Conformal elasticity of mechanism-based metamaterials

Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate symmetry due to the presence of a designer soft strain pathway. Here we show that low energy deformations of designer dilational metamaterials will be governed by a scalar field theory, conformal elasticity, in which the nonuniform, nonlinear deformations observed under generic loads correspond with the well-studied—conformal—maps. We validate this approach using experiments and finite element simulations and further show that such systems obey a holographic bulk-boundary principle, which enables an analytic method to predict and control nonuniform, nonlinear deformations. This work both presents a unique method of precise deformation control and demonstrates a general principle in which mechanisms can generate special classes of soft deformations.

The Calculation, Thresholds and Reporting of Inter-Limb Strength Asymmetry: A Systematic Review

The prevalence of inter-limb strength differences is well documented in the literature however, there are inconsistencies related to measurement and reporting, and the normative values and effects associated with inter-limb asymmetry. Therefore, the aims of this systematic review were to: 1) assess the appropriateness of existing indices for the calculation of asymmetry, 2) interrogate the evidence basis for literature reported thresholds used to define asymmetry and 3) summarise normative levels of inter-limb strength asymmetry and their effects on injury and performance. To conduct this systematic review, scientific databases (PubMed, Scopus, SPORTDiscus and Web of Science) were searched and a total of 3,594 articles were retrieved and assessed for eligibility and article quality. The robustness of each identified asymmetry index was assessed, and the evidence-basis of the identified asymmetry thresholds was appraised retrospectively using the references provided. Fifty-three articles were included in this review. Only four of the twelve identified indices were unaffected by the limitations associated with selecting a reference limb. Eighteen articles applied a threshold to original research to identify “abnormal” asymmetry, fifteen of which utilised a threshold between 10-15%, yet this threshold was not always supported by appropriate evidence. Asymmetry scores ranged between and within populations from approximate symmetry to asymmetries larger than 15%. When reporting the effects of strength asymmetries, increased injury risk and detriments to performance were often associated with larger asymmetry, however the evidence was inconsistent. Limitations of asymmetry indices should be recognised, particularly those that require selection of a reference limb. Failure to reference the origin of the evidence for an asymmetry threshold reinforces doubt over the use of arbitrary thresholds, such as 10-15%. Therefore, an individual approach to defining asymmetry may be necessary to refine robust calculation methods and to establish appropriate thresholds across various samples and methodologies that enable appropriate conclusions to be drawn.

Dominant Symmetry Plane Detection for Point-Based 3D Models

In this paper, a symmetry detection algorithm for three-dimensional point cloud model based on weighted principal component analysis (PCA) is proposed. The proposed algorithm works as follows: first, using the point element’s area as the initial weight, a weighted PCA is performed and a plane is selected as the initial symmetry plane; and then an iterative method is used to adjust the approximate symmetry plane step by step to make it tend to perfect symmetry plane (dominant symmetry plane). In each iteration, we first update the weight of each point based on a distance metric and then use the new weights to perform a weighted PCA to determine a new symmetry plane. If the current plane of symmetry is close enough to the plane of symmetry in the previous iteration or if the number of iterations exceeds a given threshold, the iteration terminates. After the iteration is terminated, the plane of symmetry in the last iteration is taken as the dominant symmetry plane of the model. As shown in experimental results, the proposed algorithm can find the dominant symmetry plane for symmetric models and it also works well for nonperfectly symmetric models.

Stochastic modelling and prediction of monthly surface temperatures: StocSIPS

<p>From hourly to decadal time scales, atmospheric fields are characterized by two scaling regimes: at high frequencies the weather, with fluctuations increasing with the time scale, and at low frequencies, macroweather with fluctuations decreasing with scale, the transition between the two at <em>τ<sub>w</sub></em>. This transition time is the lifetime of planetary structures and is therefore close to the deterministic predictability limit of conventional numerical weather prediction models. While it is thus the outer scale of deterministic weather models, conversely, it is the inner scale of stochastic macroweather models.</p><p>Here we explore the spatial dependence of this transition time. Starting at the surface (2m temperature) we found that the monthly average temperature falls in the macroweather regime for almost any location in the globe, except for parts of the tropical ocean where <em>τ<sub>w </sub></em>∼ 1 - 2 years. As we increase in altitude, the dependence of <em>τ<sub>w</sub></em> with the location becomes more homogeneous and above 850mb <em>τ<sub>w</sub></em> < 1 month almost everywhere. The longer tropical ocean transition scales are presumably the deterministic outer scales of the “ocean weather” regime.</p><p>Knowledge of <em>τ<sub>w</sub></em> is fundamental for stochastic macroweather forecasting.   Such forecasting is based on symmetries, primarily the power-law behavior of the fluctuations that implies a huge memory that can be exploited for forecasts up to several years. In addition, there is another approximate symmetry called “statistical space-time factorization” relating spatial and temporal statistics. Finally, while weather regime temperature fluctuations are highly intermittent, in macroweather the intermittency is much lower, fluctuations are quasi Gaussian.</p><p>The Stochastic Seasonal and Interannual Prediction System (StocSIPS<sup>[1,2]</sup>) is a stochastic data-driven model that exploits these symmetries to perform macroweather (long-term) forecasts. Compared to traditional global circulation models (GCM), it has the advantage of forcing predictions to converge to the real-world climate (not the model climate). It extracts the internal variability (weather noise) directly from past data and does not suffer from model drift. Some other practical advantages include much lower computational cost, no need for downscaling and no ad hoc postprocessing.</p><p>We show that StocSIPS can predict monthly average surface temperature (nearly) to its stochastic predictability limits. Using monthly to annual lead time hindcasts, we compare StocSIPS predictions with those from the CanSIPS<sup>[3]</sup> GCM. Beyond a month, and especially over land, StocSIPS generally has higher skill. For regular StocSIPS forecasts, see http://www.physics.mcgill.ca/StocSIPS/.</p><p><strong>References</strong></p><p><sup>[1]</sup> Del Rio Amador, L. and Lovejoy, S. (2019) Clim Dyn, <strong>53</strong>: 4373. https://doi.org/10.1007/s00382-019-04791-4</p><p><sup>[2]</sup> Lovejoy, S., Del Rio Amador, L., Hébert, R. (2017) In Nonlinear Advances in Geosciences, A.A. Tsonis ed. Springer Nature, 305–355 DOI: 10.1007/978-3-319-58895-7</p><p><sup>[3]</sup> Merryfield WJ, Denis B, Fontecilla JS, Lee WS, Kharin S, Hodgson J, Archambault B (2011) Rep., 51pp, Environment Canada.</p>