scholarly journals Polarity Free Magnetic Repulsion and Magnetic Bound State

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 442
Author(s):  
Hamdi Ucar
Keyword(s):  
Degrees Of Freedom ◽  
Magnetic Moments ◽  
Classical Mechanics ◽  
Magnetic Interaction ◽  
Bound State ◽  
Weak Field ◽  
Inhomogeneous Magnetic Field ◽  
Two Body Problem ◽  
New Class ◽  
Inertial Body

This is a report on a dynamic autonomous magnetic interaction which does not depend on polarities resulting in short ranged repulsion involving one or more inertial bodies and a new class of bound state based on this interaction. Both effects are new to the literature, found so far. Experimental results are generalized and reported qualitatively. Working principles of these effects are provided within classical mechanics and found consistent with observations and simulations. The effects are based on the interaction of a rigid and finite inertial body (an object having mass and moment of inertia) endowed with a magnetic moment with a cyclic inhomogeneous magnetic field which does not require to have a local minimum. Such a body having some degrees of freedom involved in driven harmonic motion by this interaction can experience a net force in the direction of the weak field regardless of its position and orientation or can find stable equilibrium with the field itself autonomously. The former is called polarity free magnetic repulsion and the latter is classified as a magnetic bound state. Experiments show that a bound state can be obtained between two free bodies having magnetic dipole moment as a solution of two-body problem. Various schemes of trapping bodies having magnetic moments by rotating fields are realized as well as rotating bodies trapped by a static dipole field in presence of gravity. Additionally, a special case of bound state called bipolar bound state between free dipole bodies is investigated.

scholarly journals Polarity Free Magnetic Repulsion and Magnetic Bound State

2020 ◽  
Author(s):  
Hamdi Ucar
Keyword(s):  
Magnetic Moments ◽  
Classical Mechanics ◽  
Magnetic Interaction ◽  
Bound State ◽  
Weak Field ◽  
Inhomogeneous Magnetic Field ◽  
New Class ◽  
Inertial Body ◽  
Special Case ◽  
Rotating Bodies

This is a report on a dynamic autonomous magnetic interaction which does not depend on polarities resulting in short ranged repulsion involving one or more inertial bodies and a new class of bound state based on this interaction. Both effects are new to the literature, found so far. Experimental results are generalized and reported qualitatively. Working principles of these effects are provided within classical mechanics and found consistent with observations and simulations. The effects are based on the interaction of a rigid and finite inertial body (an object having mass and moment of inertia) endowed with a magnetic moment with a cyclic inhomogeneous magnetic field which does not require to have a local minimum. Such a body having some DoF involved in driven harmonic motion by this interaction can experience a net force in the direction of the weak field regardless of its position and orientation or can find stable equilibrium with the field itself autonomously. The former is called polarity free magnetic repulsion and the latter magnetic bound state. Experiments show that a bound state can be obtained between two free bodies having magnetic dipole moment. Various schemes of trapping bodies having magnetic moments by rotating fields are realized as well as rotating bodies trapped by a static dipole field in presence of gravity. Also, a special case of bound state called bipolar bound state between free dipole bodies is investigated.

scholarly journals BARYONS AS THREE-FLAVOR SOLITONS

1996 ◽  
Vol 11 (14) ◽  
pp. 2419-2544 ◽  
Author(s):  
HERBERT WEIGEL
Keyword(s):  
Symmetry Breaking ◽  
Vector Meson ◽  
Degrees Of Freedom ◽  
Magnetic Moments ◽  
Axial Vector ◽  
Vector Current ◽  
Bound State ◽  
Axial Vector Current ◽  
Flavor Symmetry ◽  
Matrix Elements

The description of baryons as soliton solutions of effective meson theories for three-flavor (up, down and strange) degrees of freedom is reviewed and the phenomenological implications are illuminated. In the collective approach the soliton configuration is equipped with baryon quantum numbers by canonical quantization of the coordinates describing the flavor orientation. The baryon spectrum resulting from exact diagonalization of the collective Hamiltonian is discussed. The prediction of static properties, such as the baryon magnetic moments and the Cabibbo matrix elements for semileptonic hyperon decays, are explored with regard to the influence of flavor symmetry breaking. In particular, the role of strange degrees of freedom in the nucleon is investigated for both the vector and axial vector current matrix elements. The latter are discussed extensively within the context of the proton spin puzzle. The influence of flavor symmetry breaking on the shape of the soliton is examined, and observed to cause significant deviations from flavor-covariant predictions on the baryon magnetic moments. Short range effects are incorporated by a chirally invariant inclusion of vector meson fields. These extensions are necessary for properly describing the singlet axial vector current and the neutron–proton mass difference. The effects of the vector meson excitations on baryon properties are also considered. The bound state description of hyperons and its generalization to baryons containing a heavy quark are illustrated. In the case of the Skyrme model a comparison is made between the collective quantization scheme and the bound state approach. Finally, the Nambu–Jona-Lasinio model is employed to demonstrate that hyperons can be described as solitons in a microscopic theory of the quark flavor dynamics. This is explained for both the collective and the bound state approaches to strangeness.

Generic bifurcations of forced oscillations of integrable mechanical systems

1979 ◽  
Vol 85 (1) ◽  
pp. 125-142
Author(s):  
J. P. Cleave
Keyword(s):  
Smooth Function ◽  
Degrees Of Freedom ◽  
Standard Form ◽  
Classical Mechanics ◽  
Forced Oscillations ◽  
Positive Real ◽  
Two Body Problem ◽  
Open Set ◽  
Image Position ◽  
Small Periodic

Although integrable Hamiltonian systems are non-generic (Robinson (13)) they have some importance in classical mechanics, e.g. the two-body problem, a free rigid body not subject to a gravitational field, the Toda lattice (Moser(12)). Arnol'd (cf. (2) and (1), appendix 26) proved that under quite general conditions action-angle coordinates can be introduced. Accordingly we consider a fixed system with n degrees of freedom in the standard formwhere H0 is a smooth function of the action variables Li only and I ∈ I and I is an open set of n-tuples of positive reals. now subjected to a periodic impressed force, the resulting system, , being determined by a small, periodic perturbation of the energy functionwhere e is a small positive real and K(c, I; α0, α1, …, an) is a smooth function of parameters c ranging over a smooth r-manifold E, I ∈ I, and K has period 2π in each of the angles αi, i.e. (α0, …, αn) ∈ Tn (n-torus). The purpose of this paper is to define the forms of bifurcation of oscillations of the perturbed system (K):

scholarly journals A novel class of translationally invariant spin chains with long-range interactions

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
B. Basu-Mallick ◽  
F. Finkel ◽  
A. González-López
Keyword(s):  
Long Range ◽  
Degrees Of Freedom ◽  
Spin Chains ◽  
Open Chain ◽  
New Class ◽  
Spin Interactions ◽  
Long Range Interactions ◽  
Spin Reversal ◽  
Twisted Yangian ◽  
Internal Degrees Of Freedom

Abstract We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and (polarized) spin reversal operators, which includes the Haldane-Shastry chain as a particular degenerate case. The new class is characterized by the fact that the Hamiltonian is invariant under “twisted” translations, combining an ordinary translation with a spin flip at one end of the chain. It includes a remarkable model with elliptic spin-spin interactions, smoothly interpolating between the XXX Heisenberg model with anti-periodic boundary conditions and a new open chain with sites uniformly spaced on a half-circle and interactions inversely proportional to the square of the distance between the spins. We are able to compute in closed form the partition function of the latter chain, thereby obtaining a complete description of its spectrum in terms of a pair of independent su(1|1) and su(m/2) motifs when the number m of internal degrees of freedom is even. This implies that the even m model is invariant under the direct sum of the Yangians Y (gl(1|1)) and Y (gl(0|m/2)). We also analyze several statistical properties of the new chain’s spectrum. In particular, we show that it is highly degenerate, which strongly suggests the existence of an underlying (twisted) Yangian symmetry also for odd m.

ROTATIONS AND VIBRATIONS OF FULLERENES IN THE MOLECULAR COMPLEX C20@C80

2021 ◽  
pp. 35-48
Author(s):  
M.A. Bubenchikov ◽  
◽  
A.M. Bubenchikov ◽  
D.V. Mamontov ◽  
◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Rotation Frequency ◽  
Dynamic State ◽  
Large Molecules ◽  
Rotational Degrees Of Freedom ◽  
Rotational Motions ◽  
Centers Of Mass ◽  
The Moment

The aim of this work is to apply classical mechanics to a description of the dynamic state of C20@C80 diamond complex. Endohedral rotations of fullerenes are of great interest due to the ability of the materials created on the basis of onion complexes to accumulate energy at rotational degrees of freedom. For such systems, a concept of temperature is not specified. In this paper, a closed description of the rotation of large molecules arranged in diamond shells is obtained in the framework of the classical approach. This description is used for C20@C80 diamond complex. Two different problems of molecular dynamics, distinguished by a fixing method for an outer shell of the considered bimolecular complex, are solved. In all the cases, the fullerene rotation frequency is calculated. Since a class of possible motions for a single carbon body (molecule) consists of rotations and translational displacements, the paper presents the equations determining each of these groups of motions. Dynamic equations for rotational motions of molecules are obtained employing the moment of momentum theorem for relative motions of the system near the fullerenes’ centers of mass. These equations specify the operation of the complex as a molecular pendulum. The equations of motion of the fullerenes’ centers of mass determine vibrations in the system, i.e. the operation of the complex as a molecular oscillator.

Elements of Classical Field Theory

2021 ◽  
pp. 24-34
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Classical Field Theory ◽  
Classical Field ◽  
Lagrange Equations ◽  
Lie Group Of Transformations ◽  
Infinitesimal Transformations ◽  
Conserved Currents

The purpose of this chapter is to recall the principles of Lagrangian and Hamiltonian classical mechanics. Many results are presented without detailed proofs. We obtain the Euler–Lagrange equations of motion, and show the equivalence with Hamilton’s equations. We derive Noether’s theorem and show the connection between symmetries and conservation laws. These principles are extended to a system with an infinite number of degrees of freedom, i.e. a classical field theory. The invariance under a Lie group of transformations implies the existence of conserved currents. The corresponding charges generate, through the Poisson brackets, the infinitesimal transformations of the fields as well as the Lie algebra of the group.

Three-body Algebraic Theory

1995 ◽  
Author(s):  
F. Iachello ◽  
R. D. Levine
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Differential Operators ◽  
Algebraic Theory ◽  
Many Body ◽  
Two Body Problem ◽  
Three Body ◽  
Schrödinger Picture ◽  
Algebraic Operators

In the previous chapter we discussed the usual realization of many-body quantum mechanics in terms of differential operators (Schrödinger picture). As in the case of the two-body problem, it is possible to formulate many-body quantum mechanics in terms of algebraic operators. This is done by introducing, for each coordinate r1,r2,... and momentum p1, p2, . . . , boson creation and annihilation operators, b†iα, biα. The index i runs over the number of relevant degrees of freedom, while the index α runs from 1 to n + 1, where n is the number of space dimensions (see note 3 of Chapter 2). The boson operators satisfy the usual commutation relations, which are for i ≠ j, . . . [biα, b†jα´] = 0, [biα, bjα´] = 0,. . . . . .[bjα, b†iα´] = 0, [b†jα, b†iα´] = 0,. . . . . . [biα, b†iα´] = ẟαα´, [biα, b†iα´] = 0, [b†iα, b†iα´] = 0. . . .

scholarly journals LOCAL AND NONLOCAL DIFFERENTIAL OPERATORS: A COMPARATIVE STUDY OF HEAT AND MASS TRANSFERS IN MHD OLDROYD-B FLUID WITH RAMPED WALL TEMPERATURE

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040033 ◽  
Author(s):  
MUHAMMAD BILAL RIAZ ◽  
ABDON ATANGANA ◽  
THABET ABDELJAWAD
Keyword(s):  
Wall Temperature ◽  
Analytical Solutions ◽  
Fractional Derivatives ◽  
Differential Operators ◽  
Classical Mechanics ◽  
Rate Of Change ◽  
Dynamical Process ◽  
New Class ◽  
Mass Transfers ◽  
And Inversion

Study of heat and mass transfers is carried out for MHD Oldroyd-B fluid (OBF) over an infinite vertical plate having time-dependent velocity and with ramped wall temperature and constant concentration. It is proven in many already published articles that the heat and mass transfers do not really or always follow the classical mechanics process that is known as memoryless process. Therefore, the model using classical differentiation based on the rate of change cannot really replicate such dynamical process very accurately, thus, a different concept of differentiation is needed to capture such process. Very recently, a new class of differential operators were introduced and have been recognized to be efficient in capturing processes following the power-law, the decay law and the crossover behaviors. For the study of heat and mass transfers, we applied the newly introduced differential operators to model such flow and compare the results with integer-order derivative. Laplace transform and inversion algorithms are used for all the cases to find analytical solutions and to predict the influences of different parameters. The obtained analytical solutions were plotted for different values of fractional orders [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] on the velocity field. In comparison, Atangana–Baleanu (ABC) fractional derivatives are found to be the best to explain the memory effects than the classical, Caputo (C) and Caputo–Fabrizio (CF) fractional derivatives. Some calculated values for Nusselt number and Sherwood number are presented in tables. Moreover, from the present solutions, the already published results were found as limiting cases.

New 3-DOFs Hybrid Mechanism for Ankle and Wrist of Humanoid Robot: Modeling, Simulation, and Experiments

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Samer Alfayad ◽  
Fethi B. Ouezdou ◽  
Faycal Namoun
Keyword(s):  
Degrees Of Freedom ◽  
Humanoid Robot ◽  
Power Transmission ◽  
Mechanical Design ◽  
Humanoid Robots ◽  
Classical Solutions ◽  
Kinematic Modeling ◽  
New Class ◽  
Hybrid Mechanism ◽  
And Control

This paper deals with the design of a new class of hybrid mechanism dedicated to humanoid robotics application. Since the designing and control of humanoid robots are still open questions, we propose the use of a new class of mechanisms in order to face several challenges that are mainly the compactness and the high power to mass ratio. Human ankle and wrist joints can be considered more compact with the highest power capacity and the lowest weight. The very important role played by these joints during locomotion or manipulation tasks makes their design and control essential to achieve a robust full size humanoid robot. The analysis of all existing humanoid robots shows that classical solutions (serial or parallel) leading to bulky and heavy structures are usually used. To face these drawbacks and get a slender humanoid robot, a novel three degrees of freedom hybrid mechanism achieved with serial and parallel substructures with a minimal number of moving parts is proposed. This hybrid mechanism that is able to achieve pitch, yaw, and roll movements can be actuated either hydraulically or electrically. For the parallel submechanism, the power transmission is achieved, thanks to cables, which allow the alignment of actuators along the shin or the forearm main axes. Hence, the proposed solution fulfills the requirements induced by both geometrical, power transmission, and biomechanics (range of motion) constraints. All stages including kinematic modeling, mechanical design, and experimentation using the HYDROïD humanoid robot’s ankle mechanism are given in order to demonstrate the novelty and the efficiency of the proposed solution.

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