We formulate and solve a generalized inverse Navier–Stokes problem for the joint velocity field reconstruction and boundary segmentation of noisy flow velocity images. To regularize the problem, we use a Bayesian framework with Gaussian random fields. This allows us to estimate the uncertainties of the unknowns by approximating their posterior covariance with a quasi-Newton method. We first test the method for synthetic noisy images of two-dimensional (2-D) flows and observe that the method successfully reconstructs and segments the noisy synthetic images with a signal-to-noise ratio (SNR) of three. Then we conduct a magnetic resonance velocimetry (MRV) experiment to acquire images of an axisymmetric flow for low ( ${\simeq }6$ ) and high ( ${>}30$ ) SNRs. We show that the method is capable of reconstructing and segmenting the low SNR images, producing noiseless velocity fields and a smooth segmentation, with negligible errors compared with the high SNR images. This amounts to a reduction of the total scanning time by a factor of 27. At the same time, the method provides additional knowledge about the physics of the flow (e.g. pressure) and addresses the shortcomings of MRV (i.e. low spatial resolution and partial volume effects) that otherwise hinder the accurate estimation of wall shear stresses. Although the implementation of the method is restricted to 2-D steady planar and axisymmetric flows, the formulation applies immediately to three-dimensional (3-D) steady flows and naturally extends to 3-D periodic and unsteady flows.
BackgroundElastin-like polypeptides (ELPs) are a fascinating biomaterial that has undergone copious development for a variety of therapeutic applications including as a nanoscale drug delivery vehicle. A comprehensive understanding of ELP self-assembly is lacking and this knowledge gap impedes the advancement of ELP-based biomaterials into the clinical realm. The systematic examination of leucine-containing ELPs endeavors to expand existing knowledge about fundamental assembly–disassembly behaviours.ResultsIt was observed that these marginally soluble, short ELPs tend to behave consistently with previous observations related to assembly-related ELP phase transitions but deviated in their disassembly. It was found that chain length, concentration and overall sequence hydrophobicity may influence the irreversible formation of sub-micron particles as well as the formation of multi-micron scale, colloidally unstable aggregates. Amino acid composition affected surface charge and packing density of the particles. Particle stability upon dilution was found to vary depending upon chain length and hydrophobicity, with particles composed of longer and/or more hydrophobic ELPs being more resistant to disassembly upon isothermal dilution.ConclusionsTaken together, these results suggest marginally soluble ELPs may self-assemble but not disassemble as expected and that parameters including particle size, zeta potential and dilution resistance would benefit from widespread systematic evaluations. This information has the potential to reveal novel preparation methods capable of expanding the utility of all existing ELP-based biomaterials.Electronic supplementary materialThe online version of this article (10.1186/s12951-018-0342-5) contains supplementary material, which is available to authorized users.
Optimisation of a heterogeneous catalytic process requires characterisation of the catalyst at industrially-relevant conditions and lengthscales. Here we use magnetic resonance imaging to gain insight into Fischer-Tropsch synthesis occurring in a pilot-scale fixed-bed reactor operating at 220 °C, 37 bar, and for three H2/CO feed ratios. Molecular diffusion and carbon number of hydrocarbon products are spatially-resolved within both the reactor and individual 1 wt% Ru/TiO2 catalyst pellets. These data highlight the importance of mass transfer, in addition to nanoscale catalyst activity, on catalyst performance. In particular, a start-up time of up to 3 weeks is required for steady-state to be achieved in the catalyst pores. Further, the average carbon number present in the pores can be as much as double that in the product wax.
Self-assembling peptides are a promising class of biomaterials with desirable biocompatibility and versatility. In particular, the oligopeptide (RADA)4, consisting of arginine (R), alanine (A), and aspartic acid (D), self-assembles into nanofibers that develop into a three-dimensional hydrogel of up to 99.5% (w/v) water; yet, the organization of water within the hydrogel matrix is poorly understood. Importantly, peptide concentration and polarity are hypothesized to control the internal water structure. Using variable temperature deuterium solid-state nuclear magnetic resonance (2H NMR) spectroscopy, we measured the amount of bound water in (RADA)4-based hydrogels, quantified as the non-frozen water content. To investigate how peptide polarity affects water structure, five lysine (K) moieties were appended to (RADA)4 to generate (RADA)4K5. Hydrogels at 1 and 5% total peptide concentration were prepared from a 75:25 (w/w) blend of (RADA)4:(RADA)4K5 and similarly analyzed by 2H NMR. Interestingly, at 5% peptide concentration, there was lower mobile water content in the lysinated versus the pristine (RADA)4 hydrogel. Regardless of the presence of lysine, the 5% peptide concentration had higher non-frozen water content at temperatures as low as 217 ± 1.0 K, suggesting that bound water increases with peptide concentration. The bound water, though non-frozen, may be strongly bound to the charged lysine moiety to appear as immobilized water. Further understanding of the factors controlling water structure within hydrogels is important for tuning the transport properties of bioactive solutes in the hydrogel matrix when designing for biomedical applications.
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