38 research outputs found
Asymptotic Behavior of Inflated Lattice Polygons
We study the inflated phase of two dimensional lattice polygons with fixed
perimeter and variable area, associating a weight to a
polygon with area and bends. For convex and column-convex polygons, we
show that , where , and . The
constant is found to be the same for both types of polygons. We argue
that self-avoiding polygons should exhibit the same asymptotic behavior. For
self-avoiding polygons, our predictions are in good agreement with exact
enumeration data for J=0 and Monte Carlo simulations for . We also
study polygons where self-intersections are allowed, verifying numerically that
the asymptotic behavior described above continues to hold.Comment: 7 page
Asymptotic behaviour of convex and column-convex lattice polygons with fixed area and varying perimeter
We study the inflated phase of two dimensional lattice polygons, both convex
and column-convex, with fixed area A and variable perimeter, when a weight
\mu^t \exp[- Jb] is associated to a polygon with perimeter t and b bends. The
mean perimeter is calculated as a function of the fugacity \mu and the bending
rigidity J. In the limit \mu -> 0, the mean perimeter has the asymptotic
behaviour \avg{t}/4 \sqrt{A} \simeq 1 - K(J)/(\ln \mu)^2 + O (\mu/ \ln \mu) .
The constant K(J) is found to be the same for both types of polygons,
suggesting that self-avoiding polygons should also exhibit the same asymptotic
behaviour.Comment: 10 pages, 3 figure
Integrability as a consequence of discrete holomorphicity: the Z_N model
It has recently been established that imposing the condition of discrete
holomorphicity on a lattice parafermionic observable leads to the critical
Boltzmann weights in a number of lattice models. Remarkably, the solutions of
these linear equations also solve the Yang-Baxter equations. We extend this
analysis for the Z_N model by explicitly considering the condition of discrete
holomorphicity on two and three adjacent rhombi. For two rhombi this leads to a
quadratic equation in the Boltzmann weights and for three rhombi a cubic
equation. The two-rhombus equation implies the inversion relations. The
star-triangle relation follows from the three-rhombus equation. We also show
that these weights are self-dual as a consequence of discrete holomorphicity.Comment: 11 pages, 7 figures, some clarifications and a reference adde
On directed interacting animals and directed percolation
We study the phase diagram of fully directed lattice animals with
nearest-neighbour interactions on the square lattice. This model comprises
several interesting ensembles (directed site and bond trees, bond animals,
strongly embeddable animals) as special cases and its collapse transition is
equivalent to a directed bond percolation threshold. Precise estimates for the
animal size exponents in the different phases and for the critical fugacities
of these special ensembles are obtained from a phenomenological renormalization
group analysis of the correlation lengths for strips of width up to n=17. The
crossover region in the vicinity of the collapse transition is analyzed in
detail and the crossover exponent is determined directly from the
singular part of the free energy. We show using scaling arguments and an exact
relation due to Dhar that is equal to the Fisher exponent
governing the size distribution of large directed percolation clusters.Comment: 23 pages, 3 figures; J. Phys. A 35 (2002) 272
Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?
A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works
Leaf litter traits of invasive alien species slow down decomposition compared to Spanish natives: a broad phylogenetic comparison.
Leaf traits related to the performance of invasive alien species can influence nutrient cycling through litter decomposition. However, there is no consensus yet about whether there are consistent differences in functional leaf traits between invasive and native species that also manifest themselves through their "after life" effects on litter decomposition. When addressing this question it is important to avoid confounding effects of other plant traits related to early phylogenetic divergences and to understand the mechanism underlying the observed results to predict which invasive species will exert larger effects on nutrient cycling. We compared initial leaf litter traits, and their effect on decomposability as tested in standardized incubations, in 19 invasive-native pairs of co-familial species from Spain. They included 12 woody and seven herbaceous alien species representative of the Spanish invasive flora. The predictive power of leaf litter decomposition rates followed the order: growth form > family > status (invasive vs. native) > leaf type. Within species pairs litter decomposition tended to be slower and more dependent on N and P in invaders than in natives. This difference was likely driven by the higher lignin content of invader leaves. Although our study has the limitation of not representing the natural conditions from each invaded community, it suggests a potential slowing down of the nutrient cycle at ecosystem scale upon invasion. © Springer-Verlag 2009
A community effort in SARS-CoV-2 drug discovery.
peer reviewedThe COVID-19 pandemic continues to pose a substantial threat to human lives and is likely to do so for years to come. Despite the availability of vaccines, searching for efficient small-molecule drugs that are widely available, including in low- and middle-income countries, is an ongoing challenge. In this work, we report the results of an open science community effort, the "Billion molecules against Covid-19 challenge", to identify small-molecule inhibitors against SARS-CoV-2 or relevant human receptors. Participating teams used a wide variety of computational methods to screen a minimum of 1 billion virtual molecules against 6 protein targets. Overall, 31 teams participated, and they suggested a total of 639,024 molecules, which were subsequently ranked to find 'consensus compounds'. The organizing team coordinated with various contract research organizations (CROs) and collaborating institutions to synthesize and test 878 compounds for biological activity against proteases (Nsp5, Nsp3, TMPRSS2), nucleocapsid N, RdRP (only the Nsp12 domain), and (alpha) spike protein S. Overall, 27 compounds with weak inhibition/binding were experimentally identified by binding-, cleavage-, and/or viral suppression assays and are presented here. Open science approaches such as the one presented here contribute to the knowledge base of future drug discovery efforts in finding better SARS-CoV-2 treatments.R-AGR-3826 - COVID19-14715687-CovScreen (01/06/2020 - 31/01/2021) - GLAAB Enric