Note on Maxwell's field equations and the constitutive equations.
Maxwell field equations and constitutive equations, discussing best pedagogical formulation for electrodynamics
VELOCITY DISTRIBUTION↗
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Exact solutions of Einstein-Maxwell equations.
Exact solutions of Einstein-Maxwell equation of Petrov class N when propagation vector of gravitational field is hypersurface orthogonal
MAXWELL EQUATION↗
An Exact Solution of Einstein-Maxwell Gravity Coupled to a Scalar Field
The general solution to low-energy string theory representing static spherically symmetric solution of the Einstein-Maxwell gravity with a massless scalar field has been found. Some of the partial cases appear to coincide with known solutions to black holes, naked singularities, and gravity and electromagnetic fields.
Einstein-Maxwell gravity scalar field↗
A New Solution for Dilaton-Maxwell Gravity
A new static spherically symmetric solution corresponding to Einstein-Maxwell gravity coupled to a dilaton field with negative kinetic term has been obtained.
dilaton Maxwell gravity↗
Maxwell Duality, Lorentz Invariance, and Topological Phase
We discuss the Maxwell electromagnetic duality relations between the Aharonov-Bohm, Aharonov-Casher, and He-McKellar-Wilkens topological phases, which allows a unified description of all three phenomena.
Maxwell Duality Lorentz Invariance Topological Pha↗
X-57 “Maxwell” High-Lift Propeller Testing and Model Development
NASA’s X-57 “Maxwell” distributed electric propulsion flight demonstrator has a high-lift system that includes 12 fixed-pitch high-lift propellers located upstream of the wing leading edge for lift augmentation at low speeds. These high-lift propellers are not required at higher speeds and are folded conformally along the nacelles to reduce drag when not in operation. Aircraft performance models and flight simulations incorporate propeller performance to predict thrust, moments, and power consumption and propeller model accuracy is important in identifying safe operating regimes for this aircraft. Current high-lift propeller performance models have been verified and calibrated against numerous computational fluid dynamics analyses under a variety of flight conditions. We performed a series of full-scale wind tunnel tests at the NASA Langley Research Center Low Speed Aeroacoustic Wind Tunnel to further validate these models, to identify any adverse operating conditions for these propellers, and to assess the accuracy of the facility’s new Propeller Test Stand. The results indicate that the models accurately predicted performance and that the right-handed propeller showed lower torque and thrust for a given propeller speed compared to the left-handed version. Acoustic data support these measurements, showing higher tonal noise for the left versus right propeller. We suspect this is due to slight differences in the material properties between the early production (right) and more recent (left) blade sets leading to greater detwisting in the right-handed blades under load. Both propellers demonstrated very stable operation throughout the test including during deployment, stowing, and windmilling. Furthermore, high-speed imagery of the spinning propeller indicated no blade oscillations or instabilities for any test case. We also leveraged these images to analyze the effects of propeller loading on blade detwisting and tip position. Unfortunately, the thrust measurements varied significantly during the test due to cross-loading of the Propeller Test Stand load cell, though trends in the thrust data were still observable. The torque measurement, however, remained very precise for all test points and was used for performance comparisons. As a result of this test, we validated and improved the X-57 high-lift propeller performance models, obtained detailed propeller acoustic data and high-speed imagery, observed the propeller operating safely during a variety of dynamic events, and identified two potentially adverse, low-propeller-speed conditions which will be avoided during normal aircraft operation.
X-57↗
Polyakov’s confinement mechanism for generalized Maxwell theory
We study fractional-derivative Maxwell theory, as appears in effective descriptions of, for example, large N f QED 3 , graphene, and some types of surface defects. We argue that when the theory is realized on a lattice, monopole condensation leads to a confining phase via the Polyakov confinement mechanism.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Hot QCD phase diagram from holographic Einstein–Maxwell–Dilaton models
In this review, we provide an up-to-date account of quantitative holographic descriptions of the strongly coupled quark-gluon plasma (QGP) produced in heavy-ion collisions, based on the class of gauge-gravity Einstein-Maxwell-Dilaton (EMD) models. Holography is employed to tentatively map the QCD phase diagram at finite temperature onto a dual theory of charged, asymptotically AdS black holes in 5D. With a quantitative focus on the hot QCD phase diagram, the EMD models reviewed are adjusted to describe lattice results for the finite-temperature QCD equation of state, with 2+1 flavors and physical quark masses, at zero chemical potential and vanishing electromagnetic fields. The predictive power of EMD models is tested by quantitatively comparing their predictions for the hot QCD equation of state at nonzero baryon density and the corresponding state-of-the-art lattice QCD results. The shear and bulk viscosities predicted by these EMD models are also compared to the corresponding profiles favored by the latest phenomenological multistage models describing different heavy-ion data. We report preliminary results from a Bayesian analysis which provide systematic evidence that lattice results at finite temperature and zero baryon density strongly constrains the free parameters of EMD models. Remarkably, the set of parameters constrained by lattice results at zero chemical potential produces EMD models in quantitative agreement with lattice QCD results also at finite baryon density. We also review results for equilibrium and transport properties from magnetic EMD models, describing the QGP at finite temperatures and magnetic fields. Lastly, we provide a critical assessment of the main limitations and drawbacks of the holographic models reviewed in the present work, and point out some perspectives we believe are of fundamental importance for future developments.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Koopman wavefunctions and Clebsch variables in Vlasov–Maxwell kinetic theory
Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here, we present different approaches to Koopman's Hilbert-space formulation of classical mechanics in the context of Vlasov–Maxwell kinetic theory. The celebrated Koopman–von Neumann construction is provided with two different Hamiltonian structures: one is canonical and recovers the usual Clebsch representation of the Vlasov density, the other is non-canonical and appears to overcome certain issues emerging in the canonical formalism. Furthermore, the canonical structure is restored for a variant of the Koopman–von Neumann construction that carries a different phase dynamics. Going back to van Hove's prequantum theory, the corresponding Koopman–van Hove equation provides an alternative Clebsch representation which is then coupled to the electromagnetic fields. Finally, the role of gauge transformations in the new context is discussed in detail.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
The collisional particle-in-cell method for the Vlasov–Maxwell–Landau equations
We introduce an extension of the particle-in-cell method that captures the Landau collisional effects in the Vlasov–Maxwell–Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport–collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.
Bailo, Rafael (ORCID:0000000180183799)↗
Metriplectic foundations of gyrokinetic Vlasov–Maxwell–Landau theory
Here, this Letter reports on a metriplectic formulation of a collisional, nonlinear full-f electromagnetic gyrokinetic theory compliant with energy conservation and monotonic entropy production. In an axisymmetric background magnetic field, the toroidal angular momentum is also conserved. Notably, a new collisional current, contributing to the gyrokinetic Maxwell–Ampère equation and the gyrokinetic charge conservation law, is discovered.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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↗
Electron energy distributions in the extended gas nebulae associated with high-z AGN: Maxwell–Boltzmann versus κ distributions
ABSTRACT Emission line observations together with photoionization models provide important information about the ionization mechanisms, densities, temperatures, and metallicities in active galactic nuclei (AGN)-ionized gas. Photoionization models usually assume Maxwell–Boltzmann (M–B) electron energy distributions (EED), but it has been suggested that using κ distributions may be more appropriate and could potentially solve the discrepancies in temperatures and abundances found in HII regions and planetary nebulae. We consider the impact of the presence of κ distributions in photoionized nebulae associated with AGN and study how this might affect spectral modelling and abundance analyses for such regions. Using the photoionization code MAPPINGS 1e, we compute models adopting M–B and κ distributions of electron energies and compare the behaviour of emission line ratios for different values of κ, gas metallicity, density, ionization parameter, and SED slope. We find that the choice of EED can have a large impact on some UV and optical emission lines emitted by photoionized nebulae associated with AGN, and that the impact of adopting a κ distribution is strongly dependent on gas metallicity and ionization parameter. We compile a sample of line ratios for 143 type 2 AGN and compare our models against the observed line ratios. We find that for 98 objects, κ distributions provide a better fit to the observed line ratios than M–B distributions. In addition, we find that adopting κ-distributed electron energies results in significant changes in the inferred gas metallicity and ionization parameter in a significant fraction of objects.
Morais, S. G. (ORCID:0000000200927813)↗
Framework for phase transitions between the Maxwell and Gibbs constructions at finite temperature
The characteristics of the hadron-to-quark first-order phase transition differ depending on whether charge neutrality is locally or globally fulfilled. In 𝛽-equilibrated matter, these two possibilities correspond to the Maxwell and Gibbs constructions. Recently, we presented a new framework in which a continuously varying parameter allows one to describe a first-order phase transition in intermediate scenarios to the two extremes of fully local and fully global charge neutrality. In this work, we extend the previous framework to finite temperatures and out-of-𝛽 equilibrium conditions, making it available for simulations of core-collapse supernovae and binary neutron star mergers. We investigate its impact on key thermodynamic quantities across a range of baryon densities, temperatures, and electron fractions. We find that when matter is not in 𝛽 equilibrium, the pressure in the mixed phase is not constant even for the case of fully local charge neutrality. Moreover, we compute the thermal index using three different approaches, demonstrating that the finite-temperature extension of an equation of state using a constant thermal index can be ill defined when applied to the mixed phase.
QCD phase transitions↗
Thermodynamics of quantum measurement and Maxwell's demon's arrow of time
Here, we discuss the thermodynamic aspects of a single qubit based device, powered by weak quantum measurements, and feedback controlled by a quantum Maxwell's demon. We discuss both discrete and time-continuous operation of the measurement based device at finite temperature of the reservoir. In the discrete example where a demon acquires information via discrete weak measurements, we find that the thermodynamic variables including the heat exchanged, extractable work, and the entropy produced are completely determined by an information theoretic measure of the demon's perceived arrow of time. We also discuss a realistic time-continuous operation of the device where the feedback is applied after a sequence of weak measurements. In the time-continuous limit, we derive the exact finite-time statistics of work, heat and entropy changes along individual quantum trajectories of the quantum measurement process, and relate them to the demon's arrow of time.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Multiscale Ecosystem for solving Maxwell-Schrodinger equations of open quantum systems (OpenMS)
Light-matter interactions play an important role in many branches of physics, chemistry, energy, and materials science. In the strong coupling regime, light-matter interactions are able to tune the materials properties via the formation of new quasiparticles, such as plasmons and polaritons. However, theoretical and numerical modeling of the light-matter interaction-mediated processes remain a big challenge because light-matter interactions are fundamentally multiscale and multiphysics problems involving multiple interactions between electrons, nuclei, and photons at different time/length scales. In the current community, light-matter interactions were treated at different levels of theoretical complexity in quantum chemistry and quantum optics. In quantum optics or quantum photonics, the matter is usually simplified as a few-level system, and the light is treated quantum-mechanically. On the other hand, quantum chemistry explores first-principles methods, including both single-particle and many-body-based techniques, to describe the electronic properties of matter in detail. However, light is usually prescribed as a classical electromagnetic field, and the light-matter interaction is taken into account as an external potential via classical approximations. This software is designed to fill current modeling shortcomings by delivering a first-ever scalable multiscale platform for simulating light-matter interactions in realistic electromagnetic environments. The software solves Maxwell and Schrodinger equations self-consistent on the heterogeneous platforms. It implements HF/DFT, TDDFT, and coupled-cluster counterparts for light-matter interactions and adopts modular programming to offload massively parallel algorithms on a large number of CPU/GPUs.
Zhang, Yu↗
Adding Magnetization to the Eddy Current Approximation of Maxwell's Equations
The eddy current approximation to Maxwell's equation often omits terms associated with magnetization, removing permanent magnets from the domain of validity of the approximation. We show that adding these terms back into the eddy current approximation is relatively straightforward, and demonstrate this on using a simple material constitutive model.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Calculation of the First Moment of Energy Using D-T Reactivity Formalisms Under the Maxwell-Boltzmann Distribution (Pt. 1)
Nuclear fusion science is an example of a scientific field with a rich history of expert involvement and scientific publications, which together, form an expert-knowledge base. One example of this history is the utilization of published reaction rates from a variety of authors. Investigators for Deuterium-Tritium (D-T) ion fusion can choose from using frequently cited methods: the Bosch and Hale reactivity, thermonuclear reaction rates from Caughlan and Fowler, and the reactivity evaluation from Miley, Towner & Ivich which forms the basis of the Naval Research Lab (NRL) formulary. There are other choices available. Each of the reactivity formulations considered here, are based upon the Maxwell- Boltzmann velocity distribution for D-T fusion ion reactants. Numerical methods for computer codes simulating hot, energetic plasmas, include tabulations of the reactivity, and the first moment of energy. The purpose of this study is to answer the question: what is the first moment of energy, and how has it been formulated? This report is part of a series of reports by the authors on D-T fusion-reaction formalism. The present focus is on defining the mathematical relationship of the first moment of D-T fusion ion kinetic energy, $\langle$E$\rangle$, with the fusion crosssection, fusion reactivity and its derivative with respect to ion-temperature. Three variants of the first moment $\langle$E$\rangle$ are analytically developed and explored: 1) constant cross-section, 2) a normalized first moment, and 3) a particular function of the first moment. Much of the mathematical development is relegated to the Appendices, for a concise presentation of topics and results. A research component of this discussion is our comparison of some of the reactivity and its derivative results between evaluations (1) versus (2) and (3), which the authors have not found in any other publication to date. This investigation is useful for validation, verification (V&V) and uncertainty quantification (UQ) as it compares the work of several authors.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗