Symmetric Principle Research Articles

A frequency-domain Z-bus algorithm utilizing symmetrical components for transient analysis during capacitor switching

Abstract This paper presents a new method for digital simulation of a transmission, subtransmission or distribution system for transient analysis during capacitor switching. The method is based on the frequency-domain analysis utilizing the symmetrical component principles and the Z-bus impedance matrix in the complex frequency domain. The paper emphasizes the concepts of the method, describes the necessary boundary conditions, explains the pertinent assumptions and shows an example of the simulation on an actual subtransmission system.

Enantiomorphism of ferroelastic domains

Abstract It was shown on the basis of symmetrical principles of twinning, that under phase transitions followed by symmetry variation 43m-42m, 43m-222, 6mm-mm2, 4mm-mm2, 6mm-2, 4mm-2 ferroelastic domains may be enantiomorphic. The form of gyroelastic hysteresis loops is analised.

Symmetric variational principles and modal methods in fluid-structure interaction problems

Two new symmetric variational principles for “acoustoelastic” fluid-structure interaction problems are first derived, with simultaneous use of three variables: the structural displacements and accelerations and the fluid pressure. Thus, a total of four three-field symmetric formulations is obtained. As is then shown, these formulations can be reduced to four two-field symmetric variational principles. Each of them can lead to a single-field “limit case” formulation, which is the formulation of the “in vaccum” structure or of the “acoustic” fluid plus a frequency independent term, expressing an “added” property in its general form: the “incompressible” fluid (“in vacuum” structure plus “added mass”), the “hypercompressible” fluid (“in vacuum” structure plus “added stiffness”), the “hyperlight” structure (“acoustic” fluid plus “added compressibility”) and the “hyperflexible” structure (“acoustic” fluid plus “added rigidity”). Combinations of the above “limit case” formulations are also of interest. The impact of these formulations on the construction of modal methods is significant. A large number of methods can be constructed, since the modes of the “in vacuum”, of the “acoustic” and of the several “limit case” eigenproblems can provide basis functions for the structure and for the fluid variables, not only in the formulations of the full problem, but also in the “limit case” formulations. To demonstrate this, some new methods are proposed for the solution of the full and of the “incompressible” eigenproblems. Then, the methods based on the non-symmetric or on the three-field symmetric formulations are shown to have disadvantages, compared to the methods based on the two-field symmetric formulations. The examples provided demonstrate analytical expressions of “added properties” and verify the efficiency or the disadvantages of the model methods described. Finally, in the Appendices, the free surface conditions and the damping forces are incorporated in the various formulations and “singular cases” are treated (e.g., free bodies, “wall bounded” fluids).

Can the symmetrization principle unveil the nucleon substructure in nuclei?

We analyze the charge density distribution of 3He under the assumption that nucleons are built of quarks. Our interest is to investigate the effect of the additional terms that appear in the 3He wavefunction because of the antisymmetrization principle applied at the level of quarks as elementary constituents. We conclude from our calculation that antisymmetrization at the level of quarks may lead to a substantial ccontribution to the form factor beyond q=4 fm −1.

Topological geometrodynamics. III. Quantum theory

The description of 3-space as a spacelike 3-surface of the spaceH=M4 ×CP2 (product of Minkowski space and two-dimensional complex projective space CP2) and the idea that particles correspond to 3-surfaces of finite size inH are the basic ingredients of topological geometrodynamics, an attempt to a geometry-based unification of the fundamental interactions. The observations that the Schrodinger equation can be derived from a variational principle and that the existence of a unitaryS matrix follows from the phase symmetry of this action lead to the idea that quantum TGD should be derivable from a quadratic phase symmetric variational principle in the spaceSH, consisting of the spacelike 3-surfaces ofH. In this paper a formal realization of this idea is proposed. First, the spaceSH is endowed with the necessary geometric structures (metric, vielbein, and spinor structures) induced from the corresponding structures of the spaceH. Second, the concepts of the scalar super field inSH (both fermions and bosons should be describable by the same probability amplitude) and of super d'Alambertian are defined. It is shown that the requirement of a maximal symmetry leads to a uniqueCP-breaking super d'Alambertian and thus to a unique theory “predicting everything.” Finally, a formal expression for theS matrix of the theory is derived.

THE APPLICATION OF STABLE GROUPS TO BIOLOGICAL STRUCTURES

The properties of the stable group theory are discussed. The mathematical models of the insect legs, a pair of hands, and human chromosomes are established using stable group theory. The two postulates: the prime-number principle and the symmetric principle, and a new evolution theory in the biology are suggested. The brain structures and the structures of the nervous system can be studied using above two principles.

Curve straightening and a minimax argument for closed elastic curves

THE RESULTS obtained here have to do with the following problem. Imagine the ends of a straight length of springy wire are joined together smoothly and the wire is held in some configuration described by an immersion y of the circle into the plane or into R3. According to the Bernoulli-Euler theory of elastic rods the bending energy of the wire is proportional to the total squared curvature of y, which we will denote by F (7) = 5, k2 ds. Suppose now the wire is released and it moves so as to decrease its bending energy as efficiently as possible, i.e. following “the negative gradient of F” (so our dynamics are Aristotelian rather than Newtonian, and we are also making the physically unrealistic assumption that the wire can pass through itself freely). How does the wire evolve, and what will happen ultimately (as time goes to infinity)? Of course, one wants to know first that one can actually define such a flow on the space of immersed circles, that it exists for all time, and that one can sensibly speak of a limiting curve yrn for the trajectory through a given initial curve yo. It is shown here that this is indeed the case and that in fact the Palais-Smale condition holds for this flow. It is proved, moreover, that if y0 is a plane curve of rotation index one (e.g. if y0 is embedded) then the flow carries y0 to a circle. Our main result, however, pertains to the non-planar case, where the situation is more complicated. In a space form it is possible to integrate the equations for an elastica, i.e. for a critical point of F, and this enables one to prove, in particular, that there is a countably infinite family of (similarity classes of) closed elastic curves in R3 (see Theorem 0.1). Thus, not all wire loops in R3 will flow to a circle. On the other hand, this leaves open the possibility that ycu is a circle for almost any initial curve yO, and indeed, our concluding Theorem 3.2 states that the circle is the only stable closed elastica in R3. The proof of this theorem itself depends on the dynamical, i.e. gradient flow approach to the study of F (and avoids a detailed analysis of the Hessian of F, which is quite complicated for non-planar elastic curves). The idea is as follows. One considers a discrete group G of rotations of R3 and an associated pair of multiply covered circular elastic curves which are Gequivariantly regularly homotopic, and which are both local minima for the restriction of F to G-symmetric curves (though multiple circles are unstable with respect to general variations). An appeal to the minimax and symmetric criticality principles then enables one to conclude that there exists a non-circular elastica of “saddle type”. Comparision with the classification theorem shows that one can account in this way for all non-circular solutions, hence all are unstable. We remark that a similar critical structure occurs for “free” (length unconstrained) elastic curves in the standard two-sphere: it was shown in [S] (by an entirely different method) that all closed non-geodesic solutions in S2 are unstable and can be regarded as minimax critical points arising from symmetrical regular homotopies between certain multiple coverings of a prime geodesic (though the minimax argument in [SJ is made only heuristically). To the extent that a similar picture holds as well for manifolds of (non-constant) positive curvature one gains a new view of closed geodesics as the limits of almost all trajectories of -VF. The organization of the paper is as follows. Section 0 is a brief review of some basic facts concerning elastic curves in space forms and the classification of closed elastic curves in R3 (details can be found in [S], [6] ). Section 1 is devoted mostly to the proof ofcondition (C)for the curve straightening flow. We have included details and have attempted to keep the discussion as self-contained as possible. In Section 2 we derive a second variation formula

Continuum orbitals, complex scaling problem, and the extended virial theorem

A complex scale transformation of the time-independent Schr\"odinger equation leads to a symmetric eigenvalue problem containing both bound states and resonance (complex) eigenvalues as solutions. An extended virial theorem is stated, and its necessary fulfillment is pointed out. The latter, in conjunction with a symmetric stationary principle, allows for determination of resonance (complex) eigenvalues by means of elementary matrix manipulations. Application to the Stark effect in the hydrogen atom shows agreement with previous calculations based on numerical integration.

Atomic band structure effects on resonant scattering of atoms from solid surfaces

Bound state resonances related to the band structure of adsorbed atoms and their usefulness for determining the periodic components of atom-solid interaction potential are theoretically investigated. A variety of specular intensity patterns associated with bound state resonances near the Brillouin zone boundaries are exhibited. The (10) and (11̄) bound state resonances give rise to two split specular minima with the splitting depending essentially on v 10 for a fixed beam energy; however, the detailed features are dependent on other periodic components. For incidence along a crystal symmetry direction, symmetrization of basis states not only makes numerical computation very efficient, but also implies that there is only one specular minimum for a pair of bound states which are equivalent by symmetry. The (01) and (10) resonances along and near the x = y direction are presented to illustrate the symmetrization principle. The depth of one of the specular minima decreases and finally vanishes as the symmetry direction is approached. The single specular minimum corresponds to a resonance with the bound state which is a symmetric linear combination of (01) and (10) states in a potential well of v 0 + V 11. As expected, the shift in positions of specular minima caused by the periodic surface potential increases with decreasing beam energy.

A functional analysis of the myogenic control systems of the human Fallopian tube

Electrical and mechanical activity of segments of isolated human Fallopian tubes was recorded with the use of extracellular pore electrodes and a transducer recording tension in the longitudinal axis. Electrical activity was regularly recorded in ampullar segments of tubes from premenopausal women and consisted usually of one spike apparently preceded by prepotentials associated with each contraction. These spikes were propagated at 2 to 9 mm. per second in either direction with equal velocity. The direction or velocity of propagation was not influenced by the hormonal status of the woman from whom the tube was derived. It was concluded that the myogenic system of the human Fallopian tube was organized on a symmetrical principle, any directionality being imposed by hormonal, neuronal, or other modulating systems in vivo. Stretch was able to enhance the excitability of this system.

Megawatt HV DC Power Supplies

For the injection of heavy, multiply charged ions into accelerators or for injection of cluster ions into fusion reactors, physicists require high-voltage dc power supplies with voltages in the range of 0.5 to 3 MV and currents of the order of several hundred milliamperes, and even amperes. Several power supplies in this range have been built recently, some for particle injectors and some for testing UHV dc transmission line components. In 1974, high-voltage dc power supplies with the following output ratings were completed: 2.5 MV/200 mA, 2.2 MV/ 200 mA, 1.2 MV/100 mA, and 1.0 MV/120 mA. All power supplies are built according to the symmetrical Cockcroft-Walton generator principle and are either air-insulated open structures or built into a pressure vessel and insulated with high-pressure sulphur hexafluoride. Based upon theoretical considerations and experience gained with units previously built, it appears feasible to design even more powerful generators.

Studies on Biplane Wind Vanes, Ventilator Tubes and Cup Anemometers ( I )

In Part I, mathematical treatment of the problems, is presented to establish the theoretical support and leading principles of the experiments and actua techniques.In Part II, experimental. results based upon the mathematical principles are described for various actually designed instruments.In Chapter 1, Part I, rigorous discussions are given for the force and moment experienced by two flat plates with arbitary chord lengths, angle of stagger and decalage in two-dimensinal incompressible ideal fluid, The problem is solved after the method of I. E. Garrick but more general result due to J. Hodgkinson and E. G. C. Poole is analysed and the connection is found between them, Formulae for the cases of two plates in close proximity are given. Numerical calulations are carried out for symmetrical biplane wind vanes and fundamental principles are found for design use.In Chapter 2, Part I, exact formulae are induced for the calculation of the flux through the ventilator tubes with straight, circular, elliptic or hyperbolic sides in two-dimension. Numerical evaluations are done for the cases of straight and hyperbolic sides.In Chapter 3, Part I, basic considerations of cup anemometers are effected, and numerical calculation of the static moment of cylindrical windmill with two rotors is made for an example,In Chapter 1, Part If, three types of combined wind vane and anemometer with twin-rudder, conical tail ring, or hollow single rudder each of which may be regarded as posessing biplane characteristics, are tested in the wind tunnel. After systematic investigation based upon the theoretical oint of view one type of them is decided to be favourable for directional stability. Also anemometer windmill blades are discussed, which are indifferent to the effect of wind turbulence,In Chapter 2, Part II, systematic studies on the basic forms of straight ventilator tubes are done. Two effective. groups are found. The test was also carried out for tubes with free-running windmill. The trends of the experiments agree with theory. Numerous actual designs with, bent air passage are tested for radiosonde use. The theoretical leadership still holds in such complicated examples.Cowled windmill models are tested of their torqud and power and compared with those of windmill alan. e. The effect of the cowling is not highly promissing but several important fundamental characteristics of windmill are revealed. Free-running windmill or windmill anemometer is also treated. A full-scale windmill is experimented in natural wind.Two types of cowled hot-wire anemometer are investigated of their directional insensitiveness to the wind.In Chapter 3, Part II, cylindrical windmill' model with two rotors is tested of its troque and power, and also discussed as an anemometer.