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The case of isotropic compressible turbulence subjected to rapid isotropic compression is studied using inviscid rapid distortion theory and direct numerical simulation. An exact solution to the rapid distortion problem is given, and results are compared to those of direct numerical simulation. Implications for modelling turbulent flows are discussed.
A magnetic field sensor that isotropically senses an incident magnetic field. This is preferably accomplished by providing a magnetic field sensor device that has one or more circular shaped magnetoresistive sensor elements for sensing the incident magnetic field. The magnetoresistive material used is preferably isotropic, and may be a CMR material or some form of a GMR material. Because the sensor elements are circular in shape, shape anisotropy is eliminated. Thus, the resulting magnetic field sensor device provides an output that is relatively independent of the direction of the incident magnetic field in the sensor plane.
We present a generalised formalism for treating the porosity-associated reduction in continuum opacity that occurs when individual clumps in a stochastic medium become optically thick. As in previous work, we concentrate on developing bridging laws between the limits of optically thin and thick clumps. We consider geometries resulting in either isotropic or anisotropic effective opacity, and, in addition to an idealised model in which all clumps have the same local overdensity and scale, we also treat an ensemble of clumps with optical depths set by Markovian statistics. This formalism is then applied to the specific case of bound-free absorption of X- rays in hot star winds, a process not directly affected by clumping in the optically thin limit. We find that the Markov model gives surprisingly similar results to those found previously for the single clump model, suggesting that porous opacity is not very sensitive to details of the assumed clump distribution function. Further, an anisotropic effective opacity favours escape of X-rays emitted in the tangential direction (the venetian blind effect), resulting in a bump of higher flux close to line centre as compared to profiles computed from isotropic porosity models. We demonstrate how this characteristic line shape may be used to diagnose the clump geometry, and we confirm previous results that for optically thick clumping to significantly influence X-ray line profiles, very large porosity lengths, defined as the mean free path between clumps, are required. Moreover, we present the first X-ray line profiles computed directly from line-driven instability simulations using a 3-D patch method, and find that porosity effects from such models also are very small. This further supports the view that porosity has, at most, a marginal effect on X-ray line diagnostics in O stars, and therefore that these diagnostics do indeed provide a good clumping insensitive method for deriving O star mass-loss rates.
We present a generalised formalism for treating the porosity-associated reduction in continuum opacity that occurs when individual clumps in a stochastic medium become optically thick. As in previous work, we concentrate on developing bridging laws between the limits of optically thin and thick clumps. We consider geometries resulting in either isotropic or anisotropic effective opacity, and, in addition to an idealised model in which all clumps have the same local overdensity and scale, we also treat an ensemble of clumps with optical depths set by Markovian statistics. This formalism is then applied to the specific case of bound-free absorption of X- rays in hot star winds, a process not directly affected by clumping in the optically thin limit. We find that the Markov model gives surprisingly similar results to those found previously for the single clump model, suggesting that porous opacity is not very sensitive to details of the assumed clump distribution function. Further, an anisotropic effective opacity favours escape of X-rays emitted in the tangential direction (the venetian blind effect), resulting in a bump of higher flux close to line centre as compared to profiles computed from isotropic porosity models. We demonstrate how this characteristic line shape may be used to diagnose the clump geometry, and we confirm previous results that for optically thick clumping to significantly influence X-ray line profiles, very large porosity lengths, defined as the mean free path between clumps, are required. Moreover, we present the first X-ray line profiles computed directly from line-driven instability simulations using a 3-D patch method, and find that porosity effects from such models also are very small. This further supports the view that porosity has, at most, a marginal effect on X-ray line diagnostics in O stars, and therefore that these diagnostics do indeed provide a good clumping insensitive method for deriving O star mass-loss rates.
The performance of a three-dimensional continuum damage mechanics (CDM) model for intralaminar damage, coupled with a cohesive zone model for delamination, is examined for damage prediction in cross-ply and quasi-isotropic laminated plates subjected to quasi-static transverse indentation. Details of the CDM model based on the deformation gradient decomposition (DGD) method and the finite element (FE) modeling strategy are presented and discussed. Critical features of the damage model and FE modeling approach are assessed by comparing analysis predictions to experimental data for cross-ply and quasi-isotropic panels in which damage is dominated by complex interactions between matrix cracks and delaminations.
Dyadic Green function for moving isotropic medium
Huygen principle for analysis of electromagnetic field in moving isotropic homogeneous and linear medium
Huygen principle for electromagnetic field in moving, isotropic, homogeneous and linear medium, using Maxwell-Minkowski equations and Green function for field equation
Elastic equilibrium in isotropic plate in stationary thermal field, and bending due to temperature stresses
Gamma-ray isotropic dose, energy flux and energy current buildup factors for finite slabs calculated by Monte Carlo techniques
Time-dependent Green function for moving isotropic nondispersive medium
This study was undertaken to examine how well the 0.05 inch/min loading rate typically used to develop allowables for open hole compression strength of carbon/epoxy laminates represents structures that may experience a much lower loading rate (such as civil engineering structures) or a much higher loading rate (such as a rocket interstage at liftoff). The Composite Materials Handbook-17 (CMH-17) suggests developing strength allowables at the coupon level (lowest level of the “building block” approach) and using a rigorous statistical analysis to arrive at a strength allowable upon which the structure is to be further designed at higher levels of the building block pyramid. But do these coupon level tests truly represent meaningful stresses at which the composite in the final structure can withstand considering the effects of loading rate? Open hole compression (OHC) strength was chosen for this study since most structures are designed to some damage tolerance criteria and OHC strength testing is rather simple to perform. A quasi-isotropic lay-up was chosen since this is a very common lay-up sequence. The results show that for structures that experience a very small loading rate (0.0005 in/min) the allowables developed at the standard 0.05 in/min loading rate are higher than what the composite can withstand at this lower loading rate. Conversely, at a high loading rate of 10 in/min the strength values found at the standard test rate of 0.05 in/min are slightly lower and not “in family” using the statistics suggested in CMH-17. These results question if standardized test rates are reliable, at least to the fidelity of being “in family” per CMH-17. Some creep rupture tests were also performed to demonstrate that OHC strength values could be lower than the slowest test speed used in this study (0.0005 in/min).
This study presents experimental results of compression after impact (CAI) testing of aluminum honeycomb core sandwich structure with face sheets made of co-cured T1100/3960 quasi-isotropic carbon/epoxy when tested at +22.5⁰ and -22.5⁰ with respect to the 0⁰ fibers. In a previous study examining the CAI strengths of honeycomb sandwich structure, it was found that specimens had different CAI strengths, based on a [-45/90/+45/0]s layup, depending on whether they were tested in the 0⁰ direction (face sheet layup of [-45/90/+45/0]s) or 90⁰ direction (face sheet layup of [+45/0/-45/90]s). The CAI strength results showed that the specimens tested in the 90⁰ direction had a 19% drop in CAI strength compared to specimens tested in the 0⁰ direction. This was attributed to the 0⁰ load bearing plies in the 0⁰ direction specimens being “tucked in” at the center of the specimen thus providing more stability against microbuckling. This raised the question as to what CAI strength would specimens tested at +22.5⁰ (face sheet layup of [-22.5/- 67.5/+67.6/+22.5]s) and -22.5⁰ (face sheet layup of [-67.5/+67.5/+22.5/-22.5]s) have compared to specimens tested in the 0⁰ and 90⁰ direction. Results presented in this study show that the specimens loaded at +22.5⁰ and -22.5⁰ have a similar average CAI strength compared to the specimens loaded in the 0⁰ direction. The specimens loaded in the 90⁰ direction exhibit 16% lower average CAI strength. Additional specimens were tested in the +45⁰ direction to put the 0⁰ load bearing fibers on the outside of the specimen to see if this would decrease the strength as has been documented for undamaged strength. These specimens have average CAI strength values between the 0⁰ direction average CAI strength values and the 90⁰ direction average CAI strength values.
Hydromagnetic waves in plasma with isotropic and nonisotropic pressure perpendicular to a magnetic field
Methods for obtaining broad-angle antenna coverage from a satellite whose diameter is large compared with the signal wavelength, considering broad-band biconical and isotropic patterns
Edge dislocations in elastic isotropic half space, calculating their displacement functions and considering their electron diffraction contrast
Diffuse reflection and transmission coefficients computed for radiative transfer in homogeneous slabs of finite thickness with isotropic scattering
Spacecraft quasi-isotropic antenna system for space telemetry