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

Machine Learning Groups Patients by Early Functional Improvement Likelihood Based on Wearable Sensor Instrumented Preoperative Timed-Up-and-Go Tests

© 2019 The Author(s) Background: Wearable sensors permit efficient data collection and unobtrusive systems can be used for instrumenting knee patients for objective assessment. Machine learning can be leveraged to parse the abundant information these systems provide and segment patients into relevant groups without specifying group membership criteria. The objective of this study is to examine functional parameters influencing favorable recovery outcomes by separating patients into functional groups and tracking them through clinical follow-ups. Methods: Patients undergoing primary unilateral total knee arthroplasty (n = 68) completed instrumented timed-up-and-go tests preoperatively and at their 2-, 6-, and 12-week follow-up appointments. A custom wearable system extracted 55 metrics for analysis and a K-means algorithm separated patients into functionally distinguished groups based on the derived features. These groups were analyzed to determine which metrics differentiated most and how each cluster improved during early recovery. Results: Patients separated into 2 clusters (n = 46 and n = 22) with significantly different test completion times (12.6 s vs 21.6 s, P \u3c .001). Tracking the recovery of both groups to their 12-week follow-ups revealed 64% of one group improved their function while 63% of the other maintained preoperative function. The higher improvement group shortened their test times by 4.94 s, (P = .005) showing faster recovery while the other group did not improve above a minimally important clinical difference (0.87 s, P = .07). Features with the largest effect size between groups were distinguished as important functional parameters. Conclusion: This work supports using wearable sensors to instrument functional tests during clinical visits and using machine learning to parse complex patterns to reveal clinically relevant parameters

Comparison of Contact Kinematics in Posterior-Stabilized and Cruciate-Retaining Total Knee Arthroplasty at Long-Term Follow-Up

© 2019 Elsevier Inc. Background: There is controversy regarding the superiority of posterior-stabilizing (PS) total knee arthroplasty (TKA) and cruciate-retaining (CR) TKA. Substantial work has made comparisons between PS and CR TKA at follow-ups of less than 5 years. It was the goal of the present study to compare the kinematics at greater than 5 years postoperatively between CR and PS TKA, with a secondary goal of comparing patient function. Methods: A total of 42 knees were investigated, with equal representation in the PS and CR TKA groups. Patients underwent radiostereometric analysis imaging at 0°, 20°, 40°, 60° 80°, and 100° of flexion. Contact position, magnitude of excursion, and condylar separation on each condyle were measured. A Timed-Up-and-Go functional test was also performed by patients, with the total test time being measured. Preoperative and postoperative clinical outcome scores were also collected. Results: There were differences in contact position on both the medial and lateral condyles at multiple angles of flexion (P \u3c .05). There was no difference (P = .89) in medial excursion; however, PS TKA had greater lateral excursion than CR TKA (P \u3c .01). No difference (P \u3e .99) was found in frequency of condylar separation. PS TKA was associated with faster (P = .03) total Timed-Up-and-Go test times. There were no differences in clinical outcome scores between the groups preoperatively or postoperatively. Conclusion: We found kinematic and functional differences that favor PS TKA. Our results suggest posterior cruciate ligament insufficiency in CR TKA, indicating that perhaps the cam/post systems in PS TKA better maintain knee kinematics and function long term

Hydrodynamic stability and mode coupling in Keplerian flows: local strato-rotational analysis

Aims. Qualitative analysis of key (but yet unappreciated) linear phenomena in stratified hydrodynamic Keplerian flows: (i) the occurrence of a vortex mode, as a consequence of strato-rotational balance, with its transient dynamics; (ii) the generation of spiral-density waves (also called inertia-gravity or $g\Omega$ waves) by the vortex mode through linear mode coupling in shear flows. Methods. Non-modal analysis of linearized Boussinesq equations written in the shearing sheet approximation of accretion disk flows. Results. It is shown that the combined action of rotation and stratification introduces a new degree of freedom -- vortex mode perturbation -- which is linearly coupled with the spiral-density waves. These two modes are jointly able to extract energy from the background flow and they govern the disk dynamics in the small-scale range. The transient behavior of these modes is determined by the non-normality of the Keplerian shear flow. Tightly leading vortex mode perturbations undergo substantial transient growth, then, becoming trailing, inevitably generate trailing spiral-density waves by linear mode coupling. This course of events -- transient growth plus coupling -- is particularly pronounced for perturbation harmonics with comparable azimuthal and vertical scales and it renders the energy dynamics similar to the 3D unbounded plane Couette flow case. Conclusions. Our investigation strongly suggests that the so-called bypass concept of turbulence, which has been recently developed by the hydrodynamic community for spectrally stable shear flows, can also be applied to Keplerian disks. This conjecture may be confirmed by appropriate numerical simulations that take in account the vertical stratification and consequent mode coupling in the high Reynolds number regime.Comment: A&A (accepted

Phase-Field Model of Mode III Dynamic Fracture

We introduce a phenomenological continuum model for mode III dynamic fracture that is based on the phase-field methodology used extensively to model interfacial pattern formation. We couple a scalar field, which distinguishes between ``broken'' and ``unbroken'' states of the system, to the displacement field in a way that consistently includes both macroscopic elasticity and a simple rotationally invariant short scale description of breaking. We report two-dimensional simulations that yield steady-state crack motion in a strip geometry above the Griffith threshold.Comment: submitted to PR

Recent ecological change in ancient lakes

Ancient lakes are among the best archivists of past environmental change, having experienced more than one full glacial cycle, a wide range of climatic conditions, tectonic events, and long association with human settlements. These lakes not only record long histories of environmental variation and human activity in their sediments, but also harbor very high levels of biodiversity and endemism. Yet, ancient lakes are faced with a familiar suite of anthropogenic threats, which may degrade the unusual properties that make them especially valuable to science and society. In all ancient lakes for which data exist, significant warming of surface waters has occurred, with a broad range of consequences. Eutrophication threatens both native species assemblages and regional economies reliant on clean surface water, fisheries, and tourism. Where sewage contributes nutrients and heavy metals, one can anticipate the occurrence of less understood emerging contaminants, such as pharmaceuticals, personal care products, and microplastics that negatively affect lake biota and water quality. Human populations continue to increase in most of the ancient lakes’ watersheds, which will exacerbate these concerns. Further, human alterations of hydrology, including those produced through climate change, have altered lake levels. Co‐occurring with these impacts have been intentional and unintentional species introductions, altering biodiversity. Given that the distinctive character of each ancient lake is strongly linked to age, there may be few options to remediate losses of species or other ecosystem damage associated with modern ecological change, heightening the imperative for understanding these systems

Theory of dynamic crack branching in brittle materials

The problem of dynamic symmetric branching of an initial single brittle crack propagating at a given speed under plane loading conditions is studied within a continuum mechanics approach. Griffith's energy criterion and the principle of local symmetry are used to determine the cracks paths. The bifurcation is predicted at a given critical speed and at a specific branching angle: both correlated very well with experiments. The curvature of the subsequent branches is also studied: the sign of $T$, with $T$ being the non singular stress at the initial crack tip, separates branches paths that diverge from or converge to the initial path, a feature that may be tested in future experiments. The model rests on a scenario of crack branching with some reasonable assumptions based on general considerations and in exact dynamic results for anti-plane branching. It is argued that it is possible to use a static analysis of the crack bifurcation for plane loading as a good approximation to the dynamical case. The results are interesting since they explain within a continuum mechanics approach the main features of the branching instabilities of fast cracks in brittle materials, i.e. critical speeds, branching angle and the geometry of subsequent branches paths.Comment: 41 pages, 15 figures. Accepted to International Journal of Fractur

Microbiome and infectivity studies reveal complex polyspecies tree disease in Acute Oak Decline

Decline-diseases are complex and becoming increasingly problematic to tree health globally. Acute Oak Decline (AOD) is characterized by necrotic stem lesions and galleries of the bark-boring beetle, Agrilus biguttatus, and represents a serious threat to oak. Although multiple novel bacterial species and Agrilus galleries are associated with AOD lesions, the causative agent(s) are unknown. The AOD pathosystem therefore provides an ideal model for a systems-based research approach to address our hypothesis that AOD lesions are caused by a polymicrobial complex. Here we show that three bacterial species, Brenneria goodwinii, Gibbsiella quercinecans and Rahnella victoriana, are consistently abundant in the lesion microbiome and possess virulence genes used by canonical phytopathogens that are expressed in AOD lesions. Individual and polyspecies inoculations on oak logs and trees demonstrated that B. goodwinii and G. quercinecans cause tissue necrosis and, in combination with A. biguttatus, produce the diagnostic symptoms of AOD. We have proved a polybacterial cause of AOD lesions, providing new insights into polymicrobial interactions and tree disease. This work presents a novel conceptual and methodological template for adapting Koch’s postulates to address the role of microbial communities in disease

Prenatal hypoxia induces increased cardiac contractility on a background of decreased capillary density.

Background: Chronic hypoxia in utero (CHU) is one of the most common insults to fetal development and may be associated with poor cardiac recovery from ischaemia-reperfusion injury,yet the effects on normal cardiac mechanical performance are poorly understood. Methods: Pregnant female wistar rats were exposed to hypoxia (12% oxygen, balance nitrogen)for days 10–20 of pregnancy. Pups were born into normal room air and weaned normally. At 10 weeks of age, hearts were excised under anaesthesia and underwent retrograde 'Langendorff' perfusion. Mechanical performance was measured at constant filling pressure (100 cm H2O) with intraventricular balloon. Left ventricular free wall was dissected away and capillary density estimated following alkaline phosphatase staining. Expression of SERCA2a and Nitric Oxide Synthases (NOS) proteins were estimated by immunoblotting. Results: CHU significantly increased body mass (P < 0.001) compared with age-matched control rats but was without effect on relative cardiac mass. For incremental increases in left ventricular balloon volume, diastolic pressure was preserved. However, systolic pressure was significantly greater following CHU for balloon volume = 50 μl (P < 0.01) and up to 200 μl (P < 0.05). For higher balloon volumes systolic pressure was not significantly different from control. Developed pressures were correspondingly increased relative to controls for balloon volumes up to 250 μl (P < 0.05).Left ventricular free wall capillary density was significantly decreased in both epicardium (18%; P <0.05) and endocardium (11%; P < 0.05) despite preserved coronary flow. Western blot analysis revealed no change to the expression of SERCA2a or nNOS but immuno-detectable eNOS protein was significantly decreased (P < 0.001) in cardiac tissue following chronic hypoxia in utero. Conclusion: These data offer potential mechanisms for poor recovery following ischaemia, including decreased coronary flow reserve and impaired angiogenesis with subsequent detrimental effects of post-natal cardiac performance

Stress-corrosion mechanisms in silicate glasses

The present review is intended to revisit the advances and debates in the comprehension of the mechanisms of subcritical crack propagation in silicate glasses almost a century after its initial developments. Glass has inspired the initial insights of Griffith into the origin of brittleness and the ensuing development of modern fracture mechanics. Yet, through the decades the real nature of the fundamental mechanisms of crack propagation in glass has escaped a clear comprehension which could gather general agreement on subtle problems such as the role of plasticity, the role of the glass composition, the environmental condition at the crack tip and its relation to the complex mechanisms of corrosion and leaching. The different processes are analysed here with a special focus on their relevant space and time scales in order to question their domain of action and their contribution in both the kinetic laws and the energetic aspects.Comment: Invited review article - 34 pages Accepted for publication in J. Phys. D: Appl. Phy