Viscosity Sum Rules at Large Scattering Lengths

We use the operator product expansion (OPE) and dispersion relations to obtain new model-independent "Borel-resummed" sum rules for both shear and bulk viscosity of many-body systems of spin-1/2 fermions with predominantly short range S-wave interactions. These sum rules relate Gaussian weights of the frequency-dependent viscosities to the Tan contact parameter C(a). Our results are valid for arbitrary values of the scattering length a, but receive small corrections from operators of dimension larger than 5 in the OPE, and can be used to study transport properties in the vicinity of the infinite scattering length fixed point. In particular, we find that the exact dependence of the shear viscosity sum rule on scattering length is controlled by the function C(a). The sum rules that we obtain depend on a frequency scale w that can be optimized to maximize their overlap with low-energy data

Towards a Dynamic Interaction Network of Life to unify and expand the evolutionary theory

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Modelling Urban Tree Growth and Ecosystem Services: Review and Perspectives

Climate change in combination with increasing urbanization is a major challenge for our cities. Ecosystem services from the urban green play a significant role in mitigating the negative effects. Urban tree growth models are appropriate tools for the quantification of ecosystem services in some cases in dependence of the plant growth dynamics and of the changing environment. We report about the state of the art in modelling urban tree growth and ecosystem services and describe the background of urban tree growth and the provision of ecosystem services. Furthermore, we present basic growth model principles and describe and compare existing urban tree growth models. Finally we discuss the use of urban tree growth models, uncover advantages and disadvantages of the single urban tree growth models and indicate current limitations and future venues in modelling