scholarly journals Magnetic motion of spherical frictional charged particles on the unit sphere

2019 ◽  
Vol 65 (5 Sept-Oct) ◽  
pp. 496 ◽  
Author(s):  
Talat Körpınar ◽  
Ridvan Cem Demirkol
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Potential Energy ◽  
Frictional Force ◽  
Poynting Vector ◽  
Positive Curvature ◽  
Charged Particles ◽  
Energy Functional ◽  
Ordinary Space ◽  
Potential Energy Functional

Mathematically, the sphere unit S² is described to be a 2-sphere in an ordinary space with a positive curvature. In this study, we aim to present the manipulation of a spherical charged particle in a continuous motion with a magnetic field on the sphere S² while it is exposed to a frictional force. In other words, we effot to derive the exact geometric characterization for the spherical charged particle under the influence of a frictional force field on the unit 2-sphere. This approach also helps to discover some physical and kinematical characterizations belonging to the particle such as the magnetic motion, the torque, the potential energy functional, and the Poynting vector.

Principles of minimum potential energy and complementary energy

2020 ◽  
pp. 228-248
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Boundary Condition ◽  
Potential Energy ◽  
Displacement Field ◽  
Mixed Boundary ◽  
Energy Functional ◽  
The Body ◽  
Minimum Potential Energy ◽  
Complementary Energy ◽  
Minimum Potential ◽  
Potential Energy Functional

With the displacement field taken as the only fundamental unknown field in a mixed-boundary-value problem for linear elastostatics, the principle of minimum potential energy asserts that a potential energy functional, which is defined as the difference between the free energy of the body and the work done by the prescribed surface tractions and the body forces --- assumes a smaller value for the actual solution of the mixed problem than for any other kinematically admissible displacement field which satisfies the displacement boundary condition. This principle provides a weak or variational method for solving mixed boundary-value-problems of elastostatics. In particular, instead of solving the governing Navier form of the partial differential equations of equilibrium, one can search for a displacement field such that the first variation of the potential energy functional vanishes. A similar principle of minimum complementary energy, which is phrased in terms of statically admissible stress fields which satisfy the equilibrium equation and the traction boundary condition, is also discussed. The principles of minimum potential energy and minimum complementary energy can also be applied to derive specialized principles which are particularly well-suited to solving structural problems; in this context the celebrated theorems of Castigliano are discussed.

Two Kinds of Finite Element Variables Based on B-Spline Wavelet on Interval for Curved Beam

2019 ◽  
Vol 11 (02) ◽  
pp. 1950017 ◽  
Author(s):  
Yanfei He ◽  
Xingwu Zhang ◽  
Jia Geng ◽  
Xuefeng Chen ◽  
Zengguang Li
Keyword(s):  
Finite Element ◽  
Potential Energy ◽  
Free Vibration Analysis ◽  
Energy Functional ◽  
Curved Beam ◽  
Spline Wavelet ◽  
B Spline ◽  
Generalized Potential ◽  
Potential Energy Functional ◽  
Two Kinds Of Variables

Curved beam structure has been widely used in engineering, due to its good load-bearing and geometric characteristics. More common methods for analyzing and designing this structure are the finite element methods (FEMs), but these methods have many disadvantages. Fortunately, the multivariable wavelet FEMs can solve these drawbacks. However, the multivariable generalized potential energy functional of curved beam, used to construct this element, has not been given in previous literature. In this paper, the generalized potential energy functional for curved beam with two kinds of variables is derived initially. On this basis, the B-spline wavelet on the interval (BSWI) is used as the interpolation function to construct the wavelet curved beam element with two kinds of variables. In the end, several typical numerical examples of thin to thick curved beams are given, which show that the present element is more effective in static and free vibration analysis of curved beam structures.

Orbits of magnetized charged particles in parabolic and inverse electrostatic potentials

2016 ◽  
Vol 82 (1) ◽  
Author(s):  
P. M. Bellan
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Charged Particle ◽  
Penning Trap ◽  
Axial Magnetic Field ◽  
Charged Particles ◽  
Analytic Solutions ◽  
The Other ◽  
Particle Orbit ◽  
Slow Frequency

Analytic solutions are presented for the orbit of a charged particle in the combination of a uniform axial magnetic field and parabolic electrostatic potential. These trajectories are shown to correspond to the sum of two individually rotating vectors with one vector rotating at a constant fast frequency and the other rotating in the same sense but with a constant slow frequency. These solutions are related to Penning trap orbits and to stochastic orbits. If the lengths of the two rotating vectors are identical, the particle has zero canonical angular momentum in which case the particle orbit will traverse the origin. If the potential has an inverse dependence on distance from the source of the potential, the particle can impact the source. Axis-encircling orbits are where the length of the vector associated with the fast frequency is longer than the vector associated with the slow frequency. Non-axis-encircling orbits are the other way around.

scholarly journals CHARGED PARTICLES WITH SPIN IN A GRAVITATIONAL WAVE AND A UNIFORM MAGNETIC FIELD

2006 ◽  
Vol 15 (01) ◽  
pp. 121-130 ◽  
Author(s):  
MORTEZA MOHSENI
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Gravitational Wave ◽  
Uniform Magnetic Field ◽  
Charged Particles ◽  
Space Time ◽  
Pp Wave

We study the motion of a pseudo-classical charged particle with spin in the space–time of a gravitational pp wave in the presence of a uniform magnetic field.

A vectorizable potential energy functional for reactive scattering

1987 ◽  
Vol 72 (4) ◽  
pp. 253-264 ◽  
Author(s):  
Ernesto Garcia ◽  
Luigi Ciccarelli ◽  
Antonio Lagan�
Keyword(s):  
Potential Energy ◽  
Energy Functional ◽  
Reactive Scattering ◽  
Potential Energy Functional

Stability of the critical equilibrium of a compressed column on a Winkler foundation

2021 ◽  
pp. 108128652110615
Author(s):  
Mingzhi Gao ◽  
Ming Jin
Keyword(s):  
Potential Energy ◽  
Energy Functional ◽  
Exact Expression ◽  
Second Order ◽  
Winkler Foundation ◽  
Critical Equilibrium ◽  
Order Variation ◽  
The Stability ◽  
Potential Energy Functional ◽  
Theoretical Results

In this paper, the critical equilibrium of a simply supported compressed column on a Winkler foundation is analyzed based on Koiter’s theory. The exact expression of the potential energy functional is presented. By the Fourier series of the disturbance deflection, the second-order variation of the potential energy is expressed as a quadratic form. At critical equilibrium, the second-order variation of the potential energy is semi-positive definite, so that the stability of the critical equilibrium is determined by the sign of the fourth-order variation or sixth-order variation. It can be seen that only in two small ranges of elastic-foundation stiffness is the corresponding critical state stable and the bifurcation equilibrium upward. Then, the theoretical results of this paper are compared with previous experimental and theoretical results.

Critical Examination of a Proposed Charged-Particle Stern–Gerlach Experiment

1972 ◽  
Vol 50 (3) ◽  
pp. 185-195
Author(s):  
Thomas F. Knott
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Phase Space ◽  
Initial Phase ◽  
Initial Conditions ◽  
Transverse Velocity ◽  
Charged Particles ◽  
Transverse Magnetic ◽  
Critical Examination ◽  
Focusing Effect

It has been proposed by Enga and Bloom that combined electric and magnetic helical quadrupole fields may be used to perform a Stern–Gerlach experiment on charged particles. A detailed investigation shows that the longitudinal Lorentz force due to coupling of the transverse velocity of the particles to the transverse magnetic field produces an additional focusing effect which masks the Stern–Gerlach force in large regions of initial phase space. Consideration of uncompensated magnetic fields, produced by small random variations in conductor dimensions and location, shows that the tolerances required to preserve spin separation in the useful range of initial conditions are several orders of magnitude higher than can be achieved at this time.

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