Symmetric Density Research Articles

Variety of disc wind-driven explosions in massive rotating stars – II. Dependence on the progenitor

Abstract We assess the variance of supernova(SN)-like explosions associated with the core collapse of rotating massive stars into a black hole-accretion disc system under changes in the progenitor structure. Our model of the central engine evolves the black hole and the disc through the transfer of matter and angular momentum and includes the contribution of the disc wind. We perform two-dimensional, non-relativistic, hydrodynamics simulations using the open-source hydrodynamic code Athena++, for which we develop a method to calculate self-gravity for axially symmetric density distributions. For a fixed model of the wind injection, we explore the explosion characteristics for progenitors with zero-age main-sequence masses from 9 to 40 M⊙ and different degrees of rotation. Our outcomes reveal a wide range of explosion energies with Eexpl spanning from ∼0.3 × 1051 erg to >8 × 1051 erg and ejecta mass Mej from ∼0.6 to >10M⊙. Our results are in agreement with some range of the observational data of stripped-envelope and high-energy SNe such as broad-lined type Ic SNe, but we measure a stronger correlation between Eexpl and Mej. We also provide an estimate of the 56Ni mass produced in our models which goes from ∼0.04 M⊙ to ∼1.3 M⊙. The 56Ni mass shows a correlation with the mass and the angular velocity of the progenitor: more massive and faster rotating progenitors tend to produce a higher amount of 56Ni. Finally, we present a criterion that allows the selection of a potential collapsar progenitor from the observed explosion energy.

Self-consistent electron density with shell structure using neural network-based Pauli potential.

The orbital-free density functional theory (OF-DFT) based method is a convenient tool to carry out electronic structure calculations scaling almost linearly with the number of electrons. However, the main impediment in the application of this method is the unavailability of the accurate form for the non-interacting kinetic energy functional in terms of electron density. The Pauli kinetic energy functional is the unknown part of the kinetic energy functional, and the corresponding Pauli potential appears in the governing Euler equation. In the present study, we present a feed-forward neural network (NN) approach to represent the Pauli potential of a group of atomic systems possessing spherically symmetric ground-state densities. This NN-based representation of Pauli potential combined with the Hohenberg-Kohn variational principle yields self-consistent radial densities that accurately exhibit the correct atomic shell structure. For this approach, the electron density in the form of a grid serves as the input to the NN model. In addition, we calculated the non-interacting kinetic energy by summing the Pauli kinetic energy, derived from the NN-based Pauli potential, and the von Weizsäcker kinetic energy. Our results demonstrate high accuracy for smaller atoms, while larger atoms exhibit greater deviations when compared with smaller atoms. The method presented in this paper provides an efficient way to calculate the Pauli potential and the Pauli kinetic energy without the need for functional derivatives. Our study represents a significant step forward in the application of machine learning techniques to OF-DFT, showcasing the potential of NNs in improving the accuracy and efficiency of quantum mechanical calculations in atomic systems.

Towards a unified fold-cusp model for bond polarity scaling: electron rearrangements in the pyrolytic isomerization of cubane to cyclooctatetraene.

This study meticulously examines the criteria for assigning electron rearrangements along the intrinsic reaction coordinate (IRC) leading to bond formation and breaking processes during the pyrolytic isomerization of cubane (CUB) to 1,3,5,7-cyclooctatetraene (COT) from both thermochemical and bonding perspectives. Notably, no cusp-type function was detected in the initial thermal conversion step of CUB to bicyclo[4.2.0]octa-2,4,7-triene (BOT). Contrary to previous reports, all relevant fluxes of the pairing density must be described in terms of fold unfolding. The transannular ring opening in the second step highlights characteristics indicative of a cusp-type catastrophe, facilitating a direct comparison with fold features. This fact underscores the critical role of density symmetry persistence near topographical events in determining the type of bifurcation. A fold-cusp unified model for scaling the polarity of chemical bonds is proposed, integrating ubiquitous reaction classes such as isomerization, bimolecular nucleophilic substitution, and cycloaddition. The analysis reveals that bond polarity index (BPI) values within the [0, 10-5] au interval correlate with cusp unfolding, whereas fold spans over a broader [10-3, ∞) au spectrum. These insights emphasize that the cusp polynomial is suitable for describing chemical processes involving symmetric electron density distributions, particularly those involving homolytic bond cleavages; in contrast, fold characterizes most chemical events. Geometry optimization and frequency calculations were conducted using various DFT functionals. In line with recent findings concerning the rigorous application of BET, the characterization of bond formations and scissions via unfoldings was carried out by carefully monitoring the determinant of the Hessian matrix at all potentially degenerate CPs and their relative distance. The computed gas-phase activation enthalpies strongly align with experimental values, stressing the adequacy of the chosen levels of theory in describing the ELF topography along the IRC. The BPI was determined using the methodology proposed by Allen and collaborators.

Study of light deflection and shadow in the Rindler-like Schwarzschild solution

In this paper, we calculate the deflection angle in the non-plasma medium by expanding the Keeton–Petters approach. We use analysis to determine how non-magnetic plasma affects the shadow of a Schwarzschild–Rindler black hole. We only consider the spherically symmetric case in which the shadow is circular. It is assumed that the plasma is independent of pressure and magnetization. From a specified spherically symmetric spacetime, we compute the results for a spherically symmetric plasma density. Our main purpose is to derive analytically a formula for the orbital radius of the shadow. Due to the diffusive nature of plasma, the shadow’s radius is influenced by the frequency of the photons. The impacts of the non-magnetic plasma are important in radio establishment. We determine that the non-magnetic plasma incorporates a decreasing impact on the shadow size for a distant observer from the Schwarzschild–Rindler black hole. Moreover, we graphically analyze the impacts of different parameters on the shadow of the corresponding black hole.

Acoustic Wake in a Singular Isothermal Profile: Dynamical Friction and Gravitational-wave Emission

We consider the motion of a circularly moving perturber in a self-gravitating, collisional system with a spherically symmetric density profile. We concentrate on the singular isothermal sphere, which, despite its pathological features, admits a simple polarization function in linear response theory. This allows us to solve for the acoustic wake trailing the perturber and the resulting dynamical friction, in the limit where the self-gravity of the response can be ignored. In a steady state and for subsonic velocities v p < c s , the dynamical friction torque Fφ∝vp3 is suppressed for perturbers orbiting in an isothermal sphere relative to the infinite, homogeneous medium expectation F φ ∝ v p . For highly supersonic motions, both expectations agree and are consistent with a local approximation to the gravitational torque. At fixed resolution (a given Coulomb logarithm), the response of the system is maximal for Mach numbers near the constant circular velocity of the singular isothermal profile. This resonance maximizes the gravitational-wave (GW) emission produced by the trailing acoustic wake. For an inspiral around a massive black hole of mass 106 M ⊙ located at the center of a (truncated) isothermal sphere, this GW signal could be comparable to the vacuum GW emission of a black hole binary at subnanohertz frequencies when the small black hole enters the Bondi sphere of the massive one. The exact magnitude of this effect depends on departures from hydrostatic equilibrium and on the viscosity present in any realistic astrophysical fluid, which are not included in our simplified description.

Experimental characterization of the effective acoustic properties of anisotropic porous materials via free-field measurements

Porous media are commonly described as effective isotropic fluid materials, such that their acoustic properties can be adequately determined from their bulk modulus and dynamic density. Most acoustic absorbents, however, possess a marked anisotropy, which influences their acoustical behavior and the parameters necessary to deduce it. Specifically, the influence of anisotropy translates into a full symmetric density tensor (in place of a scalar). This study presents a method for retrieving the bulk modulus and all six components of the density tensor of a layer of porous material from reflection coefficients measured in free field with an array of microphones. The procedure consists in expressing the sound field measured in the vicinity of the layer as a superposition of plane waves, from which the surface impedance and the reflection coefficient are reconstructed. The reflection properties, as well as the pressure at the rigid backing interface, are estimated for various source positions (i.e., various angles of incidence) and an inverse problem is formulated to infer the effective fluid parameters. The validity of the method is examined experimentally on a manufactured porous material, and the resulting fluid parameters compared with experimental results obtained from reflection and transmission coefficients measured in an impedance tube.

Electric Field Features and Charge Behavior in Oil-Pressboard Composite Insulation under Impulse Voltage

Oil-pressboard/paper insulation materials are essential in transformers for ensuring their safe and stable operation, primarily due to their roles in spatial electric field distribution and charge migration mechanisms. Current spatial distribution analyses rely on computational methods that lack empirical validation, particularly for oil-pressboard/paper composites. This study leverages the principles of the Kerr electro-optic effect to develop a rapid measurement platform for electric fields within oil-pressboard/paper insulation under impulse voltage conditions, which measures the spatial electric field characteristics using Cu-Cu and Al-Al electrodes under various scenarios: with asymmetric and symmetric pressboard coverage and different numbers of insulating paper layers. Findings indicated: (1) In asymmetric pressboard models, Cu-Cu electrodes exhibit a consistent peak electric field of approximately 16 kV/mm, while Al-Al electrodes show peak values of 18.13 kV/mm and −14.98 kV/mm. Charge density patterns are similar, with Cu-Cu at about 68 μC/m2 and Al-Al at 11.2 μC/m2 and −124.8 μC/m2. (2) Symmetric models present consistent peak electric fields and charge densities for both polarities. (3) Increasing insulating paper layers elevates electric field strengths. Both electrodes show the similar peak field of about 17 kV/mm with differing paper layers due to higher charge injection from the Al electrode. (4) Utilizing the Schottky effect and field emission principles, the study clarifies charge generation and migration mechanisms. These insights could provide a theoretical foundation for designing and verifying oil-pressboard/paper insulation structures in transformers.

Comparison of different estimation methods for the inverse power perk distribution with applications in engineering and actuarial sciences

Introducing the Inverse Power Perk distribution, this paper presents a versatile probability distribution designed to model positively skewed data with unprecedented flexibility. Building upon the Perk distribution, it accommodates a wide range of shapes including right-skewed, J-shaped, reversed J-shaped, and nearly symmetric densities, as well as hazard rates exhibiting various patterns of increase and decrease. The paper delves into the mathematical properties of this novel distribution and offers a comprehensive overview of estimation techniques, including maximum likelihood estimators, ordinary least square estimators, percentile-based estimators, maximum product of spacing estimators, Cramer-von Mises, weighted least squares estimators, and Anderson-Darling estimators. To assess the performance of these estimation methods across different sample sizes, Monte Carlo simulations are conducted. Through comparisons of average absolute error and mean squared error, the efficacy of each estimator is evaluated, shedding light on their suitability for both small and large samples. In a practical application, three real datasets, including insurance data, are employed to demonstrate the versatility of the current model, when comparing to existing alternatives. The IPP distribution offers significant advantages over traditional distributions, particularly in its superior ability to model tail risks, making it an invaluable tool for practitioners dealing with extreme values and rare events. Its computational efficiency further sets it apart, enabling more robust and faster analysis in large-scale datasets.This empirical analysis further underscores the utility and adaptability of the Inverse Power Perk model in capturing the nuances of diverse datasets, thereby offering valuable insights for practitioners in various fields.

In Situ Measurement of Track Shape in Cold Spray Deposits

Cold spray is a material deposition technology with a high deposition rate and attractive material properties that has great interest for additive manufacturing (AM). Successfully cold spraying free-form parts that are close to their intended shape, however, requires knowing the fundamental shape of the sprayed track, so that a spray path can be planned that builds up a part from a progressively overlaid sequence of tracks. Several studies have measured track shape using ex situ or quasi-in situ approaches, but an in situ measurement approach has, to the authors’ knowledge, not yet been reported. Furthermore, most studies characterize the track cross section as a symmetric Gaussian probability density function (PDF) with fixed shape parameters. The present study implements a novel in situ track shape measurement technique using a custom-built nozzle-tracking laser profilometry system. The shape of the track is recorded throughout the duration of a spray, allowing a comprehensive investigation of how the track shape evolves as the deposit is built up. A skewed track shape is observed—likely due to the side-injection design of the applicator used—and a skewed Gaussian PDF—a more generalized version of the standard Gaussian PDF—is fit to the track profile. The skewed Gaussian fit parameters are studied across two principal nozzle path parameters: nozzle traverse speed and step size. Empirical relationships between the fit parameters and the nozzle path parameters are derived, and a physics-based inverse relationship between nozzle speed and powder mass deposition rate is obtained. One of the fit parameters is shown to be an effective means of monitoring deposition efficiency during spraying. Overall, the approach presents a promising means of measuring track shape, in situ, as well as modeling it using a more general shape function.

Ensemble Generalization of the Perdew-Zunger Self-Interaction Correction: A Way Out of Multiple Minima and Symmetry Breaking.

The Perdew-Zunger (PZ) self-interaction correction (SIC) is an established tool to correct unphysical behavior in density functional approximations. Yet, the PZ-SIC is well-known to sometimes break molecular symmetries. An example of this is the benzene molecule, for which the PZ-SIC predicts a symmetry-broken electron density and molecular geometry, since the method does not describe the two possible Kekulé structures on an even footing, leading to local minima [Lehtola et al. J. Chem. Theory Comput. 2016, 12, 3195]. The PZ-SIC is often implemented with Fermi-Löwdin orbitals (FLOs), yielding the FLO-SIC method, which likewise has issues with symmetry breaking and local minima [Trepte et al. J. Chem. Phys. 2021, 155, 224109]. In this work, we propose a generalization of the PZ-SIC─the ensemble PZ-SIC (E-PZ-SIC) method─which shares the asymptotic computational scaling of the PZ-SIC (albeit with an additional prefactor). The E-PZ-SIC is straightforwardly applicable to various molecules, merely requiring one to average the self-interaction correction over all possible Kekulé structures, in line with chemical intuition. We showcase the implementation of the E-PZ-SIC with FLOs, as the resulting E-FLO-SIC method is easy to realize on top of an existing implementation of the FLO-SIC. We show that the E-FLO-SIC indeed eliminates symmetry breaking, reproducing a symmetric electron density and molecular geometry for benzene. The ensemble approach suggested herein could also be employed within approximate or locally scaled variants of the PZ-SIC and its FLO-SIC versions.

A new extension of the Gumbel distribution with biomedical data analysis

In the field of biomedical research, data characteristics often exhibit significant variability, challenging the applicability of classical Gumbel distribution for biomedical data modeling. To address this, this paper introduces a novel extension of the Gumbel model known as the odd beta prime Gumbel (OBP-Gum) model. Derived from the odd beta prime family, the new distribution exhibits greater kurtosis compared to the traditional Gumbel distribution. Importantly, the proposed distribution is designed to capture right-skewed, left-skewed, and nearly symmetric density functions, as well as increasing, decreasing, constant, and upside-down bathtub shapes for its hazard rate function, providing excellent curvature features for creating flexible statistical models for biomedical research. We derive the fundamental features of the OBP-Gum model, such as the quantile function, linear representations, moment generating function, moments, skewness, kurtosis, incomplete moments, and Rényi and Tsallis entropies. Parameter estimation for this new model is conducted using the maximum likelihood estimation method. A simulation study demonstrates the performance of the model parameters. The empirical findings, based on applications to two biomedical datasets, suggest that the OBP-Gum distribution outperforms existing models, particularly in handling extreme observations. Instead of relying on conventional models for decision-making, this research provides relevant stakeholders with an improved statistical distribution for more accurate biomedical data modeling.

Helicity of magnetic fields associated with non-relativistic electron vortex beams

The helicities of the magnetic fields associated with non-relativistic electron vortex beams are considered for radially extended Bessel modes. Investigating the helicity density of this system lies in realizing the unique electric and magnetic properties of electron vortex beams that influence their interactions with matter. We have evaluated the vector potential components needed for the derivation of the magnetic helicity density and found that this has a non-zero distribution. This is attributed entirely to the cylindrically symmetric density flux of the electron beam, which scales with the winding number ℓ . It is also related to the magnetic moments of the electron oriented along the z-direction, giving rise to the z-component of the magnetic field. We obtain different helicity distributions for different signs of winding number ±ℓ , which confirms the chiral character of the magnetic fields associated with the electron vortex beam. The physical consequences of taking the spin current density into consideration are also examined. This allows a comparison to be made between the evaluated total current helicities, one with and one without including the spin-polarization.

Density functional theory from spherically symmetric densities: Ground and excited states of Coulomb systems.

Recently, Theophilou [J. Chem. Phys. 149, 074104 (2018)] proposed a peculiar version of the density functional theory by showing that the set of spherical averages of the density around the nuclei determines uniquely the external potential in atoms, molecules, and solids. Here, this novel theory is extended to individual excited states. The generalization is based on the method developed in the series of papers by Ayers, Levy, and Nagy [Phys. Rev. A 85, 042518 (2012)]. Generalized Hohenberg-Kohn theorems are proved to the set of spherically symmetric densities using constrained search. A universal variational functional for the sum of the kinetic and electron-electron repulsion energies is constructed. The functional is appropriate for the ground state and all bound excited states. Euler equations and Kohn-Sham equations for the set are derived. The Euler equations can be rewritten as Schrödinger-like equations for the square root of the radial densities, and the effective potentials in them can be expressed in terms of wave function expectation values. The Hartree plus exchange-correlation potentials can be given by the difference of the interacting and the non-interacting effective potentials.

Ultrasound‐Assisted Deposition of Sepia Melanin and Multiwalled Carbon Nanotubes on Carbon Cloth: Toward Sustainable Surface Engineering for Flexible Supercapacitors

AbstractThe rising global demand for energy requires, among others, sustainable energy storage devices. Biosourced redox‐active molecules are interesting for eco‐designed electrochemical energy storage as they increase the energy density of the electrodes adding the Faradaic (redox) storage mechanism to the electrostatic one. The engineering of the electrode surface and electrode surface/molecule interface is key to optimizing storage. Here, (i) electrodes prepared by ultrasound‐assisted modification of carbon cloth in the presence of Sepia melanin, a quinone macromolecule, and multiwalled carbon nanotubes (MWCNTs) and (ii) their use in flexible symmetric electrochemical capacitors assembled with polyvinyl alcohol (PVA)‐based hydrogel electrolyte is reported. Electrodes exhibit an areal capacitance as high as 274 mF cm−2. Corresponding semi‐solid‐state symmetric supercapacitors feature high energy density of 18 Wh kg−1, power density up to 221 W kg−1 (evaluated at 0.5 A g−1), outstanding cycling stability (100% capacitance retention, and 100% Coulombic efficiency after 10 000 cycles) along with excellent flexibility. This work contributes to the development of sustainable surface engineering approaches for environmentally benign electrochemical energy storage devices.

Asymmetric electronic deformation in graphene molecular capacitors

AbstractAsymmetric deformation density analysis is applied on bilayer graphene flakes as molecular capacitors to identify the extent of asymmetric distribution of electrons and holes when exposed to bias voltage. Three triangular, orthorhombic, and hexagonal symmetries for graphene flakes are considered in two sizes and electric field potential is applied along the vector perpendicular to graphene flakes' plane to simulate 1–4 V as the bias voltage applied to molecular‐scale capacitors The number of electrons responsible for asymmetric distribution of electrons and holes, and occupied to virtual transfer are calculated, and electric field deformation density analysis is also performed that shows distributions of electrons and holes are quite asymmetric for the orthorhombic symmetry, while for the other symmetries, they are almost image of each other. It was found that isosurfaces of deformation density distribution possess a multilayer structure and accretion and depletion of electrons can be taken place between flakes or outside the parallel flakes, and it is shown that bias voltage is able to significantly remove symmetry of electrons and holes distribution. Inspection of molecular orbitals showed that electric field could change the energetic order of molecular orbitals, so that occupancy inversion is occurred for the orthorhombic systems that is responsible for their extraordinary properties.

Fe-N co-doped carbon nanofibers with Fe3C decoration for water activation induced oxygen reduction reaction

ABSTRACT Proton activity at the electrified interface is central to the kinetics of proton-coupled electron transfer (PCET) reactions in electrocatalytic oxygen reduction reaction (ORR). Here, we construct an efficient Fe3C water activation site in Fe-N co-doped carbon nanofibers (Fe3C-Fe1/CNT) using an electrospinning-pyrolysis-etching strategy to improve interfacial hydrogen bonding interactions with oxygen intermediates during ORR. In situ Fourier transform infrared spectroscopy and density functional theory studies identified delocalized electrons as key to water activation kinetics. Specifically, the strong electronic perturbation of the Fe–N4 sites by Fe3C disrupts the symmetric electron density distribution, allowing more free electrons to activate the dissociation of interfacial water, thereby promoting hydrogen bond formation. This process ultimately controls the PCET kinetics for enhanced ORR. The Fe3C-Fe1/CNT catalyst demonstrates a half-wave potential of 0.83 V in acidic media and 0.91 V in alkaline media, along with strong performance in H2-O2 fuel cells and Al-air batteries.

Characterization of tensile properties of chain stitch structure fabric with negative Poisson’s ratio yarn

Negative Poisson’s ratio textiles have expanded deformation behavior and special mechanical properties under tension. According to the previous research, the negative Poisson’s ratio effect of fabrics was always lower than yarns. The main reason was that negative Poisson’s ratio yarns showed little structural deformation because of the fabric structures. In this study, chain stitch structure fabrics with negative Poisson’s ratio yarns as inserted weft yarns were designed and prepared. The effect of inserted weft yarns, symmetrical and parallelization arrangement and density on the Poisson’s ratio of chain stitch fabrics were tested and analyzed. The results showed that the negative Poisson’s ratio effect of fabrics was as similar as yarns and yarns in fabric. When the knitting loops provided fixation role in the fabrics, the negative Poisson’s yarns could also present obvious deformation behavior to successfully improve the expand effect of fabrics. Poisson’s ratio and porosity of fabrics under cyclic stretching were carried out to study the structure and property stability. The chain stitch structure fabrics with negative Poisson’s ratio are expected to provide more choices for improving the property and applicability.

Statistical analysis of the inverse power Zeghdoudi model: Estimation, simulation and modeling to engineering and environmental data

Abstract In this research, we investigate a brand-new two-parameter distribution as a modification of the power Zeghdoudi distribution (PZD). Using the inverse transformation technique on the PZD, the produced distribution is called the inverted PZD (IPZD). Its usefulness in producing symmetric and asymmetric probability density functions makes it the perfect choice for lifetime phenomenon modeling. It is also appropriate for a range of real data since the relevant hazard rate function has one of the following shapes: increasing, decreasing, reverse j-shape or upside-down shape. Mode, quantiles, moments, geometric mean, inverse moments, incomplete moments, distribution of order statistics, Lorenz, Bonferroni, and Zenga curves are a few of the significant characteristics and aspects explored in our study along with some graphical representations. Twelve effective estimating techniques are used to determine the distribution parameters of the IPZD. These include the Kolmogorov, least squares (LS), a maximum product of spacing, Anderson-Darling (AD), maximum likelihood, minimum absolute spacing distance, right-tail AD, minimum absolute spacing-log distance, weighted LS, left-tailed AD, Cramér-von Mises, AD left-tail second-order. A Monte Carlo simulation is used to examine the effectiveness of the obtained estimates. The visual representation and numerical results show that the maximum likelihood estimation strategy regularly beats the other methods in terms of accuracy when estimating the relevant parameters. The usefulness of the recommended distribution for modelling data is illustrated and displayed visually using two real data sets through comparisons with other distributions.

The single and double inverse Pareto–Burr XII distribution: Properties, estimation methods, and real-life data applications

Researchers consistently improve statistical tools to provide a flexible method to fit or predict. The solution needs to be more suitable since the approach is sometimes complex and complicated. Generally, statistical tools are generated from ordinary least squares and wavelet methods. However, the reliability tool provides a good fit comparable to state-of-the-art methods, including the complex posterior setting of hyperparameters. In this article, a flexible extension of the Burr XII model, which is the odd inverse Pareto–Burr XII (OIPBXII) distribution, is studied and investigated using statistical tools such as Markov chain Monte Carlo methods. The mathematical properties of the probability density distribution of OIPBXII are derived, and it shows a behavior shape, decreasing, increasing, J-shaped, reversed-J-shaped, bathtub, upside-down bathtub, decreasing–increasing–decreasing hazard rates, and right-skewed, symmetrical, and concave down densities. The OIPBXII parameters are investigated by using seven classical approaches to estimation. Extensive simulation results are presented to explore the performance of these methods for small and large samples. An application to two real-life sets of data from engineering and medicine is analyzed, showing the flexibility of the OIPBXII distribution as compared to existing Burr XII distributions.

The Helicity of Magnetic Fields Associated with Relativistic Electron Vortex Beams

For radially extended Bessel modes, the helicity density distributions of magnetic fields associated with relativistic electron vortex beams are investigated for first time in the literature. The form of the distribution is defined by the electron beam’s cylindrically symmetric density flux, which varies with the winding number ℓ and the electron spin. Different helicity distributions are obtained for different signs of the winding number ±ℓ, confirming the chiral nature of the magnetic fields associated with the electron vortex beam. The total current helicity for the spin-down state is smaller than that of the spin-up state. The different fields and helicities associated with opposite winding numbers and/or spin values will play an important role in the investigation of the interaction of relativistic electron vortices with matter and especially chiral matter. A comparison of the calculated quantities with the corresponding ones in the case of non-relativistic spin-polarized electron beams is performed.