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Shock waves driven by fast and wide coronal mass ejections (CMEs) are highly efficient particle accelerators involved in the production of solar energetic particle (SEP) events. The gradual SEP event measured by STEREO-A and B on October 11, 2013 had notable properties: (1) it occurred in isolation with very low background particle intensities, (2) it had a clear onset of SEPs measured in situ allowing detailed timing analyses, and (3) it was associated with a fast CME event magnetically connected with STA and B. These allowed us to investigate the temporal connection between the rapidly evolving shock properties, such as compression ratio, Mach number and geometry, and the intensity and composition of SEPs measured in situ. We use shock reconstruction techniques and multi-viewpoint imaging data from STA and B, SOHO, and SDO spacecraft to determine the kinematic evolution of the expanding shock wave. Using 3D magneto-hydrodynamic modelling we obtained shock wave properties along an ensemble of magnetic field lines connected to STA and B, estimating their uncertainties. Using a velocity dispersion analysis of the SEP data, we time shift the SEP time series and analyze the relations between their properties and the modeled shock ones, as well as the energy dependence of these relations. We find a very good temporal agreement between the formation of the modelled shock wave and the estimated release times for both electrons and protons. This simultaneous release suggests a common acceleration process. This early phase is marked at both STEREOs by elevated electron-to-proton ratios that coincide with the highly quasi-perpendicular phase of the shock, suggesting that the rapid evolution of the shock as it transits from the low to the high corona modifies the conditions under which particles are accelerated. We discuss these findings in terms of basic geometry and acceleration processes., Comment: 13 pages, 14 figures, submitted to A&A

Collisionless shock waves, ubiquitous in the universe, are crucial for particle acceleration in various astrophysical systems. Currently, the heliosphere is the only natural environment available for their in situ study. In this work, we showcase the collective acceleration of electrons and ions by one of the fastest in situ shocks ever recorded, observed by the pioneering Parker Solar Probe at only 34.5 million kilometers from the Sun. Our analysis of this unprecedented, near-parallel shock shows electron acceleration up to 6 MeV amidst intense multi-scale electromagnetic wave emissions. We also present evidence of a variable shock structure capable of injecting and accelerating ions from the solar wind to high energies through a self-consistent process. The exceptional capability of the probe's instruments to measure electromagnetic fields in a shock traveling at 1% the speed of light has enabled us, for the first time, to confirm that the structure of a strong heliospheric shock aligns with theoretical models of strong shocks observed in astrophysical environments. This alignment offers viable avenues for understanding astrophysical shock processes and the acceleration of charged particles., Comment: Main text: 9 pages, 4 figures, 1 table; Supplementary text: 9 pages, 6 figures

Understanding the properties and physical phase of the dense strongly interacting matter present in the cores of neutron stars or created in their binary mergers remains one of the most prominent open problems in nuclear astrophysics. While most microscopic analyses have historically relied on solvable phenomenological models of nuclear and quark matter, in recent years a model-independent approach utilizing only controlled ab-initio calculations and astrophysical observations has emerged as a viable alternative. In these lecture notes, I review recent progress in first-principles weak-coupling calculations within high-density quark matter, shedding light on its thermodynamic and transport properties. I cover the most important technical tools used in such calculations, introduce selected highlight results, and explain how this information can be used in phenomenological studies of neutron-star physics. The notes do not offer a self-consistent treatment of the topics covered, but rather aim at filling gaps in existing textbooks on thermal field theory and at connecting the dots in a story developed in several recent research articles, to which the interested reader is directed for further technical details., Comment: 55 pages, 12 figures. Lecture notes for lectures presented at the 63rd Cracow School of Theoretical Physics, held in Zakopane, Poland on 17-23 September 2023. v2: Version accepted for publication in Acta Phys. Pol. B

We consider constellations of disks which are unions of disjoint hyperbolic disks in the unit disk with fixed radii and unfixed centers. We study the problem of maximizing the conformal capacity of a constellation under constraints on the centers in two cases. In the first case the constraint is that the centers are at most at distance $R \in(0,1)$ from the origin and in the second case it is required that the centers are on the subsegment $[-R,R]$ of a diameter of the unit disk. We study also similar types of constellations with hyperbolic segments instead of the hyperbolic disks. Our computational experiments suggest that a dispersion phenomenon occurs: the disks/segments go as close to the unit circle as possible under these constraints and stay as far as possible from each other. The computation of capacity reduces to the Dirichlet problem for the Laplace equation which we solve with a fast boundary integral equation method. The results are double-checked with the $hp$-FEM method.

We prove an identity which connects the visual angle metric $v_{\mathbb{H}^2}$ and the hyperbolic metric $\rho_{\mathbb{H}^2}$ of the upper half plane $\mathbb{H}^2$. The proof is based on geometric arguments and uses computer algebra methods for formula manipulation. We also prove a sharp H\"older continuity result for quasiregular mappings with respect to the visual angle metric., Comment: 33 pages, 7 figures, 3 tables

Modern hydrodynamic simulations of core-collapse supernovae and neutron-star mergers require knowledge not only of the equilibrium properties of strongly interacting matter, but also of the system's response to perturbations, encoded in various transport coefficients. Using perturbative and holographic tools, we derive here an improved weak-coupling and a new strong-coupling result for the most important transport coefficient of unpaired quark matter, its bulk viscosity. These results are combined in a simple analytic pocket formula for the quantity that is rooted in perturbative Quantum Chromodynamics at high densities but takes into account nonperturbative holographic input at neutron-star densities, where the system is strongly coupled. This expression can be used in the modeling of unpaired quark matter at astrophysically relevant temperatures and densities., Comment: 18 pages, 6 figures

We investigate Lindel\"of and Koebe type boundary behavior results for bounded quasiregular mappings in $n$-dimensional Euclidean space. Our results give sufficient conditions for the existence of non-tangential limits at a boundary point., Comment: 14 pages

Improving the synthetic methanol production efficiency is essential for adopting carbon-neutral methanol technologies. In the present computational fluid dynamics (CFD) study, we investigate synthetic methanol (CH$_3$OH) production in a milli-duct with a rectangular cross-section. The duct involves catalytic wall reactions with CO$_2$ and H$_2$ as reactants. Direct numerical simulations are carried out at bulk Reynolds numbers $Re_\mathrm{b} =$ 100, 500, 1100 and 2200 spanning laminar and turbulent flow regimes. We investigate a high catalyst loading, corresponding to gas hourly space velocity values of GHSV = 0.086, 0.44, 0.96 and 1.93 m$^3$/(kg$_\mathrm{cat}$ h). The results consist of the following features. 1) Turbulent mixing may significantly enhance methanol production under transport-limited chemistry, increasing the methanol mass flow rate at the outlet up to 56.4 % in the duct. 2) The reaction rate reaches local minima/maxima in the turbulent ejection/sweep structures observed in the proximity of the catalytic walls, respectively. 3) The single-pass conversion efficiency of CO$_2$ and the methanol yield across the duct decrease monotonically as the Reynolds number increases (lower residence time), while in contrast, the methanol mass flow rate at the outlet increases as $Re_\mathrm{b}$ increases (higher reactant inflow). These results suggest that turbulent transport could be leveraged to improve methanol yield in straight millichannels, albeit at the cost of increased reactant recycling., Comment: 28 pages, 11 figures

Due to the invariance properties of cross-ratio, M\"obius transformations are often used to map a set of points or other geometric object into a symmetric position to simplify a problem studied. However, when the points are mapped under a M\"obius transformation, the distortion of the Euclidean geometry is rarely considered. Here, we identify several cases where the distortion caused by this symmetrization can be measured in terms of the Lipschitz constant of the M\"obius transformation in the Euclidean or the chordal metric., Comment: 14 pages, 4 figures

A boundary integral equation method is presented for fast computation of the analytic capacities of compact sets in the complex plane. The method is based on using the Kerzman--Stein integral equation to compute the Szeg\"o kernel and then the value of the Ahlfors map at the point at infinity. The proposed method can be used for domains with smooth and piecewise smooth boundaries. When combined with conformal mappings, the method can be used for compact slit sets. Several numerical examples are presented to demonstrate the efficiency of the proposed method. We recover some known exact results and corroborate the conjectural subadditivity property of analytic capacity.

The purpose of this note is to prove that the strong Christ-Goldberg maximal function is bounded. This is a matrix weighted maximal operator appearing in the theory of matrix weighted norm inequalities. Related to this we record the Rubio de Francia extrapolation theorem with bi-parameter matrix weights., Comment: 14 pages. v2: Improvements in the text. Takes into account referee comments

Using the definition of uniformly perfect sets in terms of convergent sequences, we apply lower bounds for the Hausdorff content of a uniformly perfect subset $E$ of $\mathbb{R}^n$ to prove new explicit lower bounds for the Hausdorff dimension of $E.$ These results also yield lower bounds for capacity test functions, which we introduce, and enable us to characterize domains of $\mathbb{R}^n$ with uniformly perfect boundaries. Moreover, we show that an alternative method to define capacity test functions can be based on the Whitney decomposition of the domain considered., Comment: 29 pages, 2 figures

Both nonzero temperature and chemical potentials break the Lorentz symmetry present in vacuum quantum field theory by singling out the rest frame of the heat bath. This leads to complications in the application of thermal perturbation theory, including the appearance of novel infrared divergences in loop integrals and an apparent absence of four-dimensional integration-by-parts (IBP) identities, vital for high-order computations. Here, we propose a new strategy that enables the use of IBP techniques in the evaluation of Feynman integrals, in particular vacuum or bubble diagrams, in the limit of vanishing temperature $T$ but nonzero chemical potentials $\mu$. The central elements of the new setup include a contour representation for the temporal momentum integral, the use of a small but nonzero $T$ as an IR regulator, and the systematic application of both temporal and spatial differential operators in the generation of linear relations among the loop integrals of interest. The relations we derive contain novel inhomogeneous terms featuring differentiated Fermi-Dirac distribution functions, which severely complicate calculations at nonzero temperature, but are shown to reduce to solvable lower-dimensional objects as $T$ tends to zero. Pedagogical example computations are kept at the one- and two-loop levels, but the application of the new method to higher-order calculations is discussed in some detail., Comment: 48 pages, 1 figure, structural revisions and clarifications added, matches published version (v3)

We prove several new formulas for the visual angle metric of the unit disk in terms of the hyperbolic metric and apply these to prove a sharp Schwarz lemma for the visual angle metric under quasiregular mappings., Comment: 15 pages, 9 Figures

Neutron-star cores contain matter at the highest densities in our Universe. This highly compressed matter may undergo a phase transition where nuclear matter melts into deconfined quark matter, liberating its constituent quarks and gluons. Quark matter exhibits an approximate conformal symmetry, predicting a specific form for its equation of state (EoS), but it is currently unknown whether the transition takes place inside at least some physical neutron stars. Here, we quantify this likelihood by combining information from astrophysical observations and theoretical calculations. Using Bayesian inference, we demonstrate that in the cores of maximally massive stars, the EoS is consistent with quark matter. We do this by establishing approximate conformal symmetry restoration with high credence at the highest densities probed and demonstrating that the number of active degrees of freedom is consistent with deconfined matter. The remaining likelihood is observed to correspond to EoSs exhibiting phase-transition-like behavior, treated as arbitrarily rapid crossovers in our framework., Comment: Version 2: the published version. 18 pages, 8 figs

We prove that if $E$ is a compact subset of the unit disk ${\mathbb D}$ in the complex plane, if $E$ contains a sequence of distinct points $a_n\not= 0$ for $n\geq 1$ such that $\lim_{n\to\infty} a_n=0$ and for all $n$ we have $ |a_{n+1}| \geq \frac{1}{2} |a_n| $, and if $G={\mathbb D} \setminus E$ is connected and $0\in \partial G$, then there is a constant $c>0$ such that for all $z\in G$ we have $ \lambda_{G } (z) \geq c/|z| $ where $\lambda_{G } (z)$ is the density of the hyperbolic metric in $G$.

The Hilbert metric between two points $x,y$ in a bounded convex domain $G$ is defined as the logarithm of the cross-ratio of $x,y$ and the intersection points of the Euclidean line passing through the points $x,y$ and the boundary of the domain. Here, we study this metric in the case of the unit ball $\mathbb{B}^n$. We present an identity between the Hilbert metric and the hyperbolic metric, give several inequalities for the Hilbert metric, and results related to the inclusion properties of the balls defined in the Hilbert metric. Furthermore, we study the distortion of the Hilbert metric under conformal mappings., Comment: 18 pages, 4 figures

For a fixed integer $m>2$ and $r_j>0, j=1,...,m,$ our focus is to study disjoint disks with hyperbolic radii $r_j$ and the set $E$ which is their union in the hyperbolic space, the unit disk equipped with the hyperbolic metric. Such a set is called a constellation of $m$ disks. The centers of the disks are not fixed and hence individual disks of the constellation are allowed to move under the constraints that they do not overlap and their hyperbolic radii remain invariant. Our main objective is to find computational lower bounds for the conformal capacity of this disk constellation. The capacity depends on the centers and radii in a very complicated way even in the simplest cases when $m=3$ or $m=4$. In the absence of analytic methods our work is based on numerical simulations using two different numerical methods, the boundary integral equation method and the $hp$-FEM method, resp. Our simulations combine capacity computation with minimization methods and produce extremal cases where the disks of the constellation are grouped next to each other. This resembles the behavior of animal colonies in arctic areas minimizing heat flow.

We study current bounds on strong first-order phase transitions (PTs) along the equation of state (EOS) of dense strongly interacting matter in neutron stars, under the simplifying assumption that on either side of the PT the EOS can be approximated by a simple polytropic form. We construct a large ensemble of possible EOSs of this form, anchor them to chiral effective field theory calculations at nuclear density and perturbative QCD at high densities, and subject them to astrophysical constraints from high-mass pulsars and gravitational-wave observations. Within this setup, we find that a PT permits neutron-star solutions with larger radii, but only if the transition begins below twice nuclear saturation density. We also identify a large parameter space of allowed PTs currently unexplored by numerical-relativity studies. Additionally, we locate a small region of parameter space allowing twin-star solutions, though we find them to only marginally pass the current astrophysical constraints. Finally, we find that sizeable cores of high-density matter beyond the PT may be located in the centers of some stable neutron stars, primarily those with larger masses., Comment: 10 pages, 11 figures; version accepted for publication in ApJ. Substantial change from v1 in treatment of matching to chiral EFT in a continuous manner. Figures and discussions updated. Conclusions qualitatively unchanged

We study computational methods for the approximation of special functions recurrent in geometric function theory and quasiconformal mapping theory. The functions studied can be expressed as quotients of complete elliptic integrals and as inverses of such quotients. In particular, we consider the distortion function $\varphi_K(r)$ which gives a majorant for $|f(x)|$ when $f: \mathbb{B}^2 \to \mathbb{B}^2, f(0)=0,$ is a quasiconformal mapping of the unit disk $\mathbb{B}^2.$ It turns out that the approximation method is very simple: five steps of Landen iteration is enough to achieve machine precision., Comment: 16 pages, 4 figures

We study certain points significant for the hyperbolic geometry of the unit disk. We give explicit formulas for the intersection points of the Euclidean lines and the stereographic projections of great circles of the Riemann sphere passing through these points. We prove several results related to collinearity of these intersection points, offer new ways to find the hyperbolic midpoint, and represent a formula for the chordal midpoint. The proofs utilize Gr\"obner bases from computer algebra for the solution of polynomial equations., Comment: 26 pages, 7 figures

For augmentation of the square-shaped image data of a convolutional neural network (CNN), we introduce a new method, in which the original images are mapped onto a disk with a conformal mapping, rotated around the center of this disk and mapped under such a M\"obius transformation that preserves the disk, and then mapped back onto their original square shape. This process does not result the loss of information caused by removing areas from near the edges of the original images unlike the typical transformations used in the data augmentation for a CNN. We offer here the formulas of all the mappings needed together with detailed instructions how to write a code for transforming the images. The new method is also tested with simulated data and, according the results, using this method to augment the training data of 10 images into 40 images decreases the amount of the error in the predictions by a CNN for a test set of 160 images in a statistically significant way (p-value=0.0360)., Comment: 14 pages, 3 figures

Spacecraft missions provide the unique opportunity to study the properties of collisionless shocks utilising in situ measurements. In the past years, several diagnostics have been developed to address key shock parameters using time series of magnetic field (and plasma) data collected by a single spacecraft crossing a shock front. A critical aspect of such diagnostics is the averaging process involved in the evaluation of upstream-downstream quantities. In this work, we discuss several of these techniques, with a particular focus on the shock obliquity (defined as the angle between the upstream magnetic field and the shock normal vector) estimation. We introduce a systematic variation of the upstream/downstream averaging windows, yielding to an ensemble of shock parameters, a useful tool to address the robustness of their estimation. This approach is first tested with a synthetic shock, compliant with the Rankine-Hugoniot jump conditions for a shock, including the presence of noise and disturbances. We then employ self-consistent, hybrid kinetic shock simulations to apply the diagnostics to virtual spacecraft crossing the shock front at various stages of its evolution, highlighting the role of shock-induced fluctuations in the parameters estimation. This approach has the strong advantage of retaining some important properties of collisionless shock while being able to set a known, nominal set of shock parameters. Finally, two recent observations of interplanetary shocks from the Solar Orbiter spacecraft are presented, and the approach is also tested on an interplanetary shock measured by the four spacecraft of the Magnetospheric Multiscale (MMS) mission. All the Python software developed and used for the diagnostics (SerPyShock) is made available for the public, including an example of parameter estimation for a shock wave recently observed in-situ by the Solar Orbiter spacecraft., Comment: Published in Frontiers in Astronomy and Space Sciences

Our limited understanding of the physical properties of matter at ultra-high density, high proton/neutron number asymmetry, and low temperature is presently one of the major outstanding problems in physics. As matter in this extreme state is known to only exist stably in the cores of neutron stars (NSs), complementary measurements from electromagnetic and gravitational wave astrophysical observations of NSs, combined with terrestrial laboratory constraints and further theoretical investigations, hold the promise to provide important insight into the properties of matter in a region of the quantum chromodynamics phase space that is otherwise inaccessible. This multidisciplinary endeavor imposes the following requirements for facilities and resources in the upcoming decade and beyond: * A next generation of gravitational wave detectors to uncover more double NS and neutron star-black hole mergers; * Sensitive radio telescopes to find the most massive and fastest spinning NSs; * Large-area, high-time-resolution and/or high angular resolution X-ray telescopes to constrain the NS mass-radius relation; * Suitable laboratory facilities for nuclear physics experiments to constrain the dense matter equation of state; * Funding resources for theoretical studies of matter in this regime; * The availability of modern large-scale high performance computing infrastructure. The same facilities and resources would also enable significant advances in other high-profile fields of inquiry in modern physics such as the nature of dark matter, alternative theories of gravity, nucleon superfluidity and superconductivity, as well as an array of astrophysics, including but not limited to stellar evolution, nucleosynthesis, and primordial black holes., Comment: Submitted to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021) under Cosmic Frontier (CF07: Cosmic probes of fundamental physics); 30 pages, 8 figures

We analyze envelopes of 233 and 22 $M_{\text L}$0.0 to $M_{\text L}$1.8 earthquakes induced by two geothermal stimulations in the Helsinki, Finland, metropolitan area. We separate source spectra and site terms and determine intrinsic attenuation and the scattering strength of shear waves in the 3 Hz to 200 Hz frequency range using radiative transfer based synthetic envelopes. Displacement spectra yield scaling relations with a general deviation from self-similarity, with a stronger albeit more controversial signal from the weaker 2020 stimulation. The 2020 earthquakes also tend to have a smaller local magnitude compared to 2018 earthquakes with the same moment magnitude. We discuss these connections in the context of fluid effects on rupture speed or medium properties. Site terms demonstrate that the spectral amplification relative to two reference borehole sites is not neutral at the other sensors; largest variations are observed at surface stations at frequencies larger than 30 Hz. Intrinsic attenuation is exceptionally low with $Q_{\text i}^{-1}$ values down to $2.4\times 10^{-5}$ at 20 Hz, which allows the observation of a diffuse reflection at the ${\sim}$50 km deep Moho. Scattering strength is in the range of globally observed data with $Q_{\text{sc}}^{-1}$ between $10^{-3}$ and $10^{-4}$. The application of the employed Qopen analysis program to the 2020 data in a retrospective monitoring mode demonstrates its versatility as a seismicity processing tool. The diverse results have implications for scaling relations, hazard assessment and ground motion modeling, and imaging and monitoring using ballistic and scattered wavefields in the crystalline Fennoscandian Shield environment., Comment: published in JGR: Solid Earth, v2: published version

We study inequalities between the hyperbolic metric and intrinsic metrics in convex polygonal domains in the complex plane. Special attention is paid to the triangular ratio metric in rectangles. A local study leads to an investigation of the relationship between the conformal radius at an arbitrary point of a planar domain and the distance of the point to the boundary., Comment: 20 pages, 7 figures

We study the mixed Dirichlet-Neumann problem for the Laplace equation in the complement of a bounded convex polygonal quadrilateral in the extended complex plane. The Dirichlet\,/\,Neumann conditions at opposite pairs of sides are $\{0,1\}$ and $\{0,0\},$ resp. The solution to this problem is a harmonic function in the unbounded complement of the polygon known as the \emph{potential function} of the quadrilateral. We compute the values of the potential function including its value at infinity., Comment: 14 pages, 5 figures

In this paper we discuss problems concerning the conformal condenser capacity of "hedgehogs", which are compact sets $E$ in the unit disk $\mathbb{D}=\{z:\,|z|<1\}$ consisting of a central body $E_0$ that is typically a smaller disk $\overline{\mathbb{D}}_r=\{z:\,|z|\le r\}$, $0

We determine the pressure of a cold and dense electron gas to a nearly complete next-to-next-to-next-to-leading order (N$^3$LO) in the fine-structure constant $\alpha_e$, utilizing a new result for the two-loop photon self-energy from a companion paper. Our result contains all infrared-sensitive contributions to the pressure at this order, including the coefficient of the $O(\alpha_e^3 \ln \alpha_e^{ })$ term, and leaves only a single coefficient associated with the contributions of unresummed hard momenta undetermined. Moreover, we explicitly demonstrate the complete cancellation of infrared divergences according to the effective field theory paradigm by determining part of the hard contributions at this order. Our calculation provides the first improvement to a 45-year-old milestone result and demonstrates the feasibility of the corresponding N$^3$LO calculation for cold and dense quark matter., Comment: 6 pages (main text), 6 pages (supplemental material) and 3 figures