Mode Coalescence Research Articles

Modeling borehole breakout by mixed mode crack growth, interaction, and coalescence

This technical note describes a numerical model that has been developed to simulate the progression of borehole breakout in heterogeneous and discontinuous rock

Analytic and Numerical Models of Wave-CISK with Conditional Heating

Wave-CISK with conditional heating is investigated in the equatorial zonal-height plane by analytic and numerical techniques. For two- and three-level models, previous results are extended to give additional evidence that the most unstable mode has a single wet region of infinitesimal width. A three-level model has qualitatively similar behavior as the two-level model except that propagating solutions are possible due to coalescence of internal vertical modes. Phase speeds with conditional heating are found to be slightly greater than those for unconditional heating. The structure has one circulation cell in the vertical and is asymmetric in longitude with stronger motion on the leading edge. Growth rate is inversely proportional to the width of the single wet region. That width can be limited by second-order diffusion. A general integral relationship between growth rate, viscosity, phase speed, and heating is derived. The main conclusion is that the linear wave-CISK catastrophe is modified by conditional heating but not eliminated. The preferred mode of instability has one wet region, but it occurs on the smallest possible scale. It is likely that numerical models that use conditional heating are sensitive to resolution, especially for the commonly used spectral truncations, unless there is sufficiently strong damping at the smallest scales.

Coalescence of aeroelastic modes in flutter analysis

Coalescence of aeroelastic modes in flutter analysis

Dynamic stiffness analysis of follower force

The dynamic stiffness method can predict an infinite number of natural modes of a conservative structure by means of a finite number of co-ordinates. The method is extended to non-conservative systems characterized by follower forces in this paper. Skeletal frame structures are taken as examples. The resulting matrix equations are solved by the parametric inverse iteration method with the intensity of the follower forces as parameter. The influences of shear deformation and rotatory inertia on the flutter instability are considered. The higher order flutter mode critical follower forces for a slender cantilever are found to be (2 n−0·5) 2 π 2 EI/ l 2 approximately. The flutter frequency and flutter load are calculated directly by a Newtonian method with a Romberg algorithm for the determinant derivatives. It is found that flutter may occur by coalescence of non-adjacent linear modes.

Cause of the lower-hybrid current-drive density limit.

We derive a simple model which predicts the observed lower-hybrid current-drive density limit for all major experiments to within a factor of 2. The model is based on (i) the experimentally observed upshift in ${k}_{?}$ and (ii) the ${k}_{?}$ dependence of the mode coalescence condition of the linear mode conversion of a lower-hybrid wave into a hot-plasma wave.

Bandwidth Broadening in RF-Structure

Broad bandwidth represents one of the features the most sought after in electron tubes. In linear accelerators, it ensures the insensitiveness of the RF-structure to mechanical error or beam loading. This is commonly achieved by increasing the coupling between accelerating cells. To go further however, coalescence between two passbands or more is being used. The postcoupled Alvarez structure, the side-coupled or resonant slot-coupled cavity chain, as well as the dish-and-washer structure, among others, are well known examples. More generally, coalescence can take place in complex RF-structures such as multiperiodic systems. Presently, the use of mode coalescence is extended to certain types of RF-structures in TWTs in order to avoid band-edge oscillations. The purpose of this paper is to derive rules that mode coalescence obeys. Examples will be given for illustrations.

Barotropic Instability and Rossby Wave Radiation

Abstract A detailed study of linear barotropic instability confirms that the concept of critical level overreflection is fundamental to the understanding of the entire family of unstable modes in this problem. This is in agreement with the general argument presented by Lindzen and Tung and applied by Lindzen et al.. However, our approach in the analysis is somewhat novel, and it may be seen as an extension of the exact method of calculation employed by Davis and Peltier in their work on stratified parallel flows. The practical numerical utility of the neutral stability boundaries as a basis for the determination of both the radiating unstable modes and the fundamental unstable modes is demonstrated. The actual neutral boundaries provide a much tighter restriction on the real phase speeds of the linear disturbances than the one provided by the usual semicircle theorem. Our presentation of complete stability curves for the entire family of unstable modes allows us to clarify the issue of mode coalescence th...

Propagation of the electromagnetic ion-cyclotron wave in a fusion plasma

The propagation of the electromagnetic ion-cyclotron wave in a fusion plasma described by a loss-cone structure is discussed. The wavelength is assumed to be much larger than the ion Larmour radius and the ion plasma frequency ≫ the ion-cyclotron frequency. The two modes that propagate in the plasma interact strongly and fuse together under certain conditions making the plasma unstable. The coalescence of the modes is found to decrease with an increase in electron temperature.

Optimal design of ring stiffened cylindrical shells using multiple stiffener sizes

Abstract : This report describes the solution to the singly reinforced discrete stiffener problem by direct use of an optimization scheme employing mathematical programming. The optimization formulation and procedure used here admit a large number of simultaneous buckling modes thus allowing optimization under conditions of mode coalescence, which are usual in this type of problem. This is a preliminary study, the purposes of which are; to develop and evaluate methodology for the treatment of this problem, to develop preliminary insights into how multiple frame sizes may efficiently be employed in submersible structures, to examine the nature of design improvement resulting from use of multiple size frames, and to investigate the nature of such optimal designs. (Author)

Cyclotron wave instability in the corona and origin of solar radio emission with fine structure

The results of investigation of the cyclotron wave instability in the corona for Bernstein modes and plasma waves in a hybrid band have been used to interpret zebra-pattern phenomena. Two models of the generation region of parallel drifting bands are considered: the model of the point source localized at the apex of the magnetic trap and the model of a distributed source extended along the magnetic flux tube. In the first model it is assumed that a harmonic character of zebrapattern appears either in coalescence of excited Bernstein modes at different harmonics of the gyrofrequency or in coalescence of these modes with plasma waves excited in the hybrid band. In the latter case if the magnetic field changes in time a pulsating generation regime occurs. In the second model, the emission bands appear in the regions of double plasma resonance as a result of coalescence of longitudinal waves excited in the hybrid band. Estimations of the magnetic field and the nonequilibrium component density necessary for the zebra-pattern to generate are presented.