Eshelby Forces Associated with an Advancing Crack Surrounded by Vanishingly Small Inhomogeneity

1991 ◽  
Author(s):  
Chien H. Wu
Keyword(s):  
1965 ◽  
Vol 43 (4) ◽  
pp. 640-644
Author(s):  
Som Krishan

Oscillations of a collisionless plasma in equilibrium with a magnetic field which is weakly inhomogeneous in one dimension are studied. The calculations are based on longitudinal oscillations, i.e. the electric vector is parallel to the wave vector. The procedure employed is to use Maxwell's equations and expand the velocity distribution function about its equilibrium value for finding the perturbation in the distribution. The dispersion relation so obtained is different from that of Rosenbluth et al. (1962). The system is stable for the small Landau growth rate (Landau 1946), which might become appreciable for wavelengths comparable with the Larmor radius, provided [Formula: see text], where k is the wave vector and ε is a small inhomogeneity parameter.


2008 ◽  
Vol 17 (02) ◽  
pp. 311-326 ◽  
Author(s):  
MATTEO LUCA RUGGIERO ◽  
ANGELO TARTAGLIA

After briefly reviewing the relativistic approach to positioning systems based on the introduction of the emission coordinates, we show how explicit maps can be obtained between the Cartesian coordinates and the emission coordinates, for a suitably chosen set of emitters, whose world lines are supposed to be known by the users. We consider Minkowski space–time and the space–time where a small inhomogeneity is introduced (i.e. a small a "gravitational" field), in 1 + 1 and 1 + 3 dimensions.


1977 ◽  
Vol 44 (3) ◽  
pp. 449-454 ◽  
Author(s):  
J. Tirosh

By considering the stress interaction between an inhomogeneity embedded in an elastic brittle-like solid and the preexisting microcracks (“Griffith cracks”) inherent to the solid, several puzzling phenomena concerning the apparent anomalous “size effect” on the fracture strength of solids weakened (strengthened) by a cutout (reinforcement) are explained quantitatively. The various conditions under which a cylindrical inhomogeneity in an otherwise homogeneous body enhances the strength of the body or weakens it when the body is subjected to load normal to the cylindrical axis are revealed and discussed. In particular it is shown that uniaxial tensile and compressive critical loads required to fracture material with various hole sizes are predictable as confirmed by experiments with quasi-isotropic composite materials, rocks, and high strength alloys found in the open literature. The entries to these predictive functions are the two independent fracture properties of the material; tensile strength and toughness of the virgin material, or the typical size of the Griffith cracks. As a by-product, the extremely high compressive strength of a material (with respect to its tensile strength) with vanishingly small inhomogeneity emerges.


2005 ◽  
Vol 127 (6) ◽  
pp. 2396-2401
Author(s):  
N. Ya. Kirpichnikova ◽  
L. A. Svirkina ◽  
V. B. Philippov

2005 ◽  
Vol 127 (6) ◽  
pp. 2389-2395
Author(s):  
N. Ya. Kirpichnikova ◽  
S. N. Kirpichnikov ◽  
V. B. Philippov

1992 ◽  
Vol 289 ◽  
Author(s):  
Yue Hu ◽  
Seth Fraden ◽  
J. L. Glass ◽  
L. E. Wenner

When an electric field is applied to a colloidal suspension of micronsize particles, the particles are attracted to each other in the direction of the external field. They line up to form chains and columns across the gap of the electrodes and therefore drastically change the rheological properties of the suspension. These electrorheological phenomena have been studied extensively by recent computer simulation work [1,2], and it is generally accepted that the interactions between the induced electric dipole moments of the particles are responsible for their alignment in the external fields. To avoid net migrations of particles in electric fields of small inhomogeneity, alternating fields are generally used in experiments.


Blood ◽  
1995 ◽  
Vol 85 (8) ◽  
pp. 2194-2201 ◽  
Author(s):  
JM Theler ◽  
DP Lew ◽  
ME Jaconi ◽  
KH Krause ◽  
CB Wollheim ◽  
...  

The subcellular pattern of cytosolic free Ca2+ ([Ca2+]i) changes in human polymorphonuclear neutrophils (PMNs) was studied using imaging of fura-2 fluorescence (time resolution 12.5 ratios/s) to determine whether PMNs could obtain directional information from the [Ca2+]i signal. [Ca2+]i changes were observed during initial adherence, the subsequent chemotactic movement, and the phagocytosis of opsonized yeast particles. Initial adherence was followed by a rapid increase in [Ca2+]i (from 90 +/- 10 to 290 +/- 40 nmol/L in 6.5 +/- 2.5 seconds; +/- SEM, n = 10), apparently homogeneously distributed over the entire cytoplasm, which preceded the spreading of the PMNs. [Ca2+]i increases after the contact of the PMNs with yeast particles were of lower mean amplitude; [Ca2+]i increased simultaneously throughout the cytosol. In the absence of extracellular Ca2+, multiple phagocytotic events could proceed normally without a mandatory [Ca2+]i transient. In PMNs polarized on phagocytosis, gradients in [Ca2+]i could be observed. [Ca2+]i was more elevated in the periphagosomal area than in the remaining parts. Taken together, these data show that [Ca2+]i waves do not provide the neutrophil with directional information during chemotaxis and phagocytosis. Sustained small inhomogeneity of [Ca2+]i levels are consistent with a proposed redistribution of releasable Ca2+ stores on phagocytosis.


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