skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Fine Wrinkling on Coarsely Meshed Thin Shells
We propose a new model and algorithm to capture the high-definition statics of thin shells via coarse meshes. This model predicts global, fine-scale wrinkling at frequencies much higher than the resolution of the coarse mesh; moreover, it is grounded in the geometric analysis of elasticity, and does not require manual guidance, a corpus of training examples, nor tuning of ad hoc parameters. We first approximate the coarse shape of the shell using tension field theory, in which material forces do not resist compression. We then augment this base mesh with wrinkles, parameterized by an amplitude and phase field that we solve for over the base mesh, which together characterize the geometry of the wrinkles. We validate our approach against both physical experiments and numerical simulations, and we show that our algorithm produces wrinkles qualitatively similar to those predicted by traditional shell solvers requiring orders of magnitude more degrees of freedom.  more » « less
Award ID(s):
1910274
PAR ID:
10333495
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
ACM Transactions on Graphics
Volume:
40
Issue:
5
ISSN:
0730-0301
Page Range / eLocation ID:
1 to 32
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    Nonlinear mechanics of solids is an exciting field that encompasses both beautiful mathematics, such as the emergence of instabilities and the formation of complex patterns, as well as multiple applications. Two-dimensional crystals and van der Waals (vdW) heterostructures allow revisiting this field on the atomic level, allowing much finer control over the parameters and offering atomistic interpretation of experimental observations. In this work, we consider the formation of instabilities consisting of radially oriented wrinkles around mono- and few-layer “bubbles” in two-dimensional vdW heterostructures. Interestingly, the shape and wavelength of the wrinkles depend not only on the thickness of the two-dimensional crystal forming the bubble, but also on the atomistic structure of the interface between the bubble and the substrate, which can be controlled by their relative orientation. We argue that the periodic nature of these patterns emanates from an energetic balance between the resistance of the top membrane to bending, which favors large wavelength of wrinkles, and the membrane-substrate vdW attraction, which favors small wrinkle amplitude. Employing the classical “Winkler foundation” model of elasticity theory, we show that the number of radial wrinkles conveys a valuable relationship between the bending rigidity of the top membrane and the strength of the vdW interaction. Armed with this relationship, we use our data to demonstrate a nontrivial dependence of the bending rigidity on the number of layers in the top membrane, which shows two different regimes driven by slippage between the layers, and a high sensitivity of the vdW force to the alignment between the substrate and the membrane. 
    more » « less
  2. Modelling of fluid–particle interactions is a major area of research in many fields of science and engineering. There are several techniques that allow modelling of such interactions, among which the coupling of computational fluid dynamics (CFD) and the discrete element method (DEM) is one of the most convenient solutions due to the balance between accuracy and computational costs. However, the accuracy of this method is largely dependent upon mesh size, where obtaining realistic results always comes with the necessity of using a small mesh and thereby increasing computational intensity. To compensate for the inaccuracies of using a large mesh in such modelling, and still take advantage of rapid computations, we extended the classical modelling by combining it with a machine learning model. We have conducted seven simulations where the first one is a numerical model with a fine mesh (i.e. ground truth) with a very high computational time and accuracy, the next three models are constructed on coarse meshes with considerably less accuracy and computational burden and the last three models are assisted by machine learning, where we can obtain large improvements in terms of observing fine-scale features yet based on a coarse mesh. The results of this study show that there is a great opportunity in machine learning towards improving classical fluid–particle modelling approaches by producing highly accurate models for large-scale systems in a reasonable time. 
    more » « less
  3. Abstract Leaf breakdown is an important process in forested headwater streams. A common method used to quantify the role of macroinvertebrate and microbial communities in leaf litter breakdown involves using paired mesh bags that either allow or exclude macroinvertebrate access to leaves. We examined common assumptions of the paired litterbag method to test (1) whether mesh size alters microbial respiration and (2) whether the effects of abrasive flows (e.g., from water and sediment) differ between coarse‐ and fine‐mesh litterbags. We measured rates of microbial respiration on Acer rubrum and Rhododendron maximum leaves incubated in coarse‐ and fine‐mesh litterbags. We also measured rates of abrasion using aerated concrete blocks in pairs of coarse‐ and fine‐mesh bags in ten streams across a gradient of discharge. We found that rates of microbial respiration on Acer rubrum leaves conditioned in fine‐mesh bags were 65% greater than the rates of respiration in paired coarse‐mesh bags, but respiration rates on Rhododendron maximum were similar in coarse‐ and fine‐mesh bags. Abrasion was, on average, 56% greater in coarse‐mesh than paired fine‐mesh bags, and these effects were greater in streams with higher discharge. These results suggest that more caution is required when attributing the difference in leaf breakdown between coarse‐ and fine‐mesh bags to macroinvertebrates. Because the effect of mesh size on microbial respiration of Acer leaves and abrasion are opposite in direction, the effect that dominates and creates bias likely depends on both environmental context and experimental design. 
    more » « less
  4. Flood mapping on Earth imagery is crucial for disaster management, but its efficacy is hampered by the lack of high-quality training labels. Given high-resolution Earth imagery with coarse and noisy training labels, a base deep neural network model, and a spatial knowledge base with label constraints, our problem is to infer the true high-resolution labels while training neural network parameters. Traditional methods are largely based on specific physical properties and thus fall short of capturing the rich domain constraints expressed by symbolic logic. Neural-symbolic models can capture rich domain knowledge, but existing methods do not address the unique spatial challenges inherent in flood mapping on high-resolution imagery. To fill this gap, we propose a spatial-logic-aware weakly supervised learning framework. Our framework integrates symbolic spatial logic inference into probabilistic learning in a weakly supervised setting. To reduce the time costs of logic inference on vast high-resolution pixels, we propose a multi-resolution spatial reasoning algorithm to infer true labels while training neural network parameters. Evaluations of real-world flood datasets show that our model outperforms several baselines in prediction accuracy. The code is available at https://github.com/spatialdatasciencegroup/SLWSL. 
    more » « less
  5. Abstract Understanding the observed temperature dependence of decomposition (i.e., its apparent activation energy) requires separation of direct effects of temperature on consumer metabolism (i.e., the inherent activation energy) from those driven by indirect seasonal patterns in phenology and biomass, and by longer‐term, climate‐driven shifts in acclimation, adaptation, and community assembly. Such parsing is important because studies that relate temperature to decomposition usually involve multi‐season data and/or spatial proxies for long‐term shifts, and so incorporate these indirect factors. The various effects of such factors can obscure the inherent temperature dependence of detrital processing. Separating the inherent temperature dependence of decomposition from other drivers is important for accurate prediction of the contribution of detritus‐sourced greenhouse gases to climate warming and requires novel approaches to data collection and analysis. Here, we present breakdown rates of red maple litter incubated in coarse‐ and fine‐mesh litterbags (the latter excluding macroinvertebrates) for serial approximately one‐month increments over one year in nine streams along a natural temperature gradient (mean annual: 12.8°–16.4°C) from north Georgia to central Alabama, USA. We analyzed these data using distance‐based redundancy analysis and generalized additive mixed models to parse the dependence of decomposition rates on temperature, seasonality, and shredding macroinvertebrate biomass. Microbial decomposition in fine‐mesh bags was significantly influenced by both temperature and seasonality. Accounting for seasonality corrected the temperature dependence of decomposition rate from 0.25 to 0.08 eV. Shredder assemblage structure in coarse‐mesh bags was related to temperature across both sites and seasons, shifting from “cold” stonefly‐dominated communities to “warm” communities dominated by snails or crayfish. Shredder biomass was not a significant predictor of either coarse‐mesh or macroinvertebrate‐mediated (i.e., coarse‐ minus fine‐mesh) breakdown rates, which were also jointly influenced by temperature and seasonality. Unlike fine‐mesh bags, however, temperature dependence of litter breakdown did not differ between models with and without seasonality for either coarse‐mesh (0.36 eV) or macroinvertebrate‐mediated (0.13 eV) rates. We conclude that indirect (non‐thermal) seasonal and site‐level effects play a variable and potentially strong role in shaping the apparent temperature dependence of detrital breakdown. Such effects should be incorporated into studies designed to estimate inherent temperature dependence of slow ecological processes. 
    more » « less