Electric field alignment in thin films of cylinder-forming diblock copolymer

We investigate thin films of cylinder-forming diblock copolymer confined between electrically charged parallel plates, using self-consistent-field theory ( SCFT) combined with an exact treatment for linear dielectric materials. Our study focuses on the competition between the surface interactions, which tend to orient cylinder domains parallel to the plates, and the electric field, which favors a perpendicular orientation. The effect of the electric field on the relative stability of the competing morphologies is demonstrated with equilibrium phase diagrams, calculated with the aid of a weak-field approximation. As hoped, modest electric fields are shown to have a significant stabilizing effect on perpendicular cylinders, particularly for thicker films. Our improved SCFT-based treatment removes most of the approximations implemented by previous approaches, thereby managing to resolve outstanding qualitative inconsistencies among different approximation schemes.

Use of a reduced Schiff-Base ligand to prepare novel chloro-bridged chains of rare Cu(II) trinuclear complexes with mixed azido/oxo and chloro/oxo bridges

Two mixed bridged one-dimensional (1D) polynuclear complexes, [Cu3L2(mu(1,1)-N-3)(2)(mu-Cl)Cl](n) (1) and {[Cu3L2(mu-Cl)(3)Cl]center dot 0.46CH(3)OH}(n), (2), have been synthesized using the tridentate reduced Schiff-base ligand HL (2-[(2-dimethylamino-ethylamino)-methyl]-phenol). The complexes have been characterized by X-ray structural analyses and variable-temperature magnetic susceptibility measurements. In both complexes the basic trinuclear angular units are joined together by weak chloro bridges to form a 1D chain. The trinuclear structure of 1 is composed of two terminal square planar [Cu(L)(mu(1,1)-N-3)] units connected by a central Cu(II) atom through bridging nitrogen atoms of end-on azido ligands and the phenoxo oxygen atom of the tridentate ligand. These four coordinating atoms along with a chloride ion form a distorted trigonal bipyramidal geometry around the central Cu(II). The structure of 2 is similar; the only difference being a Cl bridge replacing the mu(1,1)-N-3 bridge in the trinuclear unit. The magnetic properties of both trinuclear complexes can be very well reproduced with a simple linear symmetrical trimer model (H = JS(i)S(i+1)) with only one intracluster exchange coupling (J) including a weak intertrimer interaction (.j) reproduced with the molecular field approximation. This model provides very satisfactory fits for both complexes in the whole temperature range with the following parameters: g = 2.136(3), J = 93.9(3) cm(-1) and zj= -0.90(3) cm(-1) (z = 2) for 1 and g = 2.073(7), J = -44.9(4) cm(-1) and zJ = -1.26(6) cm(-1) (z = 2) for 2.

Coalescence of particles by differential sedimentation

We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent terminal velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with a differential sedimentation kernel. We obtain self-similar steady-state and time-dependent solutions to the kinetic equation, using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS) of moving and merging particles, and a good agreement is found.

Rovibrational energy levels of hydrogen peroxide, studied by MULTIMODE with a reaction path Hamiltonian

Recently. Carter and Handy [J. Chem. Phys. 113 (2000) 987] have introduced the theory of the reaction path Hamiltonian (RPH) [J. Chem. Phys. 72 (1980) 99] into the variational scheme MULTIMODE, for the calculation of the J = 0 vibrational levels of polyatomic molecules, which have a single large-amplitude motion. In this theory the reaction path coordinate s becomes the fourth dimension of the moment-of-inertia tensor, and must be treated separately from the remaining 3N - 7 normal coordinates in the MULTIMODE program. In the modified program, complete integration is performed over s, and the M-mode MULTIMODE coupling approximation for the evaluation of the matrix elements applies only to the 3N - 7 normal coordinates. In this paper the new algorithm is extended to the calculation of rotational-vibration energy levels (i.e. J > 0) with the RPH, following from our analogous implementation for rigid molecules [Theoret. Chem. Acc. 100 (1998) 191]. The full theory is given, and all extra terms have been included to give the exact kinetic energy operator. In order to validate the new code, we report studies on hydrogen peroxide (H2O2), where the reaction path is equivalent to torsional motion. H2O2 has previously been studied variationally using a valence coordinate Hamiltonian; complete agreement for calculated rovibrational levels is obtained between the previous results and those from the new code, using the identical potential surface. MULTIMODE is now able to calculate rovibrational levels for polyatomic molecules which have one large-amplitude motion. (C) 2003 Elsevier B.V. All rights reserved.

Strong-segregation limit of the self-consistent field theory for diblock copolymer melts

The self-consistent field theory (SCFT) introduced by Helfand for diblock copolymer melts is expected to converge to the strong-segregation theory (SST) of Semenov in the asymptotic limit, $\chi N \rightarrow \infty$. However, past extrapolations of the lamellar/cylinder and cylinder/sphere phase boundaries, within the standard unit-cell approximation, have cast some doubts on whether or not this is actually true. Here we push the comparison further by extending the SCFT calculations to $\chi N = 512,000$, by accounting for exclusion zones in the coronae of the cylindrical and spherical unit cells, and by examining finite-segregation corrections to SST. In doing so, we provide the first compelling evidence that SCFT does indeed reduce to SST.

Unit-cell approximation for diblock−copolymer brushes grafted to spherical particles

This paper examines the equilibrium phase behavior of thin diblock-copolymer films tethered to a spherical core, using numerical self-consistent field theory (SCFT). The computational cost of the calculation is greatly reduced by implementing the unit-cell approximation (UCA) routinely used in the study of bulk systems. This provides a tremendous reduction in computational time, permitting us to map out the phase behavior more extensively and allowing us to consider far larger particles. The main consequence of the UCA is that it omits packing frustration, but evidently the effect is minor for large particles. On the other hand, when the particles are small, the UCA calculation can be readily followed up with the full SCFT, the comparison to which conveniently allows one to quantitatively assess the effect of packing frustration.

A variational method to retrieve the extinction profile in liquid clouds using multiple field-of-view lidar

Liquid clouds play a profound role in the global radiation budget but it is difficult to remotely retrieve their vertical profile. Ordinary narrow field-of-view (FOV) lidars receive a strong return from such clouds but the information is limited to the first few optical depths. Wideangle multiple-FOV lidars can isolate radiation scattered multiple times before returning to the instrument, often penetrating much deeper into the cloud than the singly-scattered signal. These returns potentially contain information on the vertical profile of extinction coefficient, but are challenging to interpret due to the lack of a fast radiative transfer model for simulating them. This paper describes a variational algorithm that incorporates a fast forward model based on the time-dependent two-stream approximation, and its adjoint. Application of the algorithm to simulated data from a hypothetical airborne three-FOV lidar with a maximum footprint width of 600m suggests that this approach should be able to retrieve the extinction structure down to an optical depth of around 6, and total opticaldepth up to at least 35, depending on the maximum lidar FOV. The convergence behavior of Gauss-Newton and quasi-Newton optimization schemes are compared. We then present results from an application of the algorithm to observations of stratocumulus by the 8-FOV airborne “THOR” lidar. It is demonstrated how the averaging kernel can be used to diagnose the effective vertical resolution of the retrieved profile, and therefore the depth to which information on the vertical structure can be recovered. This work enables exploitation of returns from spaceborne lidar and radar subject to multiple scattering more rigorously than previously possible.

Inverse problems in neural field theory

We study inverse problems in neural field theory, i.e., the construction of synaptic weight kernels yielding a prescribed neural field dynamics. We address the issues of existence, uniqueness, and stability of solutions to the inverse problem for the Amari neural field equation as a special case, and prove that these problems are generally ill-posed. In order to construct solutions to the inverse problem, we first recast the Amari equation into a linear perceptron equation in an infinite-dimensional Banach or Hilbert space. In a second step, we construct sets of biorthogonal function systems allowing the approximation of synaptic weight kernels by a generalized Hebbian learning rule. Numerically, this construction is implemented by the Moore–Penrose pseudoinverse method. We demonstrate the instability of these solutions and use the Tikhonov regularization method for stabilization and to prevent numerical overfitting. We illustrate the stable construction of kernels by means of three instructive examples.

Detection of Chlamydia psittaci DNA in avian clinical samples by polymerase chain reaction

A polymerase chain reaction (PCR) assay was developed to detect Chlamydia psittaci DNA in faeces and tissue samples from avian species. Primers were designed to amplify a 264 bp product derived from part of the 5' non-translated region and part of the coding region of the ompA gene which encodes the major outer membrane protein. Amplified sequences were confirmed by Southern hybridization using an internal probe. The sensitivity of the combined assay was found to be between 60 to 600 fg of chlamydial DNA (approximately 6 to 60 genome copies). The specificity of the assay was confirmed since PCR product was not obtained from samples containing several serotypes of C. trachomatis, strains of C. pneumoniae, the type strain of C. pecorum, nor from samples containing microorganisms commonly found in the avian gut flora. In this study, 404 avian faeces and 141 avian tissue samples received by the Central Veterinary Laboratory over a 6 month period were analysed by PCR, antigen detection ELISA and where possible, cell culture isolation. PCR performed favourably compared with ELISA and cell culture, or with ELISA alone. The PCR assay was especially suited to the detection of C. psittaci DNA in avian faeces samples. The test was also useful when applied to tissue samples from small contact birds associated with a case of human psittacosis where ELISA results were negative and chlamydial isolation was a less favourable method due to the need for rapid diagnosis.

Metabifurcation analysis of a mean field model of the cortex

Mean field models (MFMs) of cortical tissue incorporate salient, average features of neural masses in order to model activity at the population level, thereby linking microscopic physiology to macroscopic observations, e.g., with the electroencephalogram (EEG). One of the common aspects of MFM descriptions is the presence of a high-dimensional parameter space capturing neurobiological attributes deemed relevant to the brain dynamics of interest. We study the physiological parameter space of a MFM of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features. These correlations are revealed by the study of bifurcation plots, which show that the model responses to changes in inhibition belong to two archetypal categories or “families”. After investigating and characterizing them in depth, we discuss their essential differences in terms of four important aspects: power responses with respect to the modeled action of anesthetics, reaction to exogenous stimuli such as thalamic input, and distributions of model parameters and oscillatory repertoires when inhibition is enhanced. Furthermore, while the complexity of sustained periodic orbits differs significantly between families, we are able to show how metamorphoses between the families can be brought about by exogenous stimuli. We here unveil links between measurable physiological attributes of the brain and dynamical patterns that are not accessible by linear methods. They instead emerge when the nonlinear structure of parameter space is partitioned according to bifurcation responses. We call this general method “metabifurcation analysis”. The partitioning cannot be achieved by the investigation of only a small number of parameter sets and is instead the result of an automated bifurcation analysis of a representative sample of 73,454 physiologically admissible parameter sets. Our approach generalizes straightforwardly and is well suited to probing the dynamics of other models with large and complex parameter spaces.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat “patchy” connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a “lattice-directed” traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.

Monte Carlo field-theoretic simulations for melts of symmetric diblock copolymer

Monte Carlo field-theoretic simulations (MCFTS) are performed on melts of symmetric diblock copolymer for invariant polymerization indexes extending down to experimentally relevant values of N̅ ∼ 10^4. The simulations are performed with a fluctuating composition field, W_−(r), and a pressure field, W_+(r), that follows the saddle-point approximation. Our study focuses on the disordered-state structure function, S(k), and the order−disorder transition (ODT). Although shortwavelength fluctuations cause an ultraviolet (UV) divergence in three dimensions, this is readily compensated for with the use of an effective Flory−Huggins interaction parameter, χ_e. The resulting S(k) matches the predictions of renormalized one-loop (ROL) calculations over the full range of χ_eN and N̅ examined in our study, and agrees well with Fredrickson−Helfand (F−H) theory near the ODT. Consistent with the F−H theory, the ODT is discontinuous for finite N̅ and the shift in (χ_eN)_ODT follows the predicted N̅^−1/3 scaling over our range of N̅.

Reconnection at the high-latitude magnetopause during northward interplanetary magnetic field conditions

The Polar spacecraft had a prolonged encounter with the high-latitude dayside magnetopause on May 29, 1996. This encounter with the magnetopause occurred when the interplanetary magnetic field was directed northward. From the three-dimensional electron and ion distribution functions measured by the Hydra instrument, it has been possible to identify nearly all of the distinct boundary layer regions associated with high-latitude reconnection. The regions that have been identified are (1) the cusp; (2) the magnetopause current layer; (3) magnetosheath field lines that have interconnected in only the Northern Hemisphere; (4) magnetosheath field lines that have interconnected in only the Southern Hemisphere; (5) magnetosheath field lines that have interconnected in both the Northern and Southern Hemispheres; (6) magnetosheath that is disconnected from the terrestrial magnetic field; and (7) high-latitude plasma sheet field lines that are participating in magnetosheath reconnection. Reconnection over this time period was occurring at high latitudes over a broad local-time extent, interconnecting the magnetosheath and lobe and/or plasma sheet field lines in both the Northern and Southern Hemispheres. Newly closed boundary layer field lines were observed as reconnection occur-red first at high latitudes in one hemisphere and then later in the other. These observations establish the location of magnetopause reconnection during these northward interplanetary magnetic field conditions as being at high latitudes, poleward of the cusp, and further reinforce the general interpretation of electron and ion phase space density signatures as indicators of magnetic reconnection and boundary layer formation.

Cusp ion steps, field-aligned currents and poleward moving auroral forms

We predict the field-aligned currents around cusp ion steps produced by pulsed reconnection between the geomagnetic field and an interplanetary magnetic field (IMF) with a B-Y component that is large in magnitude. For B-Y > 0, patches of newly opened flux move westward and eastward in the Northern and Southern Hemispheres, respectively, under the influence of the magnetic curvature force. These flow directions are reversed for B-Y < 0. The speed of this longitudinal motion initially grows with elapsed time since reconnection, but then decays as the newly opened field lines straighten. We predict sheets of field-aligned current on the boundaries between the patches produced by successive reconnection pulses, associated with the difference in the speeds of their longitudinal motion. For low elapsed times since reconnection, near the equatorward edge of the cusp region where the field lines are accelerating, the field-aligned current sheets will be downward or upward in both hemispheres for positive or negative IMF B-Y, respectively. At larger elapsed times since reconnection, as events slow and evolve from the cusp into the mantle region, these field-aligned current directions will be reversed. Observations by the Polar spacecraft on August 26,1998, show the predicted upward current sheets at steps seen in the mantle region for IMF B-Y > 0. Mapped into the ionosphere, the steps coincide with poleward moving events seen by the CUTLASS HF radar. The mapped location of the largest step also coincides with a poleward moving arc seen by the UVI imager on Polar. We show that the arc is consistent with a region of upward field-aligned current that has become unstable, such that a potential drop of about 1 kV formed below the spacecraft. The importance of these observations is that they confirm that the poleward moving events, as seen by the HF radar and the UV imager, are due to pulsed magnetopause reconnection. Milan et al. [2000] noted that the great longitudinal extent of these events means that the required reconnection pulses would have contributed almost all the voltage placed across the magnetosphere at this time. The observations also show that auroral arcs can form on open field lines in response to the pulsed application of voltage at the magnetopause.

Spatial and temporal variability of the concentration field from localized releases in a regular building array

Spatial and temporal fluctuations in the concentration field from an ensemble of continuous point-source releases in a regular building array are analyzed from data generated by direct numerical simulations. The release is of a passive scalar under conditions of neutral stability. Results are related to the underlying flow structure by contrasting data for an imposed wind direction of 0 deg and 45 deg relative to the buildings. Furthermore, the effects of distance from the source and vicinity to the plume centreline on the spatial and temporal variability are documented. The general picture that emerges is that this particular geometry splits the flow domain into segments (e.g. “streets” and “intersections”) in each of which the air is, to a first approximation, well mixed. Notable exceptions to this general rule include regions close to the source, near the plume edge, and in unobstructed channels when the flow is aligned. In the oblique (45 deg) case the strongly three-dimensional nature of the flow enhances mixing of a scalar within the canopy leading to reduced temporal and spatial concentration fluctuations within the plume core. These fluctuations are in general larger for the parallel flow (0 deg) case, especially so in the long unobstructed channels. Due to the more complex flow structure in the canyon-type streets behind buildings, fluctuations are lower than in the open channels, though still substantially larger than for oblique flow. These results are relevant to the formulation of simple models for dispersion in urban areas and to the quantification of the uncertainties in their predictions.