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Characterization of clocks and inertial sensors, such as accelerometers and gyroscopes, typically includes Allan variance analysis. Allan variance is ubiquitous in timing and navigation communities which may appear niche compared with generalized spectral analysis. This note provides some motivation for Allan Variance for audiences more familiar with spectral analysis.
Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.
William Allan Bardeen (September 15, 1941 − November 18, 2025) was an American theoretical physicist who worked at the Fermi National Accelerator Laboratory. He is renowned for his foundational work on the chiral anomaly, the Adler-Bardeen theorem, the non-Abelian anomaly and gravitational anomalies. He was instrumental in the development of quantum chromodynamics and its applications, such as semileptonic decays and the Λ $\overline{MS}$ scheme frequently used in perturbative analysis of high energy processes involving strong interactions. Bardeen also played a major role in developing a theory of dynamical breaking of electroweak symmetry via top quark condensates, leading to one of the first composite Brout-Englert-Higgs boson models. His work on the chiral symmetry dynamics of heavy-light quark bound states correctly predicted abnormally long-lived resonances which are chiral symmetry partners of the ground state.
Multiple generations of calcite and dolomite precipitated in CM chondrites during ice melting events that led to episodes of liquid water. Models and laboratory analysis have suggested a long-term transition from oxidizing to reducing conditions during aqueous alteration on the CM parent body. We found that synchrotron X-ray absorption near edge spectroscopy (XANES) can detect relative differences in the oxidation state of trace iron within these carbonates. In CM chondrites, previous work interpreted Mn abundance in calcite as an indicator of relatively early or late formation, and dolomite is understood to form relatively late. In the CM1 chondrite Meteorite Hills 01070, XANES maps reveal that Mn-poor calcite contains more oxidized iron relative to Mn-rich calcite. While these measurements of carbonates support increasing iron reduction with progressive aqueous alteration in MET 01070, comparison among different CM chondrites suggests a complex picture of redox evolution. In addition to carbonates, we performed XANES measurements of the phyllosilicate-rich matrix of Allan Hills 83,100. Pre-edge centroid analysis indicates that this CM1/2 has an oxidation state similar to typical CM2 chondrites. While additional measurements are warranted to confirm the full span of redox trends in CM carbonates, our data do not support a correlation between redox state and petrologic type.
The first very long baseline interferometry (VLBI) detections at 870$\mu$m wavelength (345$\,$GHz frequency) are reported, achieving the highest diffraction-limited angular resolution yet obtained from the surface of the Earth, and the highest-frequency example of the VLBI technique to date. These include strong detections for multiple sources observed on inter-continental baselines between telescopes in Chile, Hawaii, and Spain, obtained during observations in October 2018. The longest-baseline detections approach 11$\,$G$\lambda$ corresponding to an angular resolution, or fringe spacing, of 19$\mu$as. The Allan deviation of the visibility phase at 870$\mu$m is comparable to that at 1.3$\,$mm on the relevant integration time scales between 2 and 100$\,$s. The detections confirm that the sensitivity and signal chain stability of stations in the Event Horizon Telescope (EHT) array are suitable for VLBI observations at 870$\mu$m. Operation at this short wavelength, combined with anticipated enhancements of the EHT, will lead to a unique high angular resolution instrument for black hole studies, capable of resolving the event horizons of supermassive black holes in both space and time.
The research programme performed on the Mega Amp Spherical Tokamak (MAST) Upgrade experiment has made significant advances in developing the physics understanding of low aspect ratio tokamaks in support of the operation of ITER and design of fusion powerplants. High performance plasma scenarios have been developed to facilitate a broad programme of experiments, in which confinement is constrained by the presence of m/n = 2/1 modes that cause substantial losses of fast ions. The onset of these modes coincides with the q = 2 surface residing in a local minimum in the toroidal current density profile. The maximum electron temperature at the pedestal top, T e,ped is limited with gas fuelling to ∼350 eV to maintain regular ELMs; higher T e,ped results in a transition to a non-stationary ELM-free regime. The operational space of spherical tokamaks has been expanded into small and ELM-free regimes. Strong shaping of the last closed flux surface can induce a transition from large to small ELMs, and ELM suppression with resonant magnetic perturbations has been observed for the first time in a low aspect ratio tokamak. Negative triangularity shaping has induced a transition from ELMy H-mode to a high-performance L-mode regime for the first time in a low aspect ratio tokamak. In studies of fast ion confinement, losses of fast particles due to Global Alfvén Eigenmodes have been identified. Interactions between fast ions generated by off-axis neutral beam injection and thermal neutrals can result in significant losses of fast ions. Experiments with on- and off-axis neutral beam injection exhibit a flux pumping mechanism, where the central safety factor is held to ∼1 in the absence of sawteeth. In studies of pedestal physics, it has been found that elevated main chamber neutral pressures result in an increase in the electron density and reduction in the temperature at the pedestal top. Advances in understanding plasma exhaust include the integration of a high-performance plasma core with detached outer divertors in the X-point target configuration. A newly commissioned lower divertor cryopump reduces the lower divertor neutral pressure by up to 50%, with minimal effect on the main chamber or upper divertor. New measurements and SOLPS-ITER simulations emphasise the importance of plasma–neutral interactions on divertor detachment in the conditions accessible in experiments. Real-time control of the ionisation front location in both divertor chambers independently has been demonstrated in double null experiments, enabled by the tightly baffled divertor chambers.
Abstract Solid oxide cells (SOCs) are a promising dual‐mode technology for the production of hydrogen through high‐temperature water electrolysis, and the generation of power through a fuel cell reaction that consumes hydrogen. Switching between these two modes as the price of electricity fluctuates requires reversible SOC operation and accurate tracking of hydrogen and power production set points. Moreover, a well‐functioning control system is important to avoid cell degradation during mode‐switching operation. In this article, we apply nonlinear model predictive control (NMPC) to an SOC module and supporting equipment and compare NMPC performance to classical proportional‐integral (PI) control strategies, while switching between the modes of hydrogen and power production. While both control methods provide similar performance across various metrics during mode switching, NMPC demonstrates a significant advantage in reducing cell thermal gradients and curvatures (mixed spatial‐temporal partial derivatives), thereby helping to mitigate long‐term degradation.
ABSTRACT Changes in “blue water”, which is the total supply of fresh water available for human extraction over land, are quite closely related to changes in runoff or equivalently precipitation minus evaporation, . This article examines how climate change‐driven recent past and future changes in the regional water cycle relate to blue water availability and changes in human blue water demand. Although at the largest scales theoretical and numerical model predictions are in broad agreement with observations, at continental scales and below models predict large ranges of possible future and runoff especially at the scale of individual river catchments and for shorter timescale subseasonal floods and droughts. Nevertheless, it is expected that the occurrence and severity of floods will increase and that of droughts may increase, possibly compounded by human‐driven non‐climatic changes such as changes in land use, dam water impoundment, irrigation and extraction of groundwater. Contemporary assessments predict that increases in 21st century human water extraction in many highly‐populated regions are unlikely to be sustainable given projections of future . To reduce uncertainty in future predictions, there is an urgent need to improve modeling of atmospheric, land surface and human processes and how these components are coupled. This should be supported by maintaining the observing network and expanding it to improve measurements of land surface, oceanic and atmospheric variables. This includes the development of satellite observations stable over multiple decades and suitable for building reanalysis datasets appropriate for model evaluation.
Here, this work seeks to allow for the online operation and training of model-free reinforcement learning (RL) agents but limit the risk to system equipment and personnel. The parallel implementation of RL alongside more conventional process control (CPC) allows for the RL algorithm to learn from CPC. The past performance of both methods are assessed on a continuous basis allowing for a transition from CPC to RL and, if needed, transitioning back to CPC from RL. This allows for the RL algorithm to slowly and safely assume control of the process without significant degradation in control performance. It is shown that the RL can derive a near optimal policy even when coupled with a suboptimal CPC. It is also demonstrated that the coupled RL-CPC algorithm learns at a faster rate than traditional RL methods of exploration while the algorithm’s performance does not deteriorate below CPC, even when exposed to an unknown operating condition.
It can be difficult to identify the specific variables or equations responsible for convergence issues in large mathematical programming models. The Institute for the Design of Advanced Energy Systems Integrated Platform (IDAES-IP) contains a tool to identify poorly scaled constraints and variables by searching for rows and columns of the Jacobian matrix with small L2-norms. A singular value decomposition is then performed to identify degenerate sets of equations and remaining scaling issues. Here, this work presents a flowsheet developed for post-combustion carbon capture using a monoethanolamine (MEA) solvent system as a case study. This work takes the reader through the entire process of model diagnostics and reformulation, from a basic introduction to the mathematics behind these model diagnostics to the reformulations necessary to make the model numerically robust, including a significantly modified enhancement factor model.
Background: Deeper insights into ERBB2-driven cancers are essential to develop new treatment approaches for ERBB2+ breast cancers (BCs). We employed the Collaborative Cross (CC) mouse model to unearth genetic factors underpinning Erbb2-driven mammary tumour development and metastasis. Methods: 732 F1 hybrid female mice between FVB/N MMTV-Erbb2 and 30 CC strains were monitored for mammary tumour phenotypes. GWAS pinpointed SNPs that influence various tumour phenotypes. Multivariate analyses and models were used to construct the polygenic score and to develop a mouse tumour susceptibility gene signature (mTSGS), where the corresponding human ortholog was identified and designated as hTSGS. The importance and clinical value of hTSGS in human BC was evaluated using public datasets, encompassing TCGA, METABRIC, GSE96058, and I-SPY2 cohorts. The predictive power of mTSGS for response to chemotherapy was validated in vivo using genetically diverse MMTV-Erbb2 mice. Findings: Distinct variances in tumour onset, multiplicity, and metastatic patterns were observed in F1-hybrid female mice between FVB/N MMTV-Erbb2 and 30 CC strains. Besides lung metastasis, liver and kidney metastases emerged in specific CC strains. GWAS identified specific SNPs significantly associated with tumour onset, multiplicity, lung metastasis, and liver metastasis. Multivariate analyses flagged SNPs in 20 genes (Stx6, Ramp1, Traf3ip1, Nckap5, Pfkfb2, Trmt1l, Rprd1b, Rer1, Sepsecs, Rhobtb1, Tsen15, Abcc3, Arid5b, Tnr, Dock2, Tti1, Fam81a, Oxr1, Plxna2, and Tbc1d31) independently tied to various tumour characteristics, designated as a mTSGS. hTSGS scores (hTSGSS) based on their transcriptional level showed prognostic values, superseding clinical factors and PAM50 subtype across multiple human BC cohorts, and predicted pathological complete response independent of and superior to MammaPrint score in I-SPY2 study. The power of mTSGS score for predicting chemotherapy response was further validated in an in vivo mouse MMTV-Erbb2 model, showing that, like findings in human patients, mouse tumours with low mTSGS scores were most likely to respond to treatment. Interpretation: Our investigation has unveiled many new genes predisposing individuals to ERBB2-driven cancer. Translational findings indicate that hTSGS holds promise as a biomarker for refining treatment strategies for patients with BC.
Optimizing the performance of solid oxide electrolysis cells (SOECs) for long-term hydrogen (H 2 ) production at high temperatures is crucial, as prolonged operation leads to efficiency losses and shorter cell lifespans due to chemical degradation. Here, in this work, we adopt a quasi-steady state approach for dynamic optimization over extended operational periods to address the disparity in timescales between cell operation and degradation. Integrating a 2-D non-isothermal SOEC model with balance-of-plant (BOP) equipment, we explore three optimization objectives: minimizing terminal degradation, maximizing integral efficiency, and minimizing the levelized cost of H 2 (LCOH). Our dynamic optimization algorithm reduces LCOH by 9.5% and 16% compared to strategies focusing solely on terminal degradation and integral efficiency, respectively. For electricity prices of 0.03 $\$$/mWh and 0.3 $\$$ mWh optimal replacement schedules range from 5 to 2 years, depending on the operational mode. Furthermore, a flexible operational mode yields additional improvements in LCOH over traditional galvanostatic and potentiostatic modes.
Here, this work presents processing silicon carbide (SiC) with the laser-induced slip casting (LIS) additive manufacturing (AM). SiC was stabilized in water with polyethyleneimine (PEI) dispersant, and SiC slurries were made with rheology for LIS printing. High-density ceramic parts were printed, followed by single-step binder burnout and sintering. The printed parts achieved 93–95 % of theoretical density. X-ray computed tomography (XCT) revealed a small distribution of flaws exceeding 100 microns. The mechanical properties were measured in both parallel and perpendicular to the printing layers, and the orientation with layers perpendicular to the bending moment resulted in higher strength compared to the parallel direction. Porosity resulting from processing and large inclusions of boron carbide (B4C) were the root cause of failure in the measured samples. Despite these defects through this effort, this new approach demonstrates promise for green forming of SiC with densities greater than 95 % theoretical and tensile strengths above 250 MPa.
Here, this study develops a thermal stress model of solid-oxide electrolysis cells (SOECs) including a model for creep strain and failure probability that is integrated with a dynamic plant-wide model of a hydrogen production process. Uncertainties in key material properties of the cell are quantified to assess their impact on stress profile variability. The oxygen electrode is found to have about 10 times higher failure probability compared to the fuel electrode. The study shows that if the stack operation is not optimized, cycling operation would lead to stress build-up eventually leading to catastrophic failure. A dynamic optimization problem is set up for obtaining the optimal operational profile considering a variable hydrogen production rate. Due to the tradeoff between the efficiency and stress build-up, the dynamic optimization problem is multi-objective. It is observed that the optimizer can considerably reduce the stress build-up (i.e., can increase the stack life) albeit at the cost of a lower efficiency thus exhibiting strong tradeoffs between capital and operating costs. For example, if the stack would be replaced in 0.5 yr, specific energy requirement would be 48.5 kWh/kg H 2 while for a stack replacement time of about 6 yr, the specific energy requirement rises by about 4.2 %.
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Excessive tree mortality is a global concern and remains poorly understood as it is a complex phenomenon. We lack global and temporally continuous coverage on tree mortality data. Ground-based observations on tree mortality, e.g., derived from national inventories, are very sparse, and may not be standardized or spatially explicit. Earth observation data, combined with supervised machine learning, offer a promising approach to map overstory tree mortality in a consistent manner over space and time. However, global-scale machine learning requires broad training data covering a wide range of environmental settings and forest types. Low altitude observation platforms (e.g., drones or airplanes) provide a cost-effective source of training data by capturing high-resolution orthophotos of overstory tree mortality events at centimeter-scale resolution. Here, we introduce deadtrees.earth, an open-access platform hosting more than two thousand centimeter-resolution orthophotos, covering more than 1,000,000 ha, of which more than 58,000 ha are manually annotated with live/dead tree classifications. This community-sourced and rigorously curated dataset can serve as a comprehensive reference dataset to uncover tree mortality patterns from local to global scales using space-based Earth observation data and machine learning models. This will provide the basis to attribute tree mortality patterns to environmental changes or project tree mortality dynamics to the future. The open nature of deadtrees.earth, together with its curation of high-quality, spatially representative, and ecologically diverse data will continuously increase our capacity to uncover and understand tree mortality dynamics.
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