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The current study, as part of a PhD project on the design of a helicon thruster, aims to provide a rational methodology for the design of the helicon thruster's main component, i.e., the helicon antenna. A helicon thruster is an innovative electrodeless plasma thruster that works by exciting helicon waves in a magnetized plasma, and its antenna is capable of producing a uniform, low-temperature, high-density plasma. A magnetic nozzle is used to accelerate the exhaust plasma in order to generate a propulsive thrust. In this paper, we consider a simple helicon antenna, specifically the Nagoya type-III antenna. We consider a common experimental setup consisting of a quartz tube with finite length containing a uniform magnetized plasma and a Nagoya type-III antenna placed at the tube centre. Considering previous studies on helicon waves theory, we compare three different design methods, each based on simplifying different modelling assumptions, and evaluate the predictions of these models with results from full-wave 3D simulations. In particular, we concentrate on deriving a rational design method for the helicon antenna length, given the dimension of the quartz tube and the desired target plasma parameters. This work aims to provide a practical and fast method for dimensioning the antenna length, useful for initializing more accurate but computationally heavier full-wave simulations in 3D geometry or simply for a rapid prototyping of the helicon antenna. These results can be useful for the development of a helicon thruster but also for the design of a high-density radiofrequency plasma source.

The long root geometry $A_{n,\{1,n\}}(\mathbb{K})$ for the special linear group $\mathrm{SL}(n+1,\mathbb{K})$ admits an embedding in the (projective space of) the vector space of the traceless square matrices of order $n+1$ with entries in the field $\mathbb{K}$, usually regarded as the {\em natural} embedding of $A_{n,\{1,n\}}(\mathbb{K})$. S. Smith and H. V\"{o}lklein (A geometric presentation for the adjoint module of $\mathrm{SL}_3(\mathbb{K})$, {\em J. Algebra}, vol. 127) have proved that the natural embedding of $A_{2,\{1,2\}}(\mathbb{K})$ is relatively universal if and only if $\mathbb{K}$ is either algebraic over its minimal subfield or perfect with positive characteristic. They also give some information on the relatively universal embedding of $A_{2,\{1,2\}}(\mathbb{K})$ which covers the natural one, but that information is not sufficient to exhaustively describe it. The ``if" part of Smith-V\"{o}lklein's result also holds true for any $n$, as proved by V\"{o}lklein in his investigation of the adjoint modules of Chevalley groups (H. V\"{o}lklein, On the geometry of the adjoint representation of a Chevalley group, {\em J. Algebra}, vol. 127). In this paper we give an explicit description of the relatively universal embedding of $A_{n,\{1,n\}}(\mathbb{K})$ which covers the natural one. In particular, we prove that this relatively universal embedding has (vector) dimension equal to $\mathfrak{d}+n^2+2n$ where $\mathfrak{d}$ is the transcendence degree of $\mathbb{K}$ over its minimal subfield (if $\mathrm{char}(\mathbb{K}) = 0$) or the generating rank of $\mathbb{K}$ over ${\mathbb K}^p$ (if $\mathrm{char}(\mathbb{K}) = p > 0$). Accordingly, both the ``if" and the ``only if" part of Smith-V\"{o}lklein's result hold true for every $n \geq 2$., Comment: 23 pages

This research work is part of a PhD project aiming to design a new helicon plasma thruster for cargo space missions, within a collaboration between the School of Aerospace Engineering of La Sapienza University and the ENEA Frascati research center. A 0-D global design model of the thruster is first established to identify the main operational conditions of the thruster, starting from a targeted performance in terms of specific impulse and thrust. These operational conditions are tested with dedicated simulations on the electromagnetic plasma-wave interaction within the ionization chamber, and on the electrostatic plasma acceleration within the magnetic nozzle. The former are carried out with a finite element electromagnetic code and confirm the technical feasibility of the identified operational RF power with a predefined chamber geometry. The latter are obtained with an electrostatic particle-in-cell code, which allows to estimate more precisely the achieved thruster performance. A sub-optimal thruster with an absorbed plasma power of around 1 kW, a thrust of around 10 mN and a specific impulse higher than 1000 s is successfully simulated. The established simulation framework will serve as the basis for the next optimization of the thruster geometry and operational conditions, with the ultimate goal of building and testing a new helicon thruster prototype.

This work introduces GPTCast, a generative deep-learning method for ensemble nowcast of radar-based precipitation, inspired by advancements in large language models (LLMs). We employ a GPT model as a forecaster to learn spatiotemporal precipitation dynamics using tokenized radar images. The tokenizer is based on a Quantized Variational Autoencoder featuring a novel reconstruction loss tailored for the skewed distribution of precipitation that promotes faithful reconstruction of high rainfall rates. The approach produces realistic ensemble forecasts and provides probabilistic outputs with accurate uncertainty estimation. The model is trained without resorting to randomness, all variability is learned solely from the data and exposed by model at inference for ensemble generation. We train and test GPTCast using a 6-year radar dataset over the Emilia-Romagna region in Northern Italy, showing superior results compared to state-of-the-art ensemble extrapolation methods., Comment: 20 pages, 10 figures

In this paper we investigate the asymptotic stability of a fourth-order PDE with a fading memory forcing term and boundary conditions arising from a flexible robotics model. We carry on our study by using an abstract formulation of the problem based on the $C_0$-semigroup. To achieve our objective, we first provide new results on the existence, uniqueness, continuous dependence on initial data of either mild and strong solutions for semilinear integro-differential equations in Banach spaces. Then, we also find sufficient conditions for the uniform asymptotic stability of solutions and for the existence of attactors. As an application of these abstract results, we can ensure existence, uniqueness and continuous dependence on initial data for the solutions of the boundary value problem under investigation and, finally, we prove the uniform asymptotic stability of solutions and the existence of attactors under suitable conditions on the nonlinear term., Comment: Preprint version of a submitted article

Consider the point line-geometry ${\mathcal P}_t(n,k)$ having as points all the $[n,k]$-linear codes having minimum dual distance at least $t+1$ and where two points $X$ and $Y$ are collinear whenever $X\cap Y$ is a $[n,k-1]$-linear code having minimum dual distance at least $t+1$. We are interested in the collinearity graph $\Lambda_t(n,k)$ of ${\mathcal P}_t(n,k).$ The graph $\Lambda_t(n,k)$ is a subgraph of the Grassmann graph and also a subgraph of the graph $\Delta_t(n,k)$ of the linear codes having minimum dual distance at least $t+1$ introduced in~[M. Kwiatkowski, M. Pankov, On the distance between linear codes, Finite Fields Appl. 39 (2016), 251--263, doi:10.1016/j.ffa.2016.02.004, arXiv:1506.00215]. We shall study the structure of $\Lambda_t(n,k)$ in relation to that of $\Delta_t(n,k)$ and we will characterize the set of its isolated vertices. We will then focus on $\Lambda_1(n,k)$ and $\Lambda_2(n,k)$ providing necessary and sufficient conditions for them to be connected., Comment: 20 pages/minor corrections/updated bibliography

Radiative corrections to elastic scattering represent an important part of the interpretation of electron-induced nuclear reactions at small energy transfers, where they make for a dominant part of background. Here we present and validate a new event generator for mimicking QED radiative processes in electron-carbon scattering that exactly calculates the coherent sum of the Bethe-Heitler amplitudes for the leading diagrams and can be reliably employed for a more robust determination of inelastic cross-sections.

Let $\cal P$ be a non-degenerate polar space. In [I. Cardinali, L. Giuzzi, A. Pasini, "The generating rank of a polar grassmannian", Adv. Geom. 21:4 (2021), 515-539 doi:10.1515/advgeom-2021-0022 (arXiv:1906.10560)] we introduced an intrinsic parameter of $\cal P$, called the anisotropic gap, defined as the least upper bound of the lengths of the well-ordered chains of subspaces of $\cal P$ containing a frame; when $\cal P$ is orthogonal, we also defined two other parameters of $\cal P$, called the elliptic and parabolic gap, related to the universal embedding of $\cal P$. In this paper, assuming $\cal P$ is an orthogonal polar space, we prove that the elliptic and parabolic gaps can be described as intrinsic invariants of $\cal P$ without making recourse to the embedding., Comment: 20 pages/revised version

Ample numerical evidence from lattice calculations shows a strong connection between the confining properties of gauge theories at finite temperature and the localisation properties of the low-lying Dirac eigenmodes. In this contribution we discuss recent progress on this topic, focussing on results for QCD at imaginary chemical potential ${\mu}_I/T = \pi$ at temperatures above the Roberge-Weiss transition temperature. These confirm the general picture of low modes turning from delocalised to localised at the deconfinement transition, in a previously unexplored setup with a genuine, physical transition in the presence of dynamical fermions. This further supports the use of Dirac eigenmodes as a tool to investigate the mechanisms behind confinement and the deconfinement transition., Comment: 8 pages, 4 figures; contribution to the proceedings of the XVth Quark Confinement and Hadron Spectrum conference (ConfXV), 1-6 August 2022, University of Stavanger, Stavanger (Norway)

A polar space S is said to be symplectic if it admits an embedding e in a projective geometry PG(V) such that the e-image e(S) of S is defined by an alternating form of V. In this paper we characterize symplectic polar spaces in terms of their incidence properties, with no mention of peculiar properties of their embeddings. This is relevant especially when S admits different (non isomorphic) embeddings, as it is the case (precisely) when S is defined over a field of characteristic 2., Comment: 20 pages/extensively revised

In this preprint we present our results on the study of the electromagnetic conductivity in dense quark-gluon plasma obtained within lattice simulations with $N_f = 2 + 1$ dynamical quarks. We employ stout improved rooted staggered quarks at the physical point and the tree-level Symanzik improved gauge action. The simulations are performed at imaginary baryon chemical potential, and the Tikhonov regularisation method is used to extract the conductivity from current-current correlators. Our results indicate an increase of QGP electromagnetic conductivity with real baryon density, and this dependence is quite strong., Comment: 10 pages, 2 figures. Talk presented at the 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@Massachusetts Institute of Technology

We study the localization properties of the low-lying Dirac eigenmodes in QCD at imaginary chemical potential $\hat{\mu}_I=\pi$ at temperatures above the Roberge-Weiss transition temperature $T_{\rm RW}$. We find that modes are localized up to a temperature-dependent "mobility edge" and delocalized above it, and that the mobility edge extrapolates to zero at a temperature compatible with $T_{\rm RW}$. This supports the existence of a strong connection between localization of the low Dirac modes and deconfinement, studied here for the first time in a model with a genuine deconfinement transition in the continuum limit in the presence of dynamical fermions., Comment: 8 pages, 5 figures

Thermal monopoles, identified after Abelian projection as magnetic currents wrapping non-trivially around the thermal circle, are studied in $N_f = 2+1$ QCD at the physical point. The distribution in the number of wrappings, which in pure gauge theories points to a condensation temperature coinciding with deconfinement, points in this case to around 275 MeV, almost twice the QCD crossover temperature $T_c$; similar indications emerge looking for the formation of a percolating current cluster. The possible relation with other non-perturbative phenomena observed above $T_c$ is discussed., Comment: 6 pages, 4 figures. Fig. 4 has been updated. References added

Rockfalls pose a substantial threat to ground transportation, due to their rapidity, destructive potential and high probability of occurrence on steep topographies, found along roads and railways. Approaches for assessment of rockfall susceptibility range from purely phenomenological methods and statistical methods, suitable for modeling large areas, to purely deterministic ones, usually easier to use in local analyses. A common requirement is the need to locate potential detachment points, often found uphill on cliffs, and the subsequent assessment of the runout areas of rockfalls stemming from such points. Here, we apply a physically based model to calculate rockfall trajectories along the whole Italian railway network, within a corridor of total length of about 17,000 km and varying width. We propose a data-driven method for the location of rockfall source points based on expert mapping of potential source areas on sample representative locations. Using empirical distributions of gridded slope values in source areas mapped by experts, we derived probabilistic maps of rockfall sources in the proximity of the railway network, regardless of a particular trigger. Source areas act as starting points of simulated trajectories in the three-dimensional model STONE. The program provides a pixel-by-pixel trajectory count, covering 24,500 km2, the largest homogeneous application of the model to date. We classified the map into a vector susceptibility map of the segments of the railway, for which we provide segment-wise rockfall susceptibility. Eventually, we considered a graph representation of the network to classify the segments both on the basis of rockfall susceptibility and the role of each segment in the network, resulting in a network-ranked susceptibility. Both maps are useful for subsequent hazard assessment, and to prioritize safety improvements along the railway, at national scale., Comment: 22 pages, 9 figures, 6 tables. Published version

We study, by means of numerical lattice simulations, the properties of the reconfinement phase transition taking place in trace deformed $SU(3)$ Yang-Mills theory defined on $\mathbb{R}^3\times S^1$, in which center symmetry is recovered even for small compactification radii. We show, by means of a finite size scaling analysis, that the reconfinement phase transition is first-order, like the usual $SU(3)$ thermal phase transition. We then investigate two different physical phenomena, which are known to characterize the standard confinement/deconfinement phase transition, namely the condensation of thermal magnetic monopoles and the change in the localization properties of the eigenmodes of the Dirac operator. Regarding the latter, we show that the mobility edge signalling the Anderson-like transition in the Dirac spectrum vanishes as one enters the reconfined phase, as it happens in the standard confined phase. Thermal monopoles, instead, show a peculiar behavior: their density decreases going through reconfinement, at odds with the standard thermal theory; nonetheless, they condense at reconfinement, like at the usual confinement transition. The coincidence of monopole condensation and Dirac mode delocalization, even in a framework different from that of the standard confinement transition, suggests the existence of a strict link between them., Comment: 10 pages, 10 figures

Radiofrequency emission in the 0.4 - 3 GHz range from FTU plasmas in presence of runaway electrons (RE) has been measured with unprecedentedly high time resolution. Rapid emission bursts associated with enhanced RE pitch angle scattering reveal kinetic instabilities affecting evolution of the RE population from the buildup phase. Such measurements also provide a sensitive monitor for instabilities during early RE formation. The leading edge of radio bursts is much shorter than interleaving periods of low emission; spectral broadening during growth indicates nonlinear wave coupling as an explanation for the observed intermittency. Radiofrequency emission disappears at the beginning of post-disruption RE plateaus, and subsequently reappears in the shape of very intense bursts accompanied by strong rises of suprathermal electron cyclotron emission., Comment: 5 pages, 8 figures. To be submitted to phys. Rev. Lett. Category: physics.plasm-ph - Plasma Physics

Let $\Gamma$ be an embeddable non-degenerate polar space of finite rank $n \geq 2$. Assuming that $\Gamma$ admits the universal embedding (which is true for all embeddable polar spaces except grids of order at least $5$ and certain generalized quadrangles defined over quaternion division rings), let $\varepsilon:\Gamma\to\mathrm{PG}(V)$ be the universal embedding of $\Gamma$. Let $\cal S$ be a subspace of $\Gamma$ and suppose that $\cal S$, regarded as a polar space, has non-degenerate rank at least $2$. We shall prove that $\cal S$ is the $\varepsilon$-preimage of a projective subspace of $\mathrm{PG}(V)$., Comment: 16 pages

In this paper we study, by means of numerical simulations, the behaviour of the scalar glueball mass and the ground state of the torelon for trace deformed Yang-Mills theory defined on $ \mathbb{R}^3\times S^1$, in which center symmetry is recovered even at small compactification radii. We find, by investigating both $SU(3)$ and $SU(4)$ pure gauge theories, that the glueball mass computed in the deformed theory, when center symmetry is recovered, is compatible with its value at zero temperature and does not show any significant dependence on the compactification radius; moreover, we establish a connection between the deformation parameter and an effective compactification size, which works well at least for small deformations. In addition, we observe that the ground state of the torelon which winds around the small traced deformed circle with size $l$ acquires a pleateau for large values of the strength $h$, with values which are compatible with a $1/l$ behavior but, on the other hand, are still not in complete agreement with the asymptotic semiclassical large-$N$ predictions., Comment: 12 pages, 11 figures. In v2, in addition to SU(3) we also provide results for SU(4) at one lattice spacing. Furthermore, we provide a connection between the deformation parameter h and an effective compactification size l_eff. Major revision to the text

In this work, we report the application of Raman microspectroscopy for analysis of the refractive index of a range of tissue phantoms. Using both a custom-developed setup with visible laser source and a commercial micro-spectrometer with near infrared laser, we measured the Raman spectra of gelatin hydrogels at various concentrations. By building a calibration curve from measured refractometry data and Raman scattering intensity for different vibrational modes of the hydrogel, we determined the refractive indices of the gels from their Raman spectra, with approximately the same accuracy as that of refractometry measurements with an Abbe refractometer. This work highlights the importance of a correlative approach through Brillouin-Raman microspectroscopy for the mechano-chemical analysis of biologically relevant samples., Comment: 11 pages, 5 figures, 1 table

Let $\Gamma(n,k)$ be the Grassmann graph formed by the $k$-dimensional subspaces of a vector space of dimension $n$ over a field $\mathbb F$ and, for $t\in \mathbb{N}\setminus \{0\}$, let $\Delta_t(n,k)$ be the subgraph of $\Gamma(n,k)$ formed by the set of linear $[n,k]$-codes having minimum dual distance at least $t+1$. We show that if $|{\mathbb F}|\geq{n\choose t}$ then $\Delta_t(n,k)$ is connected and it is isometrically embedded in $\Gamma(n,k)$. This generalizes some results of [M. Kwiatkowski, M. Pankov, "On the distance between linear codes", Finite Fields Appl. 39 (2016), 251--263] and [M. Kwiatkowski, M. Pankov, A. Pasini, "The graphs of projective codes" Finite Fields Appl. 54 (2018), 15--29]., Comment: 13 pages/final version