Absence Of Axial Symmetry Research Articles

Simulations of energetic particle driven instabilities in CFQS

A nonlinear simulation of the energetic particle driven instabilities in the Chinese First Quasi-axisymmetric Stellarator (CFQS) has been conducted for the first time. MEGA, a hybrid simulation code for energetic particles interacting with a magneto-hydrodynamic fluid, was used in the present work. Both the m/n = 3/1 energetic-particle-mode (EPM) like mode and the m/n = 5/2 toroidal Alfvén eigenmode (TAE) were found, where m is the poloidal mode number and n is the toroidal mode number. Four important results were obtained as follows. First, the instability in the CFQS in three-dimensional form was shown for the first time. Second, strong toroidal mode coupling was found for the spatial profiles, and it is consistent with the theoretical prediction. Third, the resonant condition caused by the absence of axial symmetry in CFQS was demonstrated for the first time. The general resonant condition is f mode = Nf ϕ − Lf θ , where f mode, f ϕ , and f θ are mode frequency, particle toroidal transit frequency, and particle poloidal transit frequency, respectively; N and L are arbitrary integers, represent toroidal and poloidal resonance numbers. For EPM-like mode, the dominant and subdominant resonant conditions are f mode = 3f ϕ − 7f θ and f mode = f ϕ − f θ , respectively. For TAE, the dominant and subdominant resonant conditions are f mode = 4f ϕ − 9f θ and f mode = 2f ϕ − 3f θ , respectively. On the one hand, the toroidal resonance numbers are different from the toroidal mode numbers by 2. This indicates that the two-fold rotational symmetry affects the resonance condition. On the other hand, the subdominant resonances satisfy N = n, which is expected for the axisymmetric plasmas and most of the toroidal plasmas including stellarators. Fourth, the nonlinear frequency chirpings in CFQS were demonstrated for the first time. Hole and clump structures were formed in the pitch angle and energy phase space, and the particles comprising the hole and clump were kept resonant with the modes during the mode frequencies chirping.

Analytical and numerical solutions of two-dimensional problems of heat conduction and electronic optics

This work is devoted to a comparative analysis of the effectiveness of various methods for the numerical solution of a non-stationary two-dimensional problem of heat conduction in a cylindrical coordinate system in the absence of axial symmetry. The analysis is carried out on the basis of the obtained analytical solution of the two-dimensional problem of heat conduction in a steady state. The results of this work are of great applied importance in calculating the processes of gas transportation through offshore pipelines, as well as in calculating the electrostatic field of focusing systems during transportation of charged particle beams in problems of electronic optics.

Effective numerical methods for calculating non-stationary heat and glaciation dynamic processes for offshore gas pipelines

For offshore gas pipelines in the northern seas the computation of the total heat flux from ambient in every cross section of the pipeline involves solutions of various non-stationary heat problems, in particular, the one- and multidimensional single- and two-phase Stefan problems. In this paper, we have developed a novel numerical method with increased accuracy in solving one-dimensional single- and two-phase Stefan problems. Results of a comparative analysis of the various numerical techniques with respect to its effectiveness in solving to two-dimensional heat conduction problems in the absence of axial symmetry is presented. The calculation by chosen effective numerical method of the total heat flux into a gas pipeline buried in soil under different conditions presented.

Qualitative elements of early motor development that influence reaching of the erect posture. A prospective cohort study

The proposed assessment sheet aims to show in detail, which qualitative elements of motor performance are performed correctly in the 2nd month of life by children who in the 9th month reached the erect posture. Similar analysis was performed for the qualitative assessment in the 6th month. The prospective investigation of motor development involved a group of 109 children (40 girls and 69 boys). The study was based on the previously described quantity and quality assessment sheet of motor performance, validated for the 2nd and 6th month. Final investigation took place in the 9th month of life and was based on a neurological assessment.It could be shown that a completely correct assessment at the age of 2 months precludes future severe motor development disorders, especially cerebral palsy, although it does not rule out a slight delay. Prematurity and the analyzed risk factors, particularly IVH, impair the motor performance. The absence of axial symmetry, the shoulders protraction and improper position of the pelvis are the most important alarming features at the 2nd month. Distal elements observed in the prone position at the 6th month show a good prognosis for the motor performance in the 9th month. Any abnormalities, mainly related to the body axis and symmetry observed at 2 months of age should encourage one to put a child under observation.

Spin-transfer torque magnetization reversal in uniaxial nanomagnets with thermal noise

We consider the general Landau-Lifshitz-Gilbert (LLG) dynamical theory underlying the magnetization switching rates of a thin film uniaxial magnet subject to spin-torque effects and thermal fluctuations. After discussing the various dynamical regimes governing the switching phenomena, we present analytical results for the mean switching time behavior. Our approach, based on explicitly solving the first passage time problem, allows for a straightforward analysis of the thermally assisted, low spin-torque, switching asymptotics of thin film magnets. To verify our theory, we have developed an efficient Graphics Processing Unit (GPU)-based micromagnetic code to simulate the stochastic LLG dynamics out to millisecond timescales. We explore the effects of geometrical tilts between the spin-current and uniaxial anisotropy axes on the thermally assisted dynamics. We find that even in the absence of axial symmetry, the switching times can be functionally described in a form virtually identical to the collinear case.

Far-field distribution of third-harmonic generation by two crossed beams

The far-field intensity distribution of the third harmonic generated in a thin silica plate by two laser beams crossed at a small angle comprises four peaks approximately symmetric with respect to the bisector. The measurement of the intensity ratio of the inner to the outer peaks yielded values scattered from 10 to 20, surprisingly larger than the combinatorial value 9. The phase-matching factor, as determined by the full three-dimensional calculations required by the absence of axial symmetry, accounts for the observed ratio and its fluctuations.

Multipole Models of the Earth's Magnetic Field

To develop a mathematical model of rotational motion of an artificial satellite about its center of mass under the action of various forces (magnetic, Lorentz, etc.) caused by the geomagnetic field, it is necessary to know the induction of the Earth's magnetic field (EMF) as a function of the radius vector of a given point in the near-Earth space. Because the EMF possesses a complex structure and the above-mentioned functional dependence is unavailable in explicit analytic form, a set of approximate models of the EMF should be used. The simplest such model—a right dipole (aligned with the axis of rotation)—does not enable one to reveal in detail the influence of diurnal EMF rotation on the rotational motion of a satellite. The next EMF approximation—an inclined magnetic dipole—does not suffer from the above-mentioned drawback. However, it is shown that not all corrections to the magnetic induction of the EMF of the same order of magnitude are taken into account in the course of transformation from the model of aligned dipole to the model of inclined dipole. So, to develop the EMF model accurately accounting for the absence of axial symmetry of the EMF with respect to the axis of diurnal rotation of the Earth, in general, the effect of the quadrupole component of the geomagnetic potential on the EMF induction (and, probably, even the components of higher orders) must be taken into consideration. By using the International Geomagnetic Reference Field IGRF-2000, the multipole models of the EMF, corresponding to quadrupole, octupole, and higher-order approximations, were constructed and studied in this work. The EMF potential is expressed in terms of its multipole tensors. As a result, projections of the induction and induction gradient of EMF in the center of mass of the satellite onto the axes of the orbital coordinate system can be written in convenient and concise form. The expressions for the first four multipole tensors through the known geomagnetic constants are found. A method for estimating the reliability of these models is put forward, and the regions of applicability of the quadrupole and octupole models are drawn on the plane of orbital parameters.