Nonsymmetric Field Research Articles

A relativistic theory of the field II: Hamilton's principle and Bianchi's identities

As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry. Thence emerges a relativistic theory of the field by generalization of the general relativity. The derivation presented shows how naturally we can extend general relativity theory to a non-symmetric field, and that the field-equations are really the generalizations of the gravitational equations. With curvature tensor and the variational principle, we will deduce the field equations and Bianchi's identities. In consecuense, the field equations will find from Bianchi's identities.

A relativistic theory of the field

As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry, we expect the latter also to appear through the geometry. This unification has however, remained an unfulfilled goal. Thence emerges a relativistic theory of the asymmetric field by generalization of the general relativity. It will demonstrate in a new way that the field-equations chosen for the non-symmetric fields are really the natural ones.

Charged particle dynamics near an X-point of a non-symmetric magnetic field with closed field lines

Understanding particle drifts in a non-symmetric magnetic field is of primary interest in designing optimized stellarators in order to minimize the neoclassical radial loss of particles. Quasisymmetry and omnigeneity, two distinct properties proposed to ensure radial localization of collisionless trapped particles in stellarators, have been explored almost exclusively for magnetic fields with nested flux surfaces. In this work, we examine radial particle confinement when all field lines are closed. We then study charged particle dynamics in the special case of a non-symmetric vacuum magnetic field with closed field lines obtained recently by Weitzner & Sengupta (Phys. Plasmas, vol. 27, 2020, 022509). These magnetic fields can be used to construct magnetohydrodynamic equilibria for low pressure. Expanding in the amplitude of the non-symmetric fields, we explicitly evaluate the omnigeneity and quasisymmetry constraints. We show that the magnetic field is omnigeneous in the sense that the drift surfaces coincide with the pressure surfaces. However, it is not quasisymmetric according to the standard definitions.

Interplay of Linear and Nonlinear Localization Mechanisms in Spin-Torque Oscillators with a Field Well

The magnetization dynamics in a spin-torque oscillator with nonuniform profile of a static magnetic field creating a field well is studied by analytic calculations and numerical simulations. It is demonstrated that, in the case of sufficiently deep and narrow field well, the linear localization in the field well dominates the nonlinear self-localization, despite a negative nonlinear frequency shift. A change of the localization mechanism results in a qualitatively different dependence of the generation power on the driving current. For the dominant linear localization, the soft generation mode is realized, while, for the nonlinear self-localization, we observe a hard mode of auto-oscillator excitation. Simultaneously, a difference in the profiles of the excited spin-wave mode can become evident and distinguishable in experiments only in the case of a nonsymmetric field well.

Radiation of a charge in dielectric concentrator for Cherenkov radiation: Off-axis charge motion

A theoretical investigation of radiation field produced by a charge moving through the dielectric concentrator for Cherenkov radiation is performed for the general case where a charge trajectory is shifted with respect to the target axis. The idea of dielectric target with specific profile of the outer surface was presented and investigated in our previous papers for the symmetric case. Here we show how non-symmetric field components generated in the bulk of target affect field distribution near the focus where strong concentration of the energy occurs. Possible applications of this target are discussed. This version also contains corrections (Appendix C) made after publication.

Predicting Non-Linear Flow Phenomena through Different Characteristics-Based Schemes

The present work investigates the bifurcation properties of the Navier–Stokes equations using characteristics-based schemes and Riemann solvers to test their suitability to predict non-linear flow phenomena encountered in aerospace applications. We make use of a single- and multi-directional characteristics-based scheme and Rusanov’s Riemann solver to treat the convective term through a Godunov-type method. We use the Artificial Compressibility (AC) method and a unified Fractional-Step, Artificial Compressibility with Pressure-Projection (FSAC-PP) method for all considered schemes in a channel with a sudden expansion which provides highly non-linear flow features at low Reynolds numbers that produces a non-symmetrical flow field. Using the AC method, our results show that the multi-directional characteristics-based scheme is capable of predicting these phenomena while the single-directional counterpart does not predict the correct flow field. Both schemes and also Riemann solver approaches produce accurate results when the FSAC-PP method is used, showing that the incompressible method plays a dominant role in determining the behaviour of the flow. This also means that it is not just the numerical interpolation scheme which is responsible for the overall accuracy. Furthermore, we show that the FSAC-PP method provides faster convergence and higher level of accuracy, making it a prime candidate for aerospace applications.

Multi-field Dual-Mixed Variational Principles Using Non-symmetric Stress Field in Linear Elastodynamics

Three types of multi-field dual-mixed variational principles using a priori non-symmetric stress field will be derived for dynamic problems of linearly elastic solids. Starting from the functional of complementary Hamilton’s principle it is shown how this variational formulation is modified with applying the Lagrange multiplier technique, to obtain a new four-field dual-mixed functional. The independent fields of this functional will be the displacement vector, the non-symmetric stress tensor, the skew-symmetric rotation tensor and the momentum vector. Then we present how to treat appropriately the six different types of initial conditions in a weak and/or strong sense by adding a new integral expression to the four-field functional. Modifying this functional through a Legendre transformation results in a new complementary energy-based five-field dual-mixed functional which allows the momentum- and velocity vectors to be independently approximated. A complementary energy-based three-field dual-mixed variational formulation is obtained by eliminating the momentum- and velocity fields through the strong enforcement of the kinematic equation and the impulse-velocity relation from the five-field principle.

Unified Theories of Gravitational and Electromagnetic Fields in Riemannian Geometry and Higher Dimension

Some unified theories on the gravitational and electromagnetic fields are researched. We investigate mainly two new geometric unified theories. A method is that the gravitational field and the source-free electromagnetic field can be unified by the equations Rklmi = κTklmi* in the Riemannian geometry, both are contractions of im and ik, respectively. If Rklmi = κTklmi* =constant, it will be equivalent to the Yang’s gravitational equations Rkm;l –Rkl;m = 0, which include Rlm= 0. From Rlm= 0 we can obtain the Lorentz equations of motion, the first system and second source-free system of Maxwell’s field equations. This unification can be included in the gauge theory, and the unified gauge group is SL(2,C) × U(1)=GL(2,C), which is just the same as the gauge group of the Riemannian manifold. Another unified method on the general nonsymmetric metric field with high-dimensional space-time and its matrix representations are analyzed mathematically. Further, the general unified theory of five-dimensional space-time combined quantum theory and four interactions is researched. Some possible unification ways on the gravitational and electromagnetic fields are discussed. The general matrix and various corresponding theories may decompose to a sum of symmetry and antisymmetry. Moreover, we proposed an imaginative representation on the ten dimensional space-time.

Design of geocell reinforcement for supporting embankments on soft ground

The methods of design available for geocell-supported embankments are very few. Two of the earlier methods are considered in this paper and a third method is proposed and compared with them. In the first method called slip line method, plastic bearing failure of the soil was assumed and the additional resistance due to geocell layer is calculated using a non-symmetric slip line field in the soft foundation soil. In the second method based on slope stability analysis, general-purpose slope stability program was used to design the geocell mattress of required strength for embankment. In the third method proposed in this paper, geocell reinforcement is designed based on the plane strain finite element analysis of embankments. The geocell layer is modelled as an equivalent composite layer with modified strength and stiffness values. The strength and dimensions of geocell layer is estimated for the required bearing capacity or permissible deformations. These three design methods are compared through a design example. It is observed that the design method based on finite element simulations is most comprehensive because it addresses the issue of permissible deformations and also gives complete stress, deformation and strain behaviour of the embankment under given loading conditions.

Long-range surface magnetoplasmon on thin plasmon films in the Voigt configuration

This study elucidates the characteristics of a long-range surface magnetoplasmon (LRSMP) that propagates on a plasmon film with the Voigt configuration. Particle-in-cell (PIC) simulations and theoretical analyses are performed. Simulation results indicate that LRSMP has non-symmetrical fields. The proposed scheme also verifies the non-reciprocal properties of LRSMP as the direction of an applied external magnetic field is reversed. When surface waves propagate on a plasmon film across an interface on one side of which long-range surface plasmon (LRSP) is allowed while on the other side of which LRSMP is allowed, the interface behaves similar to a defect and transforms the surface waves into radiation modes owing to the mismatch between the field patterns of LRSP and LRSMP. Furthermore, PIC simulation results confirm the presence of a new high-frequency LRSMP whose frequency exceeds the plasma frequency and lacks a LRSP counterpart.

非对称磁镜场电子回旋共振氧等离子体刻蚀化学气相沉积金刚石膜

非对称磁镜场电子回旋共振氧等离子体刻蚀化学气相沉积金刚石膜

TCAD study on gate-all-around cylindrical (GAAC) transistor for CMOS scaling to the end of the roadmap

In this paper, we report TCAD study on gate-all-around cylindrical (GAAC) transistor for sub-10-nm scaling. The GAAC transistor device physics, TCAD simulation, and proposed fabrication procedure have been discussed. Among all other novel fin field effect transistor (FinFET) devices, the gate-all-around cylindrical device can be particularly used for reducing the problems of conventional multi-gate FinFET, improving device performance, and scaling-down capabilities. With gate-all-around cylindrical architecture, the transistor is controlled essentially by infinite number of gates surrounding the entire cylinder-shaped channel. Electrical integrity within the channel is improved by reducing the leakage current due to the non-symmetrical field accumulation such as the corner effect. Our proposed fabrication procedure for making devices having the gate-all-around cylindrical (GAAC) device architecture is also discussed.

LDV measurements in complex swirling flows, their physics and a database for CFD evaluations

In an earlier paper in this journal (Mocikat et al. in Exp Fluids 34:442–448, 2003) LDV measurements in a simple geometry but for a complex flow have been provided as a database for CFD evaluation purposes. With special inflow devices swirl could now be added to the flow. By changing the exit position of the test section in order to get a non-symmetric flow field, a steady swirling flow without instability induced precessing motions could be established. This flow can be interpreted as a superposition of a swirling motion to an otherwise swirl-free flow by introducing “swirl influence factors” for various aspects of the flow field. With a modified inflow device a periodically unsteady flow with swirl emerged. The turbulence features of this flow are distinctively different from the steady flow case with swirl. For all flows under consideration the three time-averaged components of the velocity vector and all components of the Reynolds stress tensor are measured in selected cross sections and provided as a data base for CFD calculations.

Irreducible tensors and their applications in problems of dynamics of solids

One difficulty encountered in solving mechanical problems with complicated interaction is to express either the moments of forces or the force function via the phase variables of the problem. Here various transformations of coordinate systems are used, because interactions are determined by a relation between tensor variables one of which refers to the body and the other refers to the field. In this connection, the usual definition of a tensor in Cartesian coordinates is inconvenient because of the fact that the components of a tensor of rank l ≥ 2 can be arranged as several linear combinations that behave differently under rotations of the coordinate system. Naturally, one needs to define tensors in such a way that their components and linear combinations of these be transformed in a unified manner under rotations of the coordinate system. This requirement is satisfied by irreducible tensors. The mathematical apparatus of irreducible tensors was created to satisfy the requirements of quantum mechanics and turned out to be rather universal. As far as the author knows, this apparatus was first used in mechanics by G. G. Denisov and the author of the present paper [1]. Using this apparatus, one can see the clear physical meaning of complicated interactions, express these interactions in invariant form, easily perform transformations from one coordinate system to another coordinate system turned relative to the first, consider rather complicated types of interactions writing them in compact form explicitly depending on the phase variables of the problem, easily use the symmetry of both the rigid body and the force field structure, and perform the averaging procedure for the entire object rather than componentwise. The present paper further develops the paper [1]. We present a brief introduction to the theory of irreducible tensors. We show that the force function of various interactions between a rigid body and a force field can be represented as the scalar product of irreducible tensors. We study general properties of evolution motions of a rigid body in axisymmetric and nonsymmetric force fields under the action of moments caused by various harmonics of the force function.

Acousto-electric well logging by eccentric source and extraction of shear wave

The nonaxisymmetric acousto-electric field excited by an eccentric acoustic source in the borehole based on Pride seismoelectric theory is considered. It is shown that the acoustic field inside the borehole, converted electric and magnetic fields and coupled fields outside the borehole are composed of an infinitude of multipole fields with different orders. The numerical results show that both the electromagnetic waves and the seismoelectric field in the borehole, and the three components of both electric field and magnetic field can be detected. Measurements on the borehole axis will be of advantage to determining shear velocity information. The components of the symmetric and nonsymmetric acoustic and electromagnetic fields can be strengthened or weakened by adding or subtracting the two full waveforms logged in some azimuths. It may be a new method of directly measuring the shear wave velocity by using the borehole seismoelectric effect.

Three dimensional nilpotent singularity and Sil’nikov bifurcation

Abstract In this paper, by using the normal form, blow-up theory and the technique of global bifurcations, we study the singularity at the origin with threefold zero eigenvalue for nonsymmetric vector fields with nilpotent linear part and 4-jet C ∞ -equivalent to y ∂ ∂ x + z ∂ ∂ y + ax 3 y ∂ ∂ z , with a ≠ 0, and analytically prove the existence of Sil’nikov bifurcation, and then of the strange attractor for certain subfamilies of the nonsymmetric versal unfoldings of this singularity under some conditions.

MicroReviews by the Book Review Editor: The Meaning of Relativity: Including the Relativistic Theory of the Non-Symmetric Field (5th edition): Albert Einstein

MicroReviews by the Book Review Editor: <i>The Meaning of Relativity: Including the Relativistic Theory of the Non-Symmetric Field</i> (5th edition): Albert Einstein

On the stability of motion of a gyrostat about a fixed point under the action of non-symmetric fields

In this work we have studied the problem of motion of a heavy magnetized gyrostat carrying electric charges and acted upon by uniform electric and magnetic fields in addition to gravity. The equilibrium positions of the gyrostat have been found and their stability studied.

Anomalous electron trapping by localized magnetic fields

We consider an electron with an anomalous magnetic moment g>2 confined to a plane and interacting with a nonzero magnetic field B perpendicular to the plane. We show that if B has compact support and the magnetic flux in the natural units is F\ge 0, the corresponding Pauli Hamiltonian has at least 1+[F] bound states, without making any assumptions about the field profile. Furthermore, in the zero-flux case there is a pair of bound states with opposite spin orientations. Using a Birman-Schwinger technique, we extend the last claim to a weak rotationally symmetric field with B(r) = O(r^{-2-\delta}) correcting thus a recent result. Finally, we show that under mild regularity assumptions the existence can be proved for non-symmetric fields with tails as well.

Transformation of a Nonsymmetric Cylindrical Field in a Nonstationary Conducting Medium in the Two-Dimensional Case

Transformation of a Nonsymmetric Cylindrical Field in a Nonstationary Conducting Medium in the Two-Dimensional Case