Covalent attachment of two important dicopper(II) systems in a one-dimensional polymeric chain: An x-ray structure of [Cu2(en)2(OH)2·Cu2(O2CMe)4](PF6)2·0.5EtOH]α showing the shortest Cucdots, three dots, centeredCu Distance in the tetraacetato core

Reaction of Cu2(O2CMe)4(H2O)2 with 1,2-diaminoethane(en) in ethanol, followed by the addition of NH4PF6, led to the formation of a covalently linked 1D polymeric copper(II) title complex showing alternating [Cu2(en)2(OH)22+] and [Cu2(O2CMe)4] units in the chain and the shortest Cucdots, three dots, centeredCu separation of 2.558(2) Å in the tetraacetato core.

Random sequential multilayer deposition of different‐sized k mers on a one dimensional infinite substrate

Kinetics of random sequential, irreversible multilayer deposition of macromolecules of two different sizes on a one dimensional infinite lattice is analyzed at the mean field level. A formal solution for the corresponding rate equation is obtained. The Jamming limits and the distribution of gaps of exact sizes are discussed. In the absence of screening, the jamming limits are shown to be the same for all the layers. A detailed analysis for the components differing by one monomer unit is presented. The small and large time behaviors and the dependence of the individual jamming limits of the k mers and (k−1) mers on k and the rate parameters are analyzed.

Exact Solution of a One-Dimensional Multicomponent Lattice Gas with Hyperbolic Interaction

We present the exact solution to a one-dimensional multicomponent quantum lattice model interacting by an exchange operator which falls off as the inverse sinh square of the distance. This interaction contains a variable range as a parameter and can thus interpolate between the known solutions for the nearest-neighbor chain and the inverse-square chain. The energy, susceptibility, charge stiffness, and the dispersion relations for low-lying excitations are explicitly calculated for the absolute ground state, as a function of both the range of the interaction and the number of species of fermions.

Generalised one-dimensional burgers'equation in relativistic fluiddynamics

This work deals with the effects of weak nonlinearity and weak dissipation on a linear wave in relativistic gasdynamics. Using perturbation and asymptotic expansions, a relativistic analogue of generalised one-dimensional Burgers' equation of classical gasdynamics is derived to describe far-field description of the wave. Steady state solution is presented for strict one-dimensional case.

Supersolid Phase in One-Dimensional Bose-Hubbard Model With Extended Range Interactions: DMRG And Field Theoretic Study at Different Densities

We use the Density Matrix Renormalization Group and the Abelian bosonization method to study the effect of density on quantum phases of one-dimensional extended Bose-Hubbard model. We predict the existence of supersolid phase and also other quantum phases for this system. We have analyzed the role of extended range interaction parameters on solitonic phase near half-filling. We discuss the effects of dimerization in nearest neighbor hopping and interaction as well as next nearest neighbor interaction on the plateau phase at half-filling.

An optimal dynamic inversion approach for controlling a class of one-dimensional nonlinear distributed parameter systems

Combining the principles of dynamic inversion and optimization theory, a new approach is presented for stable control of a class of one-dimensional nonlinear distributed parameter systems, assuming the availability a continuous actuator in the spatial domain. Unlike the existing approximate-then-design and design-then-approximate techniques, here there is no need of any approximation either of the system dynamics or of the resulting controller. Rather, the control synthesis approach is fairly straight-forward and simple. The controller formulation has more elegance because we can prove the convergence of the controller to its steady state value. To demonstrate the potential of the proposed technique, a real-life temperature control problem for a heat transfer application is solved. It has been demonstrated that a desired temperature profile can be achieved starting from any arbitrary initial temperature profile.

The mean and turbulence structure simulation of the monsoon trough boundary layer using a one-dimensional model with e-l and e-epsilon closures

An attempt has been made here to study the sensitivity of the mean and the turbulence structure of the monsoon trough boundary layer to the choice of the constants in the dissipation equation for two stations Delhi and Calcutta, using one-dimensional atmospheric boundary layer model with e-epsilon turbulence closure. An analytical discussion of the problems associated with the constants of the dissipation equation is presented. It is shown here that the choice of the constants in the dissipation equation is quite crucial and the turbulence structure is very sensitive to these constants. The modification of the dissipation equation adopted by earlier studies, that is, approximating the Tke generation (due to shear and buoyancy production) in the epsilon-equation by max (shear production, shear + buoyancy production), can be avoided by a suitable choice of the constants suggested here. The observed turbulence structure is better simulated with these constants. The turbulence structure simulation with the constants recommended by Aupoix et al (1989) (which are interactive in time) for the monsoon region is shown to be qualitatively similar to the simulation obtained with the constants suggested here, thus implying that no universal constants exist to regulate dissipation rate. Simulations of the mean structure show little sensitivity to the type of the closure parameterization between e-l and e-epsilon closures. However the turbulence structure simulation with e-epsilon closure is far better compared to the e-l model simulations. The model simulations of temperature profiles compare quite well with the observations whenever the boundary layer is well mixed (neutral) or unstable. However the models are not able to simulate the nocturnal boundary layer (stable) temperature profiles. Moisture profiles are simulated reasonably better. With one-dimensional models, capturing observed wind variations is not up to the mark.

Enhanced charge and spin currents in the one-dimensional disordered mesoscopic Hubbard ring

We consider a one-dimensional mesoscopic Hubbard ring with and without disorder and compute charge and spin stiffness as a measure of the permanent currents. For finite disorder we identify critical disorder strength beyond which the charge currents in a system with repulsive interactions are larger than those for a free system. The spin currents in the disordered repulsive Hubbard model are enhanced only for small U, where the magnetic state of the system corresponds to a charge-density wave pinned to the impurities. For large U, the state of the system corresponds to localized isolated spins and the spin currents are found to be suppressed. For the attractive Hubbard model we find that the charge currents are always suppressed compared to the free system at all length scales.

Persistent currents in a one-dimensional ring for a disordered Hubbard model

We consider a one-dimensional Hubbard model in the presence of disorder. We compute the charge stiffness for a mesoscopic ring as a function of the size L, which is a measure of the persistent currents. We find that for finite disorder the persistent currents of the system with repulsive interactions are larger than those of the system with attractive interactions. This counterintuitive result is due to the fact that local-density fluctuations are reduced in the presence of repulsive interactions.

Hydrothermal synthesis and structure of organically templated one-dimensional and three-dimensional iron fluorophosphate

Two new open-framework iron fluorophosphates, [C(4)N(2)H(12)](0.5) [FeF(HPO(4))(H(2)PO(4))] (I) and [C(4)N(2)H(12)][Fe(4)F(2)(H(2)O)(4)(PO(4))(4)]. 0.5H(2)O (II), were synthesized hydrothermally using piperazine as a templating agent. The structures were determined by single-crystal X-ray diffraction. Compound I crystallizes in the orthorhombic space group Pbca, a = 7.2126(2) Angstrom, b = 14.2071(4) Angstrom, c = 17.1338(2) Angstrom, Z = 8. The structure is composed of infinite anionic chains of [FeF(HPO(4))(H(2)PO(4))](n)(-) built by trans-fluorine sharing FeF(2)O(4) octahedra. These chains are similar to those found in tancoite-type minerals. Compound II crystallizes in the monoclinic space group P2(1)/n, a = 9.9045(3) Angstrom, b = 12.3011(3) Angstrom, c = 17.3220(4) Angstrom, beta = 103.7010(10)degrees, Z = 4. The structure of compound II has a three-dimensional (3D) architecture with an eight-membered channel along the b axis, in which protonoted piperazine molecules reside. The complex framework is built from two types of secondary building unit (SBU): one hexamer [Fe(3)F(2)(H(2)O)(2)(PO(4))(3)] (SBU6), and one dimer [FeO(4)(H(2)O)(2)PO(4)] (SBU2). The vertex sharing between these SBUs create the 3D structure.

Study of translational and rotational mobility and orientational preference of ethane in one-dimensional channels

Structural and dynamical properties of ethane in one-dimensional channels of AlPO4-5 and carbon nanotube have been investigated at dilute concentration with the help of molecular dynamics simulation. Density distributions and orientational structure of ethane have been analyzed. Repulsive interactions seem to play an important role when ethane is located in the narrow part of the AlPO4-5 channel. In AlPO4-5, parallel orientation is predominant over perpendicular orientation except when ethane is located in the broader part of the channel. Unlike in the case of single-file diffusion, our results in carbon nanotube show that at dilute concentrations the mean squared displacement, mu(2)(t) approximate to t(alpha), alpha = 1.8. The autocorrelation function for the z-component of angular velocity of ethane in space-fixed frame of reference shows a pronounced negative correlation. This is attributed to the restriction in the movement of ethane along the x- and y- directions. It is seen that the ratio of reorientational correlation times does not follow the Debye model for confined ethane but it is closer to the predictions of the Debye model for bulk ethane.

A Layered Zinc Phosphate, [C6N4H22][Zn6(PO4)4(HPO4)2], Formed by One-Dimensional Tubes

An open-framework zinc phosphate, [C6N4H22][Zn6(PO4)4(HPO4)2] (I), with alternating inorganic and organic layers has been synthesized hydrothermally from a starting mixture of ZnO, HCl, H3PO4, H2C2O4, and triethylenetetramine. Single-crystal data for I: monoclinic, space GROUP =P21/c (No. 14), a=9.881(1), b=16.857(1), c=8.286(1) Å, β=96.7(1)°, V=1370.8(1) Å3, Z=2, R1=0.06, and wR2=0.13 [1408 observed reflections with I>2σ(I)]. The structure of I comprises a network of ZnO4, PO4, and PO3(OH) tetrahedra forming one-dimensional tubes. The tubes, in turn, are linked via oxygen atoms forming macroanionic inorganic layers with eight-membered apertures. The one-dimensional tube-like architecture in I is a novel feature worthy of note.

Transformations of two-dimensional layered zinc phosphates to three-dimensional and one-dimensional structures

Transformations of the layered zinc phosphates of the compositions [C6N4H22](0.5) [Zn-2 (HPO4)(3)], I, [C3N2H12][Zn-2 (HPO4)(3)], II and [C3N2OH12][Zn-2 (HPO4)(3)], III, containing triethylenetetramine, 1,3-diaminopropane, and 1,3-diamino-2-hydroxypropane, respectively, have been investigated under different conditions. On heating in water, I transforms to a one-dimensional (1-D) ladder and a three-dimensional (3-D) structure, while II gives rise to only a two-dimensional (2-D) layered structure. In the transformation reaction of I with zinc acetate, the same ladder and 3-D structures are obtained along with a tubular layer. Under similar conditions II gives a layered structure formed by the joining of two ladder motifs. III, on the other hand, is essentially unreactive when heated with water and zinc acetate, probably because the presence of the hydroxy group in the amine which hydrogen bonds to the framework. In the presence of piperazine, I, II and III give rise to a four-membered, corner-shared linear chain which is likely to be formed via the ladder structure. In addition, 2-D and 3-D structures derived from the 1-D linear chain or ladder structures are also formed. The primary result from the study is that the layers produce 1-D ladders, which then undergo other transformations. It is noteworthy that in the various transformations carried out, most of the products are single-crystalline.

One-dimensional zinc phosphates with linear chain structure

Three one-dimensional zinc phosphates, [C5N2H14][Zn(HPO4)2], I, [C10N4H26][Zn(HPO4)2].2H2O II, and [C4N2H6]2[Zn(HPO4)], III, have been prepared employing hydro/solvothermal methods in the presence of organic amines. While I and II consist of linear chains of corner-shared four-membered rings, III is a polymeric wire where the amine molecule is directly bonded to the metal center. The wire, as well as the chain in these structures, are held together by hydrogen bond interactions involving the amine and the framework oxygens. The polymeric zinc phosphate with wire-like architecture, III, is only the second example of such architecture. Crystal data: I, monoclinic, P21/c (no. 14), a=8.603(2), b=13.529(2), c=10.880(1) Å, β=94.9(1)°, V=1261.6(1) Å3, Z=4, ρcalc.=1.893 gcm−3, μ(MoKα)=2.234 mm−1, R1=0.032, wR2=0.086, [1532 observed reflections with I>2σ(I)], II, orthorhombic, Pbca (no. 61), a=8.393(1), b=15.286(1), c=22.659(1) Å, V=2906.9(2) Å3, Z=8, ρcalc.=1.794 gcm−3, μ(MoKα)=1.957 mm−1, R1=0.055, wR2=0.11, [1565 observed reflections with I>2σ(I) and III, monoclinic, P21/c (no. 14), a=8.241(1), b=13.750(2), c=10.572(1) Å, β=90.9(1)°, V=1197.7(2) Å3, Z=4, ρcalc.=1.805 gcm−3, μ(MoKα)=2.197 mm−1, R1=0.036, wR2=0.10, [1423 observed reflections with I>2σ(I)].