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Статті в журналах з теми "Lorentz system"

Автор: Grafiati

Опубліковано: 28 травня 2022

Оновлено: 31 липня 2025

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1

Precup, Radu-Emil, Marius L. Tomescu, and Stefan Preitl. "Lorenz System Stabilization Using Fuzzy Controllers." International Journal of Computers Communications & Control 2, no. 3 (2007): 279. http://dx.doi.org/10.15837/ijccc.2007.3.2360.

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The paper suggests a Takagi Sugeno (TS) fuzzy logic controller (FLC) designed to stabilize the Lorentz chaotic systems. The stability analysis of the fuzzy control system is performed using Barbashin-Krasovskii theorem. This paper proves that if the derivative of Lyapunov function is negative semi-definite for each fuzzy rule then the controlled Lorentz system is asymptotically stable in the sense of Lyapunov. The stability theorem suggested here offers sufficient conditions for the stability of the Lorenz system controlled by TS FLCs. An illustrative example describes the application of the n

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2

Zlatanovska, Biljana, and Donc̆o Dimovski. "A modified Lorenz system: Definition and solution." Asian-European Journal of Mathematics 13, no. 08 (2020): 2050164. http://dx.doi.org/10.1142/s1793557120501648.

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Based on the approximations of the Lorenz system of differential equations from the papers [B. Zlatanovska and D. Dimovski, Systems of difference equations approximating the Lorentz system of differential equations, Contributions Sec. Math. Tech. Sci. Manu. XXXIII 1–2 (2012) 75–96, B. Zlatanovska and D. Dimovski, Systems of difference equations as a model for the Lorentz system, in Proc. 5th Int. Scientific Conf. FMNS, Vol. I (Blagoevgrad, Bulgaria, 2013), pp. 102–107, B. Zlatanovska, Approximation for the solutions of Lorenz system with systems of differential equations, Bull. Math. 41(1) (20

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3

Eremin, I. E., V. V. Neshchimenko, D. S. Shcherban, and D. V. Fomin. "System modification of the equation Lorenz–Lorentz–Clausius–Mossotti." Optik 231 (April 2021): 166327. http://dx.doi.org/10.1016/j.ijleo.2021.166327.

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4

Vodinchar, Gleb, and Evgeny Kazakov. "The Lorenz system and its generalizations as dynamo models with memory." E3S Web of Conferences 62 (2018): 02011. http://dx.doi.org/10.1051/e3sconf/20186202011.

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The one of the known applications of the classical Lorenz system is an axisymmetric αω-dynamo with a dynamical quenching of the α-effect by the helicity. In this paper we consider generalizations of the Lorentz system, which are the models of α2 - and α2ω-dynamo. The cases of finite and infinite memory in the quenching functional are considered. The conditions for the existence of stationary dynamo regimes and regimes of regular and chaotic inversions are analytically and numerically studded.

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5

Das, Mukul Chandra, and Rampada Misra. "Three Simultaneous Superimposed Rotating System." International Letters of Chemistry, Physics and Astronomy 13 (September 2013): 215–19. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.13.215.

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In inertial system, co-ordinate transformation from one frame to another is possible by using Lorentz transformation matrix. But in non-inertial or rotating system it is not applicable by using Lorentz transformation matrix. In this paper, co-ordinate transformation from one frame to another in three simultaneous superimposed rotating systems has been introduced. This also leads to assume a picture of space-time geometry of same system.

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6

Das, Mukul Chandra, and Rampada Misra. "Three Simultaneous Superimposed Rotating System." International Letters of Chemistry, Physics and Astronomy 13 (May 3, 2013): 215–19. http://dx.doi.org/10.56431/p-8ww1dq.

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Анотація:

In inertial system, co-ordinate transformation from one frame to another is possible by using Lorentz transformation matrix. But in non-inertial or rotating system it is not applicable by using Lorentz transformation matrix. In this paper, co-ordinate transformation from one frame to another in three simultaneous superimposed rotating systems has been introduced. This also leads to assume a picture of space-time geometry of same system.

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7

Bhuiyan, S. A., and A. R. Baizid. "Volume Charge Density in Most General Lorentz Transformation." Journal of Scientific Research 8, no. 3 (2016): 259–65. http://dx.doi.org/10.3329/jsr.v8i3.27133.

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Lorentz Transformations generally describe the transformations for observations between mechanical phenomenon systems in relative motion. We all know that the electrical charge of associate isolated system is relativistically invariant. We have studied the volume charge density in Special and Most General Lorentz Transformations. If one frame moves on x-axis then we will notice this in Special Lorentz Transformation. On the other hand if the motion of the moving frame is not on the x-axis relative to the rest frame however the motion is on any arbitrary direction then we will notice this formu

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8

Sem�nov, E. M. "Haar system rearrangements in Lorentz spaces." Siberian Mathematical Journal 34, no. 6 (1993): 1142–48. http://dx.doi.org/10.1007/bf00973478.

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9

Pilawa, Barbara, Andrzej Więckowski, Robert Pietrzak, and Helena Wachowska. "Microwave saturation of EPR spectra of oxidised coal." Open Chemistry 5, no. 1 (2007): 330–40. http://dx.doi.org/10.2478/s11532-006-0056-7.

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AbstractMicrowave saturation of multi-component EPR spectra of oxidized lignite Mequinenza (Spain) with a carbon content of 65.1 wt % and with a high sulphur content of 10.3 wt % was studied. The coal was oxidized with nitric acid (NHO3), peroxyacetic acid (PAA), and in O2/Na2CO3 system. Three different groups of paramagnetic centres exist in the coal samples analyzed. The EPR spectrum of the demineralised coal was a superposition of broad Gauss (ΔB pp = 0.75 mT), broad Lorentz 1 (ΔB pp = 0.42 mT) and narrow Lorentz 3 lines (ΔB pp = 0.08 mT). The three EPR components with linewidths: 0.58–0.77

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10

Das, Mukul Chandra, and Rampada Misra. "Lorentz Transformation in Super System and in Super System of Photon." International Letters of Chemistry, Physics and Astronomy 38 (September 2014): 8–14. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.38.8.

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Lorentz transformation considers that relative velocity of the frame of references in inertialsystem is less than the velocity of light. If it be such that a frame is moving with velocity same as thatof light with respect to a frame of observer then, Lorentz transformation in it will not be same as donein inertial system. Again photon is not only a particle or wave but it is a complex system due to thefact that it possesses spin and linear motion simultaneously. So, it will have some complexcharacteristics. In this work first, trial would be made to find out the process of Lorentztransformatio

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11

Das, Mukul Chandra, and Rampada Misra. "Lorentz Transformation in Super System and in Super System of Photon." International Letters of Chemistry, Physics and Astronomy 38 (September 3, 2014): 8–14. http://dx.doi.org/10.56431/p-678g22.

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Анотація:

Lorentz transformation considers that relative velocity of the frame of references in inertialsystem is less than the velocity of light. If it be such that a frame is moving with velocity same as thatof light with respect to a frame of observer then, Lorentz transformation in it will not be same as donein inertial system. Again photon is not only a particle or wave but it is a complex system due to thefact that it possesses spin and linear motion simultaneously. So, it will have some complexcharacteristics. In this work first, trial would be made to find out the process of Lorentztransformatio

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12

Alberico, Angela, Andrea Cianchi, and Carlo Sbordone. "Continuity properties of solutions to the p-Laplace system." Advances in Calculus of Variations 10, no. 1 (2017): 1–24. http://dx.doi.org/10.1515/acv-2015-0029.

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AbstractA sharp integrability condition on the right-hand side of the p-Laplace system for all its solutions to be continuous is exhibited. Their uniform continuity is also analyzed and estimates for their modulus of continuity are provided. The relevant estimates are shown to be optimal as the right-hand side ranges in classes of rearrangement-invariant spaces, such as Lebesgue, Lorentz, Lorentz–Zygmund, and Marcinkiewicz spaces, as well as some customary Orlicz spaces.

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13

Basso, Marcos L. W., and Jonas Maziero. "Complete complementarity relations and their Lorentz invariance." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2253 (2021): 20210058. http://dx.doi.org/10.1098/rspa.2021.0058.

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It is well known that entanglement under Lorentz boosts is highly dependent on the boost scenario in question. For single-particle states, a spin-momentum product state can be transformed into an entangled state. However, entanglement is just one of the aspects that completely characterizes a quantum system. The other two are known as the wave-particle duality. Although the entanglement entropy does not remain invariant under Lorentz boosts, and neither do the measures of predictability and coherence, we show here that these three measures taken together, in a complete complementarity relation

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14

Liu, Wenjuan, and Zhouyu Li. "Global weighted regularity for the 3D axisymmetric non-resistive MHD system." AIMS Mathematics 9, no. 8 (2024): 20905–18. http://dx.doi.org/10.3934/math.20241017.

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We consider the regularity criteria of axisymmetric solutions to the non-resistive MHD system with non-zero swirl in $ \mathbb{R}^{3} $. By applying a new anisotropic Hardy-Sobolev inequality in mixed Lorentz spaces, we show that strong solutions to this system can be smoothly extended beyond the possible blow-up time $ T $ if the horizontal angular component of the velocity belongs to anisotropic Lorentz spaces.

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15

Winterberg, F. "Resolution of the Ehrenfest Paradox in the Dynamic Interpretation of Lorentz Invariance." Zeitschrift für Naturforschung A 53, no. 9 (1998): 751–54. http://dx.doi.org/10.1515/zna-1998-0904.

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Abstract In the dynamic Lorentz-Poincare interpretation of Lorentz invariance, clocks in absolute motion through a preferred reference system (resp. aether) suffer a true contraction and clocks, as a result of this contraction, go slower by the same amount. With the one-way velocity of light unobservable, there is no way this older pre-Einstein interpretation of special relativity can be tested, except in cases involving rotational motion, where in the Lorentz-Poincare interpretation the interaction symmetry with the aether is broken. In this communication it is shown that Ehrenfest’s paradox,

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16

Gift, Stephan J. G. "New global positioning system (GPS) test falsifies the Lorentz transformations and special relativity." Physics Essays 34, no. 2 (2021): 231–35. http://dx.doi.org/10.4006/0836-1398-34.2.231.

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The time transformation governing the operation of the global positioning system (GPS) clocks and the time corrections required to ensure sustained clock synchronization are determined to be the Selleri time transformation and not the Lorentz time transformation. This condition, as well as GPS-demonstrated light speed anisotropy, falsifies the Lorentz transformations and special relativity.

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17

Budeanu, Maria Magdalena, and Vasile Dumitrescu. "Densities, Viscosities and Refractive Indices of Ternary System Cyclohexane + Cyclohexanol + Cyclohexanone at 293.15, 298.15 and 303.15 K." Revista de Chimie 70, no. 4 (2019): 1204–9. http://dx.doi.org/10.37358/rc.19.4.7092.

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Densities (r), viscosities (h) and refractive indices (nD) of the ternary system cyclohexane + cyclohexanol + cyclohexanone were measured at 293.15, 298.15 and 298.15 K and atmospheric pressure, over the whole composition range. The experimental values of densities and viscosities were correlated with temperature using a linear equation and Guzman equation respectively. Viscosity results were fitted with Grunberg-Nissan equation and Heric-Brewer equation. Different refractive index mixing rules (Arago-Biot, Dale-Glastone, Newton and Lorentz-Lorenz) were studied for this ternary system. The fun

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18

J. Buenker, Robert. "Lorentz Invariance and the Global Positioning System." Recent Progress in Space Technology (Formerly: Recent Patents on Space Technology) 4, no. 2 (2015): 89–98. http://dx.doi.org/10.2174/2210687104666141009225553.

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19

De Luis Pérez, Francisco Javier. "Lorentz-Invariant System with Quantum Mechanical Properties." Journal of High Energy Physics, Gravitation and Cosmology 08, no. 04 (2022): 890–95. http://dx.doi.org/10.4236/jhepgc.2022.84060.

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20

Martynyuk, Anatolii Andreevich, and Nelli Vladimirovna Nikitina. "Saddle Limit Cycles in the Lorentz System." International Applied Mechanics 39, no. 5 (2003): 613–20. http://dx.doi.org/10.1023/a:1025104112687.

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21

Goginava, U. "On Some (H p,q , L p,q )-Type Maximal Inequalities with Respect to the Walsh–Paley System." Georgian Mathematical Journal 7, no. 3 (2000): 475–88. http://dx.doi.org/10.1515/gmj.2000.475.

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Abstract The boundedness of Cesáro maximal operators for multiple Walsh–Fourier series is studied from the martingale Hardy–Lorentz space Hpq into the Lorentz space Lpq . Supremum in the maximal operators is taken over a positive cone.

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22

Kim, Young S., and Marilyn E. Noz. "Integration of Dirac’s Efforts to Construct a Quantum Mechanics Which is Lorentz-Covariant." Symmetry 12, no. 8 (2020): 1270. http://dx.doi.org/10.3390/sym12081270.

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The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be included in the Lorentz-covariant picture. In 1945, he attempted to construct a representation of the Lorentz group using a normalizable Gaussian function localized both in the space and time variables. In 1949, he introduced his instant form to exclude time-like oscillations. He also introduced the light-cone coordinate system for Lorentz boosts. Also in 1949, he stated the Lie algebra of the inhomogeneous Lorentz gro

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23

Solomon, Khmelnik. "The Lorentz force is a consequence of the system of Maxwell equations." Papers of Independent Authors, ISSN 2225-6717, 2022 55 (March 1, 2022): 30–39. https://doi.org/10.5281/zenodo.6320945.

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A new variational principle is formulated and it is proved that Maxwell's equations are a consequence of this principle. Symmetric Maxwell's equations, in which, along with electric potentials and charges, there are magnetic potentials and charges are also a consequence of this principle. Thermal losses from conduction currents are also taken into account in this principle. Maxwell's equations, supplemented by the Lorentz force formula, are also a consequence of this principle. Finally, Maxwell's equations, supplemented by the formula for the force arising from the movement of

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24

Makurat, Hanna. ""Gramatika kaszëbsczégò jãzëka" – rozpoznanie i opracowanie struktury współczesnego literackiego języka kaszubskiego. Odpowiedź na głosy krytyki." Studia z Filologii Polskiej i Słowiańskiej 53 (December 24, 2018): 331–47. http://dx.doi.org/10.11649/sfps.2018.020.

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The Grammar of the Kashubian Language – recognition and description of the structure of the contemporary Kashubian. Response to criticismThe article is a response to criticism of Hanna Makurat’s book titled The Grammar of the Kashubian Language; the book, published in 2016, is the first normative description of contemporary Kashubian. The Kashubian newspaper Skra has published a review which questioned the substantive content of the entire book. The author of the review showed incompatibilities between the book and Friedrich Lorentz’s Pomeranian Grammar, which was published in 1927–1937. Howev

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25

Glaze, Nick, Tria McNeely, Yiwen Zhu, et al. "Lorentz: Learned SKU Recommendation Using Profile Data." Proceedings of the ACM on Management of Data 2, no. 3 (2024): 1–25. http://dx.doi.org/10.1145/3654952.

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In response to diverse demands, cloud operators have significantly expanded the array of service offerings, often referred to as Stock Keeping Units (SKUs) available for computing resource configurations. Such diversity has led to increased complexity for customers to choose the appropriate SKU. In the analyzed system, only 43% of the resource capacity was rightly chosen. Although various automated solutions have attempted to resolve this issue, they often rely on the availability of enriched data, such as workload traces, which are unavailable for newly established services. Since these servi

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26

Crothers, Stephen J. "Special relativity and the Lorentz sphere." Physics Essays 33, no. 1 (2020): 15–22. http://dx.doi.org/10.4006/0836-1398-33.1.15.

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The special theory of relativity demands, by Einstein's two postulates (i) the principle of relativity and (ii) the constancy of the speed of light in vacuum, that a spherical wave of light in one inertial system transforms, via the Lorentz transformation, into a spherical wave of light (the Lorentz sphere) in another inertial system when the systems are in constant relative rectilinear motion. However, the Lorentz transformation in fact transforms a spherical wave of light into a translated ellipsoidal wave of light even though the speed of light in vacuum is invariant. The special theory of

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27

Nuha, Abdelrahman Khalid*1 Mubarak Dirar Abdallah2 Zoalnoon Ahmed Abeid Allah3 &. Sawsan Ahmed Elhouri Ahmed4. "LORENZ TRANSFORMATION FOR FREE SPACE AND FIELDS USING MAXWELL'S EQUATIONS AND NEWTON'S LAWS." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 5, no. 3 (2018): 81–85. https://doi.org/10.5281/zenodo.1206398.

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The expression of Lorentz force and Maxwell's equations were used to drive Lorentz transformation in terms of electric and magnetic fields. This expression is typical to that of special relativity. The Lorentz transformation that takes care of the effect of fields on the physical system was also derived using Newtonian laws   specially the velocity aceleration relation. The relation obtained is typical to that of generalized special relativity.

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28

UDRIŞTE, CONSTANTIN, and VINCENZO CIANCIO. "CONTROLLABILITY OF NONHOLONOMIC BLACK HOLES SYSTEMS." International Journal of Geometric Methods in Modern Physics 10, no. 02 (2012): 1250097. http://dx.doi.org/10.1142/s0219887812500971.

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This paper studies the sub-Lorentz–Vrănceanu geometry and the optimal control of nonholonomic black hole systems. This is strongly connected to the possibility of describing a nonholonomic black hole system as kernel of a Gibbs–Pfaff form or by the span of four appropriate vector fields. Joining techniques from sub-Riemannian geometry, optimal control and thermodynamics, we bring into attention new models of black holes systems. These are reflected by the original results: a Lorentz–Vrănceanu geometry on the total space, a new sub-Lorentz–Vrănceanu geometry, a new stress–energy–momentum tensor

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29

Zhou, G., and R. Chen. "Wigner distribution function of Lorentz and Lorentz–Gauss beams through a paraxial ABCD optical system." Applied Physics B 107, no. 1 (2012): 183–93. http://dx.doi.org/10.1007/s00340-012-4889-9.

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30

Du, Wen, Chengliang Zhao, and Yangjian Cai. "Propagation of Lorentz and Lorentz–Gauss beams through an apertured fractional Fourier transform optical system." Optics and Lasers in Engineering 49, no. 1 (2011): 25–31. http://dx.doi.org/10.1016/j.optlaseng.2010.09.004.

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31

Bhuiyan, S. A. "Volome Charge Density in Mixed Number Lorentz Transformation." Journal of Scientific Research 11, no. 2 (2019): 209–14. http://dx.doi.org/10.3329/jsr.v11i2.39632.

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We know charge density is changed when it observes from a moving frame of reference due to the length contraction. In this paper we have studied the volume charge density in special and mixed number Lorentz transformation. We also investigate the changes of the volume charge density of moving system in terms of rest system in mixed number Lorentz Transformations at different angles and velocities.

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32

Comay, E. "Lorentz transformation of a system carrying “Hidden Momentum”." American Journal of Physics 68, no. 11 (2000): 1007–13. http://dx.doi.org/10.1119/1.1286114.

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33

Bauer, Gernot, and Detlef Dürr. "The Maxwell-Lorentz System of a Rigid Charge." Annales Henri Poincaré 2, no. 1 (2001): 179–96. http://dx.doi.org/10.1007/pl00001030.

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34

Yao, Peter, and Timothy Sands. "Micro Satellite Orbital Boost by Electrodynamic Tethers." Micromachines 12, no. 8 (2021): 916. http://dx.doi.org/10.3390/mi12080916.

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In this manuscript, a method for maneuvering a spacecraft using electrically charged tethers is explored. The spacecraft’s velocity vector can be modified by interacting with Earth’s magnetic field. Through this method, a spacecraft can maintain an orbit indefinitely by reboosting without the constraint of limited propellant. The spacecraft-tether system dynamics in low Earth orbit are simulated to evaluate the effects of Lorentz force and torques on translational motion. With 500-meter tethers charged with a 1-amp current, a 100-kg spacecraft can gain 250 m of altitude in one orbit. By evalua

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35

Abraham A, Ungar. "Understanding Lorentz Utilizing Galilei: The Emergence of a Friendly Extended Special Relativity Theory that Admits Relativistic Multi-Particle Entanglement." Annals of Mathematics and Physics 7, no. 2 (2024): 150–57. http://dx.doi.org/10.17352/amp.000118.

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Special relativity theory stems from the Lorentz transformation of signature (1,3). The incorporation into special relativity of the Lorentz transformations of signature (m,n) for all m,n∈ℕ (n = 3 in physical applications) enriches the theory. The resulting enriched special relativity is a friendly extended special relativity that admits multi-particle entanglement, as demanded by relativistic quantum mechanics. The Lorentz transformation of signature (m,n) admits a novel physical interpretation induced by the intuitively clear interpretation of the Galilei transformation of signature (m,n) fo

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36

Akintsov, Nikolai S., Artem P. Nevecheria, Gennadii F. Kopytov, Yongjie Yang, and Tun Cao. "Special Relativity in Terms of Hyperbolic Functions with Coupled Parameters in 3+1 Dimensions." Symmetry 16, no. 3 (2024): 357. http://dx.doi.org/10.3390/sym16030357.

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This paper presents a method for parameterizing new Lorentz spacetime coordinates based on coupled parameters. The role of symmetry in rapidity in special relativity is explored, and invariance is obtained for new spacetime intervals with respect to the Lorentz transformation. Using the Euler–Hamilton equations, an additional angular rapidity and perpendicular rapidity are obtained, and the Hamiltonian and Lagrangian of a relativistic particle are expanded into rapidity spectra. A so-called passage to the limit is introduced that makes it possible to decompose physical quantities into spectra

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37

Wang, Xiaoying, Fei Jiang, and Junping Yin. "Existence and Uniqueness of the Solution of Lorentz-Rössler Systems with Random Perturbations." Abstract and Applied Analysis 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/480259.

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We consider a new chaotic system based on merging two well-known systems (the Lorentz and Rössler systems). Meanwhile, taking into account the effect of environmental noise, we incorporate whit-enoise in each equation. We prove the existence, uniqueness, and the moments estimations of the Lorentz-Rössler systems. Numerical experiments show the applications of our systems and illustrate the results.

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38

Gát, György, Ushangi Goginava, and Károly Nagy. "On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system." Studia Scientiarum Mathematicarum Hungarica 46, no. 3 (2009): 399–421. http://dx.doi.org/10.1556/sscmath.2009.1099.

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The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system is bounded from the dyadic Hardy-Lorentz space Hpq into Lorentz space Lpq for every p > 2/3 and 0 < q ≦ ∞. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system. That is, σn ( f, x1 , x2 ) → ( x1 , x2 ) a.e. as n → ∞.

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39

Birnholtz, Ofek. "Comments on initial conditions for the Abraham–Lorentz(–Dirac) equation." International Journal of Modern Physics A 30, no. 02 (2015): 1550011. http://dx.doi.org/10.1142/s0217751x15500116.

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An accelerating electric charge coupled to its own electromagnetic field both emits radiation and experiences the radiation's reaction as a (self-)force. Considering the system from an Effective Field Theory perspective, and using the physical initial conditions of no incoming radiation can help resolve many of the problems associated with the often considered "notorious" Abraham–Lorentz/Abraham–Lorentz–Dirac equations.

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40

P Morriss, Gary, and Lamberto Rondoni. "Chaos and Its Impact on the Foundations of Statistical Mechanics." Australian Journal of Physics 49, no. 1 (1996): 51. http://dx.doi.org/10.1071/ph960051.

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In this work we present a brief derivation of the periodic orbit expansion for simple dynamical systems, and then we apply it to the study of a classical statistical mechanical model, the Lorentz gas, both at equilibrium and in a nonequilibrium steady state. The results are compared with those obtained through standard molecular dynamics simulations, and they are found to be in good agreement. The form of the average using the periodic orbit expansion suggests the definition of a new dynamical partition function, which we test numerically. An analytic formula is obtained for the Lyapunov numbe

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41

SUCHY, K., and C. ALTMAN. "Reciprocity for electromagnetic–acoustic fields in compressible magnetoplasmas with anisotropic pressure." Journal of Plasma Physics 58, no. 2 (1997): 233–46. http://dx.doi.org/10.1017/s0022377897005667.

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Maxwell's curl equations and the linearized balance equations for momentum and pressure tensor for a plasma in an external magnetic field are combined in a system of first-order partial differential equations for the field quantities. With the corresponding adjoint system, the Lagrange identity is established, leading to a symmetry relation between the Green functions for the original and the adjoint fields. With temporal mapping the adjoint field can be transformed into a ‘Lorentz-adjoint’ (physical) field, leading to a reciprocity relation between the Green functions for the original and for

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42

Ostapchuk, A. K., E. M. Kuznetsova, and O. V. Dmitrieva. "Research of Cutting Processes Using the Lorentz Equation System." Bulletin of Kalashnikov ISTU 20, no. 4 (2017): 18. http://dx.doi.org/10.22213/2413-1172-2017-4-18-22.

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В настоящей работе проведено научное исследование вопроса устойчивости технологической обрабатывающей системы с разработкой математической модели - модели Лоренца. Модель построена на основе параметрического метода, разрабатываемого И. Пригожиным, а также основных законов, описывающих поведение динамических систем трения. Модель показывает, что в системе трения, включающей подсистему резца и подсистему собственного трения, при определенных условиях формируются хаотические аттракторы, что свидетельствует о присутствии детерминированного хаоса в системе. Приведены интервалы значений управляющего

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43

Vakaliuk, O., and B. Halbedel. "Lorentz Force Velocimetry using a bulk HTS magnet system." IOP Conference Series: Materials Science and Engineering 424 (October 13, 2018): 012009. http://dx.doi.org/10.1088/1757-899x/424/1/012009.

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44

Dybalski, Wojciech, and Duc Viet Hoang. "A soft-photon theorem for the Maxwell-Lorentz system." Journal of Mathematical Physics 60, no. 10 (2019): 102903. http://dx.doi.org/10.1063/1.5123592.

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45

Frank, Mariana, Ismail Turan, and Ismet Yurduşen. "The integrability of Pauli system in Lorentz violating background." Journal of High Energy Physics 2008, no. 01 (2008): 039. http://dx.doi.org/10.1088/1126-6708/2008/01/039.

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46

Oka, Koichi, and Masako Tanaka. "A simple levitation system using wireless power supply system and Lorentz force." Journal of Physics: Conference Series 744 (September 2016): 012233. http://dx.doi.org/10.1088/1742-6596/744/1/012233.

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47

Vitória, R. L. L., and H. Belich. "Effects of a Landau-Type Quantization Induced by the Lorentz Symmetry Violation on a Dirac Field." Advances in High Energy Physics 2020 (January 22, 2020): 1–7. http://dx.doi.org/10.1155/2020/4208161.

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Inspired by the extension of the Standard Model, we analyzed the effects of the spacetime anisotropies on a massive Dirac field through a nonminimal CPT-odd coupling in the Dirac equation, where we proposed a possible scenario that characterizes the breaking of the Lorentz symmetry which is governed by a background vector field and induces a Landau-type quantization. Then, in order to generalize our system, we introduce a hard-wall potential and, for a particular case, we determine the energy levels in this background. In addition, at the nonrelativistic limit of the system, we investigate the

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48

Mishra, Raja K. "Quantitative lorentz microscopy of NdFeB magnets." Proceedings, annual meeting, Electron Microscopy Society of America 46 (1988): 552–53. http://dx.doi.org/10.1017/s0424820100104820.

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It is now well established that quantitative measurement of domain wall width using Lorentz electron microscopy is nontrivial. The usual technique of extrapolating divergent wall image widths of over-focussed or under-focussed Fresnel images suffers from serious errors since it is based on geometrical considerations and does not take into account the wave optical effects of electron scattering in the microscope. These errors are overcome if one supplements the measurements with image computation for the specific electron optical system and the specimen configuration. Another way of circumventi

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49

Vasyliūnas, V. M. "The mechanical advantage of the magnetosphere: solar-wind-related forces in the magnetosphere-ionosphere-Earth system." Annales Geophysicae 25, no. 1 (2007): 255–69. http://dx.doi.org/10.5194/angeo-25-255-2007.

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Abstract. Magnetosphere-ionosphere interactions involve electric currents that circulate between the two regions; the associated Lorentz forces, existing in both regions as matched opposite pairs, are generally viewed as the primary mechanism by which linear momentum, derived ultimately from solar wind flow, is transferred from the magnetosphere to the ionosphere, where it is further transferred by collisions to the neutral atmosphere. For a given total amount of current, however, the total force is proportional to ℒB and in general, since ℒ2B~ constant by flux conservation, is much larger in

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50

Ungar, Abraham A. "A Spacetime Symmetry Approach to Relativistic Quantum Multi-Particle Entanglement." Symmetry 12, no. 8 (2020): 1259. http://dx.doi.org/10.3390/sym12081259.

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A Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, in m time and n space dimensions, is the group of pseudo-rotations of a pseudo-Euclidean space of signature (m, n). Accordingly, the Lorentz group SO(1, 3) is the common Lorentz transformation group from which special relativity theory stems. It is widely acknowledged that special relativity and quantum theories are at odds. In particular, it is known that entangled particles involve Lorentz symmetry violation. We, therefore, review studies that led to the discovery that the Lorentz group SO(m, n) forms the symmetry group b

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