On the universality of compact polymers

Fully packed loop models on the square and the honeycomb lattice constitute new classes of critical behaviour, distinct from those of the low-temperature O(n) model. A simple symmetry argument suggests that such compact phases are only possible when the underlying lattice is bipartite. Motivated by the hope of identifying further compact universality classes we therefore study the fully packed loop model on the square-octagon lattice. Surprisingly, this model is only critical for loop weights n < 1.88, and its scaling limit coincides with the dense phase of the O(n) model. For n=2 it is exactly equivalent to the selfdual 9-state Potts model. These analytical predictions are confirmed by numerical transfer matrix results. Our conclusions extend to a large class of bipartite decorated lattices.Comment: 13 pages including 4 figure

Simulations of energetic beam deposition: from picoseconds to seconds

We present a new method for simulating crystal growth by energetic beam deposition. The method combines a Kinetic Monte-Carlo simulation for the thermal surface diffusion with a small scale molecular dynamics simulation of every single deposition event. We have implemented the method using the effective medium theory as a model potential for the atomic interactions, and present simulations for Ag/Ag(111) and Pt/Pt(111) for incoming energies up to 35 eV. The method is capable of following the growth of several monolayers at realistic growth rates of 1 monolayer per second, correctly accounting for both energy-induced atomic mobility and thermal surface diffusion. We find that the energy influences island and step densities and can induce layer-by-layer growth. We find an optimal energy for layer-by-layer growth (25 eV for Ag), which correlates with where the net impact-induced downward interlayer transport is at a maximum. A high step density is needed for energy induced layer-by-layer growth, hence the effect dies away at increased temperatures, where thermal surface diffusion reduces the step density. As part of the development of the method, we present molecular dynamics simulations of single atom-surface collisions on flat parts of the surface and near straight steps, we identify microscopic mechanisms by which the energy influences the growth, and we discuss the nature of the energy-induced atomic mobility

A development of logistics management models for the Space Transportation System

A new analytic queueing approach was described which relates stockage levels, repair level decisions, and the project network schedule of prelaunch operations directly to the probability distribution of the space transportation system launch delay. Finite source population and limited repair capability were additional factors included in this logistics management model developed specifically for STS maintenance requirements. Data presently available to support logistics decisions were based on a comparability study of heavy aircraft components. A two-phase program is recommended by which NASA would implement an integrated data collection system, assemble logistics data from previous STS flights, revise extant logistics planning and resource requirement parameters using Bayes-Lin techniques, and adjust for uncertainty surrounding logistics systems performance parameters. The implementation of these recommendations can be expected to deliver more cost-effective logistics support

Promiscuous, non-catalytic, tandem carbohydrate-binding modules modulate the cell-wall structure and development of transgenic tobacco (Nicotiana tabacum) plants

We have compared heterologous expression of two types of carbohydrate binding module (CBM) in tobacco cell walls. These are the promiscuous CBM29 modules (a tandem CBM29-1-2 and its single derivative CBM29-2), derived from a non-catalytic protein1, NCP1, of the Piromyces equi cellulase/hemicellulase complex, and the less promiscuous tandem CBM2b-1-2 from the Cellulomonas fimi xylanase 11A. CBM-labelling studies revealed that CBM29-1-2 binds indiscriminately to every tissue of the wild-type tobacco stem whereas binding of CBM2b-1-2 was restricted to vascular tissue. The promiscuous CBM29-1-2 had much more pronounced effects on transgenic tobacco plants than the less promiscuous CBM2b-1-2. Reduced stem elongation and prolonged juvenility, resulting in delayed flower development, were observed in transformants expressing CBM29-1-2 whereas such growth phenotypes were not observed for CBM2b-1-2 plants. Histological examination and electron microscopy revealed layers of collapsed cortical cells in the stems of CBM29-1-2 plants whereas cellular deformation in the stem cortical cells of CBM2b-1-2 transformants was less severe. Altered cell expansion was also observed in most parts of the CBM29-1-2 stem whereas for the CBM2b-1-2 stem this was observed in the xylem cells only. The cellulose content of the transgenic plants was not altered. These results support the hypothesis that CBMs can modify cell wall structure leading to modulation of wall loosening and plant growth

Finite average lengths in critical loop models

A relation between the average length of loops and their free energy is obtained for a variety of O(n)-type models on two-dimensional lattices, by extending to finite temperatures a calculation due to Kast. We show that the (number) averaged loop length L stays finite for all non-zero fugacities n, and in particular it does not diverge upon entering the critical regime n -> 2+. Fully packed loop (FPL) models with n=2 seem to obey the simple relation L = 3 L_min, where L_min is the smallest loop length allowed by the underlying lattice. We demonstrate this analytically for the FPL model on the honeycomb lattice and for the 4-state Potts model on the square lattice, and based on numerical estimates obtained from a transfer matrix method we conjecture that this is also true for the two-flavour FPL model on the square lattice. We present in addition numerical results for the average loop length on the three critical branches (compact, dense and dilute) of the O(n) model on the honeycomb lattice, and discuss the limit n -> 0. Contact is made with the predictions for the distribution of loop lengths obtained by conformal invariance methods.Comment: 20 pages of LaTeX including 3 figure

Dense loops, supersymmetry, and Goldstone phases in two dimensions

Loop models in two dimensions can be related to O(N) models. The low-temperature dense-loops phase of such a model, or of its reformulation using a supergroup as symmetry, can have a Goldstone broken-symmetry phase for N<2. We argue that this phase is generic for -2< N <2 when crossings of loops are allowed, and distinct from the model of non-crossing dense loops first studied by Nienhuis [Phys. Rev. Lett. 49, 1062 (1982)]. Our arguments are supported by our numerical results, and by a lattice model solved exactly by Martins et al. [Phys. Rev. Lett. 81, 504 (1998)].Comment: RevTeX, 5 pages, 3 postscript figure

Bayesian Error Estimation in Density Functional Theory

We present a practical scheme for performing error estimates for Density Functional Theory calculations. The approach which is based on ideas from Bayesian statistics involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities like binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude for different systems in good agreement with existing experience.Comment: 5 pages, 3 figure

Non-CG methylation patterns shape the epigenetic landscape in Arabidopsis.

DNA methylation occurs in CG and non-CG sequence contexts. Non-CG methylation is abundant in plants and is mediated by CHROMOMETHYLASE (CMT) and DOMAINS REARRANGED METHYLTRANSFERASE (DRM) proteins; however, its roles remain poorly understood. Here we characterize the roles of non-CG methylation in Arabidopsis thaliana. We show that a poorly characterized methyltransferase, CMT2, is a functional methyltransferase in vitro and in vivo. CMT2 preferentially binds histone H3 Lys9 (H3K9) dimethylation and methylates non-CG cytosines that are regulated by H3K9 methylation. We revealed the contributions and redundancies between each non-CG methyltransferase in DNA methylation patterning and in regulating transcription. We also demonstrate extensive dependencies of small-RNA accumulation and H3K9 methylation patterning on non-CG methylation, suggesting self-reinforcing mechanisms between these epigenetic factors. The results suggest that non-CG methylation patterns are critical in shaping the landscapes of histone modification and small noncoding RNA