We report numerical results regarding the minimum sustaining coil excitation current for a RF-RF hybrid torch operating at two different frequencies. The first coil is excited at a high-frequency, while the second coil is set at a medium frequency. The filling gas is argon, at atmospheric pressure. We use the modeling software COMSOL Multiphysics to describe the evolution of key parameters when: (i) the distance between the two coils changes, (ii) the power of the high frequency coil changes. We discuss the radial temperature profiles, the axial velocities and the heat convected at the end of the medium-frequency coil. The latter is compared with the total heat conduction to the plasma confinement tube wall.

The Boltzmann equation has been a driving force behind significant mathematical research over the years. Its challenging theoretical complexity, combined with a wide variety of current scientific and technological problems that require numerical simulations based on this model, justifies such interest. This work provides a brief overview of studies and advances on the solution of the linear Boltzmann equation in one- and two-dimensional spatial dimensions. In particular, relevant aspects of the discrete ordinates approximation of the model are highlighted for neutron and photon transport applications, including nuclear safeguards, nuclear reactor shielding problems, and optical tomography. In addition, a short discussion of rarefied gas dynamics problems, relevant, for instance, to the study of micro-electro-mechanical systems, and their connection with the Linearized Boltzmann Equation, is presented. A primary goal of the work is to establish as much as possible the connections between the different phenomena described by the model and the versatility of the analytical methodology, the ADO method, in providing concise and accurate solutions, which are fundamental for numerical simulations.

The concept of inverse energy cascades has played a central role in the development of turbulence theory, with applications in two-dimensional and quasi-two-dimensional flows. We examine the presence or absence of inverse energy cascades in rotating stably stratified flows constrained to anisotropic yet fully three-dimensional domains, in a range of parameters that are relevant for planetary atmospheres. In particular, we focus on regimes with aspect ratios, Rossby, and Froude numbers similar to those found in the Earth's and other planets atmospheres. Our results show that, under certain conditions, inverse energy cascades can indeed emerge from the dry fluid dynamics solely, suggesting that this process can play a role in intermediate-scale atmospheric self-organization processes.

We study the problem of continuity of derivations over Banach algebras. More specifically, we consider a class of Banach algebras that contain a dense '$C^*$-like' subalgebra. We discuss applications to $L^p$-crossed products and symmetrized $L^p$-crossed products. As an example, our results imply that every derivation over the $L^p$-crossed product $F^p(G,X,α)$ is continuous, provided that $G$ is infinite, finitely generated, has polynomial growth, and acts freely on the compact Hausdorff space $X$.

On the example of the integrable hard rods model we study the quality of the (generalized) hydrodynamic approximation on a single coarse-grained sample. This is opposed to the traditional approach which averages over an appropriate local equilibrium state. While mathematically more ambiguous, a major advantage of the new approach is that it allows us to disentangle intrinsic diffusion from `diffusion from convection' effects. For the hard rods we find intrinsic diffusion is absent, which agrees with and clarifies recent findings. Interestingly, the results also apply to not locally thermal states, demonstrating that hydrodynamics (in this model) does not require the assumption of local equilibrium.

In 1978, Anderson and White asked whether there is a decomposition of $K_{12}$ into two graphs, one planar and one toroidal. Using theoretical arguments and a computer search of all maximal planar graphs of order 12, we show that no such decomposition exists. We further show that if $G$ is planar of order 12 and $H\subseteq\overline{G}$ is toroidal, then $H$ has at least two fewer edges than $\overline{G}$. A computer search found all 123 unique pairs $\left(G,H\right)$ that make this an equality.

In this paper we provide an explicit tableaux realization for all simple subquotients of a relation Gelfand-Tsetlin $\mathfrak{gl}(n)$-module.

We revisit the notion of equations describing pseudospherical surfaces, starting from the works by Sasaki, whose roots were influenced by the AKNS system, the works by Chern and Tenenblat, until current research topics in the field relating to Cauchy problems involving these equations and their geometric consequences.

The formation and evolution of the ultra-diffuse galaxies (UDGs) continues to remain a puzzle. Similarities and differences in the morphological and the kinematical properties of the UDGs with their possible precursors, namely low-surface brightness (LSBs), L*-type high-surface brightness (HSBs) and dwarf galaxies, may provide crucial constraints on their origin and evolution. We selected samples of UDGs, LSBs, HSBs and dwarfs from TNG50-1. We first obtained a few possible scaling relations involving some mass properties to analyse if the regression fits for UDGs are in compliance with those of the other samples. Then, we studied individual galaxy cutouts to evaluate the intrinsic shapes of their dark-matter (DM) and stellar components, orbital and kinematical properties related to their stellar velocity dispersion. Finally, we constructed the mock IFU data using the SimSpin code to extract the stellar kinematic moment maps. We observe that the UDGs and the dwarf galaxies have nearly similar regression fits in a. stellar-to-gas mass ratio vs gas mass, b. stellar-to-gas mass ratio vs total dynamical mass, c. stellar central surface density vs ratio of stellar-to-total dynamical mass, and d. total baryonic mass vs total dynamical mass parameter spaces. Next, we find that the isolated UDGs are prolate rotators similar to the dwarf population, while the tidally-bound UDGs can exhibit both prolate and oblate-rotating shapes. The DM and stellar velocity anisotropy properties of the UDGs suggest that they reside in a cored, dwarf-like halo and may be classified by early-type galaxies. Finally, the stellar kinematic properties suggest that both the UDGs and the dwarfs are slow-rotators having low to nearly no-rotations in contrast to the late-type, disc-dominated, fast-rotating LSBs and HSBs. Therefore, we may conclude that the UDGs and the dwarfs possibly have a common dynamical lineage.

Imaging polarimetry enables the spatially resolved investigation of cometary dust properties across different morphological structures. While cometary comae have been studied thoroughly in the pertinent literature, cometary tails have remained less explored. Comparing these regions can reveal differences in the size, structure, and composition of their dust. The goal of this study is to examine the size, structure and composition of the dust particles in the coma and in particular in the tail of the bright comet C/2023 A3 (Tsuchinshan-ATLAS) and to infer possible differences. For this purpose, we rely on the method of telescopic wide-field polarimetric imaging of the comet in the visible to near-infrared domain in order to obtain the dependence of the degree of linear polarization (DoLP) of the coma and tail on the phase angle across a broad range. An off-the-shelf industrial grade polarization camera was used in combination with a telescope of short aperture ratio. These observations are complemented by T-matrix and Discrete Dipole Approximation modeling using the MSTM5 and DDSCAT software framework, respectively, for simulation of light scattering by dust particles of fractal agglomerate and agglomerate debris morphology. Our observations indicate that the coma exhibits a high maximum DoLP of 0.34, which is further exceeded by a factor of about two by the DoLP of the comet's tail. Our modeling results suggest a 50:50 olivine-carbon composition. The fraction of agglomerate debris was found to be 50% in the coma and possibly higher in the tail. The differences between coma and tail in the observed maximum DoLP and the phase angle at which it occurs can be explained by a predominance of particles with radii larger than 0.6 micrometer in the coma vs. smaller sub-micrometer particles close to the Rayleigh limit in the tail [...]

In this paper we introduce and study the Maximum-Average Subtensor ($p$-MAS) problem, in which one wants to find a subtensor of size $k$ of a given random tensor of size $N$, both of order $p$, with maximum sum of entries. We are motivated by recent work on the matrix case of the problem in which several equilibrium and non-equilibrium properties have been characterized analytically in the asymptotic regime $1 \ll k \ll N$, and a puzzling phenomenon was observed involving the coexistence of a clustered equilibrium phase and an efficient algorithm which produces submatrices in this phase. Here we extend previous results on equilibrium and algorithmic properties for the matrix case to the tensor case. We show that the tensor case has a similar equilibrium phase diagram as the matrix case, and an overall similar phenomenology for the considered algorithms. Additionally, we consider out-of-equilibrium landscape properties using Overlap Gap Properties and Franz-Parisi analysis, and discuss the implications or lack-thereof for average-case algorithmic hardness.

In $\textit{total domination}$, given a graph $G=(V,E)$, we seek a minimum-size set of nodes $S\subseteq V$, such that every node in $V$ has at least one neighbor in $S$. We define a $\textit{fault-tolerant}$ version of total domination, where we require any node in $V \setminus S$ to have at least $m$ neighbors in $S$. Let $Δ$ denote the maximum degree in $G$. We prove a first $1 + \ln(Δ+ m - 1)$ approximation for fault-tolerant total domination. We also consider fault-tolerant variants of the weighted $\textit{partial positive influence dominating set}$ problem, where we seek a minimum-size set of nodes $S\subseteq V$, such that every node in $V$ is either a member of $S$ or the sum of weights of its incident edges leading to nodes in $S$ is at least half of the sum of weights over all its incident edges. We prove the first logarithmic approximations for the simple, total, and connected variants of this problem. To prove the result for the connected case, we extend the general approximation framework for non-submodular functions from integer-valued to fractional-valued functions, which we believe is of independent interest.

We introduce a systematic method for constructing polytope approximations to the quantum set in a variety of device-independent quantum random number generation (DI-QRNG) protocols. Our approach relies on two general-purpose algorithms that iteratively refine an initial outer-polytope approximation, guided by typical device behaviour and cryptographic intuition. These refinements strike a balance between computational tractability and approximation effectiveness. By integrating these approximations into the probability estimation (PE) framework [Zhang et al., PRA 2018], we obtain significantly improved certified entropy bounds in the finite-size regime. We test our method on various bipartite and tripartite DI-QRNG protocols, using both simulated and experimental data. In all cases, it yields notably higher entropy rates with fewer device uses than the existing techniques. We further extend our analysis to the more demanding task of randomness amplification, demonstrating major performance gains without added complexity. These results offer an effective and ready-to-use method to prove security-with improved certified entropy rates-in the most common practical DI-QRNG protocols. Our algorithms and entropy certification with PE tools are publicly available under a non-commercial license at https://github.com/CQCL/PE_polytope_approximation.

The efficient simulation of multijet final states presents a serious computational task for analyses of LHC data and will be even more so at the HL-LHC. We here discuss means to accelerate the generation of unweighted events based on a two-stage rejection-sampling algorithm that employs neural-network surrogates for unweighting the hard-process matrix elements. To this end, we generalise the previously proposed algorithm based on factorisation-aware neural networks to the case of multijet merging at tree-level accuracy. We thereby account for several non-trivial aspects of realistic event-simulation setups, including biased phase-space sampling, partial unweighting, and the mapping of partonic subprocesses. We apply our methods to the production of Z+jets final states at the HL-LHC using the Sherpa event generator, including matrix elements with up to six final-state partons. When using neural-network surrogates for the dominant Z+5 jets and Z+6 jets partonic processes, we find a reduction in the total event-generation time by more than a factor of 10 compared to baseline Sherpa.

Measuring the astrometric and spectroscopic data of stars orbiting the central black hole in our galaxy (Sgr A*) offers a promising way to measure relativistic effects. In principle, the "no-hair" theorem can be tested at the Galactic Center by monitoring the orbital precession of S-stars due to the angular momentum (spin) and quadrupole moment of Sgr A*. Closer-in stars, more strongly affected by the black hole's rotation, may be required. GRAVITY+ could detect such stars that are currently too faint for GRAVITY. We aim to analytically and numerically characterize orbital reorientations induced by spin-related effects of Sgr A* up to the second post-Newtonian (2PN) order. We use the two-timescale method to derive the 2PN analytical expressions of the secular evolution of the orbital parameters that are related to the observer. To study the interaction between the orbital and spin orientations, we introduce observer-independent quantities that offer insight into the Kerr geometry. We also use the post-Newtonian code OOGRE to simulate hypothetical stars orbiting closer to Sgr A*, where spin and quadrupole effects are stronger. This enables comparison with our analytical predictions. We exhibit three orbital-timescale precession rates that encode the in-plane pericenter shift and the out-of-plane redirection of the osculating ellipse. We provide the 2PN expressions of these precession rates and express the orbit-integrated associated angular shifts of the pericenter and of the ellipse axes. We relate these orbital-timescale precession rates to the secular-timescale precession of the orbital angular momentum around the black hole spin axis. We consider that the theoretical insight we provide in this article will be useful in constraining the spin effect of Sgr A* with GRAVITY+ observations.

In this paper we introduce a new two-player zero-sum game whose value function approximates the level set formulation for the geometric evolution by mean curvature of a hypersurface. In our approach the game is played with symmetric rules for the two players and probability theory is involved (the game is not deterministic).

We investigate the performance of an adiabatic evolution protocol when initialized from a Gibbs state at finite temperature. Specifically, we identify the diagonality of the final state in the energy eigenbasis, as well as the difference in energy and in energy variance with respect to the ideal adiabatic limit as key benchmarks for success and introduce metrics to quantify the off-diagonal contributions. Provided these benchmarks converge to their ideal adiabatic values, we argue that thermal expectation values of observables can be recovered, in accordance with the eigenstate thermalization hypothesis. For the transverse-field Ising model, we analytically establish that these benchmarks converge polynomially in both the quasi-adiabatic evolution time $T$ and system size. We perform numerical studies on non-integrable systems and find close quantitative agreement for the off-diagonality metrics, along with qualitatively similar behavior in the energy convergence.

We investigate interfacial fluid dynamics and heat transfer at nanoscales using an improved diffuse interface approach for liquid-vapor interfaces in non-equilibrium. Conventional Navier-Stokes-Korteweg (NSK) formulations often fail to accurately capture transport phenomena across extremely thin interfaces due to underestimation of interface resistances. In this work, we improve the NSK model by adding a production term in the momentum equation based on higher-order corrections. To enhance interface resistances, viscosity and thermal conductivity are made dependent on the density gradient, increasing resistance only within the interface region. The gradient-based coefficients are determined by fitting to solutions of the Enskog-Vlasov equation for Couette flow (see Struchtrup and Frezzotti, 2022). Applying these fitted equations to pure heat conduction and planar evaporation problems shows that the model accurately captures interfacial transport, making it a useful tool for studying nanoscale evaporation, thermal management, and droplet dynamics on solid surfaces.

Universal features of chaotic quantum dynamics underlie our understanding of thermalization in closed quantum systems and the complexity of quantum computations. Reversible automaton circuits, comprised of classical logic gates, have emerged as a tractable means to study such dynamics. Despite generating no entanglement in the computational basis, these circuits nevertheless capture many features expected from fully quantum evolutions. In this work, we demonstrate that the differences between automaton dynamics and fully quantum dynamics are revealed by the operator entanglement spectrum, much like the entanglement spectrum of a quantum state distinguishes between the dynamics of states under Clifford and Haar random circuits. While the operator entanglement spectrum under random unitary dynamics is governed by the eigenvalue statistics of random Gaussian matrices, we show evidence that under random automaton dynamics it is described by the statistics of Bernoulli random matrices, whose entries are random variables taking values $0$ or $1$. We study the crossover between automaton and generic unitary operator dynamics as the automaton circuit is doped with gates that introduce superpositions, namely Hadamard or $R_x = e^{-i\fracπ{4}X}$ gates. We find that a constant number of superposition-generating gates is sufficient to drive the operator dynamics to the random-circuit universality class, similar to earlier results on Clifford circuits doped with $T$ gates. This establishes the operator entanglement spectrum as a useful tool for probing the chaoticity and universality class of quantum dynamics.

This article considers three non-zero hypercharge triplets as an extension of the Standard Model Higgs doublet. Under extra $U(1)_{L_μ-L_τ}$ symmetry, the triplets are charged. We examine the stability of the electroweak vacuum at the two-loop and tree-levels. The two-loop $β$-functions are found to be capable of satisfying the vacuum stability up to the Planck scale. On the other hand, only up to $10^{12}$ GeV can the perturbative unitarity be satisfied because of the increase in the positive influence from triplet degrees of freedom. For the strongly electroweak first-order phase transition, the parameter space permitted by the Planck scale stability is examined. Because the triplet degrees of freedom contribute sufficiently to the cubic term, the model satisfies the strongly first order phase transition for the triplet bare mass parameters up to the TeV scale. For all mass ranges, it is found that this model predicts a strongly first-order phase transition until the degrees of freedom are heavy enough to separate from the thermal bath. The gravitational wave signatures are tested at the benchmark places that fulfill the strongly first-order phase transition. The measurable frequency range of the LISA and BBO experiments also turns out to contain the benchmark points permitted by Planck scale stability, strongly first-order phase transition.

We consider an elliptic system of Schrödinger-Bopp-Podolsky type in a bounded and smooth domain of R3 with a non constant coupling factor. This kind of system has been introduced in the mathematical literature in [14] and in the last years many contributions appeared. In particular here we present the results in [2] and [34] which show existence of solutions by means of the Ljusternik-Schnirelmann theory under different boundary conditions on the electrostatic potential.

Tensor networks like matrix product states (MPSs) and matrix product operators (MPOs) are powerful tools for representing exponentially large states and operators, with applications in quantum many-body physics, machine learning, numerical analysis, and other areas. In these applications, computing a compressed representation of the MPO--MPS product is a fundamental computational primitive. For this operation, this paper introduces a new single-pass, randomized algorithm, called successive randomized compression (SRC), that improves on existing approaches in speed or in accuracy. The performance of the new algorithm is evaluated on synthetic problems and unitary time evolution problems for quantum spin systems.

Orbiting matter misaligned with a spinning black hole undergoes Lense-Thirring precession, due to the frame-dragging effect. This phenomenon is particularly relevant for type-C QPOs observed in the hard states of low-mass X-ray binaries. However, the accretion flow in these hard states is complex, consisting of a geometrically thick, hot corona surrounded by a geometrically thin, cold disk. Recent simulations have demonstrated that, in such a truncated disk scenario, the precession of the inner hot corona slows due to its interaction with the outer cold disk. This paper aims to provide an analytical description of the precession of an inner (hot) torus in the presence of accretion torques exerted by the outer (cold) disk. Using the angular momentum conservation equation, we investigate the evolution of the torus angular momentum vector for various models of accretion torque. We find that, in general, an accretion torque tilts the axis of precession away from the black hole spin axis. In all models, if the accretion torque is sufficiently strong, it can halt the precession; any perturbation from this stalled state will cause the torus to precess around an axis that is misaligned with the black hole spin axis. The accretion torque exerted by the outer thin disk can cause precession around an axis that is neither aligned with the black hole spin axis nor perpendicular to the plane of the disk. This finding may have significant observational implications, as the jet direction, if aligned with the angular momentum axis of the torus, may no longer reliably indicate the black hole spin axis or the orientation of the outer accretion disk

The search for radio signals from exoplanets or star-planet interactions is a topic of major scientific interest, as it is likely the best way to detect and measure a planetary magnetic field and, therefore, to probe the inner structure of exoplanets. However, detecting these radio emissions is challenging, since they are anisotropic by nature, sporadic, and of low intensity because of their great distances, and because the sky cannot be monitored continuously. The aim of this article is to demonstrate the relevance of using statistical tools to detect periodic radio signals in unevenly spaced observations, and identify the implications of the measured period. The identification of periodic radio signals is achieved here by a Lomb-Scargle analysis. We first apply the technique to simulated astrophysical observations with controlled simulated noise. This allows us to characterize the origin of spurious detection peaks in the resulting periodograms, as well as to identify peaks corresponding to real periods in the studied system, and to harmonic or beat periods. We then validate this method with a real signal, using approximately 1400 hours of data from observations of Jupiter's radio emissions by the NenuFAR radio telescope over more than six years, to detect the periodicities of Jovian radio emissions (auroral and induced by the Galilean moons). We demonstrate with the simulation that the LombScargle periodogram allows us to correctly identify periodic radio signals, even in a diluted signal. On real measurements, it correctly detects the rotation period of the strong signal produced by Jupiter and the beat period of the emission triggered by the interaction between Jupiter and its Galilean moon Io, ...

For a smooth affine algebraic group $G$ over an algebraically closed field, we consider several two-variables generalizations of the affine Grassmannian $G(\!(t)\!)/G[\![t]\!]$, given by quotients of the double loop group $G(\!(x)\!)(\!(y)\!)$. We prove that they are representable by ind-schemes if $G$ is solvable. Given a smooth surface $X$ and a flag of subschemes of $X$, we provide a geometric interpretation of the two-variables Grassmannians, in terms of bundles and trivialisation data defined on appropriate loci in $X$, which depend on the flag.

We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other fundamental properties of forking calculus. Most notably, stationarity holds over arbitrary sets (in fact, every type is Lascar strong). On the other hand, we prove that stability is preserved under direct integrals of measurable fields of structures. We deduce that stability in the extremal models of an affine theory implies stability of the theory. We also deduce that the affine part of a stable continuous logic theory is affinely stable, generalising the result of preservation of stability under randomisations.

We identify the size of the largest connected component in a subcritical inhomogeneous random graph with a kernel of preferential attachment type. The component is polynomial in the graph size with an explicitly given exponent, which is strictly larger than the exponent for the largest degree in the graph. This is in stark contrast to the behaviour of inhomogeneous random graphs with a kernel of rank one. Our proof uses local approximation by branching random walks going well beyond the weak local limit and novel results on subcritical killed branching random walks.

The palette sparsification theorem (PST) of Assadi, Chen, and Khanna (SODA 2019) states that in every graph $G$ with maximum degree $Δ$, sampling a list of $O(\log{n})$ colors from $\{1,\ldots,Δ+1\}$ for every vertex independently and uniformly, with high probability, allows for finding a $(Δ+1)$ vertex coloring of $G$ by coloring each vertex only from its sampled list. PST naturally leads to a host of sublinear algorithms for $(Δ+1)$ vertex coloring, including in semi-streaming, sublinear time, and MPC models, which are all proven to be nearly optimal, and in the case of the former two are the only known sublinear algorithms for this problem. While being a quite natural and simple-to-state theorem, PST suffers from two drawbacks. Firstly, all its known proofs require technical arguments that rely on sophisticated graph decompositions and probabilistic arguments. Secondly, finding the coloring of the graph from the sampled lists in an efficient manner requires a considerably complicated algorithm. We show that a natural weakening of PST addresses both these drawbacks while still leading to sublinear algorithms of similar quality (up to polylog factors). In particular, we prove an asymmetric palette sparsification theorem (APST) that allows for list sizes of the vertices to have different sizes and only bounds the average size of these lists. The benefit of this weaker requirement is that we can now easily show the graph can be $(Δ+1)$ colored from the sampled lists using the standard greedy coloring algorithm. This way, we can recover nearly-optimal bounds for $(Δ+1)$ vertex coloring in all the aforementioned models using algorithms that are much simpler to implement and analyze.

Differential linear categories provide the categorical semantics of the multiplicative and exponential fragments of Differential Linear Logic. Briefly, a differential linear category is a symmetric monoidal category that is enriched over commutative monoids (called additive enrichment) and has a monoidal coalgebra modality that is equipped with a codereliction. The codereliction is what captures the ability of differentiating non-linear proofs via linearization in Differential Linear Logic. The additive enrichment plays an important role since it allows one to express the famous Leibniz rule. However, the axioms of a codereliction can be expressed without any sums or zeros. Therefore, it is natural to ask if one can consider a possible non-additive enriched version of differential linear categories. In this paper, we show that even if a codereliction can technically be defined in a non-additive setting, it nevertheless induces an additive enrichment via bialgebra convolution. Thus, we obtain a novel characterization of a differential linear category as a symmetric monoidal category with a monoidal bialgebra modality equipped with a codereliction. Moreover, we also show that coderelictions are, in fact, unique. We also introduce monoidal Hopf coalgebra modalities and discuss how antipodes relate to enrichment over Abelian groups.

We introduce a geometric model of shallow multiplicative exponential linear logic (MELL) using the Hilbert scheme. Building on previous work interpreting multiplicative linear logic proofs as systems of linear equations, we show that shallow MELL proofs can be modeled by locally projective schemes. The key insight is that while multiplicative linear logic proofs correspond to equations between formulas, the exponential fragment of shallow proofs corresponds to equations between these equations. We prove that the model is invariant under cut-elimination by constructing explicit isomorphisms between the schemes associated to proofs related by cut-reduction steps. A key technical tool is the interpretation of the exponential modality using the Hilbert scheme, which parameterizes closed subschemes of projective space. We demonstrate the model through detailed examples, including an analysis of Church numerals that reveals how the Hilbert scheme captures the geometric content of promoted formulas. This work establishes new connections between proof theory and algebraic geometry, suggesting broader relationships between computation and scheme theory.