2,848 research outputs found
Orientational phase transitions in the hexagonal phase of a diblock copolymer melt under shear flow
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
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
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
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 sites has order . We complement that result and show
cutoff with an -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 -window. The law of the process behind the
front plays a crucial role: Blondel showed that it converges to an invariant
measure , on which very little is known. Here we obtain quantitative
bounds on the speed of convergence to , 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
-window.Comment: 33 pages, 2 figure
Reactions at polymer interfaces: A Monte Carlo Simulation
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 . 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 -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
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
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Required conditions for and coincident 1/1-mode activity associated with the nonlocal electron heat transport effect on TFTR
A database of 71 distinct and randomly collected cold pulse cases from TFTR is analyzed. Observations show a striking parameter regime cutoff for the presence of nonlocal transient transport and coincident MHD (1/1-mode) activity as well as for changes in the radial speed of the nonlocal transport effect and changes in the sawtooth period. A nontrivial link is demonstrated between electron heat transport and MHD properties through observation of a common cutoff in the parameter n{sub e}(0)/T{sub e}(0){sup 1/2} and a common threshold in injection size for radial speed and sawtooth period changes. Auxiliary heating (via energetic neutral beams) destroys whatever process is responsible for the nonlocal transport effect, unless the discharge contains significant amounts of injected tritium. These observations are preliminary, but they represent important circumstantial evidence for mysterious propagation of changes in some MHD-related phenomenon as being responsible for a large fraction of electron heat transport. This propagation is then probably a function of n{sub e}(0)/T{sub e}(0){sup 1/2}, ion mass, and possibly beam power. An analysis of Ohmic cases shows that the cutoff in n{sub e}(0)/T{sub e}{sup 1/2} indicates the nonlocal transport effects may occur when the electrons are collisionally thermally decoupled from the ions
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Unusual Low-frequency Magnetic Perturbations in TFTR
Low-frequency magnetic perturbations (less than or equal to 30 kHz) observed in the Tokamak Fusion Test Reactor (TFTR) tokamak do not always conform to expectations from Magneto-Hydro-Dynamic (MHD) modes. The discrepancy between observations and expectations arises from the existence of three classes of magnetic perturbations in TFTR: (1) 'Edge Originated Magnetic Perturbations' (EOMP's), (2) 'Kink-like Modes' (KLM's), and (3) Tearing Modes (TM's). The EOMP class has unusual magnetic phenomenon including up/down asymmetry in poloidal intensity variation that MHD modes alone cannot generate. The contributions of MHD modes in plasma edge regions are too small to explain the magnitude of observed EOMP perturbations. At least two-thirds, possibly nearly all, of magnetic perturbations in a typical EOMP originate from sources other than MHD modes. An EOMP has a unity toroidal harmonic number and a poloidal harmonic number close to a discharge's edge q-value. It produces little temperature fluctuations, except possibly in edge regions. The KLM class produces temperature fluctuations, mostly confined within the q=1 surface with an ideal-mode-like structure, but generates little external magnetic perturbations. The TM class conforms generally to expectations from MHD modes. We propose that current flowing in the Scrape-off-layer (SOL) plasma is a possible origin of EOMP's
Interfaces in Diblocks: A Study of Miktoarm Star Copolymers
We study AB 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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