field equations
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Omar S. Daif ◽  
M. Helmy Abd El-Raouf ◽  
Mohamed Adel Esmaeel ◽  
Abd Elsamie B. Kotb

<span>In this paper, the field analysis of the sleeve rotor induction motor (IM) is carried out taking the rotor ends into consideration. Here, the field system equations are derived using the cylindrical model with applying Maxwell's field equations. It is expected that, both starting and maximum torques will increase with taking the rotor ends than that without rotor ends. A simple model is used to establish the geometry of the rotor ends current density and to investigate the air gap flux density. The magnetic flux is assumed to remain radially constant through the very small air gap length between the sleeve and stator surfaces. Variation of the field in the radial direction is ignored and the skin effect in the axial direction is considered. The axial distributions of the air gap flux density, the sleeve current density components and the force density have been determined. The motor performance is carried out taking into account the effects of the rotor ends on the starting and normal operations. The sleeve rotor resistance and leakage reactance have been obtained in terms of the cylindrical geometry of the machine. These equivalent circuit parameters have been calculated and plotted as functions of the motor speed with and without the rotor ends.</span>

Carlos Baladrón ◽  
Andrei Khrennikov

Closed timelike curves (CTCs), non-intuitive theoretical solutions of general relativity field equations can be modelled in quantum mechanics in a way, known as Deutsch-CTCs, to circumvent one of their most paradoxical implications, namely, the so-called grandfather paradox. An outstanding theoretical result of this model is the demonstration that in the presence of a Deutsch-CTC a classical computer would be computationally equivalent to a quantum computer. In the present study, the possible implications of such a striking result for the foundations of quantum mechanics and the connections between classicality and quantumness are explored. To this purpose, a model for fundamental particles that interact in physical space exchanging carriers of momentum and energy is considered. Every particle is then supplemented with an information space in which a probabilistic classical Turing machine is stored. It is analysed whether, through the action of Darwinian evolution, both a classical algorithm coding the rules of quantum mechanics and an anticipation module might plausibly be developed on the information space from initial random behaviour. The simulation of a CTC on the information space of the particle by means of the anticipation module would imply that fundamental particles, which do not possess direct intrinsic quantum features from first principles in this information-theoretic Darwinian approach, could however generate quantum emergent behaviour in real time as a consequence of Darwinian evolution acting on information-theoretic physical systems.

Quantum ◽  
2022 ◽  
Vol 6 ◽  
pp. 617
David Plankensteiner ◽  
Christoph Hotter ◽  
Helmut Ritsch

A full quantum mechanical treatment of open quantum systems via a Master equation is often limited by the size of the underlying Hilbert space. As an alternative, the dynamics can also be formulated in terms of systems of coupled differential equations for operators in the Heisenberg picture. This typically leads to an infinite hierarchy of equations for products of operators. A well-established approach to truncate this infinite set at the level of expectation values is to neglect quantum correlations of high order. This is systematically realized with a so-called cumulant expansion, which decomposes expectation values of operator products into products of a given lower order, leading to a closed set of equations. Here we present an open-source framework that fully automizes this approach: first, the equations of motion of operators up to a desired order are derived symbolically using predefined canonical commutation relations. Next, the resulting equations for the expectation values are expanded employing the cumulant expansion approach, where moments up to a chosen order specified by the user are included. Finally, a numerical solution can be directly obtained from the symbolic equations. After reviewing the theory we present the framework and showcase its usefulness in a few example problems.

2022 ◽  
Vol 21 (12) ◽  
pp. 310
Avirt S. Lighuda ◽  
Jefta M. Sunzu ◽  
Sunil D. Maharaj ◽  
Eunice W. Mureithi

Abstract We establish new charged stellar models from the Einstein-Maxwell field equations for relativistic superdense objects outfitted with three layers. The core layer is described by a linear equation of state (EoS) describing quark matter, while the intermediate layer is described by a Bose-Einstein condensate EoS for Bose-Einstein condensate matter and the envelope layers satisfying a quadratic EoS for the neutron fluid. We have specified a new choice of the electric field and one of the metric potentials. It is interesting to note that the choice of electric field in this model can be set to vanish and we can regain earlier neutral models. Plots generated depict that the matter variables, gravitational potentials and other physical conditions are consistent with astrophysical studies. The interior layers and exterior boundary are also matched.

2022 ◽  
Vol 82 (1) ◽  
Hrishikesh Chakrabarty ◽  
Debasish Borah ◽  
Ahmadjon Abdujabbarov ◽  
Daniele Malafarina ◽  
Bobomurat Ahmedov

AbstractWe study the effects of gravitational lensing on neutrino oscillations in the $$\gamma $$ γ -spacetime which describes a static, axially-symmetric and asymptotically flat solution of the Einstein’s field equations in vacuum. Using the quantum-mechanical treatment for relativistic neutrinos, we calculate the phase of neutrino oscillations in this spacetime by considering both radial and non-radial propagation. We show the dependence of the oscillation probability on the absolute neutrino masses, which in the two-flavour case also depends upon the sign of mass squared difference, in sharp contrast with the well-known results of vacuum oscillation in flat spacetime. We also show the effects of the deformation parameter $$\gamma $$ γ on neutrino oscillations and reproduce previously known results for the Schwarzschild metric. We then extend these to a more realistic three flavours neutrino scenario and study the effects of the parameter $$\gamma $$ γ and the lightest neutrino mass while using best fit values of neutrino oscillation parameters.

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