Search NASA⌕ Search

SEARCH · Search NASA

Results for “ideal gas”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Numerical Solution of the Steady-State Network Flow Equations for a Non-Ideal Gas

Herein we formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solution for a broad class of non-ideal pressure-density relations that satisfy a monotonicity property. Further, we develop a Newton-Raphson algorithm for numerical solution of the steady-state problem, which is made possible by a systematic non-dimensionalization of the equations. The developed algorithm has been extensively tested on benchmark instances and shown to converge robustly to a generalized solution. Previous results [1]-[4], indicate that the steady-state network flow equations for an ideal gas are difficult to solve by the Newton-Raphson method because of its extreme sensitivity to the initial guess. In contrast, we find that non-dimensionalization of the steady-state problem is key to robust convergence of the Newton-Raphson method. We identify criteria based on the uniqueness of solutions under which the existence of a non-physical generalized solution found by a non-linear solver implies non-existence of a physical solution, i.e., infeasibility of the problem. Finally, we compare pressure and flow solutions based on ideal and non-ideal equations of state to demonstrate the need to apply the latter in practice. The solver developed in this article is open-source and is made available for both the academic and research communities as well as the industry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Maxwell–Boltzmann statistics of the quantum ideal gas in the canonical ensemble

Abstract The Maxwell–Boltzmann statistics of the quantum ideal gas is studied through the canonical partition function by exactly counting discrete quantum states without the continuum approximation. Analytic expressions for energy, pressure, entropy, and heat capacity are expressed in terms of Jacobi theta functions and complete elliptic integrals. The results show typical effects of discrete energy levels in the low temperature limit while they reproduce thermodynamics of the classical ideal gas in the high temperature limit.

Mechanics↗
DOE OSTI2026

Relaxations of the steady optimal gas flow problem for a non-Ideal gas

Natural gas ranks second in U.S. primary energy consumption. Because most production sites are remote, gas must be transported through pipeline networks equipped with compressors, valves, and other components. For both economic efficiency and system reliability, it is desirable to operate these networks optimally. The governing physics across pipeline components entails nonlinear, non-convex equality and inequality constraints, and the most general steady-flow operations problem is a Mixed-Integer Nonlinear Program (MINLP).This work focuses on one such steady-flow problem-the Optimal Gas Flow (OGF) for a natural gas pipeline network-which minimizes production cost subject to the steady-flow physics. For day-to-day operations, the ability to quickly compute a globally optimal solution and a strong lower bound for varying demand profiles is crucial. A promising strategy is to build tight relaxations of the OGF’s nonlinear constraints. However, many nonlinearities arising from non-ideal equations of state either lack relaxations or have relaxations that do not scale to realistic network sizes. We address this gap by combining recent advances in polyhedral relaxations for univariate functions to construct tight, computationally efficient relaxations of the OGF with a non-ideal equation of state. These relaxations solve within seconds on a standard laptop. In conclusion, we demonstrate their quality through extensive numerical experiments on very large-scale test networks from the literature and find that the proposed approach proves optimality in 92% of tested instances.

03 NATURAL GAS↗
DOE OSTI2020

Using Differential Forms to Find Symmetries in the Noh Problem for an Ideal Gas in a Spherical System

The Euler equations describe inviscid, compressible gas flow and are derived using the laws of conservation of mass, momentum, and energy. From these equations a common test problem, the Noh problem, can be solved for invariant solutions in planar, cylindrical, and spherical geometries. Using Lie group analysis methods, we will solve the Noh Problem for an ideal gas in a spherical system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

GEOSH: Ideal Gas Chemical Equation of State

We present the framework and methodology for the new Los Alamos National Laboratory (LANL) G as chemical E quation O f S tate at H igher temperatures code (GEOSH) which aims to accurately model the behavior of chemically complex gaseous mixtures in equilibrium. Assuming the ideal gas approximation, GEOSH leverages the recursive nature of the Saha ionization and molecular equations in order to eliminate the molecular and ionic degrees of freedom, thereby reducing the problem size to the number of atomic species plus one for the free electrons if ions are included. This approach allows the chemical species, both molecular and ionic, of the mixture to be expressed in terms of the abundances of the elemental species. As a result, the GEOSH framework achieves a reduction in computational expense, increased processing speed, and the capability to efficiently model large-scale chemical networks. This report provides the necessary physical background and theoretical foundations for the GEOSH code, accompanied by benchmarking studies.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Spin-dependent Seebeck and Nernst effects in an ideal skyrmion gas

In this work, we theoretically and numerically study spin-dependent Seebeck and Nernst effects in 2D ferromagnetic materials with the topological spin texture (skyrmion and vortex) ideal gas. From the numerical solution of the matrix Boltzmann equation for a nonequilibrium distribution function and the Lippmann–Schwinger equation for a T-matrix we find the strong nonlinear behaviors in the thermoelectric coefficients depending on skyrmion/vortex diameters and electron concentrations. In particular, the dramatic dependences in the Seebeck and Nernst coefficients take place at larger magnetic texture sizes where the abrupt sign flip in the vortex Seebeck and Nernst coefficients occurs in the narrow region of electron concentrations. In this case the normalized Nernst coefficient changes from +5 to -7. The spin-dependent thermoelectric coefficients are proportional to T at low temperatures for all skyrmion/vortex sizes.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Temperature effects in spin-dependent Hall currents in an ideal skyrmion gas

The quest of novel reliable and fast performing logic and memory elements in classical and quantum computing requires discoveries of new effects in novel quantum materials. Skyrmions are such magnetic textures where electron scattering can essentially change the shape and location of the skyrmion, which can be used as a memory element being more efficient than domain walls as memory device in classical computing. Because the skyrmion motion is sensitive even to very small currents, we study electron scattering by skyrmions in an ideal skyrmion gas in ferromagnetic environment. In such systems, the direct and Hall currents become spin-dependent. For applications it is important to consider a Hall effect in the whole range of temperatures under the assumption of the skyrmion existence. In this study we find the nonmonotonic temperature dependence of the direct spin-up conductivity, i. e., the conductivity for the current directed along the applied electric field due to the electrons with the spin parallel to the ferromagnetic moment. Such a behavior contradicts the traditional understanding where the temperature only increases the value of the conductivity. The spin-down Hall conductivity is found to be even more dramatic exhibiting the conductivity sign change (i.e., the change in the current direction) with temperature for small skyrmion sizes. The found effects strongly depend on Fermi energy. The most pronounced dependencies take place if the Fermi energy is slightly below and above the bottom of the upper (spin-down) energy band of an ideal 2D electron gas. In addition, we also find that the direct and Hall resistivities, ρ xx and ρ xy , are independent of the exchange integral J for 2J > ε F .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

INVESTIGATION OF TURBULENT JETS, SPRAYS, AND SUPERCRITICAL MIXING BY TIME RESOLVED RAINBOW SCHLIEREN DEFLECTOMETRY

As technological advancements have enabled higher efficiency compression ignition (CI) engines (diesel engines) by operating at higher pressures and temperatures, the mechanisms of fuel-air mixing are postulated to change. Thus, there is a greater need for experimental data to develop and verify new phenomena. However, the fast time scales and harsh environments associated with CI engines present many experimental difficulties and requires high quality non-intrusive diagnostics to obtain useful data. The diagnostics itself must be validated prior to its implementation in an engine environment. The purpose of this research is to advance rainbow schlieren deflectometry (RSD) to study turbulent fuel sprays including the effects of supercritical mixing in CI engine environments. This objective is met by developing and applying quantitative RSD, for the first time, to three separate aspects of fuel sprays: 1) turbulent mixing, 2) phase boundaries, and 3) non-ideal gas mixing. First, quantitative RSD is demonstrated for turbulent mixing in a canonical helium jet. Rayleigh scattering data in the literature is used to validate the concentration measurements obtained by RSD. The results also provide explanations for phenomena occurring in the helium jet and provide data not yet present in the literature. Second, RSD is applied to high pressure multi-phase fuel sprays and new methodologies are developed to distinguish the liquid region from the vapor region and to quantify the in-between region on a probabilistic basis. Isolating liquid and vapor regions generally requires two separate diagnostics, e.g., Mie scattering (liquid region) and Rayleigh scattering (vapor region). However, the results of this study demonstrate that RSD can be used as a single diagnostic to measure both liquid and vapor boundaries. Third, the optical-to-thermodynamic relations associated with refrac-tometry are investigated under non-ideal gas mixing conditions to develop a generalized relationship valid for both ideal or non-ideal gas mixing. The last part of this research develops the theoretical tools to understand and experimentally realize supercritical mixing at diesel conditions. Guided by the theoretical analysis, RSD is applied to compare supercritical versus transcritical mixing at CI conditions using a constant pressure test rig. It is found that while fully supercritical mixing ers benefits in diesel engines, i.e, faster mixing times (50% higher velocities), the absence of droplets which cause high levels of particulate emissions, etc., it would be difficult to achieve in practice because of the requirements of fuels with low critical temperature and/or substantial fuel preheating.

02 PETROLEUM↗
DOE OSTI2022

Simple Approximation for the Ideal Reference State of Gases Adsorbed on Solid-State Surfaces

Reference states are useful as models for facilitating calculations of equilibrium constants, and they may also serve as standard states that are convenient for organizing and tabulating thermodynamic data; however, standard state conventions and appropriate reference states for adsorbed species have received less attention than those for pure substances and solutes. Here, we compare seven choices of reference states for calculations of equilibrium constants and transition state theory rate constants for flat surfaces, in particular (1) an ideal 2D harmonic oscillator, (2) an ideal rigid-molecule harmonic oscillator, (3) an ideal 2D harmonic oscillator with separable surface modes, (4) a 2D ideal gas, (5) an ideal 2D hindered translator, (6) an ideal 2D hindered translator with lowest-order barriers, and (7) a simple ideal 2D hindered translator proposed in this work. The advantage of models 5–7 is that they can treat both mobile and localized adsorbates in a consistent way, whereas models 1–3 are only appropriate for localized adsorbates, and model 4 is only appropriate for a freely translating adsorbate. Furthermore, models 6 and 7 reduce the computational cost without the user having to calculate barrier heights for diffusion. An advantage of the simple ideal 2D hindered translator is that it has a physical high-temperature limit. We also propose a reference state for nonflat surfaces. Here, the user is encouraged to choose a reference state based on the appropriateness of the model and the practicality of the calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Foundations of magnetohydrodynamics

In this tutorial, a derivation of magnetohydrodynamics (MHD) valid beyond the usual ideal gas approximation is presented. Non-equilibrium thermodynamics is used to obtain conservation equations and linear constitutive relations. When coupled with Maxwell's equations, this provides closed fluid equations in terms of material properties of the plasma, described by the equation of state and transport coefficients. These properties are connected to microscopic dynamics using the Irving–Kirkwood procedure and Green–Kubo relations. Symmetry arguments and the Onsager–Casimir relations allow one to vastly simplify the number of independent coefficients. Importantly, expressions for current density, heat flux, and stress (conventionally Ohm's law, Fourier's law, and Newton's law) take different forms in systems with a non-ideal equation of state. The traditional form of the MHD equations, which is usually obtained from a Chapman–Enskog solution of the Boltzmann equation, corresponds to the ideal gas limit of the general equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Richtmyer–Meshkov instability when a shock is reflected for fluids with arbitrary equation of state

First predicted by Richtmyer in 1960 and experimentally confirmed by Meshkov in 1969, the Richtmyer–Meshkov instability (RMI) is crucial in fields such as physics, astrophysics, inertial confinement fusion and high-energy-density physics. These disciplines often deal with strong shocks moving through condensed materials or high-pressure plasmas that exhibit non-ideal equations of state (EoS), thus requiring theoretical models with realistic fluid EoS for accurate RMI simulations. Approximate formulae for asymptotic growth rates, like those proposed by Richtmyer, are helpful but rely on heuristic prescriptions for compressible materials. These prescriptions can sometimes approximate the RMI growth rate well, but their accuracy remains uncertain without exact solutions, as the fully compressible RMI growth rate is influenced by both vorticity deposited during shock refraction and multiple sonic wave refractions. This study advances previous work by presenting an analytic, fully compressible theory of RMI for reflected shocks with arbitrary EoS. It compares theoretical predictions with heuristic prescriptions using ideal gas, van der Waals gas and three-term constitutive equations for simple metals, the latter being analysed with detailed and simplified ideal-gas-like EoS. We additionally offer an alternative explicit approximate formula for the asymptotic growth rate. The comprehensive model also incorporates the effects of constant-amplitude acoustic waves at the interface, associated with the D'yakov–Kontorovich instability in shocks.

Napieralski, Mario (ORCID:0009000692344901)↗
DOE OSTI2025

Thermodynamic consistency and fluctuations in mesoscopic stochastic simulations of reactive gas mixtures

It is essential that mesoscopic simulations of reactive systems reproduce the correct statistical distributions at thermodynamic equilibrium. By considering a compressible fluctuating hydrodynamics (FHD) simulation method of ideal gas mixtures undergoing reversible reactions described by the chemical Langevin equations, we show that thermodynamic consistency in reaction rates and the use of instantaneous temperatures for the evaluation of reaction rates is required for fluctuations for the overall system to be correct. We then formulate the required properties of a thermodynamically consistent reaction (TCR) model. As noted in the literature, while reactions are often discussed in terms of forward and reverse rates, these rates should not be modeled independently because they must be compatible with thermodynamic equilibrium for the system. Using a simple TCR model where each chemical species has constant heat capacity, we derive the explicit condition that the forward and reverse reaction rate constants must satisfy in order for the system to be thermodynamically consistent. We perform equilibrium and non-equilibrium simulations of ideal gas mixtures undergoing a reversible dimerization reaction to measure the fluctuational behavior of the system numerically. We confirm that FHD simulations with the TCR model give the correct static structure factor of equilibrium fluctuations. For the statistically steady simulation of a gas mixture between two isothermal walls with different temperatures, we show using the TCR model that the temperature variance agrees with the corresponding thermodynamic-equilibrium temperature variance in the interior of the system, whereas noticeable deviations are present in regions near walls, where chemistry is far from equilibrium.

Polimeno, Matteo [University of California, Merced↗
DOE OSTI2023

Specifications of FIPD Fission Gas Release Data

All fission gas release data stored in the Fuels Irradiation & Physics Database (FIPD) was originally measured using the Gas Assay, Sample and Recharge (GASR) System in the Hot Fuel Examination Facility (HFEF). It is therefore called GASR data in FIPD. During the measurement of a sample, such as an irradiated EBR-II fuel element/capsule, a pinhole-sized region near the top of the element plenum was melted by a laser. Plenum gas then expanded into a calibrated volume (note: in this document, “sample” and “capsule/element” are used interchangeably consistent with GASR documents in FIPD). The pressure rise in the volume was recorded. Helium backfilling and expansion was then performed to determine the sample (e.g., fuel element plenum) volume using Boyle’s Law and assuming ideal gas behavior at constant temperature. With the plenum volume and the recorded pressure rise, the sample (e.g., fuel element plenum) pressure was derived with assumption of ideal gas law behavior. The plenum volume and pressure as well as the cladding temperature during the measurement were collected (GASR data in FIPD). Other records associated with the fission gas release data include: raw GASR data records including volumes and post-puncture pressures of seal head/sealing head and manifold, calibration data, backfilling gas pressure data, and the data analysis records. A sample(s) of the fission gas released from the plenum was collected by the GASR system into sample bottles. The chemical and isotopic composition of the gas sample was analyzed separately from GASR data, and will be discussed in a separate specification. The plenum volume, pressure, and cladding temperature during the measurement are typically utilized to determine the number of moles of gas in the plenum. This quantity is often compared to the number of moles of gas generated by fission events. However, calculating these values and their associated uncertainty is beyond the scope of this document, as it necessitates additional assumptions. The most important document to understand the FIPD fission gas data is the GASR operational manual (title: Gas Assay, Sample and Recharge System (GASR) operation and maintenance manual, HFEF/N OMM 4381, DOC. NO. W0018-0032-ES-00). This manual provides: (1) description of the GASR and the functions of each component (laser drilling, welding, seal head/sealing head, manifold, vacuum system, sample system, purge and gas tag system, etc.); (2) step-by-step guidance on calibrations, operations, and measurements; and (3) maintenance procedures and other details relating to the structure and operation of the GASR. Note that the original GASR operated until 2020. A new GASR with the same design and measurement methodology was installed in 2021. The specifications of the GASR presented on the HFEF website at this time are consistent with the ones given in the operational manual. The methods to calculate the plenum volume and pressures were not included in the operational manual, but were recorded in the legacy data analysis files. Details of the methods are given in Chapter 3.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Lattice quantum chromodynamics at large isospin density

We present an algorithm to compute correlation functions for systems with the quantum numbers of many identical mesons from lattice quantum chromodynamics (QCD). The algorithm is numerically stable and allows for the computation of n-pion correlation functions for n ϵ {1, … , N} using a single N × N matrix decomposition, improving on previous algorithms. We apply the algorithm to calculations of correlation functions with up to 6144 charged pions using two ensembles of gauge field configurations generated with quark masses corresponding to a pion mass m π = 170 MeV and spacetime volumes of (4.4 3 × 8.8) fm 4 and (5.8 3 × 11.6) fm 4 . We also discuss statistical techniques for the analysis of such systems, in which the correlation functions vary over many orders of magnitude. In particular, we observe that the many-pion correlation functions are well-approximated by log-normal distributions, allowing the extraction of the energies of these systems. Using these energies, the large-isospin-density, zero-baryon-density region of the QCD phase diagram is explored. A peak is observed in the energy density at an isospin chemical potential μ I ~ 1.5m π , signaling the transition into a Bose-Einstein condensed phase. The isentropic speed of sound, c s , in the medium is seen to exceed the ideal-gas (conformal) limit ($c^{2}_{s} ≤ 1/3)$ over a wide range of chemical potential before falling towards the asymptotic expectation at μ I ~ 15m π . These, and other thermodynamic observables, indicate that the isospin chemical potential must be large for the system to be well described by an ideal gas or perturbative QCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Entropy generation from hydrodynamic mixing in inertial confinement fusion indirect-drive targets

The increase in entropy from the physical mixing of two adjacent materials in inertial confinement fusion (ICF) implosions and gas-filled hohlraums is analytically assessed. An idealized model of entropy generation from the mixing of identical ideal-gas particles across a material interface in the presence of pressure and temperature gradients is applied. Physically, mix-driven entropy generation refers to the work done by the gases in expanding into a larger common volume from atomic mixing under the condition of no internal energy change, or work needed to restore the initial unmixed state. Furthermore, the effect of a mix-generated entropy increase is analytically shown to lead to less compression of the composite ICF fluid under adiabatic conditions. The amount of entropy generation is estimated to be ~10 J for a Rayleigh–Taylor-induced micrometer-scale annular mixing layer between the solid deuterium–tritium fuel and (undoped) high-density carbon pusher of an imploding capsule at the National Ignition Facility (NIF). This level of entropy generation is consistent with lower-than-expected fuel compressions measured on the NIF [Hurricane et al., Phys. Plasmas 26, 052704 (2019)]. The degree of entropy increase from mixing of high-Z hohlraum wall material and low-Z, moderate- to high-density gas fills is estimated to lead to ~100 kJ of heat generation for NIF-scale experiments [Moody et al., Phys. Plasmas 21, 056317 (2014)]. This value represents a significant fraction of the inferred missing x-ray drive energy based on observed delays in capsule implosion times compared with mainline simulations [Jones et al., Phys. Plasmas 19, 056315 (2012)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Working Fluid Characterization and Performance Assessment of Subcritical Organic Rankine Cycles Based on the Lee–Kesler Approach for Energy Recovery

Here, a generalized model using the Lee–Kesler approach based on the corresponding states principle is developed to assess the performance of subcritical Organic Rankine Cycles operating with different working fluids. Each fluid is characterized by five parameters: the acentric factor, critical temperature, critical pressure, molar mass, and the ideal-gas ratio of specific heats at the critical temperature. The model was developed using the compressibility factor modified version of the Benedict–Webb–Rubin equation proposed by Lee and Kesler and the enthalpy and entropy functions to calculate thermodynamic state properties. The model was validated by comparing the results calculated with the model and working fluid thermodynamic properties obtained with the CoolProp database. This comparison was conducted for 91 working fluids, obtaining a relative error below 5% for 88 out of the 91 fluids (∼97%). A generalized parametric study was conducted to determine the influence of the pinch point and each fluid parameter on the performance of Organic Rankine Cycle (ORC) systems. It was found that efficiency increases with critical temperature, ideal-gas ratio of specific heats at the critical temperature, and acentric factor, reaching up to 13%. The developed model enables the evaluation of ORC system performance for existing working fluids. It also allows the formulation and evaluation of new fluids to enhance the performance of the ORC while retrieving energy from any kind of source; and likewise, the methodology can be applied to other power generation cycles.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Real-fluid behavior in rapid compression machines: Does it matter?

Rapid compression machines (RCMs) have been extensively used to quantify fuel autoignition chemistry and validate chemical kinetic models at high-pressure conditions. Historically, the analyses of experimental and modeling RCM autoignition data have been conducted based on the adiabatic core hypothesis with ideal gas assumption, where real-fluid behavior has been completely overlooked, though this might be significant at common RCM test conditions. Here, this work presents a first-of-its-kind study that addresses two significant but overlooked questions for autoignition studies within RCMs in the fundamental combustion community: (i) experiment-wise, can unaccounted-for real-fluid behavior in RCMs affect the interpretation and analysis of RCM experimental data? and (ii) simulation-wise, can unaccounted-for real-fluid behavior in RCMs affect RCM autoignition modeling and the validation of chemical kinetic models? To this end, theories for real-fluid isentropic change are newly proposed and derived based on high-order Virial EoS, and are further incorporated into an effective-volume real-fluid autoignition modeling framework newly developed for RCMs. With detailed analyses, the strong real-fluid behavior in representative RCM tests is confirmed, which can greatly influence the interpretation of RCM autoignition experiments, particularly the determination of end-of-compression temperature and evolution of the adiabatic core in the reaction chamber. Furthermore, real-fluid RCM modeling results reveal that considerable error can be introduced into simulating RCM autoignition experiments when following the community-wide accepted effective-volume approach by assuming ideal-gas behavior, which can be as high as 64% in the simulated ignition delay time at compressed pressure of 125 bar and lead to contradictory validation results of chemical kinetic models. Therefore, we recommend the community to adopt frameworks with real-fluid behavior fully accounted for (e.g., the one developed in this study) to analyze and simulate past and future RCM experiments, so as to avoid misinterpretation of RCM autoignition experiments and eliminate the potential errors that can be introduced into the simulation results with the existing RCM modeling frameworks.

High-order Virial equation of state↗
DOE OSTI2021

“Magic” Orientation Angles to Suppress Spin-Driven Hall Currents in Anisotropic 2D Materials with an Ideal Skyrmion Gas

The Hall effect depending on conduction electron spin projection becomes very different for anisotropic 2D crystals. In this case the spin-dependent electron current strongly determined by the orientation angle, θ, of the sample with respect to an applied electric eld. The spin-up and -down components of the direct and Hall charge currents oscillate with the angle 2θ. The direct and Hall components of the current have the structure where there are the angle-independent part, oscillation amplitude, and phase shift. All three quantitates strongly depend on the electron spin projection, electron mass ratio, and skyrmion size. We nd that there are "magic" orientation angles where the spin-up, spin-down, and total Hall currents vanish. There is a great interest in computations based on 2D materials with skyrmions. Such properties can be useful for computer logic operations based on skyrmions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗