Numerical investigation of localization in two-dimensional quasiperiodic mosaic lattice.

A one-dimensional lattice model with mosaic quasiperiodic potential is found to exhibit interesting localization properties, e.g. clear mobility edges (Wanget al2020Phys. Rev. Lett.125196604). We generalize this mosaic quasiperiodic model to a two-dimensional version, and numerically investigate its localization properties: the phase diagram from the fractal dimension of the wavefunction, the statistical and scaling properties of the conductance. Compared with disordered systems, our model shares many common features but also exhibits some different characteristics in the same dimensionality and the same universality class. For example, the sharp peak atg∼0of the critical distribution and the largeglimit of the universal scaling functionßresemble those behaviors of three-dimensional disordered systems.

Scaling up biodiversity-ecosystem function relationships across space and over time.

Understanding how to scale up effects of biological diversity on ecosystem functioning and services remains challenging. There is a general consensus that biodiversity loss alters ecosystem processes underpinning the goods and services upon which humanity depends. Yet most of that consensus stems from experiments performed at small spatial scales for short time frames, which limits transferability of conclusions to longer-term, landscape-scale conservation policies and management. Here we develop quantitative scaling relationships linking 374 experiments that tested plant diversity effects on biomass production across a range of scales. We show that biodiversity effects increase by factors of 1.68 and 1.10 for each 10-fold increase in experiment temporal and spatial scales, respectively. Contrary to prior studies, our analyses suggest that the time scale of experiments, rather than their spatial scale, is the primary source of variation in biodiversity effects. But consistent with earlier research, our analyses reveal that complementarity effects, rather than selection effects, drive the positive space-time interactions for plant diversity effects. Importantly, we also demonstrate complex space-time interactions and nonlinear responses that emphasize how simple extrapolations from small-scale experiments are likely to underestimate biodiversity effects in real-world ecosystems. Quantitative scaling relationships from this research are a crucial step towards bridging controlled experiments that identify biological mechanisms across a range of scales. Predictions from scaling relationships like these could then be compared with observations for fine-tuning the relationships and ultimately improving their capacities to predict consequences of biodiversity loss for ecosystem functioning and services over longer time frames across real-world landscapes.

A Pediatric Covariate Function for CYP3A-Mediated Midazolam Clearance Can Scale Clearance of Selected CYP3A Substrates in Children.

Recently a framework was presented to assess whether pediatric covariate models for clearance can be extrapolated between drugs sharing elimination pathways, based on extraction ratio, protein binding, and other drug properties. Here we evaluate when a pediatric covariate function for midazolam clearance can be used to scale clearance of other CYP3A substrates. A population PK model including a covariate function for clearance was developed for midazolam in children aged 1-17 years. Commonly used CYP3A substrates were selected and using the framework, it was assessed whether the midazolam covariate function accurately scales their clearance. For eight substrates, reported pediatric clearance values were compared numerically and graphically with clearance values scaled using the midazolam covariate function. For sildenafil, clearance values obtained with population PK modeling based on pediatric concentration-time data were compared with those scaled with the midazolam covariate function. According to the framework, a midazolam covariate function will lead to systemically accurate clearance scaling (absolute prediction error (PE) < 30%) for CYP3A substrates binding to albumin with an extraction ratio between 0.35 and 0.65 when binding < 10% in adults, between 0.05 and 0.55 when binding > 90%, and with an extraction ratio ranging between these values when binding between 10 and 90%. Scaled clearance values for eight commonly used CYP3A substrates were reasonably accurate (PE < 50%). Scaling of sildenafil clearance was accurate (PE < 30%). We defined for which CYP3A substrates a pediatric covariate function for midazolam clearance can accurately scale plasma clearance in children. This scaling approach may be useful for CYP3A substrates with scarce or no available pediatric PK information.

Frequency-dependent scaling from mesoscale to macroscale in viscoelastic random composites.

This paper investigates the scaling from a statistical volume element (SVE; i.e. mesoscale level) to representative volume element (RVE; i.e. macroscale level) of spatially random linear viscoelastic materials, focusing on the quasi-static properties in the frequency domain. Requiring the material statistics to be spatially homogeneous and ergodic, the mesoscale bounds on the RVE response are developed from the Hill-Mandel homogenization condition adapted to viscoelastic materials. The bounds are obtained from two stochastic initial-boundary value problems set up, respectively, under uniform kinematic and traction boundary conditions. The frequency and scale dependencies of mesoscale bounds are obtained through computational mechanics for composites with planar random chessboard microstructures. In general, the frequency-dependent scaling to RVE can be described through a complex-valued scaling function, which generalizes the concept originally developed for linear elastic random composites. This scaling function is shown to apply for all different phase combinations on random chessboards and, essentially, is only a function of the microstructure and mesoscale.