flow, shallow water dynamics and magneto-hydrodynamics. The first order solutions consistently improved depending on the extent of grid non-alignment to discontinuities, with the major influence due to regulation of non-convective diffusion. The application is also experimented on schemes such as Roe, Jameson-Schmidt-Turkel and some second order accurate methods. The consistent improvement in accuracy either at moderate or marked levels, for a variety of problems and with increasing grid size, reasonably indicate a scope for DDR as a regular tool to impart genuine multidimensional upwinding effect in a simpler framework. (C) 2012 Elsevier Inc. All rights reserved.

Cu-II-azide polynuclear complexes of Cu-4 building clusters with Schiff-base co-ligands: synthesis, structures, magnetic behavior and DFT studies

Three new copper-azido complexes Cu-4(N-3)(8)(L-1)(2)](n) (1), Cu-4(N-3)(6)(L-2)(2)(H2O)(2)] (2), and Cu-4(N-3)(6)(L-3)(2)](n) (3) L-1 is the imine resulting from the condensation of pyridine-2-carboxaldehyde with N-methylethylenediamine, HL2 and HL3 are the condensation products of 2-hydroxy-3-methoxybenzaldehyde with N,N-diethylethylenediamine and N-ethylethylenediamine respectively] have been synthesized by using 0.5 molar equivalents of the Schiff base ligands with Cu(NO3)(2)center dot 3H(2)O and an excess of NaN3. Single crystal X-ray structures show that the basic unit of these complexes contains very similar Cu-4(II) building blocks. While 1 and 3 have overall 1D structures, 2 forms discrete tetranuclear clusters due to blocking of two coordination sites on the tetranuclear cluster by water molecules. Magnetic susceptibility measurements over a wide range of temperatures exhibit the presence of both antiferromagnetic and ferromagnetic exchanges within the tetranuclear unit structures. Density functional theory calculations (using B3LYP functional and two different basis sets) have been performed on the complexes 1-3 to provide a qualitative theoretical interpretation of their overall magnetic behavior.