Polymer Adsorption on Curved Surfaces: Finite chain length corrections

The structural properties of polymers adsorbed onto a surface have been widely investigated using self-consistent mean-field theories. Recently, analytical mean-field theories have been applied to study polymer adsorption on curved surfaces but all in the context of the ground state dominance approximation in which the polymer chain length (N) is essentially infinite. Using an expression for the free energy by Semenov, we determine leading order (in 1/N) corrections due to the finiteness of the polymer chain length on surface tension, spontaneous curvature, and rigidity constants.Comment: 24 pages, 7 figures. Accepted for publication in Macromolecule

Density Functional Theory of a Curved Liquid-Vapour Interface: Evaluation of the rigidity constants

It is argued that to arrive at a quantitative description of the surface tension of a liquid drop as a function of its inverse radius, it is necessary to include the bending rigidity k and Gaussian rigidity k_bar in its description. New formulas for k and k_bar in the context of density functional theory with a non-local, integral expression for the interaction between molecules are presented. These expressions are used to investigate the influence of the choice of Gibbs dividing surface and it is shown that for a one-component system, the equimolar surface has a special status in the sense that both k and k_bar are then the least sensitive to a change in the location of the dividing surface. Furthermore, the equimolar value for k corresponds to its maximum value and the equimolar value for k_bar corresponds to its minimum value. An explicit evaluation using a short-ranged interaction potential between molecules, shows that k is negative with a value around minus 0.5-1.0 kT and that k_bar is positive with a value which is a bit more than half the magnitude of k. Finally, for dispersion forces between molecules, we show that a term proportional to log(R)/R^2 replaces the rigidity constants and we determine the (universal) proportionality constants.Comment: 28 pages; 5 figures; accepted for publication in J. Phys.: Condens. Matter (2013

Geometry of lipid vesicle adhesion

The adhesion of a lipid membrane vesicle to a fixed substrate is examined from a geometrical point of view. This vesicle is described by the Helfrich hamiltonian quadratic in mean curvature; it interacts by contact with the substrate, with an interaction energy proportional to the area of contact. We identify the constraints on the geometry at the boundary of the shared surface. The result is interpreted in terms of the balance of the force normal to this boundary. No assumptions are made either on the symmetry of the vesicle or on that of the substrate. The strong bonding limit as well as the effect of curvature asymmetry on the boundary are discussed.Comment: 7 pages, some major changes in sections III and IV, version published in Physical Review

Tension, rigidity and preferential curvature of interfaces between coexisting polymer solutions

The properties of the interface in a phase-separated solution of polymers with different degrees of polymerization and Kuhn segment lengths are calculated. The starting point is the planar interface, the profile of which is calculated in the so-called 'blob model', which incorporates the solvent in an implicit way. The next step is the study of a metastable droplet phase formed by imposing a chemical potential different from that at coexistence. The pressure difference across the curved interface, which corresponds to this higher chemical potential, is used to calculate the curvature properties of the droplet. Interfacial tensions, Tolman lengths and rigidities are calculated and used for predictions for a realistic experimental case. The results suggest that interfaces between phase-separated solutions of polymers exhibit, in general, a preferential curvature, which stabilizes droplets of low molecular mass polymer in a high molecular mass macroscopic phase.Comment: 21 pages; 8 figures; accepted for publication in Macromolecule

The Finite Field Kakeya Problem

A Besicovitch set in AG(n,q) is a set of points containing a line in every direction. The Kakeya problem is to determine the minimal size of such a set. We solve the Kakeya problem in the plane, and substantially improve the known bounds for n greater than 4.Comment: 13 page

Some colouring problems for Paley graphs

The Paley graph Pq, where q≡1(mod4) is a prime power, is the graph with vertices the elements of the finite field Fq and an edge between x and y if and only if x-y is a non-zero square in Fq. This paper gives new results on some colouring problems for Paley graphs and related discussion. © 2005 Elsevier B.V. All rights reserved

Molecular Dynamics Study of the Nematic-Isotropic Interface

We present large-scale molecular dynamics simulations of a nematic-isotropic interface in a system of repulsive ellipsoidal molecules, focusing in particular on the capillary wave fluctuations of the interfacial position. The interface anchors the nematic phase in a planar way, i.e., the director aligns parallel to the interface. Capillary waves in the direction parallel and perpendicular to the director are considered separately. We find that the spectrum is anisotropic, the amplitudes of capillary waves being larger in the direction perpendicular to the director. In the long wavelength limit, however, the spectrum becomes isotropic and compares well with the predictions of a simple capillary wave theory.Comment: to appear in Phys. Rev.

Behavioural and physiological consequences of acute social defeat in growing gilts: effects of the social environment

Endocrine, behavioural and immunologic processes, together with body growth, were evaluated in gilts that were defeated at 10 weeks of age in resident-intruder tests. Immediately after defeat, gilts were either separated from or reunited with a familiar conspecific (litter-mate; always a barrow). Gilts were assigned to one of four treatments: (a) DI: defeat, followed by isolation (separation from original litter-mate; n=8); (b) I: no defeat, isolation (control group; n=9); (c) DP; defeat, followed by pair-housing (reunion with original litter-mate; n=8); and (d) P: no defeat, pair-housing (control group; n=8). The following general conclusions were derived: (1) social defeat caused pronounced short-term elevations in hypothalamic-pituitary-adrenal (HPA) and sympathetic-adrenal medullary activities, and of prolactin levels. Moreover, as soon as 1 h after defeat, percentages of blood lymphocytes and neutrophilic granulocytes were, respectively, decreased and increased; (2) social defeat had some long-lasting influence on behaviour and physiology, but isolation predominantly determined responses in the longer term. Defeat, as well as isolation, resulted in increased cardiovascular activities compared to P controls, as observed in a novel object test (NOT: +7 days) and an aversion test (AVT: +14 days). Moreover, defeated as well as isolated gilts did not habituate to a repeated novel environment test (NET: -7, +2 and +7 days) in terms of frequencies of vocalising, whereas P controls did. Isolation, through the separation from any other pig, was responsible for the other observed long-term characteristics, which developed progressively. Isolated gilts showed high mobilities and high cortisol responses in the repeated NET (+7 days), not being habituated. This contrasted the reactions of pair-housed gilts, which were much reduced. In addition to their high cardiovascular activities in the NOT and the AVT, isolated gilts also displayed higher heart rates in the repeated NET and during human presence following the NOT, compared to pair-housed gilts. Finally, isolated gilts were more inhibited to approach a novel object (in the NOT) than pair-housed pigs; and (3) stress responses of defeated gilts were modulated by the subsequent social environment. Stimulation of the HPA-axis (plasma- and salivary cortisol) was prolonged in those defeated gilts which were isolated (observed in the first hour). Changes in leucocyte subsets were still observed after 3 days in DI, but were `normalised' within 1 day in DP gilts. Two days after defeat, habituation to the repeated NET in terms of mobility and salivary cortisol responses occurred in control and DP gilts, but not in DI gilts. We argue that these effects of the social environment shortly after defeat were related to a stress-reducing effect of a stable social relationship, i.e. social support.

A comparative study of the application of two horse welfare assessment protocols

Two assessment protocols for horse welfare were compared: the Swedish official protocol (OP) and a newly developed horse welfare assessment protocol (HWAP). The protocols differ in composition: the HWAP contains 20 animal-based (35.7%), 28 resource-based (50.0%) and 8 management-based (14.3%) measures whereas the OP has 4 animal-based (8.9%), 21-resource-based (46.7%), 16-management-based (35.6%) and 4-uncategorized measures (8.9%). The HWAP detected more welfare issues than the OP for 11 out of 12 welfare criteria. The OP took less time to assess (2-4h) compared to the HWAP (3h 20min to 8h 40min). The added level of detail and more animal-based measures means that the HWAP provides a more thorough assessment of welfare of the individual animal than the OP