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From an available solution for the deformation of elliptical holes in a viscous material, a criterion is developed for fracture by the growth and coalescence of cylindrical holes under any prescribed history of applied principal components of stress and strain which do not rotate relative to the material. The criterion is extended to plastic materials by extrapolation from an analysis for the growth of circular holes under equiaxial transverse stress. Experiments on Plasticine substantiate the analysis and its extrapolation. For both plastic and viscous flow, most of the applied strain to fracture is found to occur while the holes are still small compared with their spacing. The most striking result is that in plastic materials there is a very strong inverse dependence of fracture strain on hydrostatic tension. The theory also indicates the effects of anisotropy, strain-hardening, and strain gradients on ductile fracture by the growth of holes.

The existence of galaxies today implies that the early Universe must have been inhomogeneous. Some regions might have got so compressed that they underwent gravitational collapse to produce black holes. Once formed, black holes in the early Universe would grow by accreting nearby matter. A first estimate suggests that they might grow at the same rate as the Universe during the radiation era and be of the order of 10 15 to 10 17 solar masses now. The observational evidence however is against the existence of such giant black holes. This motivates a more detailed study of the rate of accretion which shows that black holes will not in fact substantially increase their original mass by accretion. There could thus be primordial black holes around now with masses from 10 −5 g upwards.

A black hole of given mass, angular momentum, and charge can have a large number of different unobservable internal configurations which reflect the possible different initial configurations of the matter which collapsed to produce the hole. The logarithm of this number can be regarded as the entropy of the black hole and is a measure of the amount of information about the initial state which was lost in the formation of the black hole. If one makes the hypothesis that the entropy is finite, one can deduce that the black holes must emit thermal radiation at some nonzero temperature. Conversely, the recently derived quantum-mechanical result that black holes do emit thermal radiation at temperature $\frac{\ensuremath{\kappa}\ensuremath{\hbar}}{2\ensuremath{\pi}kc}$, where $\ensuremath{\kappa}$ is the surface gravity, enables one to prove that the entropy is finite and is equal to $\frac{{c}^{3}A}{4G\ensuremath{\hbar}}$, where $A$ is the surface area of the event horizon or boundary of the black hole. Because black holes have negative specific heat, they cannot be in stable thermal equilibrium except when the additional energy available is less than 1/4 the mass of the black hole. This means that the standard statistical-mechanical canonical ensemble cannot be applied when gravitational interactions are important. Black holes behave in a completely random and time-symmetric way and are indistinguishable, for an external observer, from white holes. The irreversibility that appears in the classical limit is merely a statistical effect.

This article outlines the mechanism by which brokerage provides social capital. Opinion and behavior are more homogeneous within than between groups, so people connected across groups are more familiar with alternative ways of thinking and behaving. Brokerage across the structural holes between groups provides a vision of op-tions otherwise unseen, which is the mechanism by which brokerage becomes social capital. I review evidence consistent with the hy-pothesis, then look at the networks around managers in a large American electronics company. The organization is rife with struc-tural holes, and brokerage has its expected correlates. Compensation, positive performance evaluations, promotions, and good ideas are disproportionately in the hands of people whose networks span structural holes. The between-group brokers are more likely to ex-press ideas, less likely to have ideas dismissed, and more likely to have ideas evaluated as valuable. I close with implications for cre-ativity and structural change. The hypothesis in this article is that people who stand near the holes in a social structure are at higher risk of having good ideas. The argument is that opinion and behavior are more homogeneous within than between groups, so people connected across groups are more familiar with alter-

To assess the effects of a firm's network of relations on innovation, this paper elaborates a theoretical framework that relates three aspects of a firm's ego network—direct ties, indirect ties, and structural holes (disconnections between a firm's partners)—to the firm's subsequent innovation output. It posits that direct and indirect ties both have a positive impact on innovation but that the impact of indirect ties is moderated by the number of a firm's direct ties. Structural holes are proposed to have both positive and negative influences on subsequent innovation. Results from a longitudinal study of firms in the international chemicals industry indicate support for the predictions on direct and indirect ties, but in the interfirm collaboration network, increasing structural holes has a negative effect on innovation. Among the implications for interorganizational network theory is that the optimal structure of interfirm networks depends on the objectives of the network members.

We describe techniques for incorporating feedback from star formation and black hole accretion into simulations of isolated and merging galaxies. At present, the details of these processes cannot be resolved in simulations on galactic scales. Our basic approach therefore involves forming coarse-grained representations of the properties of the interstellar medium and black hole accretion starting from basic physical assumptions, so that the impact of these effects can be included on resolved scales. We illustrate our method using a multiphase description of star-forming gas. Feedback from star formation pressurises highly overdense gas, altering its effective equation of state. We show that this allows the construction of stable galaxy models with much larger gas fractions than possible in earlier numerical work. We extend the model by including a treatment of gas accretion onto central supermassive black holes in galaxies. Assuming thermal coupling of a small fraction of the bolometric luminosity of accreting black holes to the surrounding gas, we show how this feedback regulates the growth of black holes. In gas-rich mergers of galaxies, we observe a complex interplay between starbursts and central AGN activity when the tidal interaction triggers intense nuclear inflows of gas. Once an accreting supermassive black hole has grown to a critical size, feedback terminates its further growth, and expels gas from the central region in a powerful quasar-driven wind. Our simulation methodology is therefore able to address the coupled processes of gas dynamics, star formation, and black hole accretion during the formation of galaxies.