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We introduce a novel framework for optimization based on energy-conserving Hamiltonian dynamics in a strongly mixing (chaotic) regime and establish its key properties analytically and numerically. The prototype is a discretization of Born-Infeld dynamics, with a squared relativistic speed limit depending on the objective function. This class of frictionless, energy-conserving optimizers proceeds unobstructed until slowing naturally near the minimal loss, which dominates the phase space volume of the system. Building from studies of chaotic systems such as dynamical billiards, we formulate a specific algorithm with good performance on machine learning and PDE-solving tasks, including generalization. It cannot stop at a high local minimum, an advantage in non-convex loss functions, and proceeds faster than GD+momentum in shallow valleys. 

In this study, a suite of natural wastewater sources is tested to understand the effects of wastewater composition and source on electrochemically driven nitrogen and phosphorus nutrient removal. Kinetics, electrode behavior, and removal efficiency were evaluated during electrochemical precipitation, whereby a sacrificial magnesium (Mg) anode was used to drive precipitation of ammonium and phosphate. The electrochemical reactor demonstrated fast kinetics in the natural wastewater matrices, removing up to 54% of the phosphate present in natural wastewater within 1 min, with an energy input of only 0.04 kWh.m−3. After 1 min, phosphate removal followed a zero-order rate law in the 1 min - 30 min range. The zero-order rate constant (k) appears to depend upon differences in wastewater composition, where a faster rate constant is associated with higher Cl− and NH4+ concentrations, lower Ca2+ concentrations, and higher organic carbon content. The sacrificial Mg anode showed the lowest corrosion resistance in the natural industrial wastewater source, with an increased corrosion rate (vcorr) of 15.8 mm.y−1 compared to 1.9–3.5 mm.y−1 in municipal wastewater sources, while the Tafel slopes (β) showed a direct correlation with the natural wastewater composition and origin. An overall improvement of water quality was observed where important water quality parameters such as total organic carbon (TOC), total suspended solids (TSS), and turbidity showed a significant decrease. An economic analysis revealed costs based upon experimental Mg consumption are estimated to range from 0.19 $.m−3 to 0.30 $.m−3, but costs based upon theoretical Mg consumption range from 0.09 $.m−3 to 0.18 $.m−3. Overall, this study highlights that water chemistry parameters control nutrient recovery, while electrochemical treatment does not directly produce potable water, and that economic analysis should be based upon experimentally-determined Mg consumption data. 

In this work, we expand on the XENON1T nuclear recoil searches to study the individual signals of dark matter interactions from operators up to dimension eight in a chiral effective field theory (ChEFT) and a model of inelastic dark matter (iDM). We analyze data from two science runs of the XENON1T detector totaling $1\mathrm{t}\times \mathrm{yr}$exposure. For these analyses, we extended the region of interest from $[4.9,40.9]{\mathrm{keV}}_{\mathrm{NR}}$to $[4.9,54.4]{\mathrm{keV}}_{\mathrm{NR}}$to enhance our sensitivity for signals that peak at nonzero energies. We show that the data are consistent with the background-only hypothesis, with a small background overfluctuation observed peaking between 20 and $50{\mathrm{keV}}_{\mathrm{NR}}$, resulting in a maximum local discovery significance of $1.7\sigma$for the $\mathrm{Vector}\otimes {\text{Vector}}_{\text{strange}}$ChEFT channel for a dark matter particle of $70\mathrm{GeV}/c^2$and $1.8\sigma$for an iDM particle of $50\mathrm{GeV}/c^2$with a mass splitting of $100\mathrm{keV}/c^2$. For each model, we report 90% confidence level upper limits. We also report upper limits on three benchmark models of dark matter interaction using ChEFT where we investigate the effect of isospin-breaking interactions. We observe rate-driven cancellations in regions of the isospin-breaking couplings, leading to up to 6 orders of magnitude weaker upper limits with respect to the isospin-conserving case. Published by the American Physical Society2024 

This paper details the first application of a software tagging algorithm to reduce radon-induced backgrounds in liquid noble element time projection chambers, such as XENON1T and XENONnT. The convection velocity field in XENON1T was mapped out using ${}^{222}\mathrm{Rn}$and ${}^{218}\mathrm{Po}$events, and the rms convection speed was measured to be $0.30\pm 0.01\mathrm{cm}/\mathrm{s}$. Given this velocity field, ${}^{214}\mathrm{Pb}$background events can be tagged when they are followed by ${}^{214}\mathrm{Bi}$and ${}^{214}\mathrm{Po}$decays, or preceded by ${}^{218}\mathrm{Po}$decays. This was achieved by evolving a point cloud in the direction of a measured convection velocity field, and searching for ${}^{214}\mathrm{Bi}$and ${}^{214}\mathrm{Po}$decays or ${}^{218}\mathrm{Po}$decays within a volume defined by the point cloud. In XENON1T, this tagging system achieved a ${}^{214}\mathrm{Pb}$background reduction of ${6.2}_{-0.9}^{+0.4}\%$with an exposure loss of $1.8\pm 0.2\%$, despite the timescales of convection being smaller than the relevant decay times. We show that the performance can be improved in XENONnT, and that the performance of such a software-tagging approach can be expected to be further improved in a diffusion-limited scenario. Finally, a similar method might be useful to tag the cosmogenic ${}^{137}\mathrm{Xe}$background, which is relevant to the search for neutrinoless double-beta decay. Published by the American Physical Society2024 

Small molecule guests influence the functional properties of supramolecular hydrogels. Molecular-level understanding of such sol-gel compositions and structures is challenging due to the lack of long-range order and inherently heterogeneous sol-gel interface. In this study, insight into the uptake process of biologically relevant small molecules into guanosine-quartet(G4) borate hydrogels is obtained by gel-state magic-angle spinning (MAS) NMR spectroscopy. G4∙K + borate hydrogel can absorb up to 0.3 equivalent of cationic methylene blue (MB) without a significant disruption of the G4 fibrils that make up the gel, whereas the addition of over 0.3 equivalents of MB to the same gel leads to a gel-to-sol transition. The gel-to-sol transition process is characterized ex situ by analyzing and comparing the 1 H and 11 B MAS NMR spectra acquired before and after the MB uptake. In particular, 11 B isotropic chemical shifts and quadrupole interactions were determined by analyzing the 11 B MAS NMR spectra acquired at different magnetic fields, 11.7 T, 14.1 T and 20 T, which enable the different local bonding environments of borate anions in sol- and gel domains to be distinguished and identified. By comparison, uptake of heterocyclic molecules such as adenine, cytosine and 1-methylthymine into G4∙Na + borate hydrogels lead to stiff and clear gels while increasing the solubility of the nucleobases as compared to the solubility of the same compounds in water. G4∙Na + gel can uptake one equiv. of adenine with minimal disruption to the sol-gel framework, thus enhancing the adenine solubility up to an order of magnitude as compared to water. Combined multinuclear ( 1 H, 11 B and 23 Na) NMR spectroscopy analysis and vial inversion tests revealed that the nucleobases are embedded into pores of the sol phase rather than being closely interacting with the G-4 fibrils that make up the gel phase. These results indicate that G-4 hydrogels have potential applications as carrier systems for small molecules. Gel-state MAS NMR spectroscopy can be used to gain insight into host-guest interactions in complex heterogeneous sol-gel systems, which is often difficult to obtain from the conventional techniques such as X-ray scattering, electron microscopy and optical spectroscopy.