A two-dimensional X-ray scattering system for in-situ time-resolving studies of polymer structures subjected to controlled deformations

A two-dimensional X-ray scattering system developed around a CCD-based area detector is presented, both in terms of hardware employed and software designed and developed. An essential feature is the integration of hardware and software, detection and sample environment control which enables time-resolving in-situ wide-angle X-ray scattering measurements of global structural and orientational parameters of polymeric systems subjected to a variety of controlled external fields. The development and operation of a number of rheometers purpose-built for the application of such fields are described. Examples of the use of this system in monitoring degrees of shear-induced orientation in liquid-crystalline systems and crystallization of linear polymers subsequent to shear flow are presented.

Theory of enhanced magnetic anisotropy induced by Pt adatoms on two-dimensional Co clusters supported on a Pt(111) substrate

Calculations are reported of the magnetic anisotropy energy of two-dimensional (2D) Co nanostructures on a Pt(111) substrate. The perpendicular magnetic anisotropy (PMA) of the 2D Co clusters strongly depends on their size and shape, and rapidly decreases with increasing cluster size. The PMA calculated is in reasonable agreement with experimental results. The sensitivity of the results to the Co-Pt spacing at the interface is also investigated and, in particular, for a complete Co monolayer we note that the value of the spacing at the interface determines whether PMA or in-plane anisotropy occurs. We find that the PMA can be greatly enhanced by the addition of Pt adatoms to the top surface of the 2D Co clusters. A single Pt atom can induce in excess of 5 meV to the anisotropy energy of a cluster. In the absence of the Pt adatoms the PMA of the Co clusters falls below 1 meV/Co atom for clusters of about 10 atoms whereas, with Pt atoms added to the surface of the clusters, a PMA of 1 meV/Co atom can be maintained for clusters as large as about 40 atoms. The effect of placing Os atoms on the top of the Co clusters is also considered. The addition of 5d atoms and clusters on the top of ferromagnetic nanoparticles may provide an approach to tune the magnetic anisotropy and moment separately.

The two-dimensional anharmonic oscillator II: the microwave spectrum of silyl isocyanate, SiH3NCO

The J + 1 ← J transitions (J = 2, 3, 4, 5, and 6) in the microwave spectrum of SiH3NCO have been assigned for the vibrational ground state and for the vibrational states v10 = 1, 2, and 3. The results for v10 = 0 confirm earlier work. The vibration-rotation constants show a remarkable variation with v10 and l10. To a large extent the anomalous behavior of these constants has been explained in terms of a strongly anharmonic potential function for the ν10 vibrational mode.

The two-dimensional anharmonic oscillator III: the CCC bending mode of C3O2

Newly observed data on the rotational constants of carbon suboxide in excited vibrational states of the low-wavenumber bending vibration ν7 have been successfully interpreted in terms of the two-dimensional anharmonic oscillator wavefunctions associated with this vibration. By combining these results with published infrared and Raman spectra the vibrational assignment has been extended and a refined bending potential for ν7 has been derived: this has a minimum at a bending angle of about 24° at the central C atom, with an energy maximum at the linear configuration some 23 cm−1 above the minimum. From similar data on the combination and hot bands of ν7 with ν4 (1587 cm−1) and ν2 (786 cm−1) the effective ν7 bending potential has also been determined in the one-quantum excited states of ν4 and ν2. The effective ν7 potential shows significant changes from the ground vibrational state; the central hump in the ν7 potential surface is increased to about 50 cm−1 in the v4 = 1 state, and decreased to about 1 cm−1 in the v2 = 1 state. In the light of these results vibrational assignments are suggested for most of the observed bands in the infrared and Raman spectra of C3O2.

The two-dimensional anharmonic oscillator I: vibration-rotation constants of fulminic acid, HCNO

The lowest-wavenumber vibration of HCNO and DCNO, ν5, is known to involve a largeamplitude low-frequency anharmonic bending of the CH bond against the CNO frame. In this paper the anomalous vibrational dependence of the observed rotational constants B(v5, l5), and of the observed l-doubling interactions, is interpreted according to a simple effective vibration-rotation Hamiltonian in which the appropriate vibrational operators are averaged in an anharmonic potential surface over the normal coordinates (Q5x, Q5y). All of the data on both isotopes are interpreted according to a single potential surface having a minimum energy at a slightly bent configuration of the HCN angle ( 170°) with a maximum at the linear configuration about 2 cm−1 higher. The other coefficients in the Hamiltonian are also interpreted in terms of the structure and the harmonic and anharmonic force fields; the substitution structure at the “hypothetical linear configuration” determined in this way gives a CH bond length of 1.060 Å, in contrast to the value 1.027 Å determined from the ground-state rotational constants. We also discuss the difficulties in rationalizing our effective Hamiltonian in terms of more fundamental theory, as well as the success and limitations of its use in practice.

4,4 '-Dipyridyl-N,N '-dioxide complexes of metal-thiocyanate/selenocyanate: pi-stacked molecular rods as three-dimensional support for two-dimensional polymeric sheets and intra/interchain S center dot center dot center dot S interaction dependent architecture of the R-2(2)(8) synthon driven assembly of one-dimensional polymeric chains

Three supramolecular complexes of Co(II) using SCN-/SeCN- in combination with 4,4'-dipyridyl-N,N'-dioxide (dpyo), i.e., {[Co(SCN)(2)(dpyo)(2)].(dpyo)}(n) ( 1), {[Co(SCN)(2)(dpyo)(H2O)(2)].(H2O)}(n) ( 2), {[Co(SeCN)(2)(dpyo)(H2O)(2)]center dot(H2O)}(n) ( 3), have been synthesized and characterized by single-crystal X-ray analysis. Complex 1 is a rare example of a dpyo bridged two-dimensional (2D) coordination polymer, and pi-stacked dpyo supramolecular rods are generated by the lattice dpyo, passing through the rhombic grid of stacked layers, resulting in a three-dimensional (3D) superstructure. Complexes 2 and 3 are isomorphous one-dimensional (1D) coordination polymers [-Co-dpyo-Co-] that undergo self-assembly leading to a bilayer architecture derived through an R-2(2)(8) H-bonding synthon between coordinated water and dpyo oxygen. A reinvestigation of coordination polymers [Mn(SCN)(2)(dpyo)( H2O)(MeOH)](n) ( 4) and {[Fe(SCN)(2)(dpyo)(H2O)(2)]center dot(H2O)}(n) ( 5) reported recently by our group [ Manna et al. Indian J. Chem. 2006, 45A, 1813] reveals brick wall topology rather than bilayer architecture is due to the decisive role of S center dot center dot center dot S/Se center dot center dot center dot Se interactions in determining the helical nature in 4 and 5 as compared to zigzag polymeric chains in 2 and 3, although the same R-2(2)(8) synthon is responsible for supramolecular assembly in these complexes.

Characterization of the Salmonella typhimurium proteome by semi-automated two dimensional HPLC-mass spectrometry: detection of proteins implicated in multiple antibiotic resistance

The proteome of Salmonella enterica serovar Typhimurium was characterized by 2-dimensional HPLC mass spectrometry to provide a platform for subsequent proteomic investigations of low level multiple antibiotic resistance (MAR). Bacteria (2.15 +/- 0.23 x 10(10) cfu; mean +/- s.d.) were harvested from liquid culture and proteins differentially fractionated, on the basis of solubility, into preparations representative of the cytosol, cell envelope and outer membrane proteins (OMPs). These preparations were digested by treatment with trypsin and peptides separated into fractions (n = 20) by strong cation exchange chromatography (SCX). Tryptic peptides in each SCX fraction were further separated by reversed-phase chromatography and detected by mass spectrometry. Peptides were assigned to proteins and consensus rank listings compiled using SEQUEST. A total of 816 +/- 11 individual proteins were identified which included 371 +/- 33, 565 +/- 15 and 262 +/- 5 from the cytosolic, cell envelope and OMP preparations, respectively. A significant correlation was observed (r(2) = 0.62 +/- 0.10; P < 0.0001) between consensus rank position for duplicate cell preparations and an average of 74 +/- 5% of proteins were common to both replicates. A total of 34 outer membrane proteins were detected, 20 of these from the OMP preparation. A range of proteins (n = 20) previously associated with the mar locus in E. coli were also found including the key MAR effectors AcrA, TolC and OmpF.

Extensivity of two-dimensional turbulence

This study is concerned with how the attractor dimension of the two-dimensional Navier–Stokes equations depends on characteristic length scales, including the system integral length scale, the forcing length scale, and the dissipation length scale. Upper bounds on the attractor dimension derived by Constantin, Foias and Temam are analysed. It is shown that the optimal attractor-dimension estimate grows linearly with the domain area (suggestive of extensive chaos), for a sufficiently large domain, if the kinematic viscosity and the amplitude and length scale of the forcing are held fixed. For sufficiently small domain area, a slightly “super-extensive” estimate becomes optimal. In the extensive regime, the attractor-dimension estimate is given by the ratio of the domain area to the square of the dissipation length scale defined, on physical grounds, in terms of the average rate of shear. This dissipation length scale (which is not necessarily the scale at which the energy or enstrophy dissipation takes place) can be identified with the dimension correlation length scale, the square of which is interpreted, according to the concept of extensive chaos, as the area of a subsystem with one degree of freedom. Furthermore, these length scales can be identified with a “minimum length scale” of the flow, which is rigorously deduced from the concept of determining nodes.

Constraints on the spectral distribution of energy and enstrophy dissipation in forced two-dimensional turbulence

We study two-dimensional (2D) turbulence in a doubly periodic domain driven by a monoscale-like forcing and damped by various dissipation mechanisms of the form νμ(−Δ)μ. By “monoscale-like” we mean that the forcing is applied over a finite range of wavenumbers kmin≤k≤kmax, and that the ratio of enstrophy injection η≥0 to energy injection ε≥0 is bounded by kmin2ε≤η≤kmax2ε. Such a forcing is frequently considered in theoretical and numerical studies of 2D turbulence. It is shown that for μ≥0 the asymptotic behaviour satisfies ∥u∥12≤kmax2∥u∥2, where ∥u∥2 and ∥u∥12 are the energy and enstrophy, respectively. If the condition of monoscale-like forcing holds only in a time-mean sense, then the inequality holds in the time mean. It is also shown that for Navier–Stokes turbulence (μ=1), the time-mean enstrophy dissipation rate is bounded from above by 2ν1kmax2. These results place strong constraints on the spectral distribution of energy and enstrophy and of their dissipation, and thereby on the existence of energy and enstrophy cascades, in such systems. In particular, the classical dual cascade picture is shown to be invalid for forced 2D Navier–Stokes turbulence (μ=1) when it is forced in this manner. Inclusion of Ekman drag (μ=0) along with molecular viscosity permits a dual cascade, but is incompatible with the log-modified −3 power law for the energy spectrum in the enstrophy-cascading inertial range. In order to achieve the latter, it is necessary to invoke an inverse viscosity (μ<0). These constraints on permissible power laws apply for any spectrally localized forcing, not just for monoscale-like forcing.

Unsteady flow simulation of a vertical axis augmented wind turbine: a two-dimensional study

As the integration of vertical axis wind turbines in the built environment is a promising alternative to horizontal axis wind turbines, a 2D computational investigation of an augmented wind turbine is proposed and analysed. In the initial CFD analysis, three parameters are carefully investigated: mesh resolution; turbulence model; and time step size. It appears that the mesh resolution and the turbulence model affect result accuracy; while the time step size examined, for the unsteady nature of the flow, has small impact on the numerical results. In the CFD validation of the open rotor with secondary data, the numerical results are in good agreement in terms of shape. It is, however, observed a discrepancy factor of 2 between numerical and experimental data. Successively, the introduction of an omnidirectional stator around the wind turbine increases the power and torque coefficients by around 30–35% when compared to the open case; but attention needs to be given to the orientation of the stator blades for optimum performance. It is found that the power and torque coefficients of the augmented wind turbine are independent of the incident wind speed considered.

Kraichnan–Leith–Batchelor similarity theory and two-dimensional inverse cascades

We study the scaling properties and Kraichnan–Leith–Batchelor (KLB) theory of forced inverse cascades in generalized two-dimensional (2D) fluids (α-turbulence models) simulated at resolution 8192x8192. We consider α=1 (surface quasigeostrophic flow), α=2 (2D Euler flow) and α=3. The forcing scale is well resolved, a direct cascade is present and there is no large-scale dissipation. Coherent vortices spanning a range of sizes, most larger than the forcing scale, are present for both α=1 and α=2. The active scalar field for α=3 contains comparatively few and small vortices. The energy spectral slopes in the inverse cascade are steeper than the KLB prediction −(7−α)/3 in all three systems. Since we stop the simulations well before the cascades have reached the domain scale, vortex formation and spectral steepening are not due to condensation effects; nor are they caused by large-scale dissipation, which is absent. One- and two-point p.d.f.s, hyperflatness factors and structure functions indicate that the inverse cascades are intermittent and non-Gaussian over much of the inertial range for α=1 and α=2, while the α=3 inverse cascade is much closer to Gaussian and non-intermittent. For α=3 the steep spectrum is close to that associated with enstrophy equipartition. Continuous wavelet analysis shows approximate KLB scaling ℰ(k)∝k−2 (α=1) and ℰ(k)∝k−5/3 (α=2) in the interstitial regions between the coherent vortices. Our results demonstrate that coherent vortex formation (α=1 and α=2) and non-realizability (α=3) cause 2D inverse cascades to deviate from the KLB predictions, but that the flow between the vortices exhibits KLB scaling and non-intermittent statistics for α=1 and α=2.

The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.