Steiner Variations on Random Surfaces

Ambartzumian et.al. suggested that the modified Steiner action functional had desirable properties for a random surface action. However, Durhuus and Jonsson pointed out that such an action led to an ill-defined grand-canonical partition function and suggested that the addition of an area term might improve matters. In this paper we investigate this and other related actions numerically for dynamically triangulated random surfaces and compare the results with the gaussian plus extrinsic curvature actions that have been used previously.Comment: 8 page

Assessing the Quality of Semantic Sensor Data

Acknowledgements The research described here is supported by the award made by the RCUK Digital Economy programme to the dot.rural Digital Economy Hub; award reference: EP/G066051/1.Publisher PD

Phase transitions of a tethered membrane model on a torus with intrinsic curvature

A tethered surface model is investigated by using the canonical Monte Carlo simulation technique on a torus with an intrinsic curvature. We find that the model undergoes a first-order phase transition between the smooth phase and the crumpled one.Comment: 12 pages with 8 figure

Scaling in Steiner Random Surfaces

It has been suggested that the modified Steiner action functional has desirable properties for a random surface action. In this paper we investigate the scaling of the string tension and massgap in a variant of this action on dynamically triangulated random surfaces and compare the results with the gaussian plus extrinsic curvature actions that have been used previously.Comment: 7 pages, COLO-HEP-32

Making connections: an evangelism plan for Chicago First Church of the Nazarene

https://place.asburyseminary.edu/ecommonsatsdissertations/1660/thumbnail.jp

Multiple Potts Models Coupled to Two-Dimensional Quantum Gravity

We perform Monte Carlo simulations using the Wolff cluster algorithm of {\it multiple} $q=2,3,4$ state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the $c>1$ region of two-dimensional quantum gravity. Contrary to naive expectation we find no obvious signs of pathological behaviour for $c>1$. We discuss the results in the light of suggestions that have been made for a modified DDK ansatz for $c>1$.Comment: 9 page

Vertex Models on Feynman Diagrams

The statistical mechanics of spin models, such as the Ising or Potts models, on generic random graphs can be formulated economically by considering the N --> 1 limit of Hermitian matrix models. In this paper we consider the N --> 1 limit in complex matrix models, which describes vertex models of different sorts living on random graphs. From the graph theoretic perspective one is using matrix model and field theory inspired methods to count various classes of directed graphs. We also make some remarks on vertex models on planar random graphs (the N --> infinity limit) where the resulting matrix models are not generally soluble using currently known methods. Nonetheless, some particular cases may be mapped onto known models and hence solved.Comment: 10 Pages text (LaTeX), 4 eps figure

First-order phase transition of triangulated surfaces on a spherical core

We study an intrinsic curvature model defined on fixed-connectivity triangulated lattices enclosing a spherical core by using the canonical Monte Carlo simulation technique. We find that the model undergoes a discontinuous transition of shape transformation between the smooth state and a collapsed state even when the core radius $R$ is sufficiently large; the transition depends on $R$. The origin of the multitude of transitions is considered to be a degeneracy of the collapsed states. We also find that the Gaussian bond potential $S_1/N$, which is the sum of bond length squares, discontinuously changes at the transition. The discontinuity in $S_1/N$ implies a possibility of large fluctuations of the distance between lipids, or the density of lipids, in biological membranes such as giant vesicles or liposomes enclosing some materials.Comment: 10 figure

Frustrating and Diluting Dynamical Lattice Ising Spins

We investigate what happens to the third order ferromagnetic phase transition displayed by the Ising model on various dynamical planar lattices (ie coupled to 2D quantum gravity) when we introduce annealed bond disorder in the form of either antiferromagnetic couplings or null couplings. We also look at the effect of such disordering for the Ising model on general $\phi^3$ and $\phi^4$ Feynman diagrams.Comment: 7pages, LaTex , LPTHE-ORSAY-94-5

Strings with Extrinsic Curvature: An Analysis of the Crossover Regime

We present the results of a set of Monte Carlo simulations of Dynamically Triangulated Random Surfaces embedded in three dimensions with an extrinsic curvature dependent action. We analyze several observables in the crossover regime and discuss whether or not our observations are indicative of the presence of a phase transition.Comment: (Contribution to Lattice 92 Proceedings.) Latex file (5 pages), requires espcrc2.sty. 2 figures not included. Syracuse preprint SU-HEP-4241-52