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We compute quasinormal mode frequencies for static limits of physical black holes - semi-classical black hole solutions to Einstein-Hilbert gravity characterized by the finite formation time of an apparent horizon and its weak regularity. These assumptions lead to a highly constrained yet non-trivial form of the metric and components of the energy-momentum tensor near the horizon, which contain as a special case many known models of black holes. Using a two-point M-fraction approximation to construct an interpolating metric which captures the essential near-horizon and asymptotic properties of black holes, we explore a large part of the parameter space that characterizes the near-horizon geometry. We cast the perturbation problem as a discretized homogeneous eigensystem and compute the low-lying quasinormal mode frequencies for perturbations of a massless scalar field. Working in spherical symmetry, we provide rough constraints on leading and subleading deviations from the Schwarzschild solution which arise in a semi-classical setting, and demonstrate the potential for mimicking signatures of axially-symmetric geometries from a spherically-symmetric source., Comment: 17 pages, 13 figures, published version

An integrated data analysis system based on Bayesian inference has been developed for application to data from multiple diagnostics over the two-dimensional cross-section of tokamak divertors. Tests of the divertor multi-instrument Bayesian analysis system (D-MIBAS) on a synthetic data set (including realistic experimental uncertainties) generated from SOLPS-ITER predictions of the MAST-U divertor have been performed. The resulting inference was within 6\%, 5\% and 30\% median absolute percentage error of the SOLPS-predicted electron temperature, electron density and neutral atomic hydrogen density, respectively, across a two-dimensional poloidal cross-section of the MAST-U Super-X outer divertor. To accommodate molecular contributions to Balmer emission, an advanced emission model has been developed which is shown to be crucial for inference accuracy. Our D-MIBAS system utilises a mesh aligned to poloidal magnetic flux-surfaces, throughout the divertor, with plasma parameters assigned to each mesh vertex and collectively considered in the inference. This allowed comprehensive forward models to multiple diagnostics and the inclusion of expected physics. This is shown to be important for inference precision when including molecular contributions to Balmer emission. These developments pave the way for accurate two-dimensional electron temperature, electron density and neutral atomic hydrogen density inferences for MAST-U divertor experimental data for the first time., Comment: 22 pages, 8 figures

We study various aspects of modeling astrophysical black holes using the recently introduced semiclassical formalism of physical black holes (PBHs). This approach is based on the minimal requirements of observability and regularity of the horizons. We demonstrate that PBHs do not directly couple to the cosmological background in the current epoch, and their equation of state renders them unsuitable for describing dark energy. Utilizing their properties for analysis of more exotic models, we present a consistent semiclassical scenario for a black-to-white hole bounce and identify obstacles to the transformation from a black hole horizon to a wormhole mouth., Comment: 8 pages, 2 figures. Comments welcome!

The formation of horizons in finite time according to distant observers results in a number of remarkable properties of the objects they bound. Subject to this requirement, spherically-symmetric black holes can only decrease in mass, while white holes can only expand. We provide a detailed analysis of the latter scenario, focussing on the energy-momentum tensor near the horizon and the experiences of various observers. Kerr-Vaidya metrics are the simplest dynamical axially-symmetric solutions, all of which violate the null energy condition and thus are not excluded by the criterion of finite formation time. Of the four classes of Kerr-Vaidya metrics, two correspond to the allowed spherically-symmetric solutions: evaporating black holes and expanding white holes. We demonstrate a consistent description of accreting black holes based on the ingoing Kerr-Vaidya metric with increasing mass, and show that the model can be extended to cases where the angular momentum to mass ratio varies. Their apparent horizon is shown to be weakly singular. Pathologies are also identified in the evaporating white hole geometry which reinforce controversies arising from the classical and quantum instabilities of their static counterparts. We also describe a generalization of the equivalence between Rindler and Schwarzschild horizons to Kerr-Vaidya black holes, and describe the relevant geometric constructions., Comment: 18 pages, 5 figures. Minor edits. Comments welcome!

We trace the origins and development of black hole thermodynamics across the past half-century, emphasizing the framework's relation to classical thermodynamics, and the vital role played by the notions of equilibrium, stationarity, and symmetry. We discuss different interpretations of the first law of black hole mechanics, and assess the validity of its mechanical, process-based interpretation for evaporating black holes. We bring these ideas to the cosmological realm, and highlight the various difficulties that arise when formulating thermodynamics for black holes in asymptotically de Sitter backgrounds. We discuss a number of proposed solutions and the open questions that arise therein., Comment: 9 pages, 1 figure. Honorable Mention for the Gravity Research Foundation 2023 Awards for Essays on Gravitation

We investigate the thermodynamic properties of the Hayward regular black hole using both Euclidean path integral and Hamiltonian methods, in asymptotically anti-de Sitter, Minkowski, and de Sitter spacetimes. With the inclusion of matter fields which act as a source for the regular black hole geometry, an effective temperature emerges that differs from the conventional definition related to the Killing surface gravity. We posit that this temperature is the appropriate choice for studying thermodynamic phenomena, by demonstrating consistency between the Euclidean and Hamiltonian formulations in the appropriate limits. We examine the thermodynamic properties and phase structure of the Hayward black hole in the canonical ensemble and show that, counter to some earlier indications, standard mean-field theory critical behavior is observed when the cosmological constant is treated as a thermodynamic pressure. We note the absence of a Hawking-Page transition, and conjecture that quantum gravity corrections which are suitably strong to regulate the Schwarzschild singularity generically prevent the transition from occurring. We also show that the Smarr relation remains linear in all cases, despite the absence of a linearity proof for nonlinear electrodynamic theories with nonsymmetry inheriting fields., Comment: 19 pages, 10 figures, Published version. Comments welcome!

The Vaidya metric serves as a useful model-building tool that captures many essential features of dynamical and/or evaporating black hole spacetimes. Working in a semiclassical setting, we show that in the limit of slow evaporation, a general spherically symmetric metric subject to certain regularity conditions is uniquely described by a linear ingoing Vaidya metric in the near-horizon region. This suggests a universal description of the near-horizon geometry of evaporating black holes in terms of the linear Vaidya metric. We also demonstrate that the linear Vaidya metric can be brought into manifestly conformally static form, allowing us to determine the Hawking temperature associated with the Vaidya background with respect to the conformal vacuum. Since back-reaction is implicitly accounted for, we conclude that slowly evaporating black holes are indeed accurately described by quasistatic sequences of Schwarzschild metrics even when dynamical effects are present., Comment: 10 pages, 1 figure. Comments welcome

Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption of regularity of the renormalized expectation value of the energy-momentum tensor, and derive explicit coordinate transformations in the near-horizon region. We examine the boundary conditions appropriate for embedding the model into a cosmological background, describe their evaporation in the linear regime and highlight the observational consequences, while also discussing the implications for the laws of black hole mechanics., Comment: 15 pages, 1 figure. Comments welcome!

Plasma-molecular interactions generate molecular ions which react with the plasma and contribute to detachment through molecular activated recombination (MAR), reducing the ion target flux, and molecular activated dissociation (MAD), both of which create excited atoms. Hydrogenic emission from these atoms have been detected experimentally in detached TCV, JET and MAST-U deuterium plasmas. The TCV findings, however, were in disagreement with SOLPS-ITER simulations for deuterium indicating a molecular ion density ($D_2^+$) that was insufficient to lead to significant hydrogenic emission, which was attributed to underestimates of the molecular charge exchange rate ($D_2 + D^+ \rightarrow D_2^+ + D$) for deuterium (obtained by rescaling the hydrogen rates by their isotope mass). In this work, we have performed new SOLPS-ITER simulations with the default rate setup and a modified rate setup where ion isotope mass rescaling was disabled. This increased the $D_2^+$ content by $> \times 100$. By disabling ion isotope mass rescaling: 1) the total ion sinks are more than doubled due to the inclusion of MAR; 2) the additional MAR causes the ion target flux to roll-over during detachment; 3) the total $D\alpha$ emission in the divertor increases during deep detachment by roughly a factor four; 4) the neutral atom density in the divertor is doubled due to MAD, leading to a 50\% increase in neutral pressure; 5) total hydrogenic power loss is increased by up to 60\% due to MAD. These differences result in an improved agreement between the experiment and the simulations in terms of spectroscopic measurements, ion source/sink inferences and the occurrence of an ion target flux roll-over.

An influence of Mg and Si dopants on the formation energies and the concentration of point defects in yttrium aluminum garnet (YAG) is studied using the density functional approach. The formation energies of Mg and Si substitutional and interstitial defects, native point defects and defect complexes versus the oxygen chemical potential are obtained. It is shown that in YAG doped with Mg, negatively charged Mg substitutional defects are compensated by free carriers (holes) and positively charged oxygen vacancies, whereas interstitial Mg ions play a minor role. The concentration of oxygen vacancies increases under an increase in the concentration of Mg ions. In YAG doped with Si, positively charged Si substitutional defects are compensated by negatively changed isolated cation vacancies and complexes of Si ions and cation vacancies. Under an increase in the concentration of Si ions most of Al and Y vacancies bind in complexes with Si ions. As a result, the concentration of isolated cation vacancies depends nonmonotonically on the concentration of Si ions. The maximum of the concentration of isolated cation vacancies is reached at $0.02 - 0.04$ at. % of Si, depending on sintering conditions. Mg - Si complexes have very low formation energies. Due to formation of such complexes, Si and Mg increases the solubility of each other in YAG. At the same time Mg - Si complexes do not influence the concentration of anion and cation vacancies. The overall concentration of vacancies in YAG codoped with Mg and Si in equal atomic concentrations is low. At an excess concentration of Si or Mg the concentration of vacancies increases by orders of magnitude.

The mechanisms of magnetoelastic interaction in MnF$_2$ are studied using the method of acoustoelectric transformation. The temperature dependence of the piezomagnetic coupling coefficient and its anisotropy are determined in the antiferromagnetic phase. We observe a new effect consisting in the appearance of a non-diagonal component of the magnetic susceptibility tensor, which is proportional to the square of the order parameter, under the action of the shear wave. A phenomenological interpretation of the effect, which takes into account a small-angle rotation of the crystal lattice, is presented. In the paramagnetic state, the effect of acoustic deformation is reduced to the modulation of the diagonal component of the susceptibility tensor.

The generalization of Birkhoff's theorem to higher dimensions in Lovelock gravity allows for black hole solutions with horizon geometries of non-constant curvature. We investigate thermodynamic aspects of these `exotic' black hole solutions, with a particular emphasis on their phase transitions. We consider an extended phase space where the cosmological constant acts as a thermodynamic pressure, and examine both uncharged and $U(1)$ charged solutions. In $d=7$, black hole solutions are restricted to having constant-curvature horizon base manifolds. Uncharged $d=7$ black holes possess novel triple point phenomena analogous to those recently uncovered in exotic $d=6$ black holes in Gauss-Bonnet gravity, while their charged counterparts generically undergo small-large black hole phase transitions. In $d=8$, we find that both charged and uncharged black holes exhibit triple point behaviour and small-large black hole transitions. We also show that a wide range of `exotic' horizon geometries can be ruled out due to the appearance of naked singularities., Comment: 24 pages, 9 Figures

In this paper, we report the novel experimental observation of both unstable and stable Toroidicity-induced Alfv\'en Eigenmodes (TAEs) measured simultaneously in a JET tokamak plasma. The three-ion-heating scheme (D-DNBI-3He) is employed to accelerate deuterons to MeV energies, thereby destabilizing TAEs with toroidal mode numbers n = 3-5, each decreasing in mode amplitude. At the same time, the Alfv\'en Eigenmode Active Diagnostic resonantly excites a stable n = 6 TAE with total normalized damping rate $-\gamma/\omega_0 \approx$ 1%-4%. Hybrid kinetic-MHD modeling with codes NOVA-K and MEGA both find eigenmodes with similar frequencies, mode structures, and radial locations as in experiment. NOVA-K demonstrates good agreement with the n = 3, 4, and 6 TAEs, matching the damping rate of the n = 6 mode within uncertainties and identifying radiative damping as the dominant contribution. Improved agreement is found with MEGA for all modes: the unstable n = 3-5 and stable n = 2, 6 modes, with the latter two stabilized by higher intrinsic damping and lower fast ion drive, respectively. While some discrepancies remain to be resolved, this unique validation effort gives us confidence in TAE stability predictions for future fusion devices.

Understanding generation and mitigation of runaway electrons in disruptions is important for the safe operation of future tokamaks. In this paper we investigate runaway dynamics in reactor-scale spherical tokamaks. We study both the severity of runaway generation during unmitigated disruptions, as well as the effect that typical mitigation schemes based on massive material injection have on runaway production. The study is conducted using the numerical framework DREAM (Disruption Runaway Electron Analysis Model). We find that, in many cases, mitigation strategies are necessary to prevent the runaway current from reaching multi-megaampere levels. Our results indicate that with a suitably chosen deuterium-neon mixture for mitigation, it is possible to achieve a tolerable runaway current and ohmic current evolution. With such parameters, however, the majority of the thermal energy loss happens through radial transport rather than radiation, which poses a risk of unacceptable localised heat loads., Comment: 19 pages, 7 figures

Hebbian theory seeks to explain how the neurons in the brain adapt to stimuli, to enable learning. An interesting feature of Hebbian learning is that it is an unsupervised method and as such, does not require feedback, making it suitable in contexts where systems have to learn autonomously. This paper explores how molecular systems can be designed to show such proto-intelligent behaviours, and proposes the first chemical reaction network (CRN) that can exhibit autonomous Hebbian learning across arbitrarily many input channels. The system emulates a spiking neuron, and we demonstrate that it can learn statistical biases of incoming inputs. The basic CRN is a minimal, thermodynamically plausible set of micro-reversible chemical equations that can be analysed with respect to their energy requirements. However, to explore how such chemical systems might be engineered de novo, we also propose an extended version based on enzyme-driven compartmentalised reactions. Finally, we also show how a purely DNA system, built upon the paradigm of DNA strand displacement, can realise neuronal dynamics. Our analysis provides a compelling blueprint for exploring autonomous learning in biological settings, bringing us closer to realising real synthetic biological intelligence., Comment: Submitted to ACS Synthetic Biology. arXiv admin note: substantial text overlap with arXiv:2009.13207

We present the first analysis of the atomic and molecular processes at play during detachment in the MAST-U Super-X divertor using divertor spectroscopy data. Our analysis indicates detachment in the MAST-U Super-X divertor can be separated into four sequential phases: First, the ionisation region detaches from the target at detachment onset leaving a region of increased molecular densities downstream. The plasma interacts with these molecules, resulting in molecular ions ($D_2^+$ and/or $D_2^- \rightarrow D + D^-$) that further react with the plasma leading to Molecular Activated Recombination and Dissociation (MAR and MAD), which results in excited atoms and significant Balmer line emission. Second, the MAR region detaches from the target leaving a sub-eV temperature region downstream. Third, an onset of strong emission from electron-ion recombination (EIR) ensues. Finally, the electron density decays near the target, resulting in a density front moving upstream. The analysis in this paper indicates that plasma-molecule interactions have a larger impact than previously reported and play a critical role in the intensity and interpretation of hydrogen atomic line emission characteristics on MAST-U. Furthermore, we find that the Fulcher band emission profile in the divertor can be used as a proxy for the ionisation region and may also be employed as a plasma temperature diagnostic for improving the separation of hydrogenic emission arising from electron-impact excitation and that from plasma-molecular interactions. We provide evidences for the presence of low electron temperatures ($<0.5$ eV) during detachment phases III-IV based on quantitative spectroscopy analysis, a Boltzmann relation of the high-n Balmer line transitions together with an analysis of the brightness of high-n Balmer lines.

Dislocation model of the supersolid state of $^4$He was proposed in 1987 by one of the authors of the review. The model obtained strong support by numerous experimental and theoretical investigations from 2007 to date. In these investigations the validity of the idea put forward in 1987 was confirmed, and new conceptions of superclimb of dislocations and of the giant isochoric compressibility or the syringe effect were proposed. In this paper we review main achievements of theoretical and experimental studies of dislocation-induced supersolid and present current understanding of this phenomenon.

MAST-U has recently started operating with a Super-X divertor, designed to increase total flux expansion and neutral trapping, both predicted through simple analytic models and SOLPS calculations to reduce the plasma and impurity density detachment thresholds. In this study, utilising the SOLPS-ITER code, we are quantifying the possible gain allowed by the MAST-U Super-X and neutral baffling geometry, in terms of access to detachment. We show that a significant reduction of the upstream density detachment threshold (up to a factor 1.6) could be achieved in MAST-U, for the Super-X, as opposed to conventional divertor geometry, mainly through an increased total flux expansion, neutral trapping being found very similar between the different configurations. We also show that variations of the strike-point angle are complex to interpret in such a tightly baffled geometry, and that a case in which the target normal points more towards the separatrix does not necessarily imply a lower detachment threshold. As in previous calculations for TCV, we quantify the role of neutral effects through developing and applying a quantitative definition of neutral trapping.

$\beta$-VAE is a follow-up technique to variational autoencoders that proposes special weighting of the KL divergence term in the VAE loss to obtain disentangled representations. Unsupervised learning is known to be brittle even on toy datasets and a meaningful, mathematically precise definition of disentanglement remains difficult to find. Here we investigate the original $\beta$-VAE paper and add evidence to the results previously obtained indicating its lack of reproducibility. We also further expand the experimentation of the models and include further more complex datasets in the analysis. We also implement an FID scoring metric for the $\beta$-VAE model and conclude a qualitative analysis of the results obtained. We end with a brief discussion on possible future investigations that can be conducted to add more robustness to the claims.

The success of neural architecture search (NAS) has historically been limited by excessive compute requirements. While modern weight-sharing NAS methods such as DARTS are able to finish the search in single-digit GPU days, extracting the final best architecture from the shared weights is notoriously unreliable. Training-Speed-Estimate (TSE), a recently developed generalization estimator with a Bayesian marginal likelihood interpretation, has previously been used in place of the validation loss for gradient-based optimization in DARTS. This prevents the DARTS skip connection collapse, which significantly improves performance on NASBench-201 and the original DARTS search space. We extend those results by applying various DARTS diagnostics and show several unusual behaviors arising from not using a validation set. Furthermore, our experiments yield concrete examples of the depth gap and topology selection in DARTS having a strongly negative impact on the search performance despite generally receiving limited attention in the literature compared to the operations selection., Comment: Presented at the 5th Workshop on Meta-Learning at NeurIPS 2021

The interaction of Alfv\'{e}n Eigenmodes (AEs) and energetic particles is one of many important factors determining the success of future tokamaks. In JET, eight in-vessel antennas were installed to actively probe stable AEs with frequencies ranging 25-250 kHz and toroidal mode numbers $\vert n \vert < 20$. During the 2019-2020 deuterium campaign, almost 7500 resonances and their frequencies $f_0$, net damping rates $\gamma < 0$, and toroidal mode numbers were measured in almost 800 plasma discharges. From a statistical analysis of this database, continuum and radiative damping are inferred to increase with edge safety factor, edge magnetic shear, and when including non-ideal effects. Both stable AE observations and their associated damping rates are found to decrease with $\vert n \vert$. Active antenna excitation is also found to be ineffective in H-mode as opposed to L-mode; this is likely due to the increased edge density gradient's effect on accessibility and ELM-related noise's impact on mode identification. A novel measurement is reported of a marginally stable, edge-localized Ellipticity-induced AE probed by the antennas during high-power auxiliary heating (ICRH and NBI) up to 25 MW. NOVA-K kinetic-MHD simulations show good agreement with experimental measurements of $f_0$, $\gamma$, and $n$, indicating the dominance of continuum and electron Landau damping in this case. Similar experimental and computational studies are planned for the recent hydrogen and ongoing tritium campaigns, in preparation for the upcoming DT campaign.

We investigate thermodynamic aspects of black holes in the recently formulated four dimensional Gauss-Bonnet theory of gravity, focusing on its asymptotically de Sitter ($\Lambda>0$) solutions. We take a Euclidean path integral approach, where thermodynamic data is fixed at a finite radius `cavity' outside the black hole to achieve equilibrium in the presence of the cosmological horizon. Working in the extended phase space where the cosmological constant is treated as a thermodynamic pressure, we study the phase structure of both uncharged and charged solutions, uncovering a wealth of phenomena. In the uncharged case, black holes are found to undergo either the standard Hawking-Page-like transition to empty de Sitter space or a small-large transition (akin to those seen in charged AdS black holes in pure Einstein gravity) depending on the pressure. We also find a triple point where the radiation, small, and large black hole phases coexist, and a zeroth-order phase transition within a narrow range of Gauss-Bonnet coupling parameter. Reentrant phase transitions between radiation and a small black hole also exist inside a certain parameter range. Similar phenomena are found in the charged case, with the charge parameter playing a role analogous to the Gauss-Bonnet coupling parameter in determining the phase structure., Comment: 23 pages, 6 figures. Updated references

This paper shows experimental results from the TCV tokamak that indicate plasma-molecule interactions involving $D_2^+$ and possibly $D^-$ play an important role as sinks of energy (through hydrogenic radiation as well as dissociation) and particles during divertor detachment if low target temperatures ($< 3$ eV) are achieved. Both molecular activated recombination (MAR) and ion source reduction due to a power limitation effect are shown to be important in reducing the ion target flux during a density ramp. In contrast, the electron-ion recombination (EIR) ion sink is too small to play an important role in reducing the ion target flux. MAR or EIR do not occur during $N_2$ seeding induced detachment as the target temperatures are not sufficiently low. The impact of $D_2^+$ is shown to be underestimated in present (vibrationally unresolved) SOLPS-ITER simulations, which could result from an underestimated $D_2 + D^+ \rightarrow D_2^+ + D$ rate. The converged SOLPS-ITER simulations are post-processed with alternative reaction rates, resulting in considerable contributions of $D_2^+$ to particle and power losses as well as dissociation below the $D_2$ dissociation area. Those findings are in quantitative agreement with the experimental results.

Stationary waves in the condensate of electron-hole pairs in the $n-p$ bilayer system are studied. The system demonstrates the transition from a uniform (superfluid) to a nonuniform (supersolid) state. The precursor of this transition is the appearance of the roton-type minimum in the collective mode spectrum. Stationary waves occur in the flow of the condensate past an obstacle. It is shown that the roton-type minimum manifests itself in a rather complicated stationary wave pattern with several families of crests which cross one another. It is found that the stationary wave pattern is essentially modified under variation in the density of the condensate and under variation in the flow velocity. It is shown that the pattern is formed in the main part by shortwave modes in the case of a point obstacle. The contribution of longwave modes is clearly visible in the case of a weak extended obstacle, where the stationary wave pattern resembles the ship wave pattern.