A class of exact Navier-Stokes solutions for homogeneous flat-plate boundary layers and their linear stability

We introduce a new boundary layer formalism on the basis of which a class of exact solutions to the Navier–Stokes equations is derived. These solutions describe laminar boundary layer flows past a flat plate under the assumption of one homogeneous direction, such as the classical swept Hiemenz boundary layer (SHBL), the asymptotic suction boundary layer (ASBL) and the oblique impingement boundary layer. The linear stability of these new solutions is investigated, uncovering new results for the SHBL and the ASBL. Previously, each of these flows had been described with its own formalism and coordinate system, such that the solutions could not be transformed into each other. Using a new compound formalism, we are able to show that the ASBL is the physical limit of the SHBL with wall suction when the chordwise velocity component vanishes while the homogeneous sweep velocity is maintained. A corresponding non-dimensionalization is proposed, which allows conversion of the new Reynolds number definition to the classical ones. Linear stability analysis for the new class of solutions reveals a compound neutral surface which contains the classical neutral curves of the SHBL and the ASBL. It is shown that the linearly most unstable Görtler–Hämmerlin modes of the SHBL smoothly transform into Tollmien–Schlichting modes as the chordwise velocity vanishes. These results are useful for transition prediction of the attachment-line instability, especially concerning the use of suction to stabilize boundary layers of swept-wing aircraft.

Stabilization of subcritical bypass transition in the leading-edge boundary layer by suction

This work investigates the subcritical spatial transition in the swept Hiemenz boundary layer by means of direct numerical simulations (DNS). A pair of steady co-rotating vortices located at the attachment line is enforced as a primary disturbance leading to streaks which are stable. A small secondary, time-dependent disturbance interacts with these streaks such that instability and breakdown to turbulence may occur. The instability only occurs for a certain band of secondary disturbance frequencies. Positive secondary instability growth rates could be observed for Reynolds numbers as low as , whereas the linear critical Reynolds number is. Uniform wall suction is shown to stabilise this transition mechanism, analogously to results from linear stability theory. The effects of suction on the formation of primary streaks and on the secondary growth rate are decoupled. For streaks of different suction whose amplitude is held constant by adjusting the Reynolds number, the suction is shown to increase the growth rate of the secondary instability. The stabilising influence of wall suction consists in decreasing the streak amplitude only. Depending on the Reynolds number and the suction strength, breakdown may either occur locally and may be convected along the far-field streamlines, or occur globally and cover broad regions in the downstream direction.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.

Stabilization of Juxta-Physeal Distal Tibial and Fibular Fractures in a Juvenile Tiger Using a Hybrid Circular-Linear External Fixator

OBJECTIVE: To report stabilization of closed, comminuted distal metaphyseal transverse fractures of the left tibia and fibula in a tiger using a hybrid circular-linear external skeletal fixator. STUDY DESIGN: Clinical report. ANIMAL: Juvenile tiger (15 months, 90 kg). METHODS: From imaging studies, the tiger had comminuted distal metaphyseal transverse fractures of the left tibia and fibula, with mild caudolateral displacement and moderate compression. Multiple fissures extended from the fractures through the distal metaphyses, extending toward, but not involving the distal tibial and fibular physes. A hybrid circular-linear external skeletal fixator was applied by closed reduction, to stabilize the fractures. RESULTS: The fractures healed and the fixator was removed 5 weeks after stabilization. Limb length and alignment were similar to the normal contralateral limb at hospital discharge, 8 weeks after surgery. Two weeks later, the tiger had fractures of the right tibia and fibula and was euthanatized. Necropsy confirmed pathologic fractures ascribed to copper deficiency. CONCLUSION: Closed application of the hybrid construct provided sufficient stability to allow this 90 kg tiger's juxta-articular fractures to heal with minimal complications and without disrupting growth from the adjacent physes.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

Bridged bicyclic peptides as potential drug scaffolds: synthesis, structure, protein binding and stability

Double cyclization of short linear peptides obtained by solid phase peptide synthesis was used to prepare bridged bicyclic peptides (BBPs) corresponding to the topology of bridged bicyclic alkanes such as norbornane. Diastereomeric norbornapeptides were investigated by 1H-NMR, X-ray crystallography and CD spectroscopy and found to represent rigid globular scaffolds stabilized by intramolecular backbone hydrogen bonds with scaffold geometries determined by the chirality of amino acid residues and sharing structural features of β-turns and α-helices. Proteome profiling by capture compound mass spectrometry (CCMS) led to the discovery of the norbornapeptide 27c binding selectively to calmodulin as an example of a BBP protein binder. This and other BBPs showed high stability towards proteolytic degradation in serum.