A multiple scales approach to crack front waves

Perturbation of a propagating crack with a straight edge is solved using the method of matched asymptotic expansions (MAE). This provides a simplified analysis in which the inner and outer solutions are governed by distinct mechanics. The inner solution contains the explicit perturbation and is governed by a quasi-static equation. The outer solution determines the radiation of energy away from the tip, and requires solving dynamic equations in the unperturbed configuration. The outer and inner expansions are matched via the small parameter L/l defined by the disparate length scales: the crack perturbation length L and the outer length scale l associated with the loading. The method is first illustrated for a scalar crack model and then applied to the elastodynamic mode I problem. The dispersion relation for crack front waves is found by requiring that the energy release rate is unaltered under perturbation. The wave speed is calculated as a function of the nondimensional parameter kl where k is the crack front wavenumber, and dispersive properties of the crack front wave speed are described for the first time. The example problems considered here demonstrate that the potential of using MAE for moving boundary value problems with multiple scales.Comment: 25 pages, 5 figure

Conjugal amyotrophic lateral sclerosis:A case report from Scotland

Abstract Background Conjugal amyotrophic lateral sclerosis is rare, with significant effects on psychological and care needs. We report a case of conjugal amyotrophic lateral sclerosis disease from central Scotland. This case is particularly unusual as both patients were diagnosed within an 18-month period and experienced the disease simultaneously, with similar symptomatology and progression. Case presentation Patient A was a 71-year-old man who presented with unilateral arm weakness and wasting. Patient B was a 68-year-old woman who presented with unilateral shoulder and elbow weakness. Diagnosis of amyotrophic lateral sclerosis was made within a few months of presentation in both cases, based on typical clinical symptomatology together with supportive neurophysiological testing. Interventions included enteral feeding and non-invasive ventilation. The time period between symptom onset and death was 5 years for Patient A and 3.5 years for Patient B. Conclusion This case illustrates two main points: the care issues surrounding cases of conjugal neurological disease, and the psychological issues in these patients. There are significant care issues arising when co-habiting couples both develop severe functionally limiting neurological diseases at the same time. The more slowly progressive nature of Patient A’s disease may be at least partially explained by the support he was able to receive from Patient B before she developed symptoms. Secondly, there are important psychological effects of living with someone with the same – but more advanced – progressive and incurable neurological disease. Thus, Patient B was reluctant to have certain interventions that she had observed being given to her husband. Lastly, no plausible shared environmental risk factors were identified, implying that the co-occurrence of ALS in this couple was a random association

The New Unified Theory of ATP Synthesis/Hydrolysis and Muscle Contraction, Its Manifold Fundamental Consequences and Mechanistic Implications and Its Applications in Health and Disease

Complete details of the thermodynamics and molecular mechanisms of ATP synthesis/hydrolysis and muscle contraction are offered from the standpoint of the torsional mechanism of energy transduction and ATP synthesis and the rotation-uncoiling-tilt (RUT) energy storage mechanism of muscle contraction. The manifold fundamental consequences and mechanistic implications of the unified theory for oxidative phosphorylation and muscle contraction are explained. The consistency of current mechanisms of ATP synthesis and muscle contraction with experiment is assessed, and the novel insights of the unified theory are shown to take us beyond the binding change mechanism, the chemiosmotic theory and the lever arm model. It is shown from first principles how previous theories of ATP synthesis and muscle contraction violate both the first and second laws of thermodynamics, necessitating their revision. It is concluded that the new paradigm, ten years after making its first appearance, is now perfectly poised to replace the older theories. Finally, applications of the unified theory in cell life and cell death are outlined and prospects for future research are explored. While it is impossible to cover each and every specific aspect of the above, an attempt has been made here to address all the pertinent details and what is presented should be sufficient to convince the reader of the novelty, originality, breakthrough nature and power of the unified theory, its manifold fundamental consequences and mechanistic implications, and its applications in health and disease

Ethnicity, Culture Prickly Pear in South African Museums ?

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