Stability Analysis Of Cracks Propagating In Three Dimensional Solids

1995 ◽  
Vol 409 ◽  
Author(s):  
H. Larralde ◽  
A. A. Al-Falou ◽  
R. C. Ball
Keyword(s):  
Perturbation Theory ◽  
Stability Analysis ◽  
Fracture Surface ◽  
Three Dimensional ◽  
Type I ◽  
Two Dimensional ◽  
Singular Terms ◽  
First Order ◽  
Left Behind ◽  
First Order Perturbation

AbstractWe present a theory for the morphology of the fracture surface left behind by slowly propagating cracks in linear, isotropic and homogeneous three dimensional solids. Our results are based on first order perturbation theory of the equations of elasticity for cracks whose shape is slightly perturbed from planar. For cracks propagating under pure type I loading we find that all perturbation modes are linearly stable, from which we can predict the roughness of the fracture surface induced by fluctuations in the material. We compare our results with the classical results for cracks propagating in two dimensional systems, and discuss the effects in the three dimensional analysis which result from taking into account contributions from non-singular terms of the stress field, as well as the effects arising from finite speeds of crack propagation.

Upstream motions in stratified flow

1988 ◽  
Vol 187 ◽  
pp. 487-506 ◽  
Author(s):  
I. P. Castro ◽  
W. H. Snyder
Keyword(s):  
Body Height ◽  
Three Dimensional ◽  
Time Dependent ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Towing Tank ◽  
First Order ◽  
Density Perturbations ◽  
Small Obstacle ◽  
Obstacle Height

In this paper experimental measurements of the time-dependent velocity and density perturbations upstream of obstacles towed through linearly stratified fluid are presented. Attention is concentrated on two-dimensional obstacles which generate turbulent separated wakes at Froude numbers, based on velocity and body height, of less than 0.5. The form of the upstream columnar modes is shown to be largely that of first-order unattenuating disturbances, which have little resemblance to the perturbations described by small-obstacle-height theories. For two-dimensional obstacles the disturbances are similar to those found by Wei, Kao & Pao (1975) and it is shown that provided a suitable obstacle drag coefficient is specified, the lowest-order modes (at least) are quantitatively consistent with the results of the Oseen inviscid model.Discussion of some results of similar measurements upstream of three-dimensional obstacles, the importance of towing tank endwalls and the relevance of the Foster & Saffman (1970) theory for the limit of zero Froude number is also included.

Note on Interference Effects in Two-Step Reaction Processes

1975 ◽  
Vol 53 (23) ◽  
pp. 2590-2592
Author(s):  
J. Cejpek ◽  
J. Dobeš
Keyword(s):  
Perturbation Theory ◽  
Point Of View ◽  
Order Perturbation ◽  
Interference Effects ◽  
Qualitative Explanation ◽  
First Order ◽  
One Step ◽  
Step Transition ◽  
Reaction Processes ◽  
First Order Perturbation

The reaction processes in which a one-step transition is forbidden are analyzed from the point of view of the first order perturbation theory. The interference between two competing two-step reaction paths is found to be always constructive. A qualitative explanation of the experimentally observed reaction intensities is presented.

scholarly journals Quantum many-body effects on Rydberg excitons in cuprous oxide

2021 ◽  
Author(s):  
D. Semkat ◽  
H. Fehske ◽  
H. Stolz
Keyword(s):  
Perturbation Theory ◽  
Oscillator Strength ◽  
Cuprous Oxide ◽  
Many Body ◽  
Electron Hole ◽  
First Order ◽  
Electron Hole Plasma ◽  
Plasma Line ◽  
Many Body Effects ◽  
First Order Perturbation

AbstractWe investigate quantum many-body effects on Rydberg excitons in cuprous oxide induced by the surrounding electron-hole plasma. Line shifts and widths are calculated by full diagonalisation of the plasma Hamiltonian and compared to results in first order perturbation theory, and the oscillator strength of the exciton lines is analysed.

scholarly journals Steady-State Three-Dimensional Ice Flow over an Undulating Base: First-Order Theory with Linear Ice Rheology

1987 ◽  
Vol 33 (114) ◽  
pp. 177-185 ◽  
Author(s):  
Niels Reeh
Keyword(s):  
Three Dimensional ◽  
Steady Motion ◽  
Simple Shear Flow ◽  
Finite Width ◽  
Two Dimensional ◽  
Internal Layers ◽  
Ice Flow ◽  
Depth Variation ◽  
First Order ◽  
First Order Theory

AbstractThe problem of ice flow over threedimensional basal irregularities is studied by considering the steady motion of a fluid with a linear constitutive equation over sine-shaped basal undulations. The undisturbed flow is simple shear flow with constant depth. Using the ratio of the amplitude of the basal undulations to the ice thickness as perturbation parameter, equations to the first order for the velocity and pressure perturbations are set up and solved.The study shows that when the widths of the basal undulations are larger than 2–3 times their lengths, the finite width of the undulations has only a minor influence on the flow, which to a good approximation may be considered two-dimensional. However, as the ratio between the longitudinal and the transverse wavelengthL/Wincreases, the three-dimensional flow effects becomes substantial. If, for example, the ratio ofLtoWexceeds 3, surface amplitudes are reduced by more than one order of magnitude as compared to the two-dimensional case. TheL/Wratio also influences the depth variation of the amplitudes of internal layers and the depth variation of perturbation velocities and strain-rates. With increasingL/Wratio, the changes of these quantities are concentrated in a near-bottom layer of decreasing thickness. Furthermore, it is shown, that the azimuth of the velocity vector may change by up to 10° between the surface and the base of the ice sheet, and that significant transverse flow may occur at depth without manifesting itself at the surface to any significant degree.

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