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Instabilities in relativistic magnetized jets are thought to be deeply connected to their energy dissipation properties and to the consequent acceleration of the non-thermal emitting relativistic particles. Instabilities lead to the development of small-scale dissipative structures, in which magnetic energy is converted in other forms. In this paper we present three-dimensional numerical simulations of the instability evolution in highly magnetized plasma columns, considering different kinds of equilibria. In fact, the hoop stresses related to the azimuthal component of magnetic field can be balanced either by the magnetic pressure gradient (force-free equilibria, FF) or by the thermal pressure gradient (pressure-balanced equilibria, PB) or by a combination of the two. FF equilibria are prone to current-driven instabilities (CDI), while PB equilibria are prone to pressure-driven instabilities (PDI). We perform a global linear stability analysis, from which we derive the different instability properties in the two regimes, showing that PDI have larger growth rates and are also unstable for high wavenumbers. The numerical simulations of the non-linear instability evolution show similar phases of evolution in which the formation of strong current sheets is followed by a turbulent quasi-steady state. PDI are however characterized by a faster evolution, by the formation of smaller scale dissipative structures and larger magnetic energy dissipation. [ABSTRACT FROM AUTHOR]

The wave‐breaking amplitude of a strong nonlinear plasma wave has been determined in a warm plasma. Pseudopotential technique has been adopted to describe the wave‐breaking phenomena in such plasma. The solution is obtained with the consideration that the phase velocity of the plasma wave is equal to the velocity of light in vacuum. This assumption is justified since the wave which is excited usually by the relativistic charged particle bunches or laser pulses has phase speed very close to the speed of light in vacuum. The investigation shows that the breaking amplitude decreases with the increase of the electron temperature. Furthermore, the wavelength of the plasma wave is seen to decrease as we increase the electron temperature. The obtained results have relevance in the astrophysical situation as well as in the field of plasma based charged particle acceleration process. [ABSTRACT FROM AUTHOR]

Supermassive black hole (BH) mergers with spin-flips accelerate energetic particles through their relativistic precessing jets, producing high-energy neutrinos and finally gravitational waves (GWs). In star formation, massive stars form in pairs, triplets, and quadruplets, allowing second-generation mergers of the remnants with discrepant spin directions. The GW data support such a scenario. Earlier, we suggested that stellar mass BH mergers (visible in M82) with an associated spin-flip analogously allow the acceleration of energetic particles, with ensuing high-energy neutrinos and high-energy photons, and finally produce GWs. At cosmic distances, only the GWs and the neutrinos remain detectable. In this study, we generalize the argument to starburst and normal galaxies throughout their cosmic evolution and show that these galaxies may dominate over active galactic nuclei (AGN) in the flux of ultra-high-energy particles observed at Earth. All these sources contribute to the cosmic neutrino background, as well as the GW background (they detected lower frequencies). We outline a search strategy to find such episodic sources, which requires including both luminosity and flux density. [ABSTRACT FROM AUTHOR]

The Mathisson--Papapetrou equations are used to study the deviation of the spinning particle world lines and trajectories from the corresponding geodesic lines in Schwarzschild's background. The traditional form of these equations and their consequences in terms of the comoving tetrads are considered. Analytical and numerical calculations for the equatorial motions are performed. The circular, quasi-circular, and quasi-radial motions of the highly relativistic spinning particle are analyzed. Different illustrations are presented. [ABSTRACT FROM AUTHOR]

Flares from magnetically active dwarf stars should produce relativistic particles capable of creating γ-rays. So far, the only isolated main-sequence star besides the Sun to have been detected in γ-rays is TVLM 513−46546. Detecting γ-ray flares from more dwarf stars can improve our understanding of their magnetospheric properties, and could also indicate a diminished likelihood of their planets' habitability. In this work, we stack data from the Fermi Gamma-ray Space Telescope during a large number of events identified from optical and X-ray flare surveys. We report an upper limit of γ-ray emission from the population of flare stars. Stacking results towards control positions are consistent with a non-detection. We compare these results to observed solar γ-ray flares and against a model of emission from neutral pion decay. The upper limit is consistent with solar flares when scaled to the flare energies and distances of the target stars. As with solar flares, the neutral pion decay mechanism for γ-ray production is also consistent with these results. [ABSTRACT FROM AUTHOR]

The Klein–Gordon equation is a fundamental theoretical physics concept, governing the behavior of relativistic quantum particles with spin-zero. Its numerical solution is crucial in fields like quantum field theory, particle physics, and cosmology. The study explores numerical methodologies for solving this equation, highlighting their significance and challenges. This study uses the collocation method to approximate fractional Klein–Gordon models of distributed order based on Shifted Jacobi orthogonal polynomials and Shifted fractional order Jacobi orthogonal functions. While, the distributed term (integral term) was treat using Legendre–Gauss–Lobatto quadrature. It assesses residuals through finite expansion and yields accurate numerical results. The method is more factual and fair when initial and boundary conditions are enforced. Numerical simulations are presented to demonstrate the method's accuracy, particularly in fractional Klein–Gordon models of distributed order. Furthermore, we offer a few numerical test scenarios to show that the method is able to maintain the non-smooth solution of the underlying issue. [ABSTRACT FROM AUTHOR]

The issue of radiation mechanisms triggered in 1950–60s the first applications of plasma physics to understand the nature of radio galaxies. This interplay has steadily intensified during the past five decades due to the premise of in-situ acceleration of relativistic electrons occurring in the lobes of radio galaxies. This article briefly traces the chain of these remarkable developments, largely from an observational perspective. We recount several observational and theoretical milestones established along the way and the lessons drawn from them. We also present a new observational clue about in-situ acceleration of the relativistic particles radiating in the lobes of radio galaxies, gleaned by us from the very recently published sensitive radio observations of a tailed radio source in the galaxy cluster Abell 1033. [ABSTRACT FROM AUTHOR]

In light of the significance of non-commutative quaternionic algebra in modern physics, this study proposes the existence of the Klein paradox in the quaternionic (3+1)-dimensional space-time structure. By introducing quaternionic wave function, we rewrite the Klein–Gordon equation in extended quaternionic form that includes scalar and the vector fields. Because quaternionic fields are non-commutative, the quaternionic Klein–Gordon equation provides three separate sets of the probability density and probability current density of relativistic particles. We explore the significance of these probability densities by determining the reflection and transmission coefficients for the quaternionic relativistic step potential. Furthermore, we also discuss the quaternionic version of the oscillatory, tunnelling, and Klein zones for the quaternionic step potential. The Klein paradox occurs only in the Klein zone when the impacted particle's kinetic energy is less than 0 − m 0 c 2 . Therefore, it is emphasized that for the quaternionic Klein paradox, the quaternionic reflection coefficient becomes exclusively higher than value one while the quaternionic transmission coefficient becomes lower than zero. [ABSTRACT FROM AUTHOR]

Conventional formulation of QED since the 50s works very well for stationary states and for scattering problems, but with newly arisen challenges from the 80s on, where real time evolution of particles in a nonequilibrium setting are required, and quantum features such as coherence, dissipation, correlation and entanglement in a system interacting with its quantum field environment are sought after, new ways to formulate QED suitable for these purposes beckon. In this paper we present a linearized effective theory using a Gaussian wavepacket description of a charged relativistic particle coupled to quantum electromagnetic fields to study the interplay between single electrons and quantum fields in free space, at a scale well below the Schwinger limit. The proper values of the regulators in our effective theory are determined from the data of individual experiments, and will be time-dependent in the laboratory frame if the single electrons are accelerated. Using this new theoretical tool, we address the issues of decoherence of flying electrons in free space and the impact of Unruh effect on the electrons. Our result suggests that vacuum fluctuations may be a major source of blurring the interference pattern in electron microscopes. For a single electron accelerated in a uniform electric field, we identify the Unruh effect in the two-point correlators of the deviations from the electron's classical trajectory. From our calculations we also bring out some subtleties, involving the bosonic versus fermionic spectral functions. [ABSTRACT FROM AUTHOR]

In this paper, in the context of the Magueijo–Smolin (MS) model and using the Foldy–Wouthuysen transformation for relativistic spin-1/2 particles, we study the nonrelativistic limit (NRL) of the Dirac equation within the doubly special relativity. This leads to obtaining a deformed Schrödinger–Pauli equation; there, we test the influence of the MS model on the NRL of the Dirac equation. However, we also examine the efficacy and behavior of the Foldy–Wouthuysen transformation in deriving the NRL in the presence of MS model. Besides, we compute that the energies shift in the context of MS model and check if the deformed Schrödinger–Pauli equation form still shows explicitly the g-factor 2. [ABSTRACT FROM AUTHOR]

A classical theory of radiation from a relativistic charged particle linearly accelerated by a high-intensity laser pulse with modulated polarization is developed via solving the equation of motion of a charge in the electromagnetic wave field. The formulas for calculating the spectral and angular characteristics of radiation, namely, the radiation intensity of a particle and its phase- and phase-angle distributions are obtained. The graphs of dependence of the radiation characteristics on the modulation coefficient are constructed. [ABSTRACT FROM AUTHOR]

We show that the Connes–Rovelli thermal time associated with the quantum harmonic oscillator can be described as an (unsharp) observable, that is, as a positive operator valued measure. We furthermore present extensions of this result to the free massless relativistic particle in one dimension and to a hypothetical physical system whose equilibrium state is given by the noncommutative integral. [ABSTRACT FROM AUTHOR]

This paper presents a method for parameterizing new Lorentz spacetime coordinates based on coupled parameters. The role of symmetry in rapidity in special relativity is explored, and invariance is obtained for new spacetime intervals with respect to the Lorentz transformation. Using the Euler–Hamilton equations, an additional angular rapidity and perpendicular rapidity are obtained, and the Hamiltonian and Lagrangian of a relativistic particle are expanded into rapidity spectra. A so-called passage to the limit is introduced that makes it possible to decompose physical quantities into spectra in terms of elementary functions when explicit decomposition is difficult. New rapidity-dependent Lorentz spacetime coordinates are obtained. The descriptions of particle motion using the old and new Lorentz spacetime coordinates as applied to plane laser pulses are compared in terms of the particle kinetic energy. Based on a classical model of particle motion in the field of a plane monochromatic electromagnetic wave and that of a plane laser pulse, rapidity-dependent spectral decompositions into elementary functions are presented, and the Euler–Hamilton equations are derived as rapidity functions in 3+1 dimensions. The new and old Lorentz spacetime coordinates are compared with the Fermi spacetime coordinates. The proper Lorentz groups SO(1,3) with coupled parameters using the old and new Lorentz spacetime coordinates are also compared. As a special case, the application of Lorentz spacetime coordinates to a relativistic hydrodynamic system with coupled parameters in 1+1 dimensions is demonstrated. [ABSTRACT FROM AUTHOR]

In this article, we highlight that the interaction potential confining Dirac particles in a box must be invariant under the charge conjugation to avoid the Klein paradox, in which an infinite number of negative-energy particles are excited. Furthermore, we derive the quantization rules for a relativistic particle in a cylindrical box, which emulates the volume occupied by a beam of particles with a non-trivial aspect ratio. We apply our results to the evaluation of the quantum limit for emittance in particle accelerators. The developed theory allows the description of quantum beams carrying Orbital Angular Momentum (OAM). We demonstrate how the degeneracy pressure is such to increase the phase–space area of Dirac particles carrying OAM. The results dramatically differ from the classical evaluation of phase–space areas, that would foresee no increase in emittance for beams in a coherent state of OAM. We discuss the quantization of the phase–space cell's area for single Dirac particles carrying OAM, and, finally, provide an interpretation of the beam entropy as the measure of how much the phase–space area occupied by the beam deviates from its quantum limit. [ABSTRACT FROM AUTHOR]

Low-frequency radio observations show an increasing number of radio galaxies located in galaxy clusters that display peculiar morphologies and spectral profiles. This is the result of the dynamical interaction of the galaxy with the surrounding medium. Studying this phenomenon is key to understanding the evolution of low-energy relativistic particles in the intracluster medium. We present a multifrequency study of the three head–tail (HT) radio galaxies and the radio halo in the galaxy cluster ZwCl 0634.1+4747. We make use of observations at four frequencies performed with LOFAR LBA (53 MHz), HBA (144 MHz), GMRT (323 MHz), and VLA (1518 MHz) data. The use of extremely low radio frequency observations, such as LOFAR at 53 and 144 MHz, allowed us to detect the extension of the tails up to a distance of ∼1 Mpc. We extracted spectral profiles along the tails in order to identify possible departures from a pure ageing model, such as the Jaffe–Perola (JP) model, which only involves synchrotron and inverse-Compton losses. We found clear evidence of departures from this simple ageing model, such as surface brightness enhancement and spectral flattening along all of the tails. This can be interpreted as the consequence of particle re-acceleration along the tails. Possible explanations for this behaviour include the interaction between a shock and the radio tails or a turbulence-driven re-acceleration mechanism. We show that the latter scenario is able to reproduce the characteristic features that we observed in our profiles. [ABSTRACT FROM AUTHOR]

Wave particle interaction plays an important role in geospace and space weather phenomena. Whistler mode chorus emissions, characterized by non-linear growth and frequency chirping, are common in planetary magnetospheres. They are regarded as the origin of relativistic acceleration of particles in the radiation belts and pulsating aurora. Intensive theoretical investigations and spacecraft observations have revealed several important features of chorus emissions. However, there is a need to conduct high-resolution and reproducible controlled laboratory experiments to deepen the understanding of space weather. Here, we present the spontaneous excitation of chirping whistler waves in hot-electron high-β plasma (β is the ratio of the plasma pressure to the magnetic pressure) in an "artificial magnetosphere", a levitated dipole experiment. These experiments suggest that the generation and nonlinear growth of coherent chorus emissions are ubiquitous in dipole magnetic configuration. We anticipate that these experiments will accelerate the laboratory investigation of space weather phenomena. Plasma created in laboratory are useful to understand the properties of atmospheric and space plasma. Here the authors report a laboratory plasma experiment in a dipole magnetic field to show the excitation of chirping whistler waves, i.e. chorus emission. [ABSTRACT FROM AUTHOR]

In this work, we consider geometrical models describing spinning particles in the context of generalized Robertson–Walker spacetimes. We study spacelike and timelike trajectories for massive and massless particles governed by two different Lagrangians: one depending on the torsion and the other on the curvature of the trajectory. For both, we are able to relate the curvature and torsion of such trajectories with the curvature of the spatial fiber of the cosmological model. Moreover, several conserved quantities are described as well as their possible relations with physical parameters of the particle. [ABSTRACT FROM AUTHOR]

This review devoted to the centenary of Alexander Friedmann's prediction of the Universe expansion presents the results obtained by him in 1922 and 1924 and an overview of their further developments. Special attention is paid to the role of mathematics, which enabled Friedmann to perform a radical departure from the conventional practice of considering our universe as a static system. The effect of particle creation in the expanding universe is discussed concurrently with the earlier investigated phenomenon of pair creation from a vacuum by an external electric field. The numbers of scalar and spinor particles created at different stages of the Universe's evolution are presented, and the possible role of the effect of the creation of particles in the formation of relativistic plasma and cold dark matter after the inflationary period is noted. It is stressed that by introducing the concept of the expanding universe, Friedmann made a contribution towards the understanding of the world around us that is compatible with those made by Ptolemy, Copernicus, and Newton in previous epochs. [ABSTRACT FROM AUTHOR]

The IceCube Neutrino Observatory instruments about 1 km 3 of deep, glacial ice at the geographic South Pole. It uses 5160 photomultipliers to detect Cherenkov light emitted by charged relativistic particles. An unexpected light propagation effect observed by the experiment is an anisotropic attenuation, which is aligned with the local flow direction of the ice. We examine birefringent light propagation through the polycrystalline ice microstructure as a possible explanation for this effect. The predictions of a first-principles model developed for this purpose, in particular curved light trajectories resulting from asymmetric diffusion, provide a qualitatively good match to the main features of the data. This in turn allows us to deduce ice crystal properties. Since the wavelength of the detected light is short compared to the crystal size, these crystal properties include not only the crystal orientation fabric, but also the average crystal size and shape, as a function of depth. By adding small empirical corrections to this first-principles model, a quantitatively accurate description of the optical properties of the IceCube glacial ice is obtained. In this paper, we present the experimental signature of ice optical anisotropy observed in IceCube light-emitting diode (LED) calibration data, the theory and parameterization of the birefringence effect, the fitting procedures of these parameterizations to experimental data, and the inferred crystal properties. [ABSTRACT FROM AUTHOR]

Production of massless scalar particles by a relativistic semitransparent mirror of finite transverse size and longitudinal thickness in (1+3)D flat spacetime is studied. The derived particle spectrum formula is applied to two specific trajectories. One is the gravitational collapse trajectory invoked in (1+1)D perfectly reflecting moving mirror literature to mimic Hawking radiation, and the other is the plasma mirror trajectory proposed to be realizable in future experiments. It is found that the finiteness of the transverse size leads to diffraction, while the nontrivial thickness amplifies the production rate. We also estimated the particle yield as ∼ 3000 in a 20-day data acquisition based on the parameters invoked in the proposed AnaBHEL experiment. [ABSTRACT FROM AUTHOR]

According to the data from the GOES satellites and the SRS solar radio spectrograph, 112 proton events were analyzed for the time interval from November 24, 2000 to December 20, 2014, accompanied by an increase in the intensity of solar energetic particles (protons) Ip with energies Ep > 1–850 MeV and type II radio bursts in the range of 25–180 MHz. A correlation was found for the proton intensity Ip with the intensity of type II radio bursts Ii and the frequency drift rate V. The correlation coefficients between Ip and Ii, as well as between Ip and V, reach approximately 0.82 and 0.67, respectively. The correlation decreases quite sharply at Ер > 100 MeV. Nonthermal electrons responsible for type II radio bursts and energetic protons are generated at the fronts of the same shock waves, while the acceleration of relativistic particles with Ер > 100 MeV is determined by nonthermal processes in the region of flare energy release. [ABSTRACT FROM AUTHOR]

Radio relics are giant sources of diffuse synchrotron radio emission in the outskirts of galaxy clusters that are associated with shocks in the intracluster medium. Still, the origin of relativistic particles that make up relics is not fully understood. For most relics, diffusive shock acceleration (DSA) of thermal electrons is not efficient enough to explain observed radio fluxes. In this paper, we use a magnetohydrodynamic simulation of galaxy clusters in combination with Lagrangian tracers to simulate the formation of radio relics. Using a Fokker–Planck solver to compute the energy spectra of relativistic electrons, we determine the synchrotron emission of the relic. We find that re-acceleration of fossil electrons plays a major role in explaining the synchrotron emission of radio relics. Particles that pass through multiple shocks contribute significantly to the overall luminosity of a radio relic and greatly boost the effective acceleration efficiency. Furthermore, we find that the assumption that the luminosity of a radio relic can be explained with DSA of thermal electrons leads to an overestimate of the acceleration efficiency by a factor of more than 103. [ABSTRACT FROM AUTHOR]

The Thomas–Bargmann–Michel–Telegdi (TBMT) equation is derived using the Exact Foldy–Wouthuysen transformation. Extra new terms were found, and we discuss their possible physical applications. The main point of this work is to detail the procedure to get the general result. We explicitly present the choice of parametrization we used on the initial Hamiltonian and the motivations to take it. We emphasize that the final equations can depend on this choice, and it is possible to prevent the manipulations of the quadratic Hamiltonian that become extremely cumbersome. More importantly, it is done in such a way that the transformed equations allow the direct separation into mass, kinetic, and interaction correction terms to the original TBMT equation. [ABSTRACT FROM AUTHOR]

It is shown that the breaking of azimuthal symmetry during the oblique entry of relativistic particles into a thin target leads to oscillations of the spectral-angular density of polarized Cherenkov radiation along the azimuthal angle. The effect of modulation of the angular distribution of Cherenkov radiation can be observed in quartz glass on individual spectral lines in the optical and near ultraviolet ranges. The interference maxima have a small angular width not exceeding 10–2 rad. The effect can be used in the diagnostics of the angular characteristics of beams of accelerated relativistic particles. [ABSTRACT FROM AUTHOR]

We present the development of a flexible tape-drive target system to generate and control secondary high-intensity laser-plasma sources. Its adjustable design permits the generation of relativistic MeV particles and x rays at high-intensity (i.e., ≥1 × 1018 W cm−2) laser facilities, at high repetition rates (>1 Hz). The compact and robust structure shows good mechanical stability and a high target placement accuracy (<4 μm RMS). Its compact and flexible design allows for mounting in both the horizontal and vertical planes, which makes it practical for use in cluttered laser-plasma experimental setups. The design permits ∼170° of access on the laser-driver side and 120° of diagnostic access at the rear. A range of adapted apertures have been designed and tested to be easily implemented to the targetry system. The design and performance testing of the tape-drive system in the context of two experiments performed at the COMET laser facility at the Lawrence Livermore National Laboratory and at the Advanced Lasers and Extreme Photonics (ALEPH) facility at Colorado State University are discussed. Experimental data showing that the designed prototype is also able to both generate and focus high-intensity laser-driven protons at high repetition rates are also presented. [ABSTRACT FROM AUTHOR]

Earth's radiation belts are extremely important for space weather because they can store and accelerate particles to relativistic energies, which can have a potential impact on satellite functionality, communications, and navigation systems. The FORESAIL consortium wants to measure these high-energy particle fluxes to understand the dynamics of the radiation belts with its satellite mission Foresail-2. The mission aims to measure magnetic ultra low frequency waves and the plasma environment in the magnetosphere around Earth. The captured data will help to improve our understanding of space weather, and in particular the dynamics of Earth's radiation belts during periods of large disturbances inside the magnetosphere. A mission design analysis and several trade-off studies are conducted to find the requirements for the science payloads and spacecraft avionics design. Deducted from these requirements, four different payloads are proposed to gather science data in a highly elliptical orbit such as a geostationary transfer orbit. The precision magnetometer uses flux-gate technology to measure magnetic waves from 1 mHz to 10 Hz. The spin scanning particle telescope is built around a detector stack to measure electron spectra in the range of 30 keV to 10 MeV. Additionally, this mission serves as a technology demonstrator for the Coulomb drag experiment which proposes a new kind of electric solar wind sail utilising the Coulomb drag force imposed onto a 300 m long tether. The fourth payload investigates multilayer radiation shielding and single event effects. All payloads will be supported by a newly developed 6U platform using mostly commercial off-the-shelf components. Its proposed avionics face several unique design requirements rising from the payloads and the preferred highly elliptical orbit for this mission. [ABSTRACT FROM AUTHOR]

Pix.PAN is a compact cylindrical magnetic spectrometer, intended to provide excellent high energy particle measurements under high rate and hostile operating conditions in space. Its principal design is composed of two Halbach-array magnetic sectors and six Timepix4-based tracking layers; the latest hybrid silicon pixel detector readout ASIC designed. Due to Pix.PAN's compact and relatively simple design, it has the potential to be used for space missions exploring with measurements of unprecedented precision, high energy particles in radiation belts and the heliophere (solar energetic particles, anomalous and galactic cosmic rays). In this white paper, we discuss the design and expected performance of Pix.PAN for COMPASS (Comprehensive Observations of Magnetospheric Particle Acceleration, Sources, and Sinks), a mission concept submitted to NASA's Call "B.16 Heliophysics Mission Concept Studies (HMCS)" in 2021 that targets the extreme high energy particle environment of Jupiter's inner radiation belts. We also discuss PixPAN's operational conditions and interface requirements. The conceptual design shows that is possible to achieve an energy resolution of<12% for electrons in the range of 10 MeV-1 GeV and<35% for protons between ∼ 200 MeV to a few GeV. Due to the timestamp precision of Timepix4, a time resolution (on an instrument level) of about 100 ps can be achieved for time-of-flight measurements. In the most intense radiation environments of the COMPASS mission, Pix.PAN is expected to have a maximum hit rate of 44 MHz cm 2 which is below the design limit of 360 MHz cm 2 of Timepix4. Finally, a sensor design is proposed which allows the instrument to operate with a power budget of 20W without the loss of scientific performance. [ABSTRACT FROM AUTHOR]

Most bridge failures result from scouring around bridge piers, resulting in economic losses and risks to public safety. The conventional equations for predicting the depth of scour at bridge piers have several limitations: (1) They mainly use regression-based techniques that cannot robustly capture the nonlinear relationship between the scour depth and its effective variables; (2) they are applicable only to a narrow range of variability of data; and (3) they are typically calibrated using laboratory data rather than field measurements and thus cannot simulate the prototype environment. To overcome these limitations, in this study, three novel hybrid machine learning methods: particle swarm optimization - extreme gradient boosting (PSO -- XGBoost), red fox optimization - XGBoost (RFO -- XGBoost), and relativistic particle swarm optimization - XGBoost (RPSO -- XGBoost) are applied to estimate the scour depth around circular bridge piers, and their effectiveness is validated using three statistical metrics, i.e. the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²). RPSO -- XGBoost generates the best results for both dimensional and dimensionless data. Moreover, the proposed approaches outperform the state-of-the-art techniques. The SHapley Additive exPlanations (SHAP) method is used to assess the relative significance of the contributing factors for predicting the scour depth. [ABSTRACT FROM AUTHOR]

In quantum scattering theory, the time evolution of a physical system can be described as a series of unitary transformations. The operator of this transformation will be denoted S ̂ ; the corresponding matrix is the Ŝ-matrix (scattering matrix). This last object contains all the information on the broadcast process associated with the operator S ̂ The present work has two objectives: To develop the one-dimensional formalism of the scattering matrix of relativistic particles of spin-s (s = 0, 1/2) in the presence of a localized electromagnetic field on the one hand and on the other hand to analyze the solutions of the problem of scattering states of relativistic particles of spin-s in interaction with some localized scalar potentials via the S ̂ -matrix formalism. [ABSTRACT FROM AUTHOR]

Large wind kinetic power of Wolf-Rayet (WR) stars make them ideal targets in low radio frequencies to search for non-thermal emission due to relativistic particle acceleration. In this paper, we present observations of two WR stars, WR 114 and WR 142, in Band 4 (550–950 MHz) and Band 5 (1050–1450 MHz) using the upgraded Giant Meterwave Radio Telescope. Neither star is detected in the observed frequency bands, nor extended emission associated with them. The upper limit to the free–free radio emission from the stellar wind enables us to constrain the mass-loss rate of WR 114 to |$\lesssim \rm 10^{-5}\, M_{ \odot }\, yr^{-1}$|⁠ ; this is a factor three smaller than previously estimated using spectroscopic modelling. If we further assume that the WR stars are binaries, the non-detection of synchrotron emission from the putative wind collision region implies that the stars are either in very wide binary systems away from periastron, or that the stars are in close binary systems with an orbital separation <70 AU for WR 114 and <20 AU for WR 142. The non-detection of low-frequency radio emission from these two systems thus provides evidence that narrows their nature, though it does not rule them out as bona fide particle-accelerating colliding-wind binaries. [ABSTRACT FROM AUTHOR]

Electromagnetic fields of relativistic charged particles have a broad frequency spectrum and a sophisticated spatial structure. Field lines offer a visual representation of this spatial structure. In this article, we derive a general set of equations for the field lines of any moving charged particle. The electric field lines are completely determined by the unit vector from the retarding point to the observation point. After proper transformations, the field line equations describe the rotation of this vector with an angular velocity coinciding with Thomas precession. In some cases, including all planar trajectories, the field line equations reduce to linear differential equations with constant coefficients. We present a detailed derivation of these equations and their general analytical solution. We then illustrate this method by constructing field lines for the "figure eight" motion of an electric charge moving under the influence of a plane wave, including complex field lines in three dimensions. [ABSTRACT FROM AUTHOR]

A basic leapfrog integrator and its energy-preserving and variational/symplectic variants are proposed and studied for the numerical integration of the equations of motion of relativistic charged particles in an electromagnetic field. The methods are based on a four-dimensional formulation of the equations of motion. Structure-preserving properties of the numerical methods are analyzed, in particular conservation and long-time near-conservation of energy and mass shell as well as preservation of volume in phase space. In the non-relativistic limit, the considered methods reduce to the Boris algorithm for non-relativistic charged-particle dynamics and its energy-preserving and variational/symplectic variants. [ABSTRACT FROM AUTHOR]

Originating from the Hamiltonian of a single qubit system, the phenomenon of the avoided level crossing is ubiquitous in multiple branches of physics, including the Landau–Zener transition in atomic, molecular, and optical physics, the band structure of condensed matter physics and the dispersion relation of relativistic quantum physics. We revisit this fundamental phenomenon in the simple example of a spinless relativistic quantum particle traveling in (1+1)-dimensional space-time and establish its relation to a spin-1/2 system evolving under a PT -symmetric Hamiltonian. This relation allows us to simulate 1-dimensional eigenvalue problems with a single qubit. Generalizing this relation to the eigenenergy problem of a bulk system with N spatial dimensions reveals that its eigenvalue problem can be mapped onto the time evolution of the edge state with (N − 1) spatial dimensions governed by a non-Hermitian Hamiltonian. In other words, the bulk eigenenergy state is encoded in the edge state as a hologram, which can be decoded by the propagation of the edge state in the temporal dimension. We argue that the evolution will be PT -symmetric as long as the bulk system admits parity symmetry. Our work finds the application of PT -symmetric and non-Hermitian physics in quantum simulation and provides insights into the fundamental symmetries. [ABSTRACT FROM AUTHOR]

Recently, topological materials (TMs) have attracted attention from various scientists. Their electronic properties are governed by relativistic particles called Dirac fermions which, in some cases, possess no masses and move in solids with the speed of light. In addition to the unique particles, such materials exhibit unprecedented electronic properties because of the quantum effects (interference between wavefunctions). Examples include nodal-line materials (NLMs), where metallic or even superconducting properties may appear only at the surface of the single crystals of insulators. Thus far, whether they be organic or inorganic compounds, TMs have hardly been discovered except for the zero-gap conductors (ZGCs), because there is no guideline on how to develop such unusual materials. In this work, we prepared a new organic charge–transfer complex, α′-STF2IBr2 (STF = bis(ethylenedithio)diselenadithiafulvalene), which measured the electrical and magnetic properties and calculated the band structure and intermolecular interactions. A close comparison with those of α-STF2I3, being established as a ZGC at p > 12–15 kbar, revealed that α′-STF2IBr2 is also closely related to it, but belongs to a different type of TMs, namely NLMs. This finding will accelerate the successive findings of NLMs to elucidate the mechanism of their unique electronic properties. [ABSTRACT FROM AUTHOR]

We consider relativistic plasma particles subjected to an external gravitation force in a 3D half space whose boundary is a perfect conductor. When the mean free path is much bigger than the variation of electromagnetic fields, the collision effect is negligible. As an effective PDE, we study the relativistic Vlasov–Maxwell system and its local-in-time unique solvability in the space-time locally Lipschitz space, for several basic mesoscopic (kinetic) boundary conditions: the inflow, diffuse, and specular reflection boundary conditions. We construct weak solutions to these initial-boundary value problems and study their locally Lipschitz continuity with the aid of a weight function depending on the solutions themselves. Finally, we prove the uniqueness of a solution, by using regularity estimate and realizing the Gauss's law at the boundary within Lipschitz continuous space. [ABSTRACT FROM AUTHOR]

The analysis of the spatiotemporal picture of particle radiation in relativistic heavy-ion collisions in terms of correlation femtoscopy scales, emission, and source functions allows one to probe the character of the evolution of the system created in the collision. Realistic models, such as the integrated hydrokinetic model (iHKM), used in the present work, are able to simulate the entire evolution process of strongly interacting matter produced in high-energy nuclear collisions. The mentioned model describes all the stages of the system's evolution, including thermalisation and hydrodynamisation, which can help researchers figure out the specific details of the process and better understand the formation mechanisms of certain observables. In the current paper, we investigated the behaviour of the pion and kaon interferometry radii and their connection with emission functions in ultrarelativistic heavy-ion collisions at the Large Hadron Collider within iHKM. We focused on the study of the emission time scales at different energies for both particle species (pions and kaons) aiming to gain deeper insight into relation of these scales and the peculiarities of the mentioned system's collective expansion and decay with the experimentally observed femtoscopy radii. One of our main interests was the problem of the total system's lifetime estimation based on the femtoscopy analysis. [ABSTRACT FROM AUTHOR]

A molecular formalism based on a decomposed energy space constructed by a modular basis of matter and radiation is proposed for relativistic quantum mechanics. In the proposed formalism, matter radiation interactions are incorporated via the dynamical transformation of the coupled particle/antiparticle pair in a multistate quantum mechanical framework. This picture generalizes relativistic quantum mechanics at minimal cost, unlike quantum field theories, and the relativistic energy–momentum relation is interpreted as energy transformations among different modules through a multistate Schrödinger equation. The application of two-state and four-state systems using a time-dependent Schrödinger equation with pair states as a basis leads to well-defined solutions equivalent to those obtained from the Klein–Gordon equation and the Dirac equation. In addition, the particle–antiparticle relationship is well manifested through a particle conjugation group. This work provides new insights into the underlying molecular mechanism of relativistic dynamics and the rational design of new pathways for energy transformation. [ABSTRACT FROM AUTHOR]

Fast radio bursts (FRBs) are still a mystery in contemporary astrophysics. Unlike many other astronomical objects whose basic physical mechanism is already identified and the research on which focuses mainly on refining details, FRBs are still largely unknown regarding their source(s) and radiation mechanism(s). To make progress in the field, a "top-down" or "detective's approach" is desirable. I will summarize how some key observational facts have narrowed down the options to interpret FRBs and show that at least some FRBs are produced from the magnetospheres of highly magnetized neutron stars (or magnetars). I will also argue that the current data seem to favor a type of coherent inverse Compton scattering process by relativistic particle bunches off a low-frequency wave propagating in the magnetosphere. This brief contribution is a shorter version of an extended review to be published in Reviews of Modern Physics, and it was written as a tribute to the 80th anniversary of Remo Ruffini. [ABSTRACT FROM AUTHOR]

This work explores the spectral behavior of interacting many-body systems — gravitating dust solutions (galaxy formations and black hole clusters) and Brownian fluids. The eigenvalue dynamics of these systems are then represented by the two-dimensional Yang–Mills field (i.e. spectral projection). The interacting particles in the many-body systems are associated with random matrices of dimensions, N. The Painlevé II dynamical system is shown to surface at large N (N → ∞); when the mentioned Yang–Mills field is configured in a specific way. Critical phenomena (Douglas–Kazakov phase transition) of the interacting many-body systems at large N were attained via the spectral projection of the mentioned physical systems. In addition, the existence of instantons (spectral Dirac monopoles) in the strong coupling phase was shown during phase transition. [ABSTRACT FROM AUTHOR]

The new relativistic semiclassical leptonic decay widths of vector mesons as the relativistic systems of two quarks with arbitrary masses interacting by means of the funnel-type potentials with Coulomb interaction are obtained. The behavior of the relativistic leptonic decay widths of vector mesons is investigated. Comparison of the behavior for new expression with its relativistic spinless analog is given. Consideration is conducted within the framework of completely covariant quasipotential approach in the Hamiltonian formulation of quantum field theory via a transition to the relativistic configurational representation in the case of two relativistic spin particles of arbitrary masses. [ABSTRACT FROM AUTHOR]

One of the most characteristic features of relativistic particle dynamics at cyclotron resonances is the stepwise dependence of energy and momentum on time [V. A. Buts and A. G. Zagorodny, Phys. Plasmas 28(2), 022311 (2021)]. The reason for these steps is the phase synchronization of charged particles and waves. To describe other features, we introduce new dependent variables in this paper. These variables allow us to find a convenient representation of the relativistic resonance that fits the numerical results and thus establish new expressions for the stationary phase, as well as analytically describe effects that were previously visible only in numerical experiment. In particular, the temporal width of the steps, the dynamics of particles on the steps, and, most importantly, the moments of random jumps of particles from one step to another are determined. Analysis of the obtained results opens the possibility to find the conditions for the unlimited acceleration of electrons by transverse electromagnetic waves in a vacuum without an external magnetic field. [ABSTRACT FROM AUTHOR]

Relativistic jets from (supermassive) black holes are typically observed in nonthermal emission, caused by highly relativistic electrons. Here, we study the interrelation between three-dimensional (special) relativistic magnetohydrodynamics, and particle acceleration in these jets. We inject Lagrangian particles into the jet that are accelerated through diffusive shock acceleration and radiate energy via synchrotron and inverse Compton processes. We investigate the impact of different injection nozzles on the jet dynamics, propagation, and the spectral energy distribution of relativistic particles. We consider three different injection nozzles—injecting steady, variable, and precessing jets. These jets evolve with substantially different dynamics, driving different levels of turbulence and shock structures. The steady jet shows a strong, stationary shock feature, resulting from a head-on collision with an inner back-flow along the jet axis—a jet inside a jet. This shock represents a site for highly efficient particle acceleration for electrons up to a few tens of TeV and should be visible in emission as a jet knot. Overall, we find that the total number of shocks is more essential for particle acceleration than the strength of the shocks. The precessing jet is most efficient in accelerating electrons to high energies reaching even few hundred TeVs, with power-law index ranging from 2.3 to 3.1. We compare different outflow components, such as the jet and the entrained material concerning particle acceleration. For the precessing nozzle, the particle acceleration in the entrained material is as efficient as that in the jet stream. This is due to the higher level of turbulence induced by the precession motion. [ABSTRACT FROM AUTHOR]

We study the quantum evolution of many-body Fermi gases in three dimensions, in arbitrarily large domains. We consider both particles with non-relativistic and with relativistic dispersion. We focus on the high-density regime, in the semiclassical scaling, and we consider a class of initial data describing zero-temperature states. In the non-relativistic case we prove that, as the density goes to infinity, the many-body evolution of the reduced one-particle density matrix converges to the solution of the time-dependent Hartree equation, for short macroscopic times. In the case of relativistic dispersion, we show convergence of the many-body evolution to the relativistic Hartree equation for all macroscopic times. With respect to previous work, the rate of convergence does not depend on the total number of particles, but only on the density: in particular, our result allows us to study the quantum dynamics of extensive many-body Fermi gases. [ABSTRACT FROM AUTHOR]

We study the acceleration of charged particles by ultra-relativistic shocks using test-particle Monte Carlo simulations. Two field configurations are considered: (i) shocks with uniform upstream magnetic field in the plane of the shock, and (ii) shocks in which the upstream magnetic field has a cylindrical geometry. Particles are assumed to diffuse in angle due to frequent non-resonant scattering on small-scale fields. The steady-state distribution of particles' Lorentz factors is shown to approximately satisfy d N /dγ ∝ γ−2.2 provided the particle motion is scattering dominated on at least one side of the shock. For scattering dominated transport, the acceleration rate scales as t acc ∝  t 1/2, though recovers Bohm scaling t acc ∝  t if particles become magnetized on one side of the shock. For uniform field configurations, a limiting energy is reached when particles are magnetized on both sides of the shock. For the cylindrical field configuration, this limit does not apply, and particles of one sign of charge will experience a curvature drift that redirects particles upstream. For the non-resonant scattering model considered, these particles preferentially escape only when they reach the confinement limit determined by the finite system size, and the distribution approaches the escapeless limit d N /dγ ∝ γ−1. The cylindrical field configuration resembles that expected for jets launched by the Blandford & Znajek mechanism, the luminous jets of active galactic nuclei and gamma-ray bursts thus provide favourable sites for the production of ultra-high-energy cosmic rays. [ABSTRACT FROM AUTHOR]

Galaxy clusters are assembled via merging of smaller structures, in a process that generates shocks and turbulence in the intra cluster medium and produces radio diffuse emission in the form of halos and relics. The cluster pair A 399–A 401 represents a special case: both clusters host a radio halo. Recent Low Frequency Array (LOFAR) observations at 140 MHz revealed the presence of a radio bridge connecting the two clusters along with two relic candidates. These relics include one South of A 399 and the other in between the two clusters, in proximity of a shock front detected in X-ray observations. In this paper we present observations of the A 399–A 401 cluster pair at 1.7, 1.4, 1.2 GHz, and 346 MHz from the Westerbork Synthesis Radio Telescope (WSRT). We detect the radio halo in the A 399 cluster at 346 MHz, extending up to ∼650 kpc and with a 125 ± 6 mJy flux density. Its spectral index between 140 MHz and 346 MHz is α = 1.75 ± 0.14. The two candidate relics are also seen at 346 MHz and we determine their spectral indices to be α = 1.10 ± 0.14 and α = 1.46 ± 0.14. The low surface brightness bridge connecting the two clusters is below the noise level at 346 MHz therefore we constrain the bridge average spectral index to be steep, i.e. α > 1.5 at 95 per cent confidence level. This result favours the scenario where dynamically-induced turbulence is a viable mechanism to reaccelerate a population of mildly relativistic particles and amplify magnetic fields on scales of a few Mpcs. [ABSTRACT FROM AUTHOR]

The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with n wires, each corresponding to one qubit, we encode 2 n position states. The data necessary to define an arbitrary position-dependent coin operator is therefore exponential in n. Hence, the exponentiality will necessarily appear somewhere in our circuits. We first propose a circuit implementing the position-dependent coin operator, that is naive, in the sense that it has exponential depth and implements sequentially all appropriate position-dependent coin operators. We then propose a circuit that "transfers" all the depth into ancillae, yielding a final depth that is linear in n at the cost of an exponential number of ancillae. The main idea of this linear-depth circuit is to implement in parallel all coin operators at the different positions. Reducing the depth exponentially at the cost of having an exponential number of ancillae is a goal which has already been achieved for the problem of loading classical data on a quantum circuit (Araujo in Sci Rep 11:6329, 2021) (notice that such a circuit can be used to load the initial state of the walker). Here, we achieve this goal for the problem of applying a position-dependent coin operator in a discrete-time quantum walk. Finally, we extend the result of Welch (New J Phys 16:033040, 2014) from position-dependent unitaries which are diagonal in the position basis to position-dependent 2 × 2 -block-diagonal unitaries: indeed, we show that for a position dependence of the coin operator (the block-diagonal unitary) which is smooth enough, one can find an efficient quantum-circuit implementation approximating the coin operator up to an error ϵ (in terms of the spectral norm), the depth and size of which scale as O (1 / ϵ) . A typical application of the efficient implementation would be the quantum simulation of a relativistic spin-1/2 particle on a lattice, coupled to a smooth external gauge field; notice that recently, quantum spatial-search schemes have been developed which use gauge fields as the oracle, to mark the vertex to be found (Zylberman in Entropy 23:1441, 2021), (Fredon arXiv:2210.13920). A typical application of the linear-depth circuit would be when there is spatial noise on the coin operator (and hence a non-smooth dependence in the position). [ABSTRACT FROM AUTHOR]