Shear-driven size segregation of granular materials: modeling and experiment

Granular materials segregate by size under shear, and the ability to quantitatively predict the time required to achieve complete segregation is a key test of our understanding of the segregation process. In this paper, we apply the Gray-Thornton model of segregation (developed for linear shear profiles) to a granular flow with an exponential profile, and evaluate its ability to describe the observed segregation dynamics. Our experiment is conducted in an annular Couette cell with a moving lower boundary. The granular material is initially prepared in an unstable configuration with a layer of small particles above a layer of large particles. Under shear, the sample mixes and then re-segregates so that the large particles are located in the top half of the system in the final state. During this segregation process, we measure the velocity profile and use the resulting exponential fit as input parameters to the model. To make a direct comparison between the continuum model and the observed segregation dynamics, we locally map the measured height of the experimental sample (which indicates the degree of segregation) to the local packing density. We observe that the model successfully captures the presence of a fast mixing process and relatively slower re-segregation process, but the model predicts a finite re-segregation time, while in the experiment re-segregation occurs only exponentially in time

On a conjecture about Dirac's delta representation using q-exponentials

A new representation of Dirac's delta-distribution, based on the so-called q-exponentials, has been recently conjectured. We prove here that this conjecture is indeed valid

Smoothed Analysis of Tensor Decompositions

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and tensors analogs of much of the matrix algebra toolkit are unlikely to exist because of hardness results. Efficient decomposition in the overcomplete case (where rank exceeds dimension) is particularly challenging. We introduce a smoothed analysis model for studying these questions and develop an efficient algorithm for tensor decomposition in the highly overcomplete case (rank polynomial in the dimension). In this setting, we show that our algorithm is robust to inverse polynomial error -- a crucial property for applications in learning since we are only allowed a polynomial number of samples. While algorithms are known for exact tensor decomposition in some overcomplete settings, our main contribution is in analyzing their stability in the framework of smoothed analysis. Our main technical contribution is to show that tensor products of perturbed vectors are linearly independent in a robust sense (i.e. the associated matrix has singular values that are at least an inverse polynomial). This key result paves the way for applying tensor methods to learning problems in the smoothed setting. In particular, we use it to obtain results for learning multi-view models and mixtures of axis-aligned Gaussians where there are many more "components" than dimensions. The assumption here is that the model is not adversarially chosen, formalized by a perturbation of model parameters. We believe this an appealing way to analyze realistic instances of learning problems, since this framework allows us to overcome many of the usual limitations of using tensor methods.Comment: 32 pages (including appendix

COP 26: Pavilion Proposals

There is considerable interest in having a Peatland Pavilion at the up-coming UNFCCC COP26 to be held in Glasgow in November 2021. The purpose of the pavilion would be to provide a focus for discussions about the increasingly recognised importance of peatlands and their role as major global stores of soil carbon but also, in their damaged state, as large sources of carbon emissions. UEL Architecture Masters students were set the task of developing potential designs for such a pavilion with the requirement that it incorporate an installation designed by the artist and UEL lecturer Michael Pinsky. The architectural concept drawn up by Hussein Ail Kassim and Mohammed Patel offers some thought-provoking ideas for such a Peatland Pavilion and thus opens up the debate about what form, both conceptually and architecturally, such a pavilion might take. It is worth highlighting that the themes of the different environment domes envisaged by Hussein and Mohammed can each be related to particular aspects of importance to peatlands

Exploring the variability of tropical savanna tree structural allometry with terrestrial laser scanning

Individual tree carbon stock estimates typically rely on allometric scaling relationships established between field-measured stem diameter (DBH) and destructively harvested biomass. The use of DBH-based allometric equations to estimate the carbon stored over larger areas therefore, assumes that tree architecture, including branching and crown structures, are consistent for a given DBH, and that minor variations cancel out at the plot scale. We aimed to explore the degree of structural variation present at the individual tree level across a range of size-classes. We used terrestrial laser scanning (TLS) to measure the 3D structure of each tree in a 1 ha savanna plot, with coincident field-inventory. We found that stem reconstructions from TLS captured both the spatial distribution pattern and the DBH of individual trees with high confidence when compared with manual measurements (R2 = 0.98, RMSE = 0.0102 m). Our exploration of the relationship between DBH, crown size and tree height revealed significant variability in savanna tree crown structure (measured as crown area). These findings question the reliability of DBH-based allometric equations for adequately representing diversity in tree architecture, and therefore carbon storage, in tropical savannas. However, adoption of TLS outside environmental research has been slow due to considerable capital cost and monitoring programs often continue to rely on sub-plot monitoring and traditional allometric equations. A central aspect of our study explores the utility of a lower-cost TLS system not generally used for vegetation surveys. We discuss the potential benefits of alternative TLS-based approaches, such as explicit modelling of tree structure or voxel-based analyses, to capture the diverse 3D structures of savanna trees. Our research highlights structural heterogeneity as a source of uncertainty in savanna tree carbon estimates and demonstrates the potential for greater inclusion of cost-effective TLS technology in national monitoring programs

Eyes on the bog. Long-term monitoring network for UK peatlands

Eyes on the Bog provides a scientifically robust, repeatable, low tech, long-term monitoring initiative. The standardised methodology enables individual peatland sites to be consistently monitored across the UK, creating a network of comparable sites. The initiative employs cheap, simple techniques and modern technology to enable useful monitoring information to be collected by peatland community employees or volunteers on: Peat subsidence and carbon loss Carbon capture Water table behaviour Peat soil condition Vegetation status, structure and composition Historical context of change and current trajectorie

Speech diversity and speech interfaces - considering an inclusive future through stammering

The number of speech interfaces and services made available through them continue to grow. This has opened up interactions to people who rely on speech as a critical modality for interacting with systems. However, people with diverse speech patterns such as those who stammer are at risk of being negatively affected or excluded from speech interface interaction. In this paper, we consider what an inclusive speech interface future may look like for people who stammer. In doing so, we identify three key challenges: (1) developing effective speech recognition, (2) understanding the user experiences of people who stammer and (3) supporting speech interfaces designers through appropriate heuristics. We believe the interdisciplinary and cross-community strengths of venues like CUI are well positioned to address these challenges going forward