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Keywords = magnetic-flux conservation

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22 pages, 6111 KB  
Article
Adaptive Fuzzy-Based Smooth Transition Strategy for Speed Regulation Zones in IPMSM
by Xinyi Yu, Wanlu Zhu and Pengfei Zhi
World Electr. Veh. J. 2026, 17(1), 44; https://doi.org/10.3390/wevj17010044 - 14 Jan 2026
Viewed by 94
Abstract
In response to the “carbon peak and carbon neutrality” strategy, industrial energy conservation has become increasingly important. Interior Permanent Magnet Synchronous Motors (IPMSMs) exhibit significant potential for efficient flux-weakening control due to their asymmetric rotor reluctance. However, conventional control strategies often cause instability [...] Read more.
In response to the “carbon peak and carbon neutrality” strategy, industrial energy conservation has become increasingly important. Interior Permanent Magnet Synchronous Motors (IPMSMs) exhibit significant potential for efficient flux-weakening control due to their asymmetric rotor reluctance. However, conventional control strategies often cause instability during transitions across speed zones. This paper proposes a novel adaptive fuzzy-based smooth transition strategy to address this issue. First, a composite control framework integrating Maximum Torque per Ampere (MTPA) and leading-angle control is established to enhance flux-weakening capability. Then, within this framework, adaptive fuzzy controllers are designed for different weakening zones, incorporating a Lyapunov-based parameter adaptation mechanism for real-time compensation. Simulation results demonstrate that the proposed strategy achieves smooth switching across the entire speed range of IPMSMs. Quantitatively, it reduces speed overshoot by 5–15%, suppresses torque ripple by over 10%, and virtually eliminates switching current pikes compared to conventional methods, thereby significantly improving system dynamic performance and operational reliability. Full article
(This article belongs to the Section Propulsion Systems and Components)
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17 pages, 3109 KB  
Article
Simulation of Eddy Current Suppression and Efficiency Recovery in Mining MCR-WPT Systems Based on Explosion-Proof Slotting
by Yingying Wang, Jiahui Yu, Jindi Pang, Shuangli Chen and Yudong Wang
Electronics 2025, 14(19), 3899; https://doi.org/10.3390/electronics14193899 - 30 Sep 2025
Viewed by 490
Abstract
To meet safety regulations in underground coal mines, wireless power transfer (WPT) systems must house both the transmitter and receiver within explosion-proof enclosures. However, eddy currents induced on the surfaces of these non-ferromagnetic metal enclosures significantly hinder magnetic flux coupling, thereby reducing transmission [...] Read more.
To meet safety regulations in underground coal mines, wireless power transfer (WPT) systems must house both the transmitter and receiver within explosion-proof enclosures. However, eddy currents induced on the surfaces of these non-ferromagnetic metal enclosures significantly hinder magnetic flux coupling, thereby reducing transmission efficiency. This paper proposes a slotting technique applied to explosion-proof enclosures to suppress eddy currents, along with the integration of magnetic flux focusing materials into the coils to enhance coupling. Simulations were conducted to compare three system configurations: (i) a WPT system without enclosures, (ii) a system with solid (unslotted) enclosures, and (iii) a system with slotted enclosures. The results show that solid enclosures reduce efficiency to nearly zero, whereas slotted enclosures restore efficiency to 90% of the baseline system without enclosures. Joule heating remains low in the slotted explosion-proof enclosures, with energy losses of 2.552 J for the transmitter enclosure and 2.578 J for the receiver enclosure. A conservative first-order estimation confirms that the corresponding temperature rise in the enclosure surfaces remains below 50 °C, which is well within the 150 °C limit stipulated by the Chinese National Standard GB 3836.1-2021 (Explosive Atmospheres—Part 1: Equipment General Requirements). These findings confirm effective eddy current suppression and efficiency recovery without compromising explosion-proof safety. The core innovation of this work lies not merely in the physical slotting approach, but in the development of a precise equivalent circuit model that fully incorporates all mutual inductance components representing eddy current effects in non-ferromagnetic explosion-proof enclosures, and its integration into the overall MCR-WPT system circuit. Full article
(This article belongs to the Section Electronic Materials, Devices and Applications)
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48 pages, 852 KB  
Article
Energy Conservation in a Charged Retarded Field Engine
by Prachi Sharma and Asher Yahalom
Energies 2025, 18(17), 4661; https://doi.org/10.3390/en18174661 - 2 Sep 2025
Viewed by 846
Abstract
Energy conservation, rooted in the time invariance of physical laws and formalized by Noether’s theorem, requires that systems with space-time translational symmetry conserve momentum and energy. This work examines how this principle applies to a charged retarded field engine, where the rate of [...] Read more.
Energy conservation, rooted in the time invariance of physical laws and formalized by Noether’s theorem, requires that systems with space-time translational symmetry conserve momentum and energy. This work examines how this principle applies to a charged retarded field engine, where the rate of change of total energy—mechanical plus field energy—is balanced by the energy flux through the system’s boundary. Using electric and magnetic field expressions from a Taylor expansion to incorporate retardation effects, we analyze the energy equation order by order for two arbitrary charged bodies. Our results show that total energy is conserved up to the fourth order, with mechanical and field energy changes exactly offset by boundary energy flux. Consequently, the work done by the internal electromagnetic field precisely equals the engine’s gained mechanical kinetic energy, addressing the central focus of this study. Full article
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27 pages, 4593 KB  
Article
A Multiphysics Thermoelastoviscoplastic Damage Internal State Variable Constitutive Model including Magnetism
by M. Malki, M. F. Horstemeyer, H. E. Cho, L. A. Peterson, D. Dickel, L. Capolungo and M. I. Baskes
Materials 2024, 17(10), 2412; https://doi.org/10.3390/ma17102412 - 17 May 2024
Cited by 2 | Viewed by 1749
Abstract
We present a macroscale constitutive model that couples magnetism with thermal, elastic, plastic, and damage effects in an Internal State Variable (ISV) theory. Previous constitutive models did not include an interdependence between the internal magnetic (magnetostriction and magnetic flux) and mechanical fields. Although [...] Read more.
We present a macroscale constitutive model that couples magnetism with thermal, elastic, plastic, and damage effects in an Internal State Variable (ISV) theory. Previous constitutive models did not include an interdependence between the internal magnetic (magnetostriction and magnetic flux) and mechanical fields. Although constitutive models explaining the mechanisms behind mechanical deformations caused by magnetization changes have been presented in the literature, they mainly focus on nanoscale structure–property relations. A fully coupled multiphysics macroscale ISV model presented herein admits lower length scale information from the nanoscale and microscale descriptions of the multiphysics behavior, thus capturing the effects of magnetic field forces with isotropic and anisotropic magnetization terms and moments under thermomechanical deformations. For the first time, this ISV modeling framework internally coheres to the kinematic, thermodynamic, and kinetic relationships of deformation using the evolving ISV histories. For the kinematics, a multiplicative decomposition of deformation gradient is employed including a magnetization term; hence, the Jacobian represents the conservation of mass and conservation of momentum including magnetism. The first and second laws of thermodynamics are used to constrain the appropriate constitutive relations through the Clausius–Duhem inequality. The kinetic framework employs a stress–strain relationship with a flow rule that couples the thermal, mechanical, and magnetic terms. Experimental data from the literature for three different materials (iron, nickel, and cobalt) are used to compare with the model’s results showing good correlations. Full article
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26 pages, 7435 KB  
Article
Model-Free Control for Doubly Salient Permanent Magnet-Generator-Based Tidal Stream Turbine Considering Flux-Weakening Operation
by Hao Chen, Luming Liu, Yassine Amirat, Zhibin Zhou, Nadia Aϊt-Ahmed and Mohamed Benbouzid
J. Mar. Sci. Eng. 2023, 11(12), 2276; https://doi.org/10.3390/jmse11122276 - 30 Nov 2023
Viewed by 1717
Abstract
Renewable energy generation is increasingly important due to serious energy issues. A Doubly Salient Permanent Magnet Generator (DSPMG) can be an interesting candidate for tidal stream renewable energy systems. However, the special structure makes the system nonlinear and strongly coupled even after Park [...] Read more.
Renewable energy generation is increasingly important due to serious energy issues. A Doubly Salient Permanent Magnet Generator (DSPMG) can be an interesting candidate for tidal stream renewable energy systems. However, the special structure makes the system nonlinear and strongly coupled even after Park transformation and involves a larger torque ripple. Previous research mainly focused on model-based control for this machine, which is very sensitive to the parameters. Thus, to control the complex systems stably and accurately, two model-free control algorithms, Active Disturbance Rejection-Based Iterative Learning Control (ADRILC) and Active Disturbance Rejection Control–Iterative Learning Control (ADRC–ILC), are proposed for the current and speed control loops of a DSPMG-based Tidal Stream Turbine (TST), respectively. ADRC–ILC uses ADRC to deal with the external non-periodic speed ripple and adopts ILC to reduce the internal periodic speed ripple. ADRILC employs an iterative method to improve the ESO for the enhancement of the convergence rate of ILC. Considering the variable tidal speed, when the speed is above the rated value, Maximum Power Point Tracking (MPPT) must be changed to a power limitation strategy for limiting the generator power to the rated value and extending the system operating range. Thus, Optimal Tip Speed Ratio (OTSR)-based MPPT (for a low tidal current speed) and Leading Angle Flux-Weakening Control (LAFWC) (for a high tidal current speed) strategies are also proposed. According to the simulation results, the proposed ADRC–ILC + ADRILC has the lowest torque ripple, the highest control accuracy, as well as a good current tracking capability and strong robustness. At the rated speed, the proposed method reduces the torque ripple by more than 20% and the speed error by about 80% compared with PI control: the current difference is limited in 2A. The LAFWC proposed for an excessive tidal current speed is effective in conserving the electromagnetic power and increasing the generator speed. Full article
(This article belongs to the Special Issue The Development of Marine Renewable Energy)
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15 pages, 719 KB  
Article
Significance of Nanoparticle Radius and Gravity Modulation on Dynamics of Nanofluid over Stretched Surface via Finite Element Simulation: The Case of Water-Based Copper Nanoparticles
by Bagh Ali, Anum Shafiq, Meznah M. Alanazi, Awatif A. Hendi, Ahmed Kadhim Hussein and Nehad Ali Shah
Mathematics 2023, 11(5), 1266; https://doi.org/10.3390/math11051266 - 6 Mar 2023
Cited by 11 | Viewed by 2683
Abstract
This communication studies the importance of varying the radius Dp of Copper nanoparticles for microgravity-modulated mixed convection in micropolar nanofluid flux under an inclined surface subject magnetic field and heat source. In the current era, extremely pervasive modernized technical implementations have drawn [...] Read more.
This communication studies the importance of varying the radius Dp of Copper nanoparticles for microgravity-modulated mixed convection in micropolar nanofluid flux under an inclined surface subject magnetic field and heat source. In the current era, extremely pervasive modernized technical implementations have drawn attention to free convection governed by g-jitter force connected with microgravity. Therefore, fixed inter-spacing of nanoparticles and effects of g-jitter on the inclined surface are taken into consideration. A mathematical formulation based on conservation principles was non-dimensionalized by enforcement of similarity transformation, yielding a related set of ODEs. The convective non-linearity and coupling, an FE discretization, was implemented and executed on the Matlab platform. The numerical process’ credibility was ensured for its acceptable adoption with the defined outcomes. Then, the computational endeavor was continued to elucidate the impacts of various inputs of Dp, the amplitude of modulation ϵ, material parameter β, mixed convection parameter λ, inclination angle γ, and magnetic parameter M. The enlarging size of nanoparticles accelerated the nanofluid flow due to the depreciation of viscosity and receded the fluid temperature by reducing the surface area for heat transportation. The modulated Nusselt number, couple stress, and skin friction coefficient are significantly affected by the variation of Dp, M, β, λ, and ϵ. These results would benefit experts dealing with upper space transportation and materials’ performance, such as the effectualness of chemical catalytic reactors and crystals. Full article
(This article belongs to the Special Issue Numerical and Analytical Study of Fluid Dynamics)
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20 pages, 8035 KB  
Article
Torque Control for PMSG-Based Wind-Power System Using Stationary abc-Reference Frame
by Israel Divan Lopes da Costa, Danilo Iglesias Brandao, Seleme Isaac Seleme and Lenin Martins Ferreira Morais
Energies 2022, 15(21), 8060; https://doi.org/10.3390/en15218060 - 29 Oct 2022
Cited by 2 | Viewed by 3835
Abstract
The power system of wind farms is generally characterized by a weak grid, in which voltages may be heavily distorted and imbalanced, challenging the control scheme of wind-power converters that must be impervious to such disturbances. The control scheme in the stationary natural [...] Read more.
The power system of wind farms is generally characterized by a weak grid, in which voltages may be heavily distorted and imbalanced, challenging the control scheme of wind-power converters that must be impervious to such disturbances. The control scheme in the stationary natural abc-frame has shown good performance under non-ideal voltage conditions, and then this paper proposes to analyze the operational performance of a wind-power system based on a permanent magnet synchronous generator subject to non-ideal conditions of the grid voltage, with its control scheme devised in the abc-reference frame. The proposed control scheme considers the torque control decoupling the flux and torque for the generator-side, showing the possibility to implement the machine torque control, without any coordinates transformation using a closed loop dot-product approach, between the field flux and stator currents. For the grid-side converter, the load current compensation is proposed, using the load current decomposition and conservative power theory (CPT), improving the grid power quality. The simulation results estimate the performance of the grid-side control under distorted and asymmetrical voltages, and the generator-side control against torque disturbances due to wind speed variation. Finally, experimental results in a small-scale test bench validate the proposed control scheme in injecting active and reactive power into the grid, and the torque control under wind speed variation. Full article
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25 pages, 2947 KB  
Article
Near-Field Behaviors of Internal Energy Flows of Free-Space Electromagnetic Waves Induced by Electric Point Dipoles
by Hyoung-In Lee
Optics 2022, 3(3), 313-337; https://doi.org/10.3390/opt3030029 - 16 Sep 2022
Cited by 5 | Viewed by 3423
Abstract
Both orbital and spin energy fluxes constitute the internal flows decomposed from a Poynting vector. For generic electromagnetic waves propagating through source-free media, these energy fluxes are quadratic in field variables so that their properties are not easily predictable. Notwithstanding, their near-field behaviors [...] Read more.
Both orbital and spin energy fluxes constitute the internal flows decomposed from a Poynting vector. For generic electromagnetic waves propagating through source-free media, these energy fluxes are quadratic in field variables so that their properties are not easily predictable. Notwithstanding, their near-field behaviors play important roles in nanoscale photonics. For time-oscillatory fields, we found two hitherto-overlooked distinctions between the two internal flows. The first is an unequal level between them because the vorticity of an orbital energy flux plays a role comparable to a spin energy flux itself. The second is regarding the electric-magnetic dual symmetry in handling the two internal flows, whence the reactive helicity plays a role as important as the electromagnetic helicity. By helicity conservation, an inter-electric-magnetic transport is possible for the spin angular momentum density, while the electric and magnetic constituents of orbital energy fluxes admit only respective intra-electric and intra-magnetic transports. We have tested the validities of all these claims by exemplarily taking the electromagnetic fields induced by an electric point dipole, either a linear or a circular one. We have thus made new contributions not only in deriving explicit forms of the internal energy flows but also in revealing the magnetic activities hidden under the electromagnetic waves induced by electric point dipoles. Full article
(This article belongs to the Section Photonics and Optical Communications)
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63 pages, 1303 KB  
Review
New Developments in Relativistic Magnetohydrodynamics
by Koichi Hattori, Masaru Hongo and Xu-Guang Huang
Symmetry 2022, 14(9), 1851; https://doi.org/10.3390/sym14091851 - 5 Sep 2022
Cited by 40 | Viewed by 10725
Abstract
Relativistic magnetohydrodynamics (RMHD) provides an extremely useful description of the low-energy long-wavelength phenomena in a variety of physical systems from quark–gluon plasma in heavy-ion collisions to matters in supernova, compact stars, and early universe. We review the recent theoretical progresses of RMHD, such [...] Read more.
Relativistic magnetohydrodynamics (RMHD) provides an extremely useful description of the low-energy long-wavelength phenomena in a variety of physical systems from quark–gluon plasma in heavy-ion collisions to matters in supernova, compact stars, and early universe. We review the recent theoretical progresses of RMHD, such as a formulation of RMHD from the perspective of magnetic flux conservation using the entropy–current analysis, the nonequilibrium statistical operator approach applied to quantum electrodynamics, and the relativistic kinetic theory. We discuss how the transport coefficients in RMHD are computed in kinetic theory and perturbative quantum field theories. We also explore the collective modes and instabilities in RMHD with a special emphasis on the role of chirality in a parity-odd plasma. We also give some future prospects of RMHD, including the interaction with spin hydrodynamics and the new kinetic framework with magnetic flux conservation. Full article
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16 pages, 4248 KB  
Article
High-Efficiency Flicker-Free LED Driver with Soft-Switching Feature
by Hung-Liang Cheng, Lain-Chyr Hwang, Heidi H. Chang, Qi-You Wang and Chun-An Cheng
Micromachines 2022, 13(5), 797; https://doi.org/10.3390/mi13050797 - 20 May 2022
Cited by 3 | Viewed by 2987
Abstract
A novel interleaved DC-DC buck converter is proposed to drive high-brightness light-emitting diodes (LEDs). The circuit configuration mainly consists of two buck converters, which are connected in parallel and use interleaved operation. Through interleaved operation, the power capability of the converter is doubled. [...] Read more.
A novel interleaved DC-DC buck converter is proposed to drive high-brightness light-emitting diodes (LEDs). The circuit configuration mainly consists of two buck converters, which are connected in parallel and use interleaved operation. Through interleaved operation, the power capability of the converter is doubled. Traditionally, two individual inductors are used in the two buck converters. The difference between conventional parallel-operated buck converters using two energy storage inductors and the proposed circuit is that the proposed circuit uses two small inductors and a coupled inductor that replace the two inductors of the buck converters. In this way, both buck converters can be designed to operate in discontinuous-current mode (DCM), even if the magnetizing inductance of the coupled inductor is large. Therefore, the freewheeling diodes can achieve zero-current switching off (ZCS). Applying the principle of conservation of magnetic flux, the magnetizing current is converted between the two windings of the coupled inductor. Because nearly constant magnetizing current continuously flows into the output, the output voltage ripple can be effectively reduced without the use of large-value electrolytic capacitors. In addition, each winding current can drop from positive to negative, and this reverse current can discharge the parasitic capacitor of the active switch to zero volts. In this way, the active switches can operate at zero-voltage switching on (ZVS), leading to low switching losses. A 180 W prototype LED driver was built and tested. Our experimental results show satisfactory performance. Full article
(This article belongs to the Section D:Materials and Processing)
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12 pages, 5118 KB  
Article
Nonlinear Varying-Network Magnetic Circuit Analysis of Consequent-Pole Permanent-Magnet Motor for Electric Vehicles
by Hui Wang, Kwok Tong Chau, Christopher H. T. Lee, C. C. Chan and Tengbo Yang
World Electr. Veh. J. 2021, 12(4), 254; https://doi.org/10.3390/wevj12040254 - 1 Dec 2021
Cited by 5 | Viewed by 3355
Abstract
To conserve rare earth resources, consequent-pole permanent-magnet (CPPM) machine has been studied, which employs iron-pole to replace half PM poles. Meanwhile, to increase flux-weakening ability, hybrid excitation CPPM machine with three-dimensional (3-D) flux flow has been proposed. Considering finite element method (FEM) is [...] Read more.
To conserve rare earth resources, consequent-pole permanent-magnet (CPPM) machine has been studied, which employs iron-pole to replace half PM poles. Meanwhile, to increase flux-weakening ability, hybrid excitation CPPM machine with three-dimensional (3-D) flux flow has been proposed. Considering finite element method (FEM) is time-consuming, for the analysis of the CPPM machine, this paper presents a nonlinear varying-network magnetic circuit (NVNMC), which can analytically calculate the corresponding electromagnetic performances. The key is to separate the model of CPPM machine into different elements reasonably; thus, the reluctances and magnetomotive force (MMF) sources in each element can be deduced. While taking into account magnetic saturation in the iron region, the proposed NVNMC method can accurately predict the 3-D magnetic field distribution, hence determining the corresponding back-electromotive force and electromagnetic power. Apart from providing fast calculation, this analytical method can provide physical insight on how to optimize the design parameters of this CPPM machine. Finally, the accuracy of the proposed model is verified by comparing the analytical results with the results obtained by using FEM. As a result, with so many desired attributes, this method can be employed for machine initial optimization to achieve higher power density. Full article
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15 pages, 2709 KB  
Article
Significant Involvement of Double Diffusion Theories on Viscoelastic Fluid Comprising Variable Thermophysical Properties
by Muhammad Sohail, Umar Nazir, Omar Bazighifan, Rami Ahmad El-Nabulsi, Mahmoud M. Selim, Hussam Alrabaiah and Phatiphat Thounthong
Micromachines 2021, 12(8), 951; https://doi.org/10.3390/mi12080951 - 12 Aug 2021
Cited by 33 | Viewed by 2359
Abstract
This report examines the heat and mass transfer in three-dimensional second grade non-Newtonian fluid in the presence of a variable magnetic field. Heat transfer is presented with the involvement of thermal relaxation time and variable thermal conductivity. The generalized theory for mass flux [...] Read more.
This report examines the heat and mass transfer in three-dimensional second grade non-Newtonian fluid in the presence of a variable magnetic field. Heat transfer is presented with the involvement of thermal relaxation time and variable thermal conductivity. The generalized theory for mass flux with variable mass diffusion coefficient is considered in the transport of species. The conservation laws are modeled in simplified form via boundary layer theory which results as a system of coupled non-linear partial differential equations. Group similarity analysis is engaged for the conversion of derived conservation laws in the form of highly non-linear ordinary differential equations. The solution is obtained vial optimal homotopy procedure (OHP). The convergence of the scheme is shown through error analysis. The obtained solution is displayed through graphs and tables for different influential parameters. Full article
(This article belongs to the Special Issue Non-Newtonian Microfluidics)
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14 pages, 1019 KB  
Article
Variable Energy Fluxes and Exact Relations in Magnetohydrodynamics Turbulence
by Mahendra Verma, Manohar Sharma, Soumyadeep Chatterjee and Shadab Alam
Fluids 2021, 6(6), 225; https://doi.org/10.3390/fluids6060225 - 15 Jun 2021
Cited by 7 | Viewed by 3090
Abstract
In magnetohydrodynamics (MHD), there is a transfer of energy from the velocity field to the magnetic field in the inertial range itself. As a result, the inertial-range energy fluxes of velocity and magnetic fields exhibit significant variations. Still, these variable energy fluxes satisfy [...] Read more.
In magnetohydrodynamics (MHD), there is a transfer of energy from the velocity field to the magnetic field in the inertial range itself. As a result, the inertial-range energy fluxes of velocity and magnetic fields exhibit significant variations. Still, these variable energy fluxes satisfy several exact relations due to conservation of energy. In this paper, using numerical simulations, we quantify the variable energy fluxes of MHD turbulence, as well as verify several exact relations. We also study the energy fluxes of Elsässer variables that are constant in the inertial range. Full article
(This article belongs to the Special Issue Fluids in Magnetic/Electric Fields)
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21 pages, 3382 KB  
Review
Axion-like Particle Searches with IACTs
by Ivana Batković, Alessandro De Angelis, Michele Doro and Marina Manganaro
Universe 2021, 7(6), 185; https://doi.org/10.3390/universe7060185 - 5 Jun 2021
Cited by 10 | Viewed by 4056 | Correction
Abstract
The growing interest in axion-like particles (ALPs) stems from the fact that they provide successful theoretical explanations of physics phenomena, from the anomaly of the CP-symmetry conservation in strong interactions to the observation of an unexpectedly large TeV photon flux from [...] Read more.
The growing interest in axion-like particles (ALPs) stems from the fact that they provide successful theoretical explanations of physics phenomena, from the anomaly of the CP-symmetry conservation in strong interactions to the observation of an unexpectedly large TeV photon flux from astrophysical sources, at distances where the strong absorption by the intergalactic medium should make the signal very dim. In this latter condition, which is the focus of this review, a possible explanation is that TeV photons convert to ALPs in the presence of strong and/or extended magnetic fields, such as those in the core of galaxy clusters or around compact objects, or even those in the intergalactic space. This mixing affects the observed γ-ray spectrum of distant sources, either by signal recovery or the production of irregularities in the spectrum, called ‘wiggles’, according to the specific microscopic realization of the ALP and the ambient magnetic field at the source, and in the Milky Way, where ALPs may be converted back to γ rays. ALPs are also proposed as candidate particles for the Dark Matter. Imaging Atmospheric Cherenkov telescopes (IACTs) have the potential to detect the imprint of ALPs in the TeV spectrum from several classes of sources. In this contribution, we present the ALP case and review the past decade of searches for ALPs with this class of instruments. Full article
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34 pages, 1138 KB  
Article
Neoclassical Navier–Stokes Equations Considering the Gyftopoulos–Beretta Exposition of Thermodynamics
by Janusz Badur, Michel Feidt and Paweł Ziółkowski
Energies 2020, 13(7), 1656; https://doi.org/10.3390/en13071656 - 2 Apr 2020
Cited by 8 | Viewed by 2910
Abstract
The seminal Navier–Stokes equations were stated even before the creation of the foundations of thermodynamics and its first and second laws. There is a widespread opinion in the literature on thermodynamic cycles that the Navier–Stokes equations cannot be taken as a thermodynamically correct [...] Read more.
The seminal Navier–Stokes equations were stated even before the creation of the foundations of thermodynamics and its first and second laws. There is a widespread opinion in the literature on thermodynamic cycles that the Navier–Stokes equations cannot be taken as a thermodynamically correct model of a local “working fluid”, which would be able to describe the conversion of “heating” into “working” (Carnot’s type cycles) and vice versa (Afanasjeva’s type cycles). Also, it is overall doubtful that “cycle work is converted into cycle heat” or vice versa. The underlying reason for this situation is that the Navier–Stokes equations come from a time when thermodynamic concepts such as “internal energy” were still poorly understood. Therefore, this paper presents a new exposition of thermodynamically consistent Navier–Stokes equations. Following that line of reasoning—and following Gyftopoulos and Beretta’s exposition of thermodynamics—we introduce the basic concepts of thermodynamics such as “heating” and “working” fluxes. We also develop the Gyftopoulos and Beretta approach from 0D into 3D continuum thermodynamics. The central role within our approach is played by “internal energy” and “energy conversion by fluxes.” Therefore, the main problem of exposition relates to the internal energy treated here as a form of “energy storage.” Within that context, different forms of energy are discussed. In the end, the balance of energy is presented as a sum of internal, kinetic, potential, chemical, electrical, magnetic, and radiation energies in the system. These are compensated by total energy flux composed of working, heating, chemical, electrical, magnetic, and radiation fluxes at the system boundaries. Therefore, the law of energy conservation can be considered to be the most important and superior to any other law of nature. This article develops and presents in detail the neoclassical set of Navier–Stokes equations forming a thermodynamically consistent model. This is followed by a comparison with the definition of entropy (for equilibrium and non-equilibrium states) within the context of available energy as proposed in the Gyftopoulos and Beretta monograph. The article also discusses new possibilities emerging from this “continual” Gyftopoulos–Beretta exposition with special emphasis on those relating to extended irreversible thermodynamics or Van’s “universal second law”. Full article
(This article belongs to the Section J: Thermal Management)
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