Autonomy and Singularity in Dynamic Fracture

The recently developed weakly nonlinear theory of dynamic fracture predicts $1/r$ corrections to the standard asymptotic linear elastic $1/\sqrt{r}$ displacement-gradients, where $r$ is measured from the tip of a tensile crack. We show that the $1/r$ singularity does not automatically conform with the notion of autonomy (autonomy means that any crack tip nonlinear solution is uniquely determined by the surrounding linear elastic $1/\sqrt{r}$ fields) and that it does not automatically satisfy the resultant Newton's equation in the crack parallel direction. We show that these two properties are interrelated and that by requiring that the resultant Newton's equation is satisfied, autonomy of the $1/r$ singular solution is retained. We further show that the resultant linear momentum carried by the $1/r$ singular fields vanishes identically. Our results, which reveal the physical and mathematical nature of the new solution, are in favorable agreement with recent near tip measurements.Comment: 4 pages, 2 figures, related papers: arXiv:0902.2121 and arXiv:0807.486

Some exact results for the velocity of cracks propagating in non-linear elastic models

We analyze a piece-wise linear elastic model for the propagation of a crack in a stripe geometry under mode III conditions, in the absence of dissipation. The model is continuous in the propagation direction and discrete in the perpendicular direction. The velocity of the crack is a function of the value of the applied strain. We find analytically the value of the propagation velocity close to the Griffith threshold, and close to the strain of uniform breakdown. Contrary to the case of perfectly harmonic behavior up to the fracture point, in the piece-wise linear elastic model the crack velocity is lower than the sound velocity, reaching this limiting value at the strain of uniform breakdown. We complement the analytical results with numerical simulations and find excellent agreement.Comment: 9 pages, 13 figure

The dynamics of cracks in torn thin sheets

Motivated by recent experiments, we present a study of the dynamics of cracks in thin sheets. While the equations of elasticity for thin plates are well known, there remains the question of path selection for a propagating crack. We invoke a generalization of the principle of local symmetry to provide a criterion for path selection and demonstrate qualitative agreement with the experimental findings. The nature of the singularity at the crack tip is studied with and without the interference of nonlinear terms.Comment: 7 pages, 11 figure

Cracks Cleave Crystals

The problem of finding what direction cracks should move is not completely solved. A commonly accepted way to predict crack directions is by computing the density of elastic potential energy stored well away from the crack tip, and finding a direction of crack motion to maximize the consumption of this energy. I provide here a specific case where this rule fails. The example is of a crack in a crystal. It fractures along a crystal plane, rather than in the direction normally predicted to release the most energy. Thus, a correct equation of motion for brittle cracks must take into account both energy flows that are described in conventional continuum theories and details of the environment near the tip that are not.Comment: 6 page

Supersonic crack propagation in a class of lattice models of Mode III brittle fracture

We study a lattice model for mode III crack propagation in brittle materials in a stripe geometry at constant applied stretching. Stiffening of the material at large deformation produces supersonic crack propagation. For large stretching the propagation is guided by well developed soliton waves. For low stretching, the crack-tip velocity has a universal dependence on stretching that can be obtained using a simple geometrical argument.Comment: 4 pages, 3 figure

Frictional sliding without geometrical reflection symmetry

The dynamics of frictional interfaces play an important role in many physical systems spanning a broad range of scales. It is well-known that frictional interfaces separating two dissimilar materials couple interfacial slip and normal stress variations, a coupling that has major implications on their stability, failure mechanism and rupture directionality. In contrast, interfaces separating identical materials are traditionally assumed not to feature such a coupling due to symmetry considerations. We show, combining theory and experiments, that interfaces which separate bodies made of macroscopically identical materials, but lack geometrical reflection symmetry, generically feature such a coupling. We discuss two applications of this novel feature. First, we show that it accounts for a distinct, and previously unexplained, experimentally observed weakening effect in frictional cracks. Second, we demonstrate that it can destabilize frictional sliding which is otherwise stable. The emerging framework is expected to find applications in a broad range of systems.Comment: 14 pages, 5 figures + Supplementary Material. Minor change in the title, extended analysis in the second par

Host preference by Saperda calcarata Say (Coleoptera: Cerambycidae)

We conducted five laboratory and one field experiments to examine potential host selection mechanisms of Saperda calcarata Say in British Columbia. Olfactory bioassays indicated that female (and possibly male) beetles were attracted to volatiles from leafy twigs of trembling aspen, Populus tremuloides Michaux. However, wounding of the bole, ethanol baiting, or both, did not result in significant orientation toward or attack of trembling aspens in the field. Feeding preferences for trembling aspen were strong for both sexes in choice bioassays, but in no-choice bioassays, females did not discriminate between trembling aspen and black cottonwood, P. trichocarpa Torrey & Gray. Scouler's willow, Salix scouleriana Barrat in Hooker, was fed upon the least by both sexes. When diameter of bolts offered as oviposition hosts was equalized, frequency of oviposition was similar among the three hosts. Our data suggest that feeding preference is the predominant mechanism of host selection by S. calcarata

Velocity Fluctuations in Dynamical Fracture: the Role of Microcracks

We address the velocity fluctuations of fastly moving cracks in stressed materials. One possible mechanism for such fluctuations is the interaction of the main crack with micro cracks (irrespective whether these are existing material defects or they form during the crack evolution). We analyze carefully the dynamics (in 2 space dimensions) of one macro and one micro crack, and demonstrate that their interaction results in a {\em large} and {\em rapid} velocity fluctuation, in qualitative correspondence with typical velocity fluctuations observed in experiments. In developing the theory of the dynamical interaction we invoke an approximation that affords a reduction in mathematical complexity to a simple set of ordinary differential equations for the positions of the cracks tips; we propose that this kind of approximation has a range of usefulness that exceeds the present context.Comment: 7 pages, 7 figure

Cloudbus Toolkit for Market-Oriented Cloud Computing

This keynote paper: (1) presents the 21st century vision of computing and identifies various IT paradigms promising to deliver computing as a utility; (2) defines the architecture for creating market-oriented Clouds and computing atmosphere by leveraging technologies such as virtual machines; (3) provides thoughts on market-based resource management strategies that encompass both customer-driven service management and computational risk management to sustain SLA-oriented resource allocation; (4) presents the work carried out as part of our new Cloud Computing initiative, called Cloudbus: (i) Aneka, a Platform as a Service software system containing SDK (Software Development Kit) for construction of Cloud applications and deployment on private or public Clouds, in addition to supporting market-oriented resource management; (ii) internetworking of Clouds for dynamic creation of federated computing environments for scaling of elastic applications; (iii) creation of 3rd party Cloud brokering services for building content delivery networks and e-Science applications and their deployment on capabilities of IaaS providers such as Amazon along with Grid mashups; (iv) CloudSim supporting modelling and simulation of Clouds for performance studies; (v) Energy Efficient Resource Allocation Mechanisms and Techniques for creation and management of Green Clouds; and (vi) pathways for future research.Comment: 21 pages, 6 figures, 2 tables, Conference pape

A Serendipitous Mutation Reveals the Severe Virulence Defect of a Klebsiella pneumoniae fepB Mutant

ABSTRACT Klebsiella pneumoniae is considered a significant public health threat because of the emergence of multidrug-resistant strains and the challenge associated with treating life-threatening infections. Capsule, siderophores, and adhesins have been implicated as virulence determinants of K. pneumoniae , yet we lack a clear understanding of how this pathogen causes disease. In a previous screen for virulence genes, we identified a potential new virulence locus and constructed a mutant ( smr ) with this locus deleted. In this study, we characterize the smr mutant and show that this mutation renders K. pneumoniae avirulent in a pneumonia model of infection. The smr mutant was expected to have a deletion of three genes, but subsequent genome sequencing indicated that a much larger deletion had occurred. Further analysis of the deleted region indicated that the virulence defect of the smr mutant could be attributed to the loss of FepB, a periplasmic protein required for import of the siderophore enterobactin. Interestingly, a Δ fepB mutant was more attenuated than a mutant unable to synthesize enterobactin, suggesting that additional processes are affected. As FepB is highly conserved among the members of the family Enterobacteriaceae , therapeutic targeting of FepB may be useful for the treatment of Klebsiella and other bacterial infections. IMPORTANCE In addition to having a reputation as the causative agent of several types of hospital-acquired infections, Klebsiella pneumoniae has gained widespread attention as a pathogen with a propensity for acquiring antibiotic resistance. It is capable of causing a range of infections, including urinary tract infections, pneumonia, and sepsis. Because of the rapid emergence of carbapenem resistance among Klebsiella strains, there is a dire need for a better understanding of virulence mechanisms and identification of new drug targets. Here, we identify the periplasmic transporter FepB as one such potential target