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Fundamentals of Electric Field
Published in Sivaji Chakravorti, Electric Field Analysis, 2017
ABSTRACT Leaving aside nuclear interactions, there are two non-contact forces that act at a distance, namely, gravitational and electric forces. Gravitational force is dominant at large distances whereas electric forces are dominant at shorter distances. The root cause of electric forces is electric charge. The effect of electric charge is spread over the entire space around it, but it falls rapidly with distance. The presence of an electric field is detected by observing the force on a charged body located within the field region. Electric field intensity is obtained by dividing the electric force by the magnitude of the test charge. To have an electric field parameter, which is independent of the charge of the test body, electric potential is introduced in the analysis, such that electric field intensity, which is a vector quantity, is the spatial derivative of electric potential, which is a scalar quantity. For a given material, electric field intensity depends on the electric flux density, which in turn depends on the amount of source charges present in the field region. For the purpose of electric field analysis, several types of charge configurations are considered, such as point, line, ring and disc charges.
Parallel curves
Published in International Journal of Mathematical Education in Science and Technology, 2022
Richard Dexter Sauerheber, Tony Stewart
The orbital paths of planets around the sun form concentric elliptic curves on a plane (Figure 11) but are not actually parallel curves, while appearing nearly so, having only a slight eccentricity. As proven mathematically by Isaac Newton, this deviation from circular is necessary to drive oscillations that cause orbiting bodies in space to propagate in perpetuity from a non-contact force from a distance. Graphs of ellipses given by x2//4 + y2/9 = 1 or = 2 or = 3, in a manner analogous to parallel curves generated from equations for circles having differing radii, were examined. The ellipses are not parallel, since the lengths of perpendicular segments along the X axis are different than the corresponding segment lengths along the Y axis. Applying this test on the elliptic equations for the planets with radii given as a function of angle θ, τhe lengths of line segments perpendicular to the orbit paths is not constant throughout the domain (not shown). Thus the concentric ellipses of the planetary orbits are not parallel curves.
Simulation of pedestrian behavior during the flashing green signal using a modified social force model
Published in Transportmetrica A: Transport Science, 2019
Zhuping Zhou, Yang Zhou, Ziyuan Pu, Yongneng Xu
Although SFM is recognized to be a simulation model which accurately reflects pedestrians’ movement, there are still some shortcomings (e.g. low operating efficiency, difficult and complex process for parameter calibration, and the overlap among pedestrians in the model simulation). A large number of studies were carried out on the improvement, development and application of SFM. Helbing revised the interaction force between individuals by introducing the anisotropy of force from other pedestrians. Yu et al. (2005) modified the form of non-contact force with a function of centrifugal force. Lakoba, Kaup, and Finkelstein (2005) calculated the binary interaction by considering the deflection angle. Hu, Fang, and Deng (2009) redefined the interaction scope among pedestrians to improve the model operating efficiency. And the overlap phenomenon was solved by revising the relative speed among pedestrians.
CFD-DEM combined the fictitious domain method with monte carlo method for studying particle sediment in fluid
Published in Particulate Science and Technology, 2018
Shengli Ma, Zhengying Wei, Xueli Chen
Discrete element method belongs to the Lagrange group of methods, where each particle is tracked, and the Newton theorem is used to solve the problem. The contact force and the non-contact force are applied to the particle. The force balance for the particle with an index i is written as: where Fext is external force field like gravity, electrostatic, or magnetic forces, and Fpp is the particle-particle contact force that is the sum of normal force Fi,n and tangential force Fi,t, and it will be described in detail in the next section. Fpw is the particle-wall contact force, and Fpf is the fluid force applied to the particle that is equal to the fdrag in equation (17). Ti,r is an additional torque on the particle.