Invariant Modes Research Articles

Gravitational coupling of neutrinos to matter vorticity. II. Microscopic asymmetries in angular momentum modes.

Microscopic asymmetries in neutrino physics are examined, which are due to the presence of a vorticity field of matter. We extend the results of an earlier paper to a complete basis of invariant angular momentum and energy modes. These modes provide a representation basis for the algebra of the total angular momentum of the system. The angular momentum space appears to be polarized along the direction determined by the local vorticity field \ensuremath{\Omega}\ensuremath{\rightarrow}. The neutrino asymmetry of currents is calculated for these modes.

The crystallography of the δ to α martensitic transformation in plutonium alloys

The CRAB formulation of the theory of martensite crystallography has been applied to the δ to α phase transformation in plutonium alloys. The low symmetry of the monoclinic α-phase results in 41 lattice invariant transformation shear modes being considered possible. The predictions, when these shears are used with the three available correspondences have been analysed and the 20 most likely mechanisms selected for presentation. Because of the lack of experimental information with which to compare the results it is difficult to select the best mechanism. However twinning of the product phase on (001) using the third correspondence is suggested. This has a habit plane near {258} δ which is the crucial piece of information which needs to be checked experimentally. Further theoretical work on the atomic shuffles associated with the correspondence also needs to be carried out.

A Method of Correcting the Superfish-Calculated Value of ZT2/Q for Cavities with Truncated Beam Tubes

The performance of an accelerating cavity can be characterized by the values of ZT/sup 2//Q for each of the cavity's resonant modes. For cylindrically symmetric structures, the program SUPERFISH can be used to find the field patterns of the azimuthally - invariant (''accelerating'') modes. However, SUPERFISH is limited to lossless regions of space entirely enclosed by Dirichlet or Neumann boundaries i.e., standing-wave solutions, and so cannot correctly treat the physical case of a cavity with open beam tubes through which energy can propagate. Instead, it is necessary to truncate the beam tubes with perfect reflectors, which introduce large amplitude standing-waves in the beam tubes, and consequently large errors in the calculated accelerating voltage and ZT/sup 2//Q. In the past, these errors have been avoided by employing long tapered beam tubes. This technique requires a considerable amount of additional computer memory, and cannot be used when memory is at a premium. In this paper, the authors describe a new technique which evaluates the errors in the accelerating voltage due to the truncated beam tubes. The method requires no special geometries or time-consuming calculations, and the results are in excellent agreement with other cavity calculations.

On a martensitic phase transformation in zirconia (ZrO 2)—II. Crystallographic aspects

Crystallographic aspects of the martensitic tetragonal → monoclinic phase transformation in zirconia single crystals have been studied experimentally and compared with predictions of the phenomenological theory of martensite crystallography. Two different orientation relationships have been observed between the high and low temperature phases. Above 1000°C, the transformation occurs according to the orientation relations (100) m∥~(100) t and [010] m∥~[001] t, while below 1000°C, (100) m~(100) t and [001] m∥~[001] t were observed. These results indicate that the habit planes of the plate-like martensite products reported in the first paper of this series [ Acta Met. 20, 1281 (1972)] had been incorrectly indexed; this occurred because of an incorrect assumption that a single crystal undergoing a monoclinie → tetragonal → monoclinic cycle would return to its original orientation at the end of the cycle. Application of the phenomenological theory of martensite crystallography indicates that the observed habit planes can be predicted using a single Bain correspondence, implied by the lower temperature orientation relations, combined with different lattice invariant deformation modes.

Рассеяние конечных общектов в сжимаюшейся плаэме

The problem of scattering by finite objects in the compressible electron gas in the absence of the d.c. magnetic field is studied from the classical viewpoint. Using a set of linearized plasma equations, the vector field is decomposed into three components, each of which is represented by a scalar potential function. The general solution of the problem is constructed in a straightforward manner. As an illustration, particular attention is paid to the problem of scattering by a plasma column. The general condition for natural oscillations and various scattering formulas are derived. From the general expression, the following types of coupling are exhibited: i) the coupling between the transversetype oscillations and the longitudinal-type oscillations, and ii) the coupling between the translational invariant modes and the angularly symmetric modes. Various limiting cases are discussed, and the problem of scattering by conducting cylinders is studied by introducing a conductivity coefficientσ for the plasma column. It is shown that simplified results can be obtained by taking the limitσ → ∞.

THE RANDOM SPATIAL ECONOMY: AN EXPLORATION IN SETTLEMENT THEORY

HE spatial arrangement and spatial operation of human activities are very complex so that the development of the branch of our science concerned with their explanation is inevitably slow. The difficulties may be grouped under three heads: (1) spatial specification; (2) decision rules used to organize behavior; (3) expression of the logical consequences of the interrelations of the two factors above. In physical geography, progress is easier because invariant modes of conduct are easier to come by, and either very limited situations are handled or the phenomena dealt with may be massively and yet meaningfully aggregated so that in any event the spatial specification problem is simpler. This paper attempts to cut the Gordian knot posed by the complicated interrelations involved by asserting randomness of behavior and/or randomness of location and using probability theory as a language. As it turns out, the results of various models formulated resemble the real world. At first sight such findings may be bewildering but their reasonableness improves with acquaintance. This paper attempts to explain some features of settlement in the U.S.A. Clearly the large numbers of relevant variables have to be pruned and aggregated to the point where they are analytically tractable. Randomness is postulated as affording a convenient technique for investigating the overall properties of this field. Such a formulation is neutral as to rationality whether socially or economically oriented: every decision may be optimal from a particular point of view and yet the resulting actions as a whole may appear as random. Lack of information, social ties, and so on will change an economic optimizing solution but not the randomness formulation. Clearly such reasoning is useful only in particular contexts, especially in general location problems, and leaves more restricted, and more urgent, problems unanswered.