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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. 

Abstract Radiogenic neutrons emitted by detector materials are one of the most challenging backgrounds for the direct search of dark matter in the form of weakly interacting massive particles (WIMPs). To mitigate this background, the XENONnT experiment is equipped with a novel gadolinium-doped water Cherenkov detector, which encloses the xenon dual-phase time projection chamber (TPC). The neutron veto (NV) can tag neutrons via their capture on gadolinium or hydrogen, which release$$\gamma $$ $\gamma$-rays that are subsequently detected as Cherenkov light. In this work, we present the first results of the XENONnT NV when operated with demineralized water only, before the insertion of gadolinium. Its efficiency for detecting neutrons is$$({82\pm 1}){\%}$$ $\left(82\pm 1\right)\%$, the highest neutron detection efficiency achieved in a water Cherenkov detector. This enables a high efficiency of$$({53\pm 3}){\%}$$ $\left(53\pm 3\right)\%$for the tagging of WIMP-like neutron signals, inside a tagging time window of$${250}~{\upmu }\hbox {s}$$ $250\mu \text{s}$between TPC and NV, leading to a livetime loss of$${1.6}{\%}$$ $1.6\%$during the first science run of XENONnT. 

We report on a blinded search for dark matter with single- and few-electron signals in the first science run of XENONnT relying on a novel detector response framework that is physics model dependent. We derive 90% confidence upper limits for dark matter-electron interactions. Heavy and light mediator cases are considered for the standard halo model and dark matter up-scattered in the Sun. We set stringent new limits on dark matter-electron scattering via a heavy mediator with a mass within $10–20\mathrm{MeV}/c^2$and electron absorption of axionlike particles and dark photons for $m_{\chi }$below $0.03\mathrm{keV}/c^2$. Published by the American Physical Society2025