Wide-angle X-ray scattering for swollen and glassy poly(2-hydroxyethyl methacrylate)

The wide angle X-ray scattering from glassy poly(2-hydroxyethyl methacrylate) (1) is presented together with that obtained from oriented and swollen samples. The scattering is compared with that previously reported for poly(methyl methacrylate) (PMMA) and the structure discussed in relation to this polymer. The chain conformation is similar to that of PMMA, although some measure of molecular interlocking appears to reduce the main interchain peak while correlated regions of inaccessible free volume between the substantial side groups are held responsible for the main peak at s = 1,25 Å−1.

Application of cylindrical distribution functions to wide-angle X-ray scattering from oriented polymers

A systematic approach is presented for obtaining cylindrical distribution functions (CDF's) of noncrystalline polymers which have been oriented by extension. The scattering patterns and CDF's are also sharpened by the method proposed by Deas and by Ruland. Data from atactic poly(methyl methacrylate) and polystyrene are analysed by these techniques. The methods could also be usefully applied to liquid crystals.

Conformational analysis of oriented non-crystalline polymers using wide angle X-ray scattering

A procedure is presented for obtaining conformational parameters from oriented but non-crystalline polymers. This is achieved by comparison of the experimental wide angle X-ray scattering with that calculated from models but in such a way that foreknowledge of the orientation distribution function is not required. X-ray scattering intensity values for glassy isotactic poly(methylmethacrylate) are analysed by these techniques. The method could be usefully applied to other oriented molecular systems such as liquid crystalline materials.

Contact angle of a hemispherical bubble: an analytical approach

We have calculated the equilibrium shape of the axially symmetric Plateau border along which a spherical bubble contacts a flat wall, by analytically integrating Laplace’s equation in the presence of gravity, in the limit of small Plateau border sizes. This method has the advantage that it provides closed-form expressions for the positions and orientations of the Plateau border surfaces. Results are in very good overall agreement with those obtained from a numerical solution procedure, and are consistent with experimental data. In particular we find that the effect of gravity on Plateau border shape is relatively small for typical bubble sizes, leading to a widening of the Plateau border for sessile bubbles and to a narrowing for pendant bubbles. The contact angle of the bubble is found to depend even more weakly on gravity.

Synthesis and crystal structures of μ-oxido- and μ-hydroxido-bridged dinuclear iron(III) complexes with an N2O donor ligand - a theoretical study on the influence of weak forces on the Fe-O-Fe bridging angle

The synthesis and crystal structures of three nonheme di-iron(III) complexes with a tridentate N,N,O Schiff-base ligand, 2-({[2-(dimethylamino) ethyl] imino} methyl) phenol (HL), are reported. Complexes [Fe2OL2(NCO)(2)] (1a) and [Fe2OL2(SAL)(2)]center dot H2O [SAL = o-(CHO)C6H4O-] (1b) are unsupported mu-oxido-bridged dimers, and [Fe-2(OH)L-2(HCOO)(2)-(Cl)] (2) is a mu-hydroxido-bridged dimer supported by a formato bridging ligand. All complexes have been characterized by X-ray crystallography and spectroscopic analysis. Complex 1b has been reported previously; however, it has been reinvestigated to confirm the presence of a crucial water molecule in the solid state. Structural analyses show that in 1a the iron atoms are pentacoordinate with a bent Fe-O-Fe angle [142.7(2)degrees], whereas in 2 the metal centers are hexacoordinate with a normal Fe-OH-Fe bridging angle [137.9(2)degrees]. The Fe-O-Fe angles in complexes 1a and 1b differ significantly to those usually shown by (mu-oxido) Fe-III complexes. A theoretical study has been performed in order to rationalize this deviation. Moreover, the influence of the water molecule observed in the solid-state structure of 1b on the Fe-O-Fe angle is also analyzed theoretically.

On the existence of two-dimensional Euler flows satisfying energy-Casimir stability criteria

The energy-Casimir stability method, also known as the Arnold stability method, has been widely used in fluid dynamical applications to derive sufficient conditions for nonlinear stability. The most commonly studied system is two-dimensional Euler flow. It is shown that the set of two-dimensional Euler flows satisfying the energy-Casimir stability criteria is empty for two important cases: (i) domains having the topology of the sphere, and (ii) simply-connected bounded domains with zero net vorticity. The results apply to both the first and the second of Arnold’s stability theorems. In the spirit of Andrews’ theorem, this puts a further limitation on the applicability of the method. © 2000 American Institute of Physics.

Nonlinear stability of Euler flows in two-dimensional periodic domains

The non-quadratic conservation laws of the two-dimensional Euler equations are used to show that the gravest modes in a doubly-periodic domain with aspect ratio L = 1 are stable up to translations (or structurally stable) for finite-amplitude disturbances. This extends a previous result based on conservation of energy and enstrophy alone. When L 1, a saturation bound is established for the mode with wavenumber |k| = L −1 (the next-gravest mode), which is linearly unstable. The method is applied to prove nonlinear structural stability of planetary wave two on a rotating sphere.

Control and analysis of oriented thin films of lipid inverse bicontinuous cubic phases using grazing incidence small-angle X‑ray scattering

Lipid cubic phases are complex nanostructures that form naturally in a variety of biological systems, with applications including drug delivery and nanotemplating. Most X-ray scattering studies on lipid cubic phases have used unoriented polydomain samples as either bulk gels or suspensions of micrometer-sized cubosomes. We present a method of investigating cubic phases in a new form, as supported thin films that can be analyzed using grazing incidence small-angle X-ray scattering (GISAXS). We present GISAXS data on three lipid systems: phytantriol and two grades of monoolein (research and industrial). The use of thin films brings a number of advantages. First, the samples exhibit a high degree of uniaxial orientation about the substrate normal. Second, the new morphology allows precise control of the substrate mesophase geometry and lattice parameter using a controlled temperature and humidity environment, and we demonstrate the controllable formation of oriented diamond and gyroid inverse bicontinuous cubic along with lamellar phases. Finally, the thin film morphology allows the induction of reversible phase transitions between these mesophase structures by changes in humidity on subminute time scales, and we present timeresolved GISAXS data monitoring these transformations.

Curl free pressure gradients over orography in a solution of the fully compressible Euler equations with implicit treatment of acoustic and gravity waves

Steep orography can cause noisy solutions and instability in models of the atmosphere. A new technique for modelling flow over orography is introduced which guarantees curl free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain following grids. Curl-free gradients are achieved by using the co-variant components of velocity over orography rather than the usual horizontal and vertical components. In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves. Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous. Results of gravity waves over orography are insensitive to the placement of terrain-following layers. The model with implicit gravity waves is stable in strongly stratified conditions, with N∆t up to at least 10 (where N is the Brunt-V ̈ais ̈al ̈a frequency). A warm bubble rising over orography is simulated and the curl free pressure gradient formulation gives much more accurate results for this test case than a model without this mimetic property.

Modeling the observed proton aurora and ionospheric convection responses to changes in the IMF clock angle: 2. Persistence of ionospheric convection

We apply a numerical model of time-dependent ionospheric convection to two directly driven reconnection pulses during a 15-min interval of southward IMF on 26 November 2000. The model requires an input magnetopause reconnection rate variation, which is here derived from the observed variation in the upstream IMF clock angle, q. The reconnection rate is mapped to an ionospheric merging gap, the MLT extent of which is inferred from the Doppler-shifted Lyman-a emission on newly opened field lines, as observed by the FUV instrument on the IMAGE spacecraft. The model is used to reproduce a variety of features observed during this event: SuperDARN observations of the ionospheric convection pattern and transpolar voltage; FUV observations of the growth of patches of newly opened flux; FUVand in situ observations of the location of the Open-Closed field line Boundary (OCB) and a cusp ion step. We adopt a clock angle dependence of the magnetopause reconnection electric field, mapped to the ionosphere, of the form Enosin4(q/2) and estimate the peak value, Eno, by matching observed and modeled variations of both the latitude, LOCB, of the dayside OCB (as inferred from the equatorward edge of cusp proton emissions seen by FUV) and the transpolar voltage FPC (as derived using the mapped potential technique from SuperDARN HF radar data). This analysis also yields the time constant tOCB with which the open-closed boundary relaxes back toward its equilibrium configuration. For the case studied here, we find tOCB = 9.7 ± 1.3 min, consistent with previous inferences from the observed response of ionospheric flow to southward turnings of the IMF. The analysis confirms quantitatively the concepts of ionospheric flow excitation on which the model is based and explains some otherwise anomalous features of the cusp precipitation morphology.

Modeling the observed proton aurora and ionospheric convection responses to changes in the IMF clock angle: 1. Persistence of cusp proton aurora

We employ a numerical model of cusp ion precipitation and proton aurora emission to fit variations of the peak Doppler-shifted Lyman-a intensity observed on 26 November 2000 by the SI-12 channel of the FUV instrument on the IMAGE satellite. The major features of this event appeared in response to two brief swings of the interplanetary magnetic field (IMF) toward a southward orientation. We reproduce the observed spatial distributions of this emission on newly opened field lines by combining the proton emission model with a model of the response of ionospheric convection. The simulations are based on the observed variations of the solar wind proton temperature and concentration and the interplanetary magnetic field clock angle. They also allow for the efficiency, sampling rate, integration time and spatial resolution of the FUV instrument. The good match (correlation coefficient 0.91, significant at the 98% level) between observed and modeled variations confirms the time constant (about 4 min) for the rise and decay of the proton emissions predicted by the model for southward IMF conditions. The implications for the detection of pulsed magnetopause reconnection using proton aurora are discussed for a range of interplanetary conditions.

Energy and pitch-angle dispersions of LLBL/cusp ions seen at middle altitudes: predictions by the open magnetosphere model

Numerical simulations are presented of the ion distribution functions seen by middle-altitude spacecraft in the low-latitude boundary layer (LLBL) and cusp regions when reconnection is, or has recently been, taking place at the equatorial magnetopause. From the evolution of the distribution function with time elapsed since the field line was opened, both the observed energy/observation-time and pitch-angle/energy dispersions are well reproduced. Distribution functions showing a mixture of magnetosheath and magnetospheric ions, often thought to be a signature of the LLBL, are found on newly opened field lines as a natural consequence of the magnetopause effects on the ions and their flight times. In addition, it is shown that the extent of the source region of the magnetosheath ions that are detected by a satellite is a function of the sensitivity of the ion instrument . If the instrument one-count level is high (and/or solar-wind densities are low), the cusp ion precipitation detected comes from a localised region of the mid-latitude magnetopause (around the magnetic cusp), even though the reconnection takes place at the equatorial magnetopause. However, if the instrument sensitivity is high enough, then ions injected from a large segment of the dayside magnetosphere (in the relevant hemisphere) will be detected in the cusp. Ion precipitation classed as LLBL is shown to arise from the low-latitude magnetopause, irrespective of the instrument sensitivity. Adoption of threshold flux definitions has the same effect as instrument sensitivity in artificially restricting the apparent source region.