Numerical construction of Green’s functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations

This thesis consists of two parts. In Part I, we describe an algorithm for approximating the Green\u27s function for elliptic problems with variable coefficients in arbitrary dimension. The basis for our approach is the separated representation, which appears as a way of approximating functions of many variables by sums of products of univariate functions. While the differential operator we wish to invert is typically ill-conditioned, its conditioning may be improved by first applying the Green\u27s function for the constant coefficient problem. This function may be computed either numerically or, in some case, analytically in a separated format. The variable coefficient Green\u27s function is then computed using a quadratically convergent iteration on the preconditioned operator, with sparsity maintained via representation in a wavelet basis. Of particular interest is that the method scales linearly in the number of dimensions, a feature that very desirable in high dimensional problems in which the curse of dimensionality must be reckoned with. As a corollary to this work, we described a randomized algorithm for maintaining low separation rank of the functions used in the construction of the Green\u27s function. For certain functions of practical interest, one can avoid the cost of using standard methods such as alternating least squares (ALS) to reduce the separation rank. Instead, terms from the separated representation may be selected using a randomized approach based on matrix skeletonization and the interpolative decomposition. The use of random projections can greatly reduce the cost of rank reduction, as well as calculation of the Frobenius norm and term-wise Gram matrices. In Part II of the thesis, we highlight three practical applications of sparse and separable approximations to the analysis of renewable energy data. In the first application, error estimates gleaned from repeated measurements are incorporated into sparse regression algorithms (LASSO and the Dantzig selector) to minimize the statistical uncertainty of the resulting model. Applied to real biomass data, this approach leads to sparser regression coefficients corresponding to improved accuracy as measured by k-fold cross validation error. In the second application, a regression model based on separated representations is fit to reliability data for cadmium telluride (CdTe) thin-film solar cells. The data is inherently multi-way, and our approach avoids artificial matricization that would typically be performed for use with standard regression algorithms. Two distinct modes of degradation, corresponding to short- and long-term decrease in cell efficiency, are identified. In the third application, some theoretical properties of a popular chemometrics algorithm called orthogonal projections to latent structures (O-PLS) are derived

Non-Stationary Policy Learning for Multi-Timescale Multi-Agent Reinforcement Learning

In multi-timescale multi-agent reinforcement learning (MARL), agents interact across different timescales. In general, policies for time-dependent behaviors, such as those induced by multiple timescales, are non-stationary. Learning non-stationary policies is challenging and typically requires sophisticated or inefficient algorithms. Motivated by the prevalence of this control problem in real-world complex systems, we introduce a simple framework for learning non-stationary policies for multi-timescale MARL. Our approach uses available information about agent timescales to define a periodic time encoding. In detail, we theoretically demonstrate that the effects of non-stationarity introduced by multiple timescales can be learned by a periodic multi-agent policy. To learn such policies, we propose a policy gradient algorithm that parameterizes the actor and critic with phase-functioned neural networks, which provide an inductive bias for periodicity. The framework's ability to effectively learn multi-timescale policies is validated on a gridworld and building energy management environment.Comment: Accepted at IEEE CDC'23. 7 pages, 6 figure

Signatures of exciton coupling in paired nanoemitters

An exciton formed by the delocalized electronic excitation of paired nanoemitters is interpreted in terms of the electromagnetic emission of the pair and their mutual coupling with a photodetector. A formulation directly tailored for fluorescence detection is identified, giving results which are strongly dependent on geometry and selection rules. Signature symmetric and antisymmetric combinations are analyzed and their distinctive features identified

Operational experience on the generation and control of high brightness electron bunch trains at SPARC-LAB

Sub-picosecond, high-brightness electron bunch trains are routinely produced at SPARC-LAB via the velocity bunching technique. Such bunch trains can be used to drive multi-color Free Electron Lasers (FELs) and plasma wake field accelerators. In this paper we present recent results at SPARC-LAB on the generation of such beams, highlighting the key points of our scheme. We will discuss also the on-going machine upgrades to allow driving FELs with plasma accelerated beams or with short electron pulses at an increased energy

Gold remobilisation and formation of high grade ore shoots driven by dissolution-reprecipitation replacement and Ni substitution into auriferous arsenopyrite

Both gold-rich sulphides and ultra-high grade native gold oreshoots are common but poorly understood phenomenon in orogenic-type mineral systems, partly because fluids in these systems are considered to have relatively low gold solubilities and are unlikely to generate high gold concentrations. The world-class Obuasi gold deposit, Ghana, has gold-rich arsenopyrite spatially associated with quartz veins, which have extremely high, localised concentrations of native gold, contained in microcrack networks within the quartz veins where they are folded. Here, we examine selected samples from Obuasi using a novel combination of quantitative electron backscatter diffraction analysis, ion microprobe imaging, synchrotron XFM mapping and geochemical modelling to investigate the origin of the unusually high gold concentrations. The auriferous arsenopyrites are shown to have undergone partial replacement (~15%) by Au-poor, nickeliferous arsenopyrite, during localised crystal-plastic deformation, intragranular microfracture and metamorphism (340-460 °C, 2 kbars). Our results show the dominant replacement mechanism was pseudomorphic dissolution-reprecipitation, driven by small volumes of an infiltrating fluid that had relatively low fS2 and carried aqueous NiCl2. We find that arsenopyrite replacement produced strong chemical gradients at crystal-fluid interfaces due to an increase in fS2 during reaction, which enabled efficient removal of gold to the fluid phase and development of anomalously gold-rich fluid (potentially 10 ppm or more depending on sulphur concentration). This process was facilitated by precipitation of ankerite, which removed CO2 from the fluid, increasing the relative proportion of sulphur for gold complexation and inhibited additional quartz precipitation. Gold re-precipitation occurred over distances of 10 µm to several tens of metres and was likely a result of sulphur activity reduction through precipitation of pyrite and other sulphides. We suggest this late remobilisation process may be relatively common in orogenic belts containing abundant mafic/ultramafic rocks, which act as a source of Ni and Co scavenged by chloride-bearing fluids. Both the preference of the arsenopyrite crystal structure for Ni and Co, rather than gold, and the release of sulphur during reaction, can drive gold remobilisation in many deposits across broad regions

Search for heavy neutral lepton production in K+ decays

A search for heavy neutral lepton production in K + decays using a data sample collected with a minimum bias trigger by the NA62 experiment at CERN in 2015 is reported. Upper limits at the 10−7 to 10−6 level are established on the elements of the extended neutrino mixing matrix |Ue4| 2 and |Uμ4| 2 for heavy neutral lepton mass in the ranges 170–448 MeV/c2 and 250–373 MeV/c2, respectively. This improves on the previous limits from HNL production searches over the whole mass range considered for |Ue4|2 and above 300 MeV/c2 for |Uμ4|2