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Nearly, all dense suspensions undergo dramatic and abrupt thickening transitions in their flow behavior when sheared at high stresses. Such transitions occur when the dominant interactions between the suspended particles shift from hydrodynamic to frictional. Here, we interpret abrupt shear thickening as a precursor to a rigidity transition and give a complete theory of the viscosity in terms of a universal crossover scaling function from the frictionless jamming point to a rigidity transition associated with friction, anisotropy, and shear. Strikingly, we find experimentally that for two different systems—cornstarch in glycerol and silica spheres in glycerol—the viscosity can be collapsed onto a single universal curve over a wide range of stresses and volume fractions. The collapse reveals two separate scaling regimes due to a crossover between frictionless isotropic jamming and frictional shear jamming, with different critical exponents. The material-specific behavior due to the microscale particle interactions is incorporated into a scaling variable governing the proximity to shear jamming, that depends on both stress and volume fraction. This reformulation opens the door to importing the vast theoretical machinery developed to understand equilibrium critical phenomena to elucidate fundamental physical aspects of the shear thickening transition.

 

Topological data analysis, which allows systematic investigations of the “shape” of data, has yielded fascinating insights into many physical systems. 

Leaf hydraulic networks play an important role not only in fluid transport but also in maintaining whole-plant water status through transient environmental changes in soil-based water supply or air humidity. Both water potential and hydraulic resistance vary spatially throughout the leaf transport network, consisting of xylem, stomata and water-storage cells, and portions of the leaf areas far from the leaf base can be disproportionately disadvantaged under water stress. Besides the suppression of transpiration and reduction of water loss caused by stomatal closure, the leaf capacitance of water storage, which can also vary locally, is thought to be crucial for the maintenance of leaf water status. In order to study the fluid dynamics in these networks, we develop a spatially explicit, capacitive model which is able to capture the local spatiotemporal changes of water potential and flow rate in monocotyledonous and dicotyledonous leaves. In electrical-circuit analogs described by Ohm's law, we implement linear capacitors imitating water storage, and we present both analytical calculations of a uniform one-dimensional model and numerical simulation methods for general spatially explicit network models, and their relation to conventional lumped-element models. Calculation and simulation results are shown for the uniform model, which mimics key properties of a monocotyledonous grass leaf. We illustrate water status of a well-watered leaf, and the lowering of water potential and transpiration rate caused by excised water source or reduced air humidity. We show that the time scales of these changes under water stress are hugely affected by leaf capacitance and resistances to capacitors, in addition to stomatal resistance. Through this modeling of a grass leaf, we confirm the presence of uneven water distribution over leaf area, and also discuss the importance of considering the spatial variation of leaf hydraulic traits in plant biology. 

The dense populations that inhabit global coastlines have an uncertain future due to increased flooding, storms, and human modification. The channel networks of deltas and marshes that plumb these coastlines present diverse architectures, including well‐studied dendritic topologies. However, the quasi‐stable loops that exist in nearly all coastal networks have not yet been explained. We present a model for self‐organizing networks inspired by vascular biophysics to show that loops emerge when the relative forcings between rivers and tides are comparable, resulting in interplay between hydrodynamic forcings at short time scales relative to network evolution. Using field data and satellite imaging, we confirm this control on 21 field networks. Our comparison provides compelling evidence that hydrodynamic fluctuations are capable of stabilizing loops in geophysical systems.

 

Nature is rife with networks that are functionally optimized to propagate inputs to perform specific tasks. Whether via genetic evolution or dynamic adaptation, many networks create functionality by locally tuning interactions between nodes. Here we explore this behavior in two contexts: strain propagation in mechanical networks and pressure redistribution in flow networks. By adding and removing links, we are able to optimize both types of networks to perform specific functions. We define a single function as a tuned response of a single “target” link when another, predetermined part of the network is activated. Using network structures generated via such optimization, we investigate how many simultaneous functions such networks can be programed to fulfill. We find that both flow and mechanical networks display qualitatively similar phase transitions in the number of targets that can be tuned, along with the same robust finite-size scaling behavior. We discuss how these properties can be understood in the context of constraint–satisfaction problems.