Topological interactions in systems of mutually interlinked polymer rings

The topological interaction arising in interlinked polymeric rings such as DNA catenanes is considered. More specifically, the free energy for a pair of linked random walk rings is derived where the distance $R$ between two segments each of which is part of a different ring is kept constant. The topology conservation is imposed by the Gauss invariant. A previous approach (M.Otto, T.A. Vilgis, Phys.Rev.Lett. {\bf 80}, 881 (1998)) to the problem is refined in several ways. It is confirmed, that asymptotically, i.e. for large $R\gg R_G$ where $R_G$ is average size of single random walk ring, the effective topological interaction (free energy) scales $\propto R^4$.Comment: 16 pages, 3 figur

Analytical study of the effect of recombination on evolution via DNA shuffling

We investigate a multi-locus evolutionary model which is based on the DNA shuffling protocol widely applied in \textit{in vitro} directed evolution. This model incorporates selection, recombination and point mutations. The simplicity of the model allows us to obtain a full analytical treatment of both its dynamical and equilibrium properties, for the case of an infinite population. We also briefly discuss finite population size corrections

Mutator Dynamics on a Smooth Evolutionary Landscape

We investigate a model of evolutionary dynamics on a smooth landscape which features a ``mutator'' allele whose effect is to increase the mutation rate. We show that the expected proportion of mutators far from equilibrium, when the fitness is steadily increasing in time, is governed solely by the transition rates into and out of the mutator state. This results is a much faster rate of fitness increase than would be the case without the mutator allele. Near the fitness equilibrium, however, the mutators are severely suppressed, due to the detrimental effects of a large mutation rate near the fitness maximum. We discuss the results of a recent experiment on natural selection of E. coli in the light of our model.Comment: 4 pages, 3 figure

Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

We study a singular-limit problem arising in the modelling of chemical reactions. At finite {\epsilon} > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1/{\epsilon}, and in the limit {\epsilon} -> 0, the solution concentrates onto the two wells, resulting into a limiting system that is a pair of ordinary differential equations for the density at the two wells. This convergence has been proved in Peletier, Savar\'e, and Veneroni, SIAM Journal on Mathematical Analysis, 42(4):1805-1825, 2010, using the linear structure of the equation. In this paper we re-prove the result by using solely the Wasserstein gradient-flow structure of the system. In particular we make no use of the linearity, nor of the fact that it is a second-order system. The first key step in this approach is a reformulation of the equation as the minimization of an action functional that captures the property of being a curve of maximal slope in an integrated form. The second important step is a rescaling of space. Using only the Wasserstein gradient-flow structure, we prove that the sequence of rescaled solutions is pre-compact in an appropriate topology. We then prove a Gamma-convergence result for the functional in this topology, and we identify the limiting functional and the differential equation that it represents. A consequence of these results is that solutions of the {\epsilon}-problem converge to a solution of the limiting problem.Comment: Added two sections, corrected minor typos, updated reference

Inventories of extreme weather events and impacts: Implications for loss and damage from and adaptation to climate extremes

Extreme and impactful weather events of the recent past provide a vital but under-utilised data source for understanding present and future climate risks. Extreme event attribution (EEA) enables us to quantify the influence of anthropogenic climate change (ACC) on a given event in a way that can be tailored to stakeholder needs, thereby enhancing the potential utility of studying past events. Here we set out a framework for systematically recording key details of high-impact events on a national scale (using the UK and Puerto Rico as examples), combining recent advances in event attribution with the risk framework. These ‘inventories’ inherently provide useful information depending on a user’s interest. For example, as a compilation of the impacts of ACC, we find that in the UK since 2000, at least 1500 excess deaths are directly attributable to human-induced climate change, while in Puerto Rico the increased intensity of Hurricane Maria alone led to the deaths of up to 3670 people. We also explore how inventories form a foundation for further analysis, learning from past events. This involves identifying the most damaging hazards and crucially also vulnerabilities and exposure characteristics over time. To build a risk assessment for heat-related mortality in the UK we focus on a vulnerable group, elderly urban populations, and project changes in the hazard and exposure within the same framework. Without improved preparedness, the risk to this group is likely to increase by ~50% by 2028 and ~150% by 2043. In addition, the framework allows the exploration of the likelihood of otherwise unprecedented events, or 'Black Swans’. Finally, not only does it aid disaster preparedness and adaptation at local and national scales, such inventories also provide a new source of evidence for global stocktakes on adaptation and loss and damage such as mandated by the Paris Climate Agreement

Elasticity of entangled polymer loops: Olympic gels

In this note we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the non affine deformation regime where the free energy scales linear with the deformation. In the large (affine) deformation regime the free energy is shown to scale as $F \propto \lambda^{5/2}$ where $\lambda$ is the deformation ratio. Thus a highly non Hookian stress - strain relation is predicted.Comment: latex, no figures, accepted in PRE Rapid Communicatio

Nitrogen recovery efficiency for corn intercropped with palisade grass.

Intercropping corn and palisade grass is a technique to increase straw production, soil C contents, nutrient cycling and crop yield. However, concerns arise from nitrogen (N) uptake by the intercropping crop causing reduction in the yield of the corn. Our objective was to evaluate N recovery efficiency (NRE), and the N dynamics in the soil-plant system in corn intercropped with palisade grass. A field trial was carried out in Bahia, Brazil, evaluating two cropping systems: corn (monoculture) and corn intercropped with palisade grass sowed between rows on the same day as the corn crop, with four replicates in a completely randomized block design. Nitrogen (150 kg∙ha?1of 15N-urea) was applied at sowing to determine NRE, which means the amounts of N-fertilizer uptake in corn and palisade grass, the amounts of N-fertilizer in soil and the 15N-fertilizer balance. Neither the NRE (63.3% in monoculture and 57.2% in intercropping) nor corn grain yield (9,800 kg∙ha?1 in monoculture and 9,671 kg∙ha?1 in intercropping) was affected by intercropping, which accumulated only 2.1 kg∙ha?1 of N-fertilizer or 1.4% N rate. In addition, palisade grass yielded 2,265 kg∙ha?1 of dry matter. The balance indicated that 82.4% of N-fertilizer was recovered in the monoculture and 86.9% in the intercropping. Intercropping palisade grass does not affect grain yield or N corn nutrition and has the potential to increase straw production contributing to maintenance of no-till

Particle approximation of the one dimensional Keller-Segel equation, stability and rigidity of the blow-up

We investigate a particle system which is a discrete and deterministic approximation of the one-dimensional Keller-Segel equation with a logarithmic potential. The particle system is derived from the gradient flow of the homogeneous free energy written in Lagrangian coordinates. We focus on the description of the blow-up of the particle system, namely: the number of particles involved in the first aggregate, and the limiting profile of the rescaled system. We exhibit basins of stability for which the number of particles is critical, and we prove a weak rigidity result concerning the rescaled dynamics. This work is complemented with a detailed analysis of the case where only three particles interact