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.

Rheology of magmas with bimodal crystal size and shape distributions: insights from analog experiments

Magmas in volcanic conduits commonly contain microlites in association with preexisting phenocrysts, as often indicated by volcanic rock textures. In this study, we present two different experiments that inves- tigate the flow behavior of these bidisperse systems. In the first experiments, rotational rheometric methods are used to determine the rheology of monodisperse and polydisperse suspensions consisting of smaller, prolate particles (microlites) and larger, equant particles (phenocrysts) in a bubble‐free Newtonian liquid (silicate melt). Our data show that increasing the relative proportion of prolate microlites to equant pheno- crysts in a magma at constant total particle content can increase the relative viscosity by up to three orders of magnitude. Consequently, the rheological effect of particles in magmas cannot be modeled by assuming a monodisperse population of particles. We propose a new model that uses interpolated parameters based on the relative proportions of small and large particles and produces a considerably improved fit to the data than earlier models. In a second series of experiments we investigate the textures produced by shearing bimodal suspensions in gradually solidifying epoxy resin in a concentric cylinder setup. The resulting textures show the prolate particles are aligned with the flow lines and spherical particles are found in well‐organized strings, with sphere‐depleted shear bands in high‐shear regions. These observations may explain the measured variation in the shear thinning and yield stress behavior with increasing solid fraction and particle aspect ratio. The implications for magma flow are discussed, and rheological results and tex- tural observations are compared with observations on natural samples.

Effect of salt on the compression of polyelectrolyte brushes in a theta solvent

Classical strong-stretching theory (SST) predicts that, as opposing polyelectrolyte brushes are compressed together in a salt-free theta solvent, they contract so as to maintain a finite polymer-free gap, which offers a potential explanation for the ultra-low frictional forces observed in experiments even with the application of large normal forces. However, the SST ignores chain fluctuations, which would tend to close the gap resulting in physical contact and in turn significant friction. In a preceding study, we examined the effect of fluctuations using self-consistent field theory (SCFT) and illustrated that high normal forces can still be applied before the gap is destroyed. We now look at the effect of adding salt. It is found to reduce the long-range interaction between the brushes but has little effect on the short-range part, provided the concentration does not enter the salted-brush regime. Consequently, the maximum normal force between two planar brushes at the point of contact is remarkably unaffected by salt. For the crossed-cylinder geometry commonly used in experiments, however, there is a gradual reduction because in this case the long-range part of the interaction contributes to the maximum normal force.

Development of biomimetic squid-inspired suckers

Biomechanical properties of squid suckers were studied to provide inspiration for the development of sucker artefacts for a robotic octopus. Mechanical support of the rings found inside squid suckers was studied by bending tests. Tensile tests were carried out to study the maximum possible sucking force produced by squid suckers based on the strength of sucker stalks, normalized by the sucking areas. The squid suckers were also directly tested to obtain sucking forces by a special testing arrangement. Inspired by the squid suckers, three types of sucker artefacts were developed for the arm skin of an octopus inspired robot. The first sucker artefact made of knitted nylon sheet reinforced silicone rubber has the same shape as the squid suckers. Like real squid suckers, this type of artefact also has a stalk that is connected to the arm skin and a ring to give radial support.The second design is a straight cylindrical structure with uniform wall thickness made of silicone rubber. One end of the cylinder is directly connected to the arm skin and the other end is open. The final design of the sucker has a cylindrical base and a concave meniscus top. The meniscus was formed naturally using the surface tension of silicone gel, which leads to a higher level of the liquid around the edge of a container. The wall thickness decreases towards the tip of the sucker opening. Sucking forces of all three types of sucker artefacts were measured. Advantages and isadvantages of each sucker type were discussed. The final design of suckers has been implemented to the arm skin prototypes.

Approximate solution of second kind integral equations on infinite cylindrical surfaces

The paper considers second kind integral equations of the form $\phi (x) = g(x) + \int_S {k(x,y)} \phi (y)ds(y)$ (abbreviated $\phi = g + K\phi $), in which S is an infinite cylindrical surface of arbitrary smooth cross section. The “truncated equation” (abbreviated $\phi _a = E_a g + K_a \phi _a $), obtained by replacing S by $S_a $, a closed bounded surface of class $C^2 $, the boundary of a section of the interior of S of length $2a$, is also discussed. Conditions on k are obtained (in particular, implying that K commutes with the operation of translation in the direction of the cylinder axis) which ensure that $I - K$ is invertible, that $I - K_a $ is invertible and $(I - K_a )^{ - 1} $ is uniformly bounded for all sufficiently large a, and that $\phi _a $ converges to $\phi $ in an appropriate sense as $a \to \infty $. Uniform stability and convergence results for a piecewise constant boundary element collocation method for the truncated equations are also obtained. A boundary integral equation, which models three-dimensional acoustic scattering from an infinite rigid cylinder, illustrates the application of the above results to prove existence of solution (of the integral equation and the corresponding boundary value problem) and convergence of a particular collocation method.

Analytical and numerical solutions describing the inward solidification of a binary melt

We present a mathematical model describing the inward solidification of a slab, a circular cylinder and a sphere of binary melt kept below its equilibrium freezing temperature. The thermal and physical properties of the melt and solid are assumed to be identical. An asymptotic method, valid in the limit of large Stefan number is used to decompose the moving boundary problem for a pure substance into a hierarchy of fixed-domain diffusion problems. Approximate, analytical solutions are derived for the inward solidification of a slab and a sphere of a binary melt which are compared with numerical solutions of the unapproximated system. The solutions are found to agree within the appropriate asymptotic regime of large Stefan number and small time. Numerical solutions are used to demonstrate the dependence of the solidification process upon the level of impurity and other parameters. We conclude with a discussion of the solutions obtained, their stability and possible extensions and refinements of our study.

Spectral analysis and the Aharonov-Bohm\~ effect on certain almost-Riemannian manifold

We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalised Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

Emergence dynamics of barnyardgrass and jimsonweed from two depths when switching from conventional to reduced and no-till conditions

A cylinder experiment was conducted in northern Greece during 2005 and 2006 to assess emergence dynamics of barnyardgrass (Echinochloa crus-galli (L.) Beauv.) and jimsonweed (Datura stramonium L.) in the case of a switch from conventional to conservation tillage systems (CT). Emergence was surveyed from two burial depths (5 and 10 cm) and with simulation of reduced tillage (i.e. by soil disturbance) and no-till conditions. Barnyardgrass emergence was significantly affected by burial depth, having greater emergence from 5 cm depth (96%) although even 78% of seedlings emerged from 10 cm depth after the two years of study. Emergence of barnyardgrass was stable across years from the different depths and tillage regimes. Jimsonweed seeds showed lower germination than barnyardgrass during the study period, whereas its emergence was significantly affected by soil disturbance having 41% compared to 28% without disturbance. A burial depth x soil disturbance interaction was also determined, which showed higher emergence from 10 cm depth with soil disturbance. Jimsonweed was found to have significantly higher emergence from 10 cm depth with soil disturbance in Year 2. Seasonal emergence timing of barnyardgrass did not vary between the different burial depth and soil disturbance regimes, as it started in April and lasted until end of May in both years. Jimsonweed showed a bimodal pattern, with first emergence starting end of April until mid-May and the second ranging from mid-June to mid-August from 10 cm burial depth and from mid-July to mid-August from 5 cm depth, irrespective of soil disturbance in both cases.