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

Engineering the surface properties of a human monoclonal antibody prevents self-association and rapid clearance in vivo

Uncontrolled self-association is a major challenge in the exploitation of proteins as therapeutics. Here we describe the development of a structural proteomics approach to identify the amino acids responsible for aberrant self-association of monoclonal antibodies and the design of a variant with reduced aggregation and increased serum persistence in vivo. We show that the human monoclonal antibody, MEDI1912, selected against nerve growth factor binds with picomolar affinity, but undergoes reversible self-association and has a poor pharmacokinetic profile in both rat and cynomolgus monkeys. Using hydrogen/deuterium exchange and cross-linking-mass spectrometry we map the residues responsible for self-association of MEDI1912 and show that disruption of the self-interaction interface by three mutations enhances its biophysical properties and serum persistence, whilst maintaining high affinity and potency. Immunohistochemistry suggests that this is achieved via reduction of non-specific tissue binding. The strategy developed represents a powerful and generic approach to improve the properties of therapeutic proteins

Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

This paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory

Multi-Task Drug Bioactivity Classification with Graph Labeling Ensembles

Abstract. We present a new method for drug bioactivity classification based on learning an ensemble of multi-task classifiers. As the base classifiers of the ensemble we use Max-Margin Conditional Random Field (MMCRF) models, which have previously obtained the state-of-the-art accuracy in this problem. MMCRF relies on a graph structure coupling the set of tasks together, and thus turns the multi-task learning problem into a graph labeling problem. In our ensemble method the graphs of the base classifiers are random, constructed by random pairing or random spanning tree extraction over the set of tasks. We compare the ensemble approaches on datasets containing the cancer inhibition potential of drug-like molecules against 60 cancer cell lines. In our experiments we find that ensembles based on random graphs surpass the accuracy of single SVM as well as a single MMCRF model relying on a graph built from auxiliary data