A mixed formulation for the direct approximation of L2L^2-weighted controls for the linear heat equation

This paper deals with the numerical computation of null controls for the linear heat equation. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a given positive time. In [Fernandez-Cara \& Münch, Strong convergence approximations of null controls for the 1D heat equation, 2013], a so-called primal method is described leading to a strongly convergent approximation of distributed control: the controls minimize quadratic weighted functionals involving both the control and the state and are obtained by solving the corresponding optimality conditions. In this work, we adapt the method to approximate the control of minimal square integrable-weighted norm. The optimality conditions of the problem are reformulated as a mixed formulation involving both the state and its adjoint. We prove the well-posedeness of the mixed formulation (in particular the inf-sup condition) then discuss several numerical experiments. The approach covers both the boundary and the inner situation and is valid in any dimension

Determining fPAR and leaf area index of several land cover classes in the Pot River and Tsitsa River catchments of the Eastern Cape, South Africa

Determining the quantum (both annual maxima and minima) and the temporal variation in the leaf area index (LAI), and the fraction of photosynthetically active radiation (fPAR), are three fundamental biophysical characteristics of the plant canopy that should parameterise ecophysiological models of water use (evapotranspiration) and carbon sequestration. Although Earth observation provides values and time series for both these parameters, in-field validation of these values is necessary. Following a very wet summer season, we conducted field surveys of several land cover classes within two quaternary catchments in the Eastern Cape province, South Africa, to determine maximum values of LAI and fPAR that occur within each of these land cover classes. To assist in up-scaling these point measures to the landscape, we present a regression relationship between Landsat 8 NDVI and LAI measured using an Accupar Ceptometer (r2 = 0.92). Peak wet season LAI varied from extremely high (>7.0) under the canopy of invasive black wattle (Acacia mearnsii) trees to ~2.0 under the canopy of a Eucalyptus plantation. Ungrazed native grassland displayed an intermediate LAI value of 3.84. The black wattle stand absorbed 97% of the available PAR, whereas the mature Eucalyptus plantation only absorbed 66% of PAR.Keywords: agroforestry, ecosystem ecology, remote sensin

Investigating 16O with the 15N(p,{\alpha})12C reaction

The 16O nucleus was investigated through the 15N(p,{\alpha})12C reaction at excitation energies from Ex = 12 231 to 15 700 keV using proton beams from a 5 MeV Van de Graaff accelerator at beam energies of Ep = 331 to 3800 keV. Alpha decay from resonant states in 16O was strongly observed for ten known excited states in this region. The candidate 4-alpha cluster state at Ex = 15.1 MeV was investigated particularly intensely in order to understand its particle decay channels.Comment: Submitted for Proceedings of Fourth International Workshop on State of the Art in Nuclear Cluster Physics (SOTANCP4), held from May 13 - 18, 2018 in Galveston, TX, US

Exploring the invasion of rangelands by Acacia mearnsii (black wattle): biophysical characteristics and management implications

Australian acacias have spread to many parts of the world. In South Africa, species such as A. mearnsii and A. dealbata are invasive. Consequently, more effort has focused on their clearing. In a context of increasing clearing costs, it is crucial to develop innovative ways of managing invasions. Our aim was to understand the biophysical properties of A. mearnsii in grasslands as they relate to grass production and to explore management implications. Aboveground biomass (AGB) of A. mearnsii was determined using a published allometric equation in invaded grasslands of the northern Eastern Cape, South Africa. The relationships among the A. mearnsii leaf area index (LAI), normalised difference vegetation index (NDVI) and AGB were investigated. The influence of A. mearnsii LAI and terrain slope on grass cover was also investigated. Strong linear relationships between NDVI, LAI and AGB were developed. Acacia mearnsii canopy adversely impacted grass production more than terrain slope (p < 0.05) and when LAI approached 2.1, grass cover dropped to below 10% in infested areas. Reducing A. mearnsii canopy could promote grass production while encouraging carbon sequestration. Given the high AGB and clearing costs, it may be prudent to adopt the ‘novel ecosystems’ approach in managing infested landscapes.Keywords: grassland, invasive plants, landscape ecology, rangeland conditio

Approximating Continuous Functions on Persistence Diagrams Using Template Functions

The persistence diagram is an increasingly useful tool from Topological Data Analysis, but its use alongside typical machine learning techniques requires mathematical finesse. The most success to date has come from methods that map persistence diagrams into $\mathbb{R}^n$, in a way which maximizes the structure preserved. This process is commonly referred to as featurization. In this paper, we describe a mathematical framework for featurization using template functions. These functions are general as they are only required to be continuous and compactly supported. We discuss two realizations: tent functions, which emphasize the local contributions of points in a persistence diagram, and interpolating polynomials, which capture global pairwise interactions. We combine the resulting features with classification and regression algorithms on several examples including shape data and the Rossler system. Our results show that using template functions yields high accuracy rates that match and often exceed those of existing featurization methods. One counter-intuitive observation is that in most cases using interpolating polynomials, where each point contributes globally to the feature vector, yields significantly better results than using tent functions, where the contribution of each point is localized. Along the way, we provide a complete characterization of compactness in the space of persistence diagrams