Discrete kink dynamics in hydrogen-bonded chains I: The one-component model

We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in quasi-one-dimensional networks of hydrogen bonds, where the on-site potential plays role of the proton potential in the hydrogen bond. The system supports a rich variety of stationary kink solutions with different symmetry properties. We study the stability and bifurcation structure of all these stationary kink states. An exactly solvable model with a piecewise ``parabola-constant'' approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete travelling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity of the Morse potential and the cooperativity of the hydrogen bond (the coupling constant of the interaction between nearest-neighbor protons).Comment: 12 pages, 20 figure

Plant functional and taxonomic diversity in European grasslands along climatic gradients

Aim: European grassland communities are highly diverse, but patterns and drivers of their continental-scale diversity remain elusive. This study analyses taxonomic and functional richness in European grasslands along continental-scale temperature and precipitation gradients. Location: Europe. Methods: We quantified functional and taxonomic richness of 55,748 vegetation plots. Six plant traits, related to resource acquisition and conservation, were analysed to describe plant community functional composition. Using a null-model approach we derived functional richness effect sizes that indicate higher or lower diversity than expected given the taxonomic richness. We assessed the variation in absolute functional and taxonomic richness and in functional richness effect sizes along gradients of minimum temperature, temperature range, annual precipitation, and precipitation seasonality using a multiple general additive modelling approach. Results: Functional and taxonomic richness was high at intermediate minimum temperatures and wide temperature ranges. Functional and taxonomic richness was low in correspondence with low minimum temperatures or narrow temperature ranges. Functional richness increased and taxonomic richness decreased at higher minimum temperatures and wide annual temperature ranges. Both functional and taxonomic richness decreased with increasing precipitation seasonality and showed a small increase at intermediate annual precipitation. Overall, effect sizes of functional richness were small. However, effect sizes indicated trait divergence at extremely low minimum temperatures and at low annual precipitation with extreme precipitation seasonality. Conclusions: Functional and taxonomic richness of European grassland communities vary considerably over temperature and precipitation gradients. Overall, they follow similar patterns over the climate gradients, except at high minimum temperatures and wide temperature ranges, where functional richness increases and taxonomic richness decreases. This contrasting pattern may trigger new ideas for studies that target specific hypotheses focused on community assembly processes. And though effect sizes were small, they indicate that it may be important to consider climate seasonality in plant diversity studies