Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices

Model lattices consisting of balls connected by central-force springs provide much of our understanding of mechanical response and phonon structure of real materials. Their stability depends critically on their coordination number $z$. $d$-dimensional lattices with $z=2d$ are at the threshold of mechanical stability and are isostatic. Lattices with $z<2d$ exhibit zero-frequency "floppy" modes that provide avenues for lattice collapse. The physics of systems as diverse as architectural structures, network glasses, randomly packed spheres, and biopolymer networks is strongly influenced by a nearby isostatic lattice. We explore elasticity and phonons of a special class of two-dimensional isostatic lattices constructed by distorting the kagome lattice. We show that the phonon structure of these lattices, characterized by vanishing bulk moduli and thus negative Poisson ratios and auxetic elasticity, depends sensitively on boundary conditions and on the nature of the kagome distortions. We construct lattices that under free boundary conditions exhibit surface floppy modes only or a combination of both surface and bulk floppy modes; and we show that bulk floppy modes present under free boundary conditions are also present under periodic boundary conditions but that surface modes are not. In the the long-wavelength limit, the elastic theory of all these lattices is a conformally invariant field theory with holographic properties, and the surface waves are Rayleigh waves. We discuss our results in relation to recent work on jammed systems. Our results highlight the importance of network architecture in determining floppy-mode structure.Comment: 12 pages, 7 figure

Aerial and surface rivers: downwind impacts on water availability from land use changes in Amazonia

The abundant evapotranspiration provided by the Amazon forests is an important component of the hydrological cycle, both regionally and globally. Since the last century, deforestation and expanding agricultural activities have been changing the ecosystem and its provision of moisture to the atmosphere. However, it remains uncertain how the ongoing land use change will influence rainfall, runoff, and water availability as findings from previous studies differ. Using moisture tracking experiments based on observational data, we provide a spatially detailed analysis recognizing potential teleconnection between source and sink regions of atmospheric moisture. We apply land use scenarios in upwind moisture sources and quantify the corresponding rainfall and runoff changes in downwind moisture sinks. We find spatially varying responses of water regimes to land use changes, which may explain the diverse results from previous studies. Parts of the Peruvian Amazon and western Bolivia are identified as the sink areas most sensitive to land use change in the Amazon and we highlight the current water stress by Amazonian land use change on these areas in terms of the water availability. Furthermore, we also identify the influential source areas where land use change may considerably reduce a given target sink's water reception (from our example of the Ucayali River basin outlet, rainfall by 5–12ĝ€% and runoff by 19–50ĝ€% according to scenarios). Sensitive sinks and influential sources are therefore suggested as hotspots for achieving sustainable land–water management

Climate impacts on human livelihoods: Where uncertainty matters in projections of water availability

Climate change will have adverse impacts on many different sectors of society, with manifold consequences for human livelihoods and well-being. However, a systematic method to quantify human well-being and livelihoods across sectors is so far unavailable, making it difficult to determine the extent of such impacts. Climate impact analyses are often limited to individual sectors (e.g. food or water) and employ sector-specific target measures, while systematic linkages to general livelihood conditions remain unexplored. Further, recent multi-model assessments have shown that uncertainties in projections of climate impacts deriving from climate and impact models, as well as greenhouse gas scenarios, are substantial, posing an additional challenge in linking climate impacts with livelihood conditions. This article first presents a methodology to consistently measure what is referred to here as AHEAD (Adequate Human livelihood conditions for wEll-being And Development). Based on a trans-disciplinary sample of concepts addressing human well-being and livelihoods, the approach measures the adequacy of conditions of 16 elements. We implement the method at global scale, using results from the Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP) to show how changes in water availability affect the fulfilment of AHEAD at national resolution. In addition, AHEAD allows for the uncertainty of climate and impact model projections to be identified and differentiated. We show how the approach can help to put the substantial inter-model spread into the context of country-specific livelihood conditions by differentiating where the uncertainty about water scarcity is relevant with regard to livelihood conditions – and where it is not. The results indicate that livelihood conditions are compromised by water scarcity in 34 countries. However, more often, AHEAD fulfilment is limited through other elements. The analysis shows that the water-specific uncertainty ranges of the model output are outside relevant thresholds for AHEAD for 65 out of 111 countries, and therefore do not contribute to the overall uncertainty about climate change impacts on livelihoods. In 46 of the countries in the analysis, water-specific uncertainty is relevant to AHEAD. The AHEAD method presented here, together with first results, forms an important step towards making scientific results more applicable for policy decisions

Aerial and surface rivers: Downwind impacts on water availability from land use changes in Amazonia

The abundant evapotranspiration provided by the Amazon forests is an important component of the hydrological cycle, both regionally and globally. Since the last century, deforestation and expanding agricultural activities have been changing the ecosystem and its provision of moisture to the atmosphere. However, it remains uncertain how the ongoing land use change will influence rainfall, runoff, and water availability as findings from previous studies differ. Using moisture tracking experiments based on observational data, we provide a spatially detailed analysis recognizing potential teleconnection between source and sink regions of atmospheric moisture. We apply land use scenarios in upwind moisture sources and quantify the corresponding rainfall and runoff changes in downwind moisture sinks. We find spatially varying responses of water regimes to land use changes, which may explain the diverse results from previous studies. Parts of the Peruvian Amazon and western Bolivia are identified as the sink areas most sensitive to land use change in the Amazon and we highlight the current water stress by Amazonian land use change on these areas in terms of the water availability. Furthermore, we also identify the influential source areas where land use change may considerably reduce a given target sink's water reception (from our example of the Ucayali River basin outlet, rainfall by 5–12ĝ€% and runoff by 19–50ĝ€% according to scenarios). Sensitive sinks and influential sources are therefore suggested as hotspots for achieving sustainable land–water management

Promoting self-regulation through school-based martial arts training

Abstract The impact of school-based Tae Kwon Do training on self-regulatory abilities was examined. A self-regulation framework including three domains (cognitive, affective, and physical) was presented. Children (N = 207) from kindergarten through Grade 5 were randomly assigned by homeroom class to either the intervention (martial arts) group or a comparison (traditional physical education) group. Outcomes were assessed using multidimensional, multimodal assessments. After a 3-month intervention, results indicated that the martial arts group demonstrated greater improvements than the comparison group in areas of cognitive self-regulation, affective self-regulation, prosocial behavior, classroom conduct, and performance on a mental math test. A significant Group  Gender interaction was found for cognitive self-regulation and classroom conduct, with boys showing greater improvements than girls. Possible explanations of this interaction as well as implications for components of martial arts training for the development of self-regulation in school-age children are discussed

Mechanical Metamaterials with Negative Compressibility Transitions

When tensioned, ordinary materials expand along the direction of the applied force. Here, we explore network concepts to design metamaterials exhibiting negative compressibility transitions, during which a material undergoes contraction when tensioned (or expansion when pressured). Continuous contraction of a material in the same direction of an applied tension, and in response to this tension, is inherently unstable. The conceptually similar effect we demonstrate can be achieved, however, through destabilisations of (meta)stable equilibria of the constituents. These destabilisations give rise to a stress-induced solid-solid phase transition associated with a twisted hysteresis curve for the stress-strain relationship. The strain-driven counterpart of negative compressibility transitions is a force amplification phenomenon, where an increase in deformation induces a discontinuous increase in response force. We suggest that the proposed materials could be useful for the design of actuators, force amplifiers, micro-mechanical controls, and protective devices.Comment: Supplementary information available at http://www.nature.com/nmat/journal/v11/n7/abs/nmat3331.htm

A characteristic lengthscale causes anomalous size effects and boundary programmability in mechanical metamaterials

The architecture of mechanical metamaterialsis designed to harness geometry, non-linearity and topology to obtain advanced functionalities such as shape morphing, programmability and one-way propagation. While a purely geometric framework successfully captures the physics of small systems under idealized conditions, large systems or heterogeneous driving conditions remain essentially unexplored. Here we uncover strong anomalies in the mechanics of a broad class of metamaterials, such as auxetics, shape-changers or topological insulators: a non-monotonic variation of their stiffness with system size, and the ability of textured boundaries to completely alter their properties. These striking features stem from the competition between rotation-based deformations---relevant for small systems---and ordinary elasticity, and are controlled by a characteristic length scale which is entirely tunable by the architectural details. Our study provides new vistas for designing, controlling and programming the mechanics of metamaterials in the thermodynamic limit.Comment: Main text has 4 pages, 4 figures + Methods and Supplementary Informatio

Static non-reciprocity in mechanical metamaterials

Reciprocity is a fundamental principle governing various physical systems, which ensures that the transfer function between any two points in space is identical, regardless of geometrical or material asymmetries. Breaking this transmission symmetry offers enhanced control over signal transport, isolation and source protection. So far, devices that break reciprocity have been mostly considered in dynamic systems, for electromagnetic, acoustic and mechanical wave propagation associated with spatio-temporal variations. Here we show that it is possible to strongly break reciprocity in static systems, realizing mechanical metamaterials that, by combining large nonlinearities with suitable geometrical asymmetries, and possibly topological features, exhibit vastly different output displacements under excitation from different sides, as well as one-way displacement amplification. In addition to extending non-reciprocity and isolation to statics, our work sheds new light on the understanding of energy propagation in non-linear materials with asymmetric crystalline structures and topological properties, opening avenues for energy absorption, conversion and harvesting, soft robotics, prosthetics and optomechanics.Comment: 19 pages, 3 figures, Supplementary information (11 pages and 5 figures