First-order transition of tethered membranes in 3d space

We study a model of phantom tethered membranes, embedded in three-dimensional space, by extensive Monte Carlo simulations. The membranes have hexagonal lattice structure where each monomer is interacting with six nearest-neighbors (NN). Tethering interaction between NN, as well as curvature penalty between NN triangles are taken into account. This model is new in the sense that NN interactions are taken into account by a truncated Lennard-Jones potential including both repulsive and attractive parts. The main result of our study is that the system undergoes a first-order crumpling transition from low temperature flat phase to high temperature crumpled phase, in contrast with early numerical results on models of tethered membranes.Comment: 5 pages, 6 figure

Phase transitions of an intrinsic curvature model on dynamically triangulated spherical surfaces with point boundaries

An intrinsic curvature model is investigated using the canonical Monte Carlo simulations on dynamically triangulated spherical surfaces of size upto N=4842 with two fixed-vertices separated by the distance 2L. We found a first-order transition at finite curvature coefficient \alpha, and moreover that the order of the transition remains unchanged even when L is enlarged such that the surfaces become sufficiently oblong. This is in sharp contrast to the known results of the same model on tethered surfaces, where the transition weakens to a second-order one as L is increased. The phase transition of the model in this paper separates the smooth phase from the crumpled phase. The surfaces become string-like between two point-boundaries in the crumpled phase. On the contrary, we can see a spherical lump on the oblong surfaces in the smooth phase. The string tension was calculated and was found to have a jump at the transition point. The value of \sigma is independent of L in the smooth phase, while it increases with increasing L in the crumpled phase. This behavior of \sigma is consistent with the observed scaling relation \sigma \sim (2L/N)^\nu, where \nu\simeq 0 in the smooth phase, and \nu=0.93\pm 0.14 in the crumpled phase. We should note that a possibility of a continuous transition is not completely eliminated.Comment: 15 pages with 10 figure

Mapping urban green infrastructure : a novel landscape-based approach to incorporating land-use and land-cover in the mapping of human-dominated systems

Common approaches to mapping green infrastructure in urbanized landscapes invariably focus on measures of land-use or land-cover and associated functional or physical traits. However, such one-dimensional perspectives do not accurately capture the character and complexity of the landscapes in which urban inhabitants live. The new approach presented in this paper demonstrates how open-source, high spatial and temporal resolution data with global coverage can be used to measure and represent the landscape qualities of urban environments. Through going beyond simple metrics of quantity, such as percentage green and blue cover it is now possible to explore the extent to which landscape quality helps to unpick the mixed evidence presented in the literature on the benefits of urban nature to human well-being. Here we present a landscape approach, employing remote sensing, GIS and data reduction techniques, to map urban green infrastructure elements in a large UK city-region. Comparison with existing urban datasets demonstrates considerable improvement in terms of coverage and thematic detail. The characterisation of landscapes, using census tracts as spatial units, and subsequent exploration of associations with social-ecological attributes highlights the further detail which can be uncovered with the approach. For example, eight urban landscape types identified for the case study city exhibited associations with distinct socio-economic conditions accountable not only to quantities but also qualities of green and blue space. The identification of individual landscape features through simultaneous measures of land-use and land cover demonstrated unique and significant associations between the former and indicators of human health and ecological condition. The approach may therefore provide a promising basis for developing further insight into the processes and characteristics which affect human health and wellbeing in urban areas, both in the UK and beyond

Fluctuation spectrum of fluid membranes coupled to an elastic meshwork: jump of the effective surface tension at the mesh size

We identify a class of composite membranes: fluid bilayers coupled to an elastic meshwork, that are such that the meshwork's energy is a function $F_\mathrm{el}[A_\xi]$ \textit{not} of the real microscopic membrane area $A$, but of a \textit{smoothed} membrane's area $A_\xi$, which corresponds to the area of the membrane coarse-grained at the mesh size $\xi$. We show that the meshwork modifies the membrane tension $\sigma$ both below and above the scale $\xi$, inducing a tension-jump $\Delta\sigma=dF_\mathrm{el}/dA_\xi$. The predictions of our model account for the fluctuation spectrum of red blood cells membranes coupled to their cytoskeleton. Our results indicate that the cytoskeleton might be under extensional stress, which would provide a means to regulate available membrane area. We also predict an observable tension jump for membranes decorated with polymer "brushes"

Folding transitions of the triangular lattice with defects

A recently introduced model describing the folding of the triangular lattice is generalized allowing for defects in the lattice and written as an Ising model with nearest-neighbor and plaquette interactions on the honeycomb lattice. Its phase diagram is determined in the hexagon approximation of the cluster variation method and the crossover from the pure Ising to the pure folding model is investigated, obtaining a quite rich structure with several multicritical points. Our results are in very good agreement with the available exact ones and extend a previous transfer matrix study.Comment: 16 pages, latex, 5 postscript figure

Deconfinement transition and string tensions in SU(4) Yang-Mills Theory

We present results from numerical lattice calculations of SU(4) Yang-Mills theory. This work has two goals: to determine the order of the finite temperature deconfinement transition on an $N_t = 6$ lattice and to study the string tensions between static charges in the irreducible representations of SU(4). Motivated by Pisarski and Tytgat's argument that a second-order SU($\infty$) deconfinement transition would explain some features of the SU(3) and QCD transitions, we confirm older results on a coarser, $N_t = 4$, lattice. We see a clear two-phase coexistence signal, characteristic of a first-order transition, at $8/g^2 = 10.79$ on a $6\times 20^3$ lattice, on which we also compute a latent heat of $\Delta\epsilon\approx 0.6 \epsilon_{SB}$. Computing Polyakov loop correlation functions we calculate the string tension at finite temperature in the confined phase between fundamental charges, $\sigma_1$, between diquark charges, $\sigma_2$, and between adjoint charges $\sigma_4$. We find that $1 < \sigma_2/\sigma_1 < 2$, and our result for the adjoint string tension $\sigma_4$ is consistent with string breaking.Comment: 10 pages with included figures. For version 2: New calculation and discussion of latent heat added; 2 new figures and 1 new table. Typo in abstract corrected for v3. To appear in Physical Review

Coulomb-gas formulation of SU(2) branes and chiral blocks

We construct boundary states in $SU(2)_k$ WZNW models using the bosonized Wakimoto free-field representation and study their properties. We introduce a Fock space representation of Ishibashi states which are coherent states of bosons with zero-mode momenta (boundary Coulomb-gas charges) summed over certain lattices according to Fock space resolution of $SU(2)_k$. The Virasoro invariance of the coherent states leads to families of boundary states including the B-type D-branes found by Maldacena, Moore and Seiberg, as well as the A-type corresponding to trivial current gluing conditions. We then use the Coulomb-gas technique to compute exact correlation functions of WZNW primary fields on the disk topology with A- and B-type Cardy states on the boundary. We check that the obtained chiral blocks for A-branes are solutions of the Knizhnik-Zamolodchikov equations.Comment: 14 pages, 3 figures, revtex4. Essentially the published versio

Phase transition of meshwork models for spherical membranes

We have studied two types of meshwork models by using the canonical Monte Carlo simulation technique. The first meshwork model has elastic junctions, which are composed of vertices, bonds, and triangles, while the second model has rigid junctions, which are hexagonal (or pentagonal) rigid plates. Two-dimensional elasticity is assumed only at the elastic junctions in the first model, and no two-dimensional bending elasticity is assumed in the second model. Both of the meshworks are of spherical topology. We find that both models undergo a first-order collapsing transition between the smooth spherical phase and the collapsed phase. The Hausdorff dimension of the smooth phase is H\simeq 2 in both models as expected. It is also found that H\simeq 2 in the collapsed phase of the second model, and that H is relatively larger than 2 in the collapsed phase of the first model, but it remains in the physical bound, i.e., H<3. Moreover, the first model undergoes a discontinuous surface fluctuation transition at the same transition point as that of the collapsing transition, while the second model undergoes a continuous transition of surface fluctuation. This indicates that the phase structure of the meshwork model is weakly dependent on the elasticity at the junctions.Comment: 21 pages, 12 figure

Adding a Myers Term to the IIB Matrix Model

We show that Yang-Mills matrix integrals remain convergent when a Myers term is added, and stay in the same topological class as the original model. It is possible to add a supersymmetric Myers term and this leaves the partition function invariant.Comment: 8 pages, v2 2 refs adde