Search

Isotropic $\alpha$-stable distributions are central in the theory of heavy-tailed distributions and play a role similar to that of the Gaussian density among finite second-moment laws. Given a sequence of $n$ observations, we are interested in characterizing the performance of Likelihood Ratio Tests where two hypotheses are plausible for the observed quantities: either isotropic Cauchy or isotropic Gaussian. Under various setups, we show that the probability of error of such detectors is not always exponentially decaying with $n$ with the leading term in the exponent shown to be logarithmic instead and we determine the constants in that leading term. Perhaps surprisingly, the optimal Bayesian probabilities of error are found to exhibit different asymptotic behaviors.

Climate change not only threatens agricultural producers but also strains financial institutions. These important food system actors include government entities tasked with both insuring grower livelihoods and supporting response to continued global warming. We use an artificial neural network to predict future maize yields in the U.S. Corn Belt, finding alarming changes to institutional risk exposure within the Federal Crop Insurance Program. Specifically, our machine learning method anticipates more frequent and more severe yield losses that would result in the annual probability of Yield Protection (YP) claims to more than double at mid-century relative to simulations without continued climate change. Furthermore, our dual finding of relatively unchanged average yields paired with decreasing yield stability reveals targeted opportunities to adjust coverage formulas to include variability. This important structural shift may help regulators support grower adaptation to continued climate change by recognizing the value of risk-reducing strategies such as regenerative agriculture. Altogether, paired with open source interactive tools for deeper investigation, our risk profile simulations fill an actionable gap in current understanding, bridging granular historic yield estimation and climate-informed prediction of future insurer-relevant loss., Comment: 24 pages, 6 figures

This article tackles the spectral analysis of the Robin Laplacian on a smooth bounded two-dimensional domain in the presence of a constant magnetic field. In the semiclassical limit, a uniform description of the spectrum located between the Landau levels is obtained. The corresponding eigenfunctions, called edge states, are exponentially localized near the boundary. By means of a microlocal dimensional reduction, our unifying approach allows on the one hand to derive a very precise Weyl law and a proof of quantum magnetic oscillations for excited states, and on the other hand to refine simultaneously old results about the low-lying eigenvalues in the Robin case and recent ones about edge states in the Dirichlet case.

Enhancing properties and performances of aluminium alloys by a control of their solidification is pivotal in automotive and aerospace industries. The fundamental role of the structure-diffusion relationship is investigated for Al-Mg-Si liquid alloys taken as a prototype of Al-6xxx. For this purpose, first principles-based molecular dynamics simulations were performed for various Si and Mg content for Al-rich compositions, including the binary alloy counterparts. Results indicate that Mg and/or Si in alloys create a more compact ordering around Al than in pure Al, lowering diffusion. Mg promotes icosahedral short-range order, while Si displays a preference towards cubic local ordering, impacting diffusion based on their respective content. It suggests a mechanism whereby an increase in Mg content generally lowers the diffusion of each species, whereas an increase in Si content enhances their diffusion, providing insights for future alloy design., Comment: 5 figues, 18 pages

The NEXT experiment aims at the sensitive search of the neutrinoless double beta decay in $^{136}$Xe, using high-pressure gas electroluminescent time projection chambers. The NEXT-White detector is the first radiopure demonstrator of this technology, operated in the Laboratorio Subterr\'aneo de Canfranc. Achieving an energy resolution of 1% FWHM at 2.6 MeV and further background rejection by means of the topology of the reconstructed tracks, NEXT-White has been exploited beyond its original goals in order to perform a neutrinoless double beta decay search. The analysis considers the combination of 271.6 days of $^{136}$Xe-enriched data and 208.9 days of $^{136}$Xe-depleted data. A detailed background modeling and measurement has been developed, ensuring the time stability of the radiogenic and cosmogenic contributions across both data samples. Limits to the neutrinoless mode are obtained in two alternative analyses: a background-model-dependent approach and a novel direct background-subtraction technique, offering results with small dependence on the background model assumptions. With a fiducial mass of only 3.50$\pm$0.01 kg of $^{136}$Xe-enriched xenon, 90% C.L. lower limits to the neutrinoless double beta decay are found in the T$_{1/2}^{0\nu}>5.5\times10^{23}-1.3\times10^{24}$ yr range, depending on the method. The presented techniques stand as a proof-of-concept for the searches to be implemented with larger NEXT detectors.

The search for neutrinoless double beta decay ($0\nu\beta\beta$) remains one of the most compelling experimental avenues for the discovery in the neutrino sector. Electroluminescent gas-phase time projection chambers are well suited to $0\nu\beta\beta$ searches due to their intrinsically precise energy resolution and topological event identification capabilities. Scalability to ton- and multi-ton masses requires readout of large-area electroluminescent regions with fine spatial resolution, low radiogenic backgrounds, and a scalable data acquisition system. This paper presents a detector prototype that records event topology in an electroluminescent xenon gas TPC via VUV image-intensified cameras. This enables an extendable readout of large tracking planes with commercial devices that reside almost entirely outside of the active medium.Following further development in intermediate scale demonstrators, this technique may represent a novel and enlargeable method for topological event imaging in $0\nu\beta\beta$., Comment: 30 Pages, 22 figures, Updated to match current JINST submission

We present a tunable metal ion beam that delivers controllable ion currents in the picoamp range for testing of dry-phase ion sensors. Ion beams are formed by sequential atomic evaporation and single or multiple electron impact ionization, followed by acceleration into a sensing region. Controllability of the ionic charge state is achieved through tuning of electrode potentials that influence the retention time in the ionization region. Barium, lead, and cobalt samples have been used to test the system, with ion currents identified and quantified using a quadrupole mass analyzer. Realization of a clean $\mathrm{Ba^{2+}}$ ion beam within a bench-top system represents an important technical advance toward the development and characterization of barium tagging systems for neutrinoless double beta decay searches in xenon gas. This system also provides a testbed for investigation of novel ion sensing methodologies for environmental assay applications, with dication beams of Pb$^{2+}$ and Cd$^{2+}$ also demonstrated for this purpose.

Polytetrafluoroethylene (PTFE) is an excellent diffuse reflector widely used in light collection systems for particle physics experiments. In noble element systems, it is often coated with tetraphenyl butadiene (TPB) to allow detection of vacuum ultraviolet scintillation light. In this work this dependence is investigated for PTFE coated with TPB in air for light of wavelengths of 200~nm, 260~nm, and 450~nm. The results show that TPB-coated PTFE has a reflectance of approximately 92\% for thicknesses ranging from 5~mm to 10~mm at 450~nm, with negligible variation as a function of thickness within this range. A cross-check of these results using an argon chamber supports the conclusion that the change in thickness from 5~mm to 10~mm does not affect significantly the light response at 128~nm. Our results indicate that pieces of TPB-coated PTFE thinner than the typical 10~mm can be used in particle physics detectors without compromising the light signal.

If neutrinos are their own antiparticles, the otherwise-forbidden nuclear reaction known as neutrinoless double beta decay ($\beta\beta 0\nu$) can occur, with a characteristic lifetime which is expected to be very long, making the suppression of backgrounds a daunting task. It has been shown that detecting (``tagging'') the Ba$^{+2}$ dication produced in the double beta decay ${}^{136}\mathrm{Xe} \rightarrow {}^{136}$Ba$^{+2}+ 2 e + (2 \nu)$ in a high pressure gas experiment, could lead to a virtually background free experiment. To identify these \Bapp, chemical sensors are being explored as a key tool by the NEXT collaboration . Although used in many fields, the application of such chemosensors to the field of particle physics is totally novel and requires experimental demonstration of their suitability in the ultra-dry environment of a xenon gas chamber. Here we use a combination of complementary surface science techniques to unambiguously show that Ba$^{+2}$ ions can be trapped (chelated) in vacuum by an organic molecule, the so-called fluorescent bicolour indicator (FBI) (one of the chemosensors developed by NEXT), immobilized on a surface. We unravel the ion capture mechanism once the molecules are immobilised on Au(111) surface and explain the origin of the emission fluorescence shift associated to the trapping of different ions. Moreover, we prove that chelation also takes place on a technologically relevant substrate, as such, demonstrating the feasibility of using FBI indicators as building blocks of a Ba$^{+2}$ detector.

We report a measurement of the half-life of the ${}^{136}$Xe two-neutrino double beta decay performed with a novel direct background subtraction technique. The analysis relies on the data collected with the NEXT-White detector operated with ${}^{136}$Xe-enriched and ${}^{136}$Xe-depleted xenon, as well as on the topology of double-electron tracks. With a fiducial mass of only 3.5 kg of Xe, a half-life of $2.34^{+0.80}_{-0.46}\textrm{(stat)}^{+0.30}_{-0.17}\textrm{(sys)}\times10^{21}~\textrm{yr}$ is derived from the background-subtracted energy spectrum. The presented technique demonstrates the feasibility of unique background-model-independent neutrinoless double beta decay searches., Comment: 9 pages, 7 figures, and 1 appendix

We obtain large $N$ asymptotics for $N \times N$ Hankel determinants corresponding to non-negative symbols with Fisher-Hartwig (FH) singularities in the multi-cut regime. Our result includes the explicit computation of the multiplicative constant. More precisely, we consider symbols of the form $\omega e^{f-NV}$, where $V$ is a real-analytic potential whose equilibrium measure $\mu_V$ is supported on several intervals, $f$ is analytic in a neighborhood of $\textrm{supp}(\mu_V)$, and $\omega$ is a function with any number of jump- and root-type singularities in the interior of $\textrm{supp}(\mu_V)$. While the special cases $\omega\equiv1$ and $\omega e^f\equiv1$ have been considered previously in the literature, we also prove new results for these special cases. No prior asymptotics were available in the literature for symbols with FH singularities in the multi-cut setting. As an application of our results, we discuss a connection between the spectral fluctuations of random Hermitian matrices in the multi-cut regime and the Gaussian free field on the Riemann surface associated to $\mu_V$. As a second application, we obtain new rigidity estimates for random Hermitian matrices in the multi-cut regime., Comment: 143 pages, 11 figures

This paper is devoted to the asymptotic analysis of the eigenvalues of the Laplace operator with a strong magnetic field and Robin boundary condition on a smooth planar domain and with a negative boundary parameter. We study the singular limit when the Robin parameter tends to infinity which is equivalent to a semi-classical limit involving a small positive semi-classical parameter. The main result is a comparison between the spectrum of the Robin Laplacian with an effective operator defined on the boundary of the domain via the Born-Oppenheimer approximation. More precisely, the low-lying eigenvalue of the Robin Laplacian is approximated by the those of the effective operator. When the curvature has a unique non-degenerate maximum, we estimate the spectral gap and find that the magnetic field does not contribute to the three-term expansion of the eigenvalues. In the case of the disc domains, the eigenvalue asymptotics displays the contribution of the magnetic field explicitly.

Radio-frequency (RF) carpets with ultra-fine pitches are examined for ion transport in gases at atmospheric pressures and above. We develop new analytic and computational methods for modeling RF ion transport at densities where dynamics are strongly influenced by buffer gas collisions. An analytic description of levitating and sweeping forces from phased arrays is obtained, then thermodynamic and kinetic principles are used to calculate ion loss rates in the presence of collisions. This methodology is validated against detailed microscopic SIMION simulations. We then explore a parameter space of special interest for neutrinoless double beta decay experiments: transport of barium ions in xenon at pressures from 1 to 10 bar. Our computations account for molecular ion formation and pressure dependent mobility as well as finite temperature effects. We discuss the challenges associated with achieving suitable operating conditions, which lie beyond the capabilities of existing devices, using presently available or near-future manufacturing techniques., Comment: 26 pages, 16 figures v2: author list update and pre-journal submission adjustments

We analyze families of primal high-order hybridizable discontinuous Galerkin (HDG) methods for solving degenerate (second-order) elliptic problems. One major trouble regarding this class of PDEs concerns its mathematical nature, which may be nonuniform over the domain. Due to the local degeneracy of the diffusion term, it can be purely hyperbolic in a subregion and elliptic in the rest. This problem is thus quite delicate to solve since the exact solution is discontinuous at interfaces separating both elliptic and hyperbolic parts. The proposed HDG method is developed in a unified and compact fashion. It can efficiently handle pure diffusive or advective regimes and intermediate regimes that combine the above mechanisms for a wide range of P\'eclet numbers, including the delicate situation of local evanescent diffusion. To this end, an adaptive stabilization strategy based on the addition of jump-penalty terms is then considered. A $\theta$-upwind-based scheme is favored for the hyperbolic region, and an inspired Scharfetter--Gummel-based technique is preferred for the elliptic region. The well-posedness of the HDG method is also discussed by analyzing the consistency and discrete coercivity properties. Extensive numerical experiments are finally considered to verify the model's robustness for all the abovementioned regimes., Comment: 22 pages, 5 figures

In this paper, we derive improved a priori error estimates for families of hybridizable interior penalty discontinuous Galerkin (H-IP) methods using a variable penalty for second-order elliptic problems. The strategy is to use a penalization function of the form $\mathcal{O}(1/h^{1+\delta})$, where $h$ denotes the mesh size and $\delta$ is a user-dependent parameter. We then quantify its direct impact on the convergence analysis, namely, the (strong) consistency, discrete coercivity, and boundedness (with $h^{\delta}$-dependency), and we derive updated error estimates for both discrete energy- and $L^{2}$-norms. The originality of the error analysis relies specifically on the use of conforming interpolants of the exact solution. All theoretical results are supported by numerical evidence., Comment: 11 pages, 7 figures, 1 table

We consider the probability of two large gaps (intervals without eigenvalues) in the bulk scaling limit of the Gaussian Unitary Ensemble of random matrices. We determine the multiplicative constant in the asymptotics. We also provide the full explicit asymptotics (up to decreasing terms) for the transition between one and two large gaps., Comment: 63 pages

We study the fluctuations of linear statistics with polynomial test functions for Multiple Orthogonal Polynomial Ensembles. Multiple Orthogonal Polynomial Ensembles form an important class of determinantal point processes that include random matrix models such as the GUE with external source, complex Wishart matrices, multi-matrix models and others. Our analysis is based on the recurrence matrix for the multiple orthogonal polynomials, that is constructed out of the nearest neighbor recurrences. If the coefficients for the nearest neighbor recurrences have limits, then we show that the right-limit of this recurrence matrix is a matrix that can be viewed as representation of a Toeplitz operator with respect to a non-standard basis. This will allow us to prove Central Limit Theorems for linear statistics of Multiple Orthogonal Polynomial Ensembles. A particular novelty is the use of the Baker--Campbell--Hausdorff formula to prove that the higher cumulants of the linear statistics converge to zero. We illustrate the main results by discussing Central Limit Theorems for the Gaussian Unitary Ensembles with external source, complex Wishart matrices and specializations of the Schur measure related to multiple Charlier, multiple Krawtchouk and multiple Meixner polynomials., Comment: 56 pages; Minor corrections and extended example section