2,848 research outputs found

    Orientational phase transitions in the hexagonal phase of a diblock copolymer melt under shear flow

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    We generalize the earlier theory by Fredrickson [J. Rheol. v.38, 1045 (1994)] to study the orientational behaviour of the hexagonal phase of diblock copolymer melt subjected to steady shear flow. We use symmetry arguments to show that the orientational ordering in the hexagonal phase is a much weaker effect than in the lamellae. We predict the parallel orientation to be stable at low and the perpendicular orientation at high shear rates. Our analysis reproduces the experimental results by Tepe et al. [Macromolecules v.28, 3008 (1995)] and explains the difficulties in experimental observation of the different orientations in the hexagonal phase.Comment: 21 pages, 6 eps figures, submitted to Physical Review

    Surface states in nearly modulated systems

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    A Landau model is used to study the phase behavior of the surface layer for magnetic and cholesteric liquid crystal systems that are at or near a Lifshitz point marking the boundary between modulated and homogeneous bulk phases. The model incorporates surface and bulk fields and includes a term in the free energy proportional to the square of the second derivative of the order parameter in addition to the usual term involving the square of the first derivative. In the limit of vanishing bulk field, three distinct types of surface ordering are possible: a wetting layer, a non-wet layer having a small deviation from bulk order, and a different non-wet layer with a large deviation from bulk order which decays non-monotonically as distance from the wall increases. In particular the large deviation non-wet layer is a feature of systems at the Lifshitz point and also those having only homogeneous bulk phases.Comment: 6 pages, 7 figures, submitted to Phys. Rev.

    Simple model with facilitated dynamics for granular compaction

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    A simple lattice model is used to study compaction in granular media. As in real experiments, we consider a series of taps separated by large enough waiting times. The relaxation of the density exhibits the characteristic inverse logarithmic law. Moreover, we have been able to identify analytically the relevant time scale, leading to a relaxation law independent of the specific values of the parameters. Also, an expression for the asymptotic density reached in the compaction process has been derived. The theoretical predictions agree fairly well with the results from the Monte Carlo simulation.Comment: 15 pages, 4 figures, REVTeX file; no changes except for single-spacing to save paper (previous version 22 pages

    Cutoff for the East process

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    The East process is a 1D kinetically constrained interacting particle system, introduced in the physics literature in the early 90's to model liquid-glass transitions. Spectral gap estimates of Aldous and Diaconis in 2002 imply that its mixing time on LL sites has order LL. We complement that result and show cutoff with an O(L)O(\sqrt{L})-window. The main ingredient is an analysis of the front of the process (its rightmost zero in the setup where zeros facilitate updates to their right). One expects the front to advance as a biased random walk, whose normal fluctuations would imply cutoff with an O(L)O(\sqrt{L})-window. The law of the process behind the front plays a crucial role: Blondel showed that it converges to an invariant measure ν\nu, on which very little is known. Here we obtain quantitative bounds on the speed of convergence to ν\nu, finding that it is exponentially fast. We then derive that the increments of the front behave as a stationary mixing sequence of random variables, and a Stein-method based argument of Bolthausen ('82) implies a CLT for the location of the front, yielding the cutoff result. Finally, we supplement these results by a study of analogous kinetically constrained models on trees, again establishing cutoff, yet this time with an O(1)O(1)-window.Comment: 33 pages, 2 figure

    Reactions at polymer interfaces: A Monte Carlo Simulation

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    Reactions at a strongly segregated interface of a symmetric binary polymer blend are investigated via Monte Carlo simulations. End functionalized homopolymers of different species interact at the interface instantaneously and irreversibly to form diblock copolymers. The simulations, in the framework of the bond fluctuation model, determine the time dependence of the copolymer production in the initial and intermediate time regime for small reactant concentration ρ0Rg3=0.163...0.0406\rho_0 R_g^3=0.163 ... 0.0406. The results are compared to recent theories and simulation data of a simple reaction diffusion model. For the reactant concentration accessible in the simulation, no linear growth of the copolymer density is found in the initial regime, and a t\sqrt{t}-law is observed in the intermediate stage.Comment: to appear in Macromolecule

    CHARACTERIZING FORAGING PATTERNS AMONG CATTLE AND BONDED AND NON-BONDED SMALL RUMINANTS USING SPATIAL POINT PROCESS TECHNIQUES

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    This paper uses the technique of spatial point processes to describe the spatial patterns of freeranging cattle and small ruminants. Two mixed-species livestock groups were monitored while foraging on 410 ha of brush-infested Southern New Mexico rangeland during July and August 1988. The groups consisted of crossbred Bos taurus and Bos indicus beef cattle with white-faced sheep (Ovis aries) and mohair goats (Capra hircus). The bonded group consisted of small ruminants that had their behaviours modified through socialization with cattle to form a ‘flerd’ in which small ruminants consistently remained near cattle. Small ruminants in the non-bonded group had not been socialized with cattle. A subset of animal location data measured during the morning and afternoon over five days for both the bonded and non-bonded groups was analyzed for spatial patterns. Only data for five morning periods (7:00-8:00 a.m.) are reported because morning and afternoon spatial patterns were similar. Observed nearest neighbor distances, mean number of small ruminant near an arbitrary cow, and point-to-animal distances were compared to Monte Carlo simulations of independently and uniformly distributed animal locations. Bonded and non-bonded groups were also compared. Results suggested bonded and non-bonded groups were similar in spatial patterns of intra-specific distances for both cattle and small ruminants. However, bonding changed the repulsive relationship observed between cattle and non-bonded small ruminants stocked together to one of inter-specific attraction. Bonded small ruminants remained close to and formed inter-specific clusters with cattle. In addition, the mean number of bonded small ruminants near an arbitrary cow was consistently higher than for non-bonded small ruminants. Finally, the spatial pattern of cattle across the paddock did not differ between bonded and non-bonded groups, while bonded small ruminants tended to disperse slightly more uniformly across the paddock than did non-bonded small ruminants. These findings indicate the usefulness of spatial point processes techniques to analyze such animal location data, substantiate on a larger scale conclusions of previous, replicated studies about the effect of bonding small ruminants to cattle, and suggest utilization of paddock landscapes may be positively influenced using flerds compared to flocks and herds

    Interfaces in Diblocks: A Study of Miktoarm Star Copolymers

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    We study ABn_n miktoarm star block copolymers in the strong segregation limit, focussing on the role that the AB interface plays in determining the phase behavior. We develop an extension of the kinked-path approach which allows us to explore the energetic dependence on interfacial shape. We consider a one-parameter family of interfaces to study the columnar to lamellar transition in asymmetric stars. We compare with recent experimental results. We discuss the stability of the A15 lattice of sphere-like micelles in the context of interfacial energy minimization. We corroborate our theory by implementing a numerically exact self-consistent field theory to probe the phase diagram and the shape of the AB interface.Comment: 12 pages, 11 included figure
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