1,236 research outputs found
Monte Carlo Study of an Extended 3-State Potts Model on the Triangular Lattice
By introducing a chiral term into the Hamiltonian of the 3-state Potts model
on a triangular lattice additional symmetries are achieved between the
clockwise and anticlockwise states and the ferromagnetic state. This model is
investigated using Monte Carlo methods. We investigate the full phase diagram
and find evidence for a line tricritical points separating the ferromagnetic
and antiferromagnetic phases.Comment: 6 pages, 10 figure
Hodge Theory on Metric Spaces
Hodge theory is a beautiful synthesis of geometry, topology, and analysis,
which has been developed in the setting of Riemannian manifolds. On the other
hand, spaces of images, which are important in the mathematical foundations of
vision and pattern recognition, do not fit this framework. This motivates us to
develop a version of Hodge theory on metric spaces with a probability measure.
We believe that this constitutes a step towards understanding the geometry of
vision.
The appendix by Anthony Baker provides a separable, compact metric space with
infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version,
to appear in Foundations of Computational Mathematics. Minor changes and
addition
Incorporating interactive 3-dimensional graphics in astronomy research papers
Most research data collections created or used by astronomers are
intrinsically multi-dimensional. In contrast, all visual representations of
data presented within research papers are exclusively 2-dimensional. We present
a resolution of this dichotomy that uses a novel technique for embedding
3-dimensional (3-d) visualisations of astronomy data sets in electronic-format
research papers. Our technique uses the latest Adobe Portable Document Format
extensions together with a new version of the S2PLOT programming library. The
3-d models can be easily rotated and explored by the reader and, in some cases,
modified. We demonstrate example applications of this technique including: 3-d
figures exhibiting subtle structure in redshift catalogues, colour-magnitude
diagrams and halo merger trees; 3-d isosurface and volume renderings of
cosmological simulations; and 3-d models of instructional diagrams and
instrument designs.Comment: 18 pages, 7 figures, submitted to New Astronomy. For paper with
3-dimensional embedded figures, see http://astronomy.swin.edu.au/s2plot/3dpd
Derivation of a Non-Local Interfacial Hamiltonian for Short-Ranged Wetting II: General Diagrammatic Structure
In our first paper, we showed how a non-local effective Hamiltionian for
short-ranged wetting may be derived from an underlying Landau-Ginzburg-Wilson
model. Here, we combine the Green's function method with standard perturbation
theory to determine the general diagrammatic form of the binding potential
functional beyond the double-parabola approximation for the
Landau-Ginzburg-Wilson bulk potential. The main influence of cubic and quartic
interactions is simply to alter the coefficients of the double parabola-like
zig-zag diagrams and also to introduce curvature and tube-interaction
corrections (also represented diagrammatically), which are of minor importance.
Non-locality generates effective long-ranged many-body interfacial interactions
due to the reflection of tube-like fluctuations from the wall. Alternative wall
boundary conditions (with a surface field and enhancement) and the diagrammatic
description of tricritical wetting are also discussed.Comment: (14 pages, 2 figures) Submitted J. Phys. Condens. Matte
Vibrational spectra of C60C8H8 and C70C8H8 in the rotor-stator and polymer phases
C60-C8H8 and C70-C8H8 are prototypes of rotor-stator cocrystals. We present
infrared and Raman spectra of these materials and show how the rotor-stator
nature is reflected in their vibrational properties. We measured the
vibrational spectra of the polymer phases poly(C60C8H8) and poly(C70C8H8)
resulting from a solid state reaction occurring on heating. Based on the
spectra we propose a connection pattern for the fullerene in poly(C60C8H8),
where the symmetry of the C60 is D2h. On illuminating the C60-C8H8 cocrystal
with green or blue light a photochemical reaction was observed leading to a
similar product to that of the thermal polymerization.Comment: 26 pages, 8 figures, to appear in Journal of Physical Chemistry B 2nd
version: minor changes in wording, accepted version by journa
Droplet shapes on structured substrates and conformal invariance
We consider the finite-size scaling of equilibrium droplet shapes for fluid
adsorption (at bulk two-phase co-existence) on heterogeneous substrates and
also in wedge geometries in which only a finite domain of the
substrate is completely wet. For three-dimensional systems with short-ranged
forces we use renormalization group ideas to establish that both the shape of
the droplet height and the height-height correlations can be understood from
the conformal invariance of an appropriate operator. This allows us to predict
the explicit scaling form of the droplet height for a number of different
domain shapes. For systems with long-ranged forces, conformal invariance is not
obeyed but the droplet shape is still shown to exhibit strong scaling
behaviour. We argue that droplet formation in heterogeneous wedge geometries
also shows a number of different scaling regimes depending on the range of the
forces. The conformal invariance of the wedge droplet shape for short-ranged
forces is shown explicitly.Comment: 20 pages, 7 figures. (Submitted to J.Phys.:Cond.Mat.
Kinetics of Phase Separation in Thin Films: Simulations for the Diffusive Case
We study the diffusion-driven kinetics of phase separation of a symmetric
binary mixture (AB), confined in a thin-film geometry between two parallel
walls. We consider cases where (a) both walls preferentially attract the same
component (A), and (b) one wall attracts A and the other wall attracts B (with
the same strength). We focus on the interplay of phase separation and wetting
at the walls, which is referred to as {\it surface-directed spinodal
decomposition} (SDSD). The formation of SDSD waves at the two surfaces, with
wave-vectors oriented perpendicular to them, often results in a metastable
layered state (also referred to as ``stratified morphology''). This state is
reminiscent of the situation where the thin film is still in the one-phase
region but the surfaces are completely wet, and hence coated with thick wetting
layers. This metastable state decays by spinodal fluctuations and crosses over
to an asymptotic growth regime characterized by the lateral coarsening of
pancake-like domains. These pancakes may or may not be coated by precursors of
wetting layers. We use Langevin simulations to study this crossover and the
growth kinetics in the asymptotic coarsening regime.Comment: 39 pages, 19 figures, submitted to Phys.Rev.
Grain Dynamics in a Two-dimensional Granular Flow
We have used particle tracking methods to study the dynamics of individual
balls comprising a granular flow in a small-angle two-dimensional funnel. We
statistically analyze many ball trajectories to examine the mechanisms of shock
propagation. In particular, we study the creation of, and interactions between,
shock waves. We also investigate the role of granular temperature and draw
parallels to traffic flow dynamics.Comment: 17 pages, 24 figures. To appear in Phys.Rev.E. High res./color
figures etc. on http://www.nbi.dk/CATS/Granular/GrainDyn.htm
Inter-Edge interaction in the Quantum Hall Effect
We consider effects of the interaction between electrons drifting along the
opposite sides of a narrow sample under the conditions of the quantum Hall
effect. A spatial variation of this interaction leads to backward scattering of
collective excitations propagating along the edges. Experiments on propagation
of the edge modes in samples with constrictions may give information about the
strength of the inter-edge electron interaction in the quantum Hall regime.Comment: 12 Pages, Latex, Accepted for publication in PRL
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