Plane wave analysis of conical and exponential pipes with incompressible mean flow

The general equation for one-dimensional wave propagation at low flow Mach numbers (M less-than-or-equals, slant0·2) is derived and is solved analytically for conical and exponential shapes. The transfer matrices are derived and shown to be self-consistent. Comparison is also made with the relevant data available in the literature. The transmission loss behaviour of conical and exponential pipes, and mufflers involving these shapes, are studied. Analytical expressions of the same are given for the case of a stationary medium. The mufflers involving conical and exponential pipes are shown to be inferior to simple expansion chambers (of similar dimensions) at higher frequencies from the point of view of noise abatement, as was observed earlier experimentally.

Self-similar solutions of laser produced blast waves

The aerodynamics of the blast wave produced by laser ablation is studied using the piston analogy. The unsteady one-dimensional gasdynamic equations governing the flow an solved under assumption of self-similarity. The solutions are utilized to obtain analytical expressions for the velocity, density, pressure and temperature distributions. The results predict. all the experimentally observed features of the laser produced blast waves.

Estimation of surface temperature from MONTBLEX data

It is observed that the daily mean temperature of the soil is linear with depth and the variation of the temperature is sinusoidal with a period of a day. Based on these observations the one-dimensional heat conduction equation for the soil can be solved which gives the amplitude and phase variation of the temperature wave with depth. Given the temperature data at three levels below the surface, the amplitude and phase variation and hence the surface temperature variation over the day are estimated. The daily mean temperature of the surface is estimated from linear extrapolation of the daily means at the three levels below the surface. Estimated values of soil thermal diffusivity show a subtantial change after sudden and heavy rains.

Magnetic field-induced metal-insulator transitions in graphite and diluted magnetic semiconductors - Discussion

Two topical subjects related with the effect of magnetic field on electrical conduction and the metal-insulator transition are discussed. The first topic is an electronic phase transition in graphite, which is interpreted as a manifestation of a nestingtype instability inherent to a one-dimensional narrow Landau sub-band. The second topic is spin-dependent tranport in III-V based diluted magnetic semiconductors; in particular, a large negative magnetoresistance observed in the vicinity of metal-nonmetal transition.

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.

Quantum-confinement effects on the ordering of the lowest-lying excited states in conjugated chains

The symmetrized density-matrix renormalization-group approach is applied within the extended Hubbard-Peierls model (with parameters U/t, V/t, and bond alternation delta) to study the ordering of the lowest one-photon (1(1)B(u)(-)) and two-photon (2(1)A(g)(+)) states in one-dimensional conjugated systems with chain lengths N up to N = 80 sites. Three different types of crossovers are studied, as a function of U/t, delta, and N. The ''U crossover'' emphasizes the larger ionic character of the 2A(g) state compared to the lowest triplet excitation. The ''delta crossover'' shows strong dependence on both N and U/t. the ''N crossover'' illustrates the more localized nature of the 2A(g) excitation relative to the 1B(u) excitation at intermediate correlation strengths.

Regular versus alternating (FeS4)(n) chains: Magnetism in KFeS2 and CsFeS2

We report crystal magnetic susceptibility results of two S = 1/2 one-dimensional Heisenberg antiferromagnets, KFeS2 and CsFeS2. Both compounds consist of (FeS4)(n) chains with an average Fe-Fe distance of 2.7 Angstrom. In KFeS2, all intrachain Fe-Fe distances are identical. Its magnetic susceptibility is typical of a regular antiferromagnetic chain with spin-spin exchange parameter J = -440.7 K. In CsFeS2, however, the Fe-Fe distances alternate between 2.61 and 2.82 Angstrom. This is reflected in its magnetic susceptibility, which could be fitted with J = -640 K, and the degree of alternation, alpha = 0.3. These compounds form a unique pair, and allow for a convenient experimental comparison of the magnetic properties of regular versus alternating Heisenberg chains.

Spin distributions in antiferromagnetically coupled Mn2+Cu2+ systems: from the pair to the infinite chain

Probably the most informative description of the ground slate of a magnetic molecular species is provided by the spin density map. Such a map may be experimentally obtained from polarized neutron diffraction (PND) data or theoretically calculated using quantum chemical approaches. Density functional theory (DFT) methods have been proved to be well-adapted for this. Spin distributions in one-dimensional compounds may also be computed using the density matrix renormalization group (DMRG) formalism. These three approaches, PND, DFT, and DMRG, have been utilized to obtain new insights on the ground state of two antiferromagnetically coupled Mn2+Cu2+ compounds, namely [Mn(Me-6-[14]ane-N-4)Cu(oxpn)](CF3SO3)(2) and MnCu(pba)(H2O)(3) . 2H(2)O, with Me-6-[14]ane-N-4 = (+/-)-5,7,7,12,14,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane, oxpn = N,N'-bis(3-aminopropyl)oxamido and pba = 1,3-propylenebis(oxamato). Three problems in particular have been investigated: the spin distribution in the mononuclear precursors [Cu(oxpn)] and [Cu(pba)](2-), the spin density maps in the two Mn2+Cu2+ compounds, and the evolution of the spin distributions on the Mn2+ and Cu2+ sites when passing from a pair to a one-dimensional ferrimagnet.

Synthesis, crystal structure and magnetic properties of a polymeric copper(II) Schiff-base complex having binuclear units covalently linked by isonicotinate ligands

The polynuclear copper(II) complex [{Cu2L(O2CC5H4N)}. C2H5OH](x) (1), where H3L is a 1∶2 Schiff base derived from 1,3-diaminopropan-2-ol and salicylaldehyde, has been prepared and structurally characterized. The structure consists of a one-dimensional zigzag chain in which the binuclear [Cu2L](+) units are covalently linked by isonicotinate ligands to give a syndiotactic arrangement of the copper ions protruding outside the chain. In the basic unit, the copper(II) centres are bridged by an alkoxo and a carboxylato ligand, giving a Cu ... Cu distance of 3.492(3) Angstrom and a Cu-O-Cu angle of 130.9(2)degrees. While one copper centre has a square-planar geometry, the other copper is square-pyramidal with the pyridine nitrogen being the axial ligand. The visible electronic spectrum of 1 shows a broad d-d band at 615 nm. The complex shows a rhombic X-band EPR spectral pattern in the polycrystalline phase at 77 K. Magnetic susceptibility measurements in the temperature range 22 to 295 K demonstrate the antiferromagnetic behaviour of 1. A theoretical fit to the magnetic data is based on a model assuming 1 as an equimolar mixture of copper atoms belonging to an antiferromagnetically coupled one-dimensional Heisenberg chain with the other copper atoms outside the chain behaving like paramagnetic centres.

Correlated conformation and charge transport in multiwall carbon nanotube-conducting polymer nanocomposites

The strikingly different charge transport behaviours in nanocomposites of multiwall carbon nanotubes (MWNTs) and conducting polymer polyethylenedioxythiophene-polystyrene-sulfonic-acid (PEDOT-PSS) at low temperatures are explained by probing their conformational properties using small-angle x-ray scattering (SAXS). The SAXS studies indicate the assembly of elongated PEDOT-PSS globules on the walls of nanotubes, coating them partially, thereby limiting the interaction between the nanotubes in the polymer matrix. This results in a charge transport governed mainly by small polarons in the conducting polymer despite the presence of metallic MWNTs. At T > 4 K, hopping of the charge carriers following one-dimensional variable range hopping is evident which also gives rise to a positive magnetoresistance (MR) with an enhanced localization length (similar to 5 nm) due to the presence of MWNTs. However, at T < 4 K, the observation of an unconventional positive temperature coefficient of resistivity is attributed to small polaron tunnelling. The exceptionally large negative MR observed in this temperature regime is conjectured to be due to the presence of quasi-1D MWNTs that can aid in lowering the tunnelling barrier across the nanotube-polymer boundary resulting in large delocalization.

An open-framework zincoborate formed by Zn6B12O24 clusters

A novel zincoborate, Zn(H2O)B2O4.xH(2)O (xapproximate to0.12), I, with open architecture has been synthesized hydrothermally. The 3-dimensional structure is built up of Zn6B12O24 clusters formed by the capping of the polycyclic borate anion, B12O2412-, by Zn3O3 clusters. The open-framework structure of I has one-dimensional 8-membered channels wherein the water molecules reside. Formation of trimeric Zn3O3 clusters as well as the presence of boron in dual coordination, both triangular and tetrahedral, are important structural features of this new zincoborate.

Topological phases, Majorana modes and quench dynamics in a spin ladder system

We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections between spin phases and topologically non-trivial phases of non-interacting fermionic systems, demonstrating the equivalence between the spontaneous breaking of global Z(2) symmetry in spin systems and the existence of isolated Majorana modes. In the Kitaev ladder, we investigate topological properties of the system in different sectors characterized by the presence or absence of a vortex in each plaquette of the ladder. We show that vortex patterns can yield a rich parameter space for tuning into topologically non-trivial phases. We introduce and employ a new topological invariant for explicitly determining the presence of zero energy Majorana modes at the boundaries of such phases. Finally, we discuss dynamic quenching between topologically non-trivial phases in the Kitaev ladder and, in particular, the post-quench dynamics governed by tuning through a quantum critical point.

Modeling re-ignition and chuffing in solid rocket motors

A nonlinear model is developed to numerically simulate dynamic combustion inside a solid rocket motor chamber. Using this model, the phenomena of re-ignition and chuffing are investigated under low-L* conditions. The model consists of two separate submodels (coupled to each other), one for unsteady burning of propellant and the other for unsteady conservation of mass and energy within the chamber. The latter yields instantaneous pressure and temperature within the chamber. The instantaneous burning rate is calculated using a one-dimensional, nonlinear, transient gas-phase model previously developed by the authors. The results presented in this paper show that the model predicts not only the critical L*, but also the various regimes of L*-instabihty. Specifically, the results exhibit (1) amplifying pressure oscillations leading to extinction, and (2) re-ignition after a dormant period following extinction. The re-ignition could be observed only when a radiation heat flux (from the combustion chamber to the propellant surface) was included. Certain high-frequency oscillations, possibly due to intrinsic instability, are observed when the pressure overshoots during re-ignition. At very low values of initial L*, successive cycles of extinction/reignition displaying typical characteristics of chuffing are predicted. Variations of the chuffing frequency and the thickness of propellant burned off during a chuff with L* are found to be qualitatively the same as that reported from experimental observations.

Persistent passive hopping and juggling is possible even with plastic collisions

We describe simple one-dimensional models of passive (no energy input, no control), generally dissipative, vertical hopping and one-ball juggling. The central observation is that internal passive system motions can conspire to eliminate collisions in these systems. For hopping, two point masses are connected by a spring and the lower mass has inelastic collisions with the ground. For juggling, a lower point-mass hand is connected by a spring to the ground and an upper point-mass ball is caught with an inelastic collision and then re-thrown into gravitational free flight. The two systems have identical dynamics. Despite inelastic collisions between non-zero masses, these systems have special symmetric energy-conserving periodic motions where the collision is at zero relative velocity. Additionally, these special periodic motions have a non-zero sized, one-sided region of attraction on the higher-energy side. For either very large or very small mass ratios, the one-sided region of attraction is large. These results persist for mildly non-linear springs and non-constant gravity. Although non-collisional damping destroys the periodic motions, small energy injection makes the periodic motions stable, with a two-sided region of attraction. The existence of such special energy conserving solutions for hopping and juggling points to possibly useful strategies for both animals and robots. The lossless motions are demonstrated with a table-top experiment.

Phase diagram of a two-species lattice model with a linear instability

We discuss the properties of a one-dimensional lattice model of a driven system with two species of particles in which the mobility of one species depends on the density of the other. This model was introduced by Lahiri and Ramaswamy (Phys. Rev. Lett., 79, 1150 (1997)) in the context of sedimenting colloidal crystals, and its continuum version was shown to exhibit an instability arising from linear gradient couplings. In this paper we review recent progress in understanding the full phase diagram of the model. There are three phases. In the first, the steady state can be determined exactly along a representative locus using the condition of detailed balance. The system shows phase separation of an exceptionally robust sort, termed strong phase separation, which survives at all temperatures. The second phase arises in the threshold case where the first species evolves independently of the second, but the fluctuations of the first influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, in which long-range order coexists with fluctuations which do not damp down in the large-size limit. This fluctuation-dominated phase ordering is associated with power law decays in cluster size distributions and a breakdown of the Porod law. The third phase is one with a uniform overall density, and along a representative locus the steady state is shown to have product measure form. Density fluctuations are transported by two kinematic waves, each involving both species and coupled at the nonlinear level. Their dissipation properties are governed by the symmetries of these couplings, which depend on the overall densities. In the most interesting case,, the dissipation of the two modes is characterized by different critical exponents, despite the nonlinear coupling.