Miracle-dz/UniFAR-FTUs huggingface dataset:
Mathematical study of degenerate boundary layers: A Large Scale Ocean Circulation Problem

This paper is concerned with a complete asymptoticanalysis as $\mathfrak{E} \to 0$ of the stationary Munk equation $\partial\_x\psi-\mathfrak{E} \Delta^2 \psi=\tau$ in a domain $\Omega\subset \mathbf{R}^2$, supplemented with boundaryconditions for $\psi $ and $\partial\_n \psi$. This equation is a simplemodel for the circulation of currents in closed basins, the variables$x$ and $y$ being respectively the longitude and the latitude. A crudeanalysis shows that as $\mathfrak{E} \to 0$, the weak limit of $\psi$ satisfiesthe so-called Sverdrup transport equation inside the domain, namely$\partial\_x \psi^0=\tau$, while boundary layers appear in the vicinity ofthe boundary.These boundary layers, which are the main center of interest of thepresent paper, exhibit several types of peculiar behaviour. First, thesize of the boundary layer on the western and eastern boundary, whichhad already been computed by several authors, becomes formally verylarge as one approaches northern and southern portions of the boudary,i.e. pieces of the boundary on which the normal is vertical. Thisphenomenon is known as geostrophic degeneracy. In order to avoid suchsingular behaviour, previous studies imposed restrictive assumptionson the domain $\Omega$ and on the forcing term $\tau$. Here, we provethat a superposition of two boundary layers occurs in the vicinity ofsuch points: the classical western or eastern boundary layers, andsome northern or southern boundary layers, whose mathematicalderivation is completely new. The size of northern/southern boundarylayers is much larger than the one of western boundary layers($\mathfrak{E}^{1/4}$ vs. $\mathfrak{E}^{1/3}$). We explain in detail how the superpositiontakes place, depending on the geometry of the boundary.Moreover, when the domain $\Omega$ is not connex in the $x$ direction,$\psi^0$ is not continuous in $\Omega$, and singular layers appear inorder to correct its discontinuities. These singular layers areconcentrated in the vicinity of horizontal lines, and thereforepenetrate the interior of the domain $\Omega$. Hence we exhibit some kindof boundary layer separation. However, we emphasize that we remainable to prove a convergence theorem, so that the singular layerssomehow remain stable, in spite of the separation.Eventually, the effect of boundary layers is non-local in severalaspects. On the first hand, for algebraic reasons, the boundary layerequation is radically different on the west and east parts of theboundary. As a consequence, the Sverdrup equation is endowed with aDirichlet condition on the East boundary, and no condition on the Westboundary. Therefore western and eastern boundary layers have in factan influence on the whole domain $\Omega$, and not only near theboundary. On the second hand, the northern and southern boundary layerprofiles obey a propagation equation, where the space variable $x$plays the role of time, and are therefore not local.
CORRELATION OF γ-RAY AND HIGH-ENERGY COSMIC RAY FLUXES FROM THE GIANT LOBES OF CENTAURUS A

The spectral energy distribution of giant lobes shows one main peak detected by the Wilkinson Microwave Anisotropy Probe at the low energy of 10−5 eV and a faint γ-ray flux imaged by the Fermi Large Area Telescope at an energy of ⩾100 MeV. On the other hand, the Pierre Auger Observatory associated some ultra-high-energy cosmic rays with the direction of Centaurus A and IceCube reported 28 neutrino-induced events in a TeV–PeV energy range, although none of them related with this direction. In this work, we describe the spectra for each of the lobes, the main peak with synchrotron radiation, and the high-energy emission with p–p interactions. After obtaining a good description of the main peak, we deduce the magnetic fields, electron densities, and the age of the lobes. Successfully describing the γ-ray emission by p–p interactions and considering thermal particles in the lobes with density in the range 10−10–10−4 cm−3 as targets, we calculate the number of ultra-high-energy cosmic rays. Although the γ-spectrum is well described with any density in the range, only when 10−4 cm−3 is considered are the expected number of events very similar to that observed by the Pierre Auger Observatory, otherwise we obtain an excessive luminosity. In addition, correlating the γ-ray and neutrino fluxes through p–p interactions, we calculate the number of high-energy neutrinos expected in IceCube. Our analysis indicates that neutrinos above 1 TeV cannot be produced in the lobes of Centaurus A, which is consistent with the results recently published by the IceCube Collaboration.
Asymptotic flatness at null infinity in arbitrary dimensions

We define the asymptotic flatness and discuss asymptotic symmetry at null infinity in arbitrary dimensions using the Bondi coordinates. To define the asymptotic flatness, we solve the Einstein equations and look at the asymptotic behavior of gravitational fields. Then we show the asymptotic symmetry and the Bondi mass loss law with the well-defined definition.
Sufficient conditions for the forcing theorem, and turning proper classes into sets

We present three natural combinatorial properties for class forcing notions, which imply the forcing theorem to hold. We then show that all known sufficent conditions for the forcing theorem (except for the forcing theorem itself), including the three properties presented in this paper, imply yet another regularity property for class forcing notions, namely that proper classes of the ground model cannot become sets in a generic extension, that is they do not have set-sized names in the ground model. We then show that over certain models of G\"odel-Bernays set theory without the power set axiom, there is a notion of class forcing which turns a proper class into a set, however does not satisfy the forcing theorem. Moreover, we show that the property of not turning proper classes into sets can be used to characterize pretameness over such models of G\"odel-Bernays set theory.
Information, uncertainty and holographic action

In this short note we show through simple derivation the explicit relation between information flow and the theories of the emergence of space-time and gravity, specifically for Newton's second law of motion. Next, in a rather straightforward derivation the Heisenberg uncertainty relation is uncovered from the universal bound on information flow. A relation between the universal bound on information flow and the change in bulk action is also shown to exist.
γ-rays and the far-infrared–radio continuum correlation reveal a powerful Galactic Centre wind

We consider the thermal and non-thermal emission from the inner 200 pc of the Galaxy. The radiation from this almost star-burst-like region is ultimately driven dominantly by on-going massive star formation. We show that this region’s radio continuum (RC) emission is in relative decit with respect to the expectation aorded by the Farinfrared{Radio Continuum Correlation (FRC). Likewise we show that the region’s -ray emission falls short of that expected given its star formation and resultant supernova rates. These facts are compellingly explained by positing that a powerful (400-1200 km/s) wind is launched from the region. This wind probably plays a number of important roles including advecting positrons into the Galactic bulge thus explaining the observed kpc extension of the 511 keV positron annihilation signal around the GC. We also show that the large-scale GC magnetic eld falls in the range 100-300 G and that { in the time they remain in the region { GC cosmic rays do not penetrate into the region’s densest molecular material.
The bullet cluster is not a cosmological anomaly

The Bullet Cluster (1E0657-56) merger is of exceptional interest for testing the standard cold-dark-matter plus cosmological constant cosmological model, and for investigating the possible existence of a long- or short-range ``fifth-force'' in the dark sector and possible need for modifications of general relativity or even of Newtonian gravity. The most recent previous simulations of the Bullet Cluster merger required an initial infall velocity far in excess of what would be expected within the standard cosmological model, at least in the absence of additional forces or modifications to gravity. We have recently carried out much more detailed simulations than previously had been done, making pixel-by-pixel fits to 2D data-maps of the mass distribution and X-ray emission, allowing for triaxial initial configurations and including MHD and cooling. Here, we compare the initial conditions of the Bullet Cluster merger as found in our new simulations to the initial conditions in similar-mass merging clusters in the Horizon cosmological simulation. We conclude that our initial infall velocity, 2900 km/s at a separation of 2.5 Mpc, is consistent with ΛCDM, given the inferred main cluster mass of 2 × 1015 M⊙. The initial concentration and shape found for the smaller (Bullet) cluster are typical for clusters of this mass range, but both quantities seem somewhat low for the larger (Main) cluster. Due to the paucity of examples of clusters with such a high mass in simulations, these features of the main cluster cannot presently be used to test ΛCDM.
Integral field spectroscopy of the circum-nuclear region of the radio Galaxy Pictor A

We present optical integral field spectroscopy of the inner 2.5×3.4kpc 2 of the broadline radio galaxy Pictor A, at a spatial resolution of � 400pc. Line emission is observed over the whole field-of-view, being strongest at the nucleus and in an elongated linear feature (ELF) crossing the nucleus from the south-west to the north-east along PA � 70 ◦ . Although the broad double-peaked Hα line and the [Oi]6300/Hα and [Sii]6717+31/Hα ratios are typical of AGNs, the [Nii]6584/Hα ratio (0.15 0.25) is unusually low. We suggest that this is due to the unusually low metallicity of the gas. Centroid velocity maps show mostly blueshifts to the south and redshifts to the north of the nucleus, but the velocity field is not well fitted by a rotation model. Velocity dispersions are low (< 100kms −1 ) along the ELF, ruling out a jet-cloud interaction as the origin of this structure. The ELF shows both blueshifts and redshifts in channel maps, suggesting that it is close to the plane of the sky. The ELF is evidently photoionized by the AGN, but its kinematics and inferred low metallicity suggest that this structure may have originated in a past merger event with another galaxy. We suggest that the gas acquired in this interaction may be feeding the ELF.
Rigidity theorem for presheaves with Witt-transfers

The rigidity theorem for homotopy invariant presheaves with Witt-transfers on the category of smooth affine varieties over a field $k$ with characteristic not equal to 2 is proved. Namely for such a presheaf $\mathcal F$ the isomorphism $\mathcal F(U)\simeq \mathcal F(x)$ where $U$ is henseliation of a variety at smooth closed point with separable residue field (over $k$) is proved. The rigidity for presheaves $W^i(X\times -)$ where $X$ is smooth variety and $W^i(-)$ are derived Witt-groups ($i\in \mathbb Z/4\mathbb Z$) follows as corollary.
Compactness and lower semicontinuity in $GSBD$

In this paper, we prove a compactness and semicontinuity result in $GSBD$ for sequences with bounded Griffith energy. This generalises classical results in $(G)SBV$ by Ambrosio and $SBD$ by Bellettini-Coscia-Dal Maso. As a result, the static problem in Francfort-Marigo's variational approach to crack growth admits (weak) solutions. Moreover, we obtain a compactness property for minimisers of suitable Ambrosio-Tortorelli's type energies, for which we have recently shown the $\Gamma$-convergence to Griffith energy.
Evidence for spin-triplet odd-parity superconductivity close to type-II van Hove singularities

Searching for unconventional Cooper pairing states has been at the heart of superconductivity research since the discovery of BCS superconductors. In particular, spin-triplet odd-parity pairing states were recently revisited due to the possibility of tuning towards topological superconductors. In this context, it is interesting to note a recent proposal that such a spin-triplet pairing instability occurs when the band filling is near van Hove singularities (vHS) associated with momenta away from time-reversal invariant momenta named type-II vHS. However, this result was obtained within a weak coupling renormalization group with Fermi surface patch approximation. To explore superconducting instabilities beyond this weak coupling Fermi surface patch approximation, we perform systematic study on Hubbard model in a two-dimensional square lattice using three different methods: random phase approximation, large-scale dynamical mean field theory simulations with continuous time quantum Monte Carlo (CTQMC) impurity solver, and large-scale dynamical cluster simulations with CTQMC cluster solver. We find, in a wide doping range centered around the type-II van Hove filling, a two-fold degenerate, spin-triplet, odd-parity $p$-wave pairing state emerges due to repulsive interaction, when the Fermi surface is not sufficiently nested. Possible relevance of our findings to the recently discovered superconductors LaO$_{1-x}$F$_{x}$BiS$_{2}$, Ir$_{1-x}$Pt$_{x}$Te$_{2}$ and proposed doped BC$_{3}$ are also discussed.
Construction and analysis of sticky reflected diffusions

We give a Dirichlet form approach for the construction of distorted Brownian motion in a bounded domain $\Omega$ of $\mathbb{R}^d$, $d \geq 1$, with boundary $\Gamma$, where the behavior at the boundary is sticky. The construction covers the case of a static boundary behavior as well as the case of a diffusion on the hypersurface $\Gamma$ (for $d \geq 2)$. More precisely, we consider the state space $\overline{\Omega}=\Omega \stackrel{. }{\cup} \Gamma$, the process is a diffusion process inside $\Omega$, the occupation time of the process on the boundary $\Gamma$ is positive and the process may diffuse on $\Gamma$ as long as it sticks on the boundary. The problem is formulated in an $L^2$-setting and the construction is formulated under weak assumptions on the coefficients and $\Gamma$. In order to analyze the process we assume a $C^2$-boundary and some weak differentiability conditions. In this case, we deduce that the process is also a solution to a given SDE for quasi every starting point in $\overline{\Omega}$ with respect to the underyling Dirichlet form. Under the addtional condition that $\{ \varrho =0 \}$ is of capacity zero, we prove ergodicity of the constructed process and consequently, we verify that the boundary behavior is indeed sticky. Moreover, we show ($\mathcal{L}^p$-)strong Feller properties which allow to characterize the constructed process even for every starting point in $\overline{\Omega} \backslash \{ \varrho=0\}$.
Pulsars in gamma rays: What Fermi is teaching us

Abstract The 2nd Fermi-LAT pulsar catalog includes 117 γ-ray pulsars, of which roughly one third are millisecond pulsars (MSPs) while the remaining two thirds split evenly into young radio-loud and radio-quiet pulsars. Although this large population will enable future, detailed studies of emission mechanisms and the evolution of the underlying neutron star population, some nearly-universal properties are already clear and unequivocal. We discuss some of these aspects below, including the altitude of the γ-ray emission site, the shape of the γ-ray spectrum, and the implications of the latter for the radiation mechanism.
Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion

It is natural to investigate if the quantization of integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of motion quadratic in the momenta. The procedure of quantization here considered transforms the Hamiltonian into the Laplace-Beltrami operator plus a scalar potential. In order to transform the constants of motion into symmetry operators of the quantum Hamiltonian, additional scalar potentials, known as quantum corrections, must be introduced, depending on the Riemannian structure of the manifold. We give here a complete geometric characterization of the quantum corrections necessary for the case considered. In particular, Stackel systems are studied in detail. Examples in conformally and non-conformally flat manifolds are given.
Generalized cosmological term from Maxwell symmetries

By gauging the Maxwell spacetime algebra the standard geometric framework of Einstein gravity with cosmological constant term is extended by adding six fourvector fields A_\mu^{ab}(x) associated with the six abelian tensorial charges in the Maxwell algebra. In the simplest Maxwell extension of Einstein gravity this leads to a generalized cosmological term that includes a contribution from these vector fields. We also consider going beyond the basic gravitational model by means of bilinear actions for the new Abelian gauge fields. Finally, an analogy with the supersymmetric generalization of gravity is indicated. In an Appendix, we propose an equivalent description of the model in terms of a shift of the standard spin connection by the A_\mu^{ab}(x) fields.
States Reimagined: COVID-19, the Ordinary, and Extraordinary in Aotearoa/New Zealand

ABSTRACT Shifting public imaginaries have played a vital role in shaping government and citizen responses to COVID-19 in Aotearoa/New Zealand. During the nation’s first COVID-19 lockdown, the general public expressed support, and at times even enthusiasm, for strict measures put in place to curb the spread of the virus. Less than a year later, what had begun as a nationalistic rallying cry to ‘unite together’ and ‘be kind’ while ‘combatting COVID-19’ took on more sinister tones through government-sponsored moral panic, including the blaming and shaming of those who did not or could not uphold COVID-19 regulations. At the same time, growing dissent, particularly by those protesting COVID-19 vaccine mandates, steadily chipped away at government-promoted images of national solidarity. By early 2022, with the spread of omicron, the government stepped away from attempting to eradicate the virus and jettisoned its collectivist message, highlighting instead each New Zealander’s ‘personal responsibility’ to try and stay well. This article traces how citizen-State relations have been reimagined in Aotearoa/NZ over the first two years of the pandemic, the effects of various pubic- and government-supported moral imaginaries in enabling the government to exercise ‘extra-ordinary’ powers, and the power and fragility of national consensus-building in the midst of crisis. I suggest how examining the pandemic and pandemic responses as a ‘collective critical event’ enables us to trace not only how it altered citizens’ visions of the State, but their active engagements in reconfiguring and reimagining various states of social, economic, and cultural life.
Long-term observations of three nulling pulsars

We present an analysis of approximately 200 hours of observations of the pulsars J1634$-$5107, J1717$-$4054 and J1853$+$0505, taken over the course of 14.7 yr. We show that all of these objects exhibit long term nulls and radio-emitting phases (i.e. minutes to many hours), as well as considerable nulling fractions (NFs) in the range $\sim67\,\% - 90\,\%$. PSR J1717$-$4054 is also found to exhibit short timescale nulls ($1 - 40~P$) and burst phases ($\lesssim 200~P$) during its radio-emitting phases. This behaviour acts to modulate the NF, and therefore the detection rate of the source, over timescales of minutes. Furthermore, PSR J1853$+$0505 is shown to exhibit a weak emission state, in addition to its strong and null states, after sufficient pulse integration. This further indicates that nulls may often only represent transitions to weaker emission states which are below the sensitivity thresholds of particular observing systems. In addition, we detected a peak-to-peak variation of $33\pm1\,\%$ in the spin-down rate of PSR J1717$-$4054, over timescales of hundreds of days. However, no long-term correlation with emission variation was found.
Configuration space of intervals with partially summable labels.

A configuration space of intervals in $\mathbb R^1$ with partially summable labels is constructed. It is a kind of an extension of the configuration space with partially summable labels constructed by the second author and at the same time a generalization of the configuration space of intervals with labels in a based space constructed by the first author. An approximation theorem of the preceding configuration space is generalized to our case. When partially summable labels are given by a partial abelian monoid $M,$ we prove that it is weakly homotopy equivalent to the space of based loops on the classifying space of $M$ under some assumptions on $M$.
Females alter their mate preferences depending on hybridization risk

Mating with another species is often maladaptive because it generally results in no or low-fitness offspring. When hybridization is sufficiently costly, individuals should avoid mating with heterospecifics even if it reduces their ability to mate with high-quality conspecifics that resemble heterospecifics. Here, we used spadefoot toads, Spea multiplicata, to evaluate whether females alter their preferences for conspecific male sexual signals (call rate) depending on heterospecific presence. When presented with conspecific signals against a background including both conspecific and heterospecific signals, females preferred male traits that were most dissimilar to heterospecifics—even though these signals are potentially associated with lower-quality mates. However, when these same females were presented with a background that included only conspecific signals, some females switched their preferences, choosing conspecific signals that were exaggerated and indicative of high-quality conspecific mates. Because only some females switched their preferences between these two chorus treatments, there was no population-level preference for exaggerated conspecific male signals in the absence of heterospecifics. These results show that hybridization risk can alter patterns of mate choice and, consequently, sexual selection on male signals. Moreover, they emphasize that the strength and expression of reproductive barriers between species (such as mate choice) can be context-dependent.
Associations between indoor relative humidity and global COVID-19 outcomes

Globally, the spread and severity of COVID-19 have been distinctly non-uniform. Seasonality was suggested as a contributor to regional variability, but the relationship between weather and COVID-19 remains unclear and the focus of attention has been on outdoor conditions. Because humans spend most of their time indoors and because most transmission occurs indoors, we here, instead, investigate the hypothesis that indoor climate—particularly indoor relative humidity (RH)—may be the more relevant modulator of outbreaks. To study this association, we combined population-based COVID-19 statistics and meteorological measurements from 121 countries. We rigorously processed epidemiological data to reduce bias, then developed and experimentally validated a computational workflow to estimate indoor conditions based on outdoor weather data and standard indoor comfort conditions. Our comprehensive analysis shows robust and systematic relationships between regional outbreaks and indoor RH. In particular, we found intermediate RH (40–60%) to be robustly associated with better COVID-19 outbreak outcomes (versus RH < 40% or >60%). Together, these results suggest that indoor conditions, particularly indoor RH, modulate the spread and severity of COVID-19 outbreaks.