A Note on the Gravitoelectromagnetic Analogy

We discuss the linear gravitoelectromagnetic approach used to solve Einstein’s equations in the weak-field and slow-motion approximation, which is a powerful tool to explain, by analogy with electromagnetism, several gravitational effects in the solar system, where the approximation holds true. In particular, we discuss the analogy, according to which Einstein’s equations can be written as Maxwell-like equations, and focus on the definition of the gravitoelectromagnetic fields in non-stationary conditions. Furthermore, we examine to what extent, starting from a given solution of Einstein’s equations, gravitoelectromagnetic fields can be used to describe the motion of test particles using a Lorentz-like force equation.

Temporal Ion Velocity Variation with Obliqueness in Magnetized Plasma Sheath

A narrow region having sharp gradients in physical parameters is formed whenever plasma comes into contact with a material wall. In this work, the temporal velocity variation of ions in such a sheath has been studied in the presence of an external oblique magnetic field. The Lorentz force equation has been solved for the given boundary conditions using Runge-Kutta method. In order to satisfy the Bohm criterion, ions enter the sheath region with ion acoustic velocity. It is observed that all components of the velocity waves are damped in plasma in the time scale of one second. The computed oscillatory part of ion velocity match with the equation of the damped harmonic oscillator. Thus obtained damping constants as well as the frequency of all three components are nearly equal for obliqueness less than 600 after which they are distinctly different. This is due to the fact that the magnetic field becomes almost parallel to the wall. In earlier studies, only the final velocity profiles are reported and hence this study is useful in understanding how the ion velocities evolve in time as they move from sheath entrance towards the wall.

A Nonlinear CFD/Multibody Incremental-Dynamic Model for A Constrained Mechanism

Numerical analysis of a multibody mechanism moving in the air is a complicated problem in computational fluid dynamics (CFD). Analyzing the motion of a multibody mechanism in a commercial CFD software, i.e., ANSYS Fluent®, is a challenging issue. This is because the components of a mechanism have to be constrained next to each other during the movement in the air to have a reliable numerical aerodynamics simulation. However, such constraints cannot be numerically modeled in a commercial CFD software, and needs to be separately incorporated into models through the programming environment, such as user-defined functions (UDF). This study proposes a nonlinear-incremental dynamic CFD/multibody method to simulate constrained multibody mechanisms in the air using UDF of ANSYS Fluent®. To testify the accuracy of the proposed method, Newton–Euler dynamic equations for a two-link mechanism are solved using Matlab® ordinary differential equations (ODEs), and the numerical results for the constrained mechanisms are compared. The UDF results of ANSYS Fluent® shows good agreement with Matlab®, and can be applied to constrained multibody mechanisms moving in the air. The proposed UDF of ANSYS Fluent® calculates the aerodynamic forces of a flying multibody mechanism in the air for a low simulation cost than the constraint force equation (CFE) method. The results could have implications in designing and analyzing flying robots to help human rescue teams, and nonlinear dynamic analyses of the aerodynamic forces applying on a moving object in the air, such as airplanes, birds, flies, etc.

Modulation frequency and velocity variation of ions in a magnetized plasma sheath for different obliqueness of the field

The understanding of ion dynamics in magnetized plasma sheath is crucial for all applications of plasma. The velocity variation as well as modulation frequency of ions in a magnetized plasma sheath has been studied for different obliqueness of the magnetic field. The governing Lorentz force equation has been solved numerically for the given boundary conditions as applicable in the kinetic simulation of the sheath. For different obliqueness of the magnetic field, the average values, maximum amplitude, damping factor as well as frequency of oscillation are studied. The oscillating velocity components change at different rates depending on their orientation with respect to the field direction. Significant changes in the damping factor and modulation frequency has been observed for all components of velocity; however, the frequency of oscillation remains the same. As the obliqueness increases, shoulder natures in the components of velocity are observed. BIBECHANA 18 (2021) 134-139

Directional magnetic and electric vortex lines and their geometries in Minkowski space

In this study, we firstly introduce a different type of directional Fermi-Walker transportations along with vortex lines of a non-vanishing vector field in three-dimensional Minkowski space. Then we consider some geometric quantities, which are used to characterize vortex lines, in order to express angular velocity vector (Darboux vector) of the system in terms of these quantities. Later we present timelike directional magnetic vortex lines by computing the Lorentz force. Hence, we reach a remarkable relation between timelike directional magnetic vortex lines and angular velocity vector of vortex lines with a nonrotating frame in Minkowski space. We also determine the timelike directional electric vortex lines by considering the electromagnetic force equation. We finally investigate the conditions of being uniform for magnetic fields of timelike directional magnetic vortex lines and we improve such a remarkable approach to find the electromagnetic curvature which contains many geometrical features belonging to timelike directional magnetic and electric vortex line.

Combination of Kharrat-Toma Transform and Homotopy Perturbation Method to Solve a Strongly Nonlinear Oscillators Equation.

This article introduces a new hybridization between the Kharrat-Toma transform and the homotopy perturbation method for solving a strongly nonlinear oscillator with a cubic and harmonic restoring force equation that arising in the applications of physical sciences. The proposed method is based on applying our new integral transform "Kharrat-Toma Transform" and then using the homotopy perturbation method. The objective of this paper is to illustrate the efficiency of this hybrid method and suggestion modified it. The results showed that the modified method is effectiveness and more accurate.

On the Equivalence Principle and Relativistic Quantum Mechanics

Einstein’s Equivalence Principle implies that the Lorentz force equation can be derived from a geodesic equation by imposing a certain (necessary) condition on the electromagnetic potential (Trzetrzelewski, EPL 120:4, 2018). We analyze the quantization of that constraint and find the corresponding differential equations for the phase of the wave function. We investigate these equations in the case of Coulomb potential and show that physically acceptable solutions do not exist. This result signals an inconsistency between Einstein’s Equivalence Principle and Relativistic Quantum Mechanics at an atomic level.

A Highschooler’s Guide to GeV-Range Electromagnetism

The following article has been written primarily by the high school students who make up the team “Cryptic Ontics”, one of the two winning teams in the 2018 edition of CERN’s Beamline for Schools (BL4S) competition, and is based on the set of experiments the students endeavoured to conduct over the course of a two-week period at CERN. Reconstructing influential physical theories from scratch often helps in uncovering hitherto unknown logical connections and eliciting instructive empirical checkpoints within said theory. With this in mind, in the following article, a top-down reconstruction (beginning with the experimental observations and ending at the theoretical framework) of the Lorentz force equation is performed, and potentially interesting questions which come up are explored. In its most common form, the equation is written out as: [Formula: see text]. Only the term that includes the magnetic field [Formula: see text] will be dealt with for this article. The independent parameters we use are (i) the momenta of the particles, (ii) the charge (rather, the types) of particles, either positive or negative, and (iii) the current passing through the dipole generating the electromagnetic field. We then measure the angle by which particles get deflected while varying these three parameters and derive an empirical relationship between them.