Probing the Nanoscale Heterogeneous Mixing in a High-Performance Polymer Blend

The blend of polyetheretherketone (PEEK) and polybenzimidazole (PBI) produces a high-performance blend (PPB) that is a potential replacement material in several industries due to its high temperature stability and desirable tribological properties. Understanding the nanoscale structure and interface of the two domains of the blend is critical for elucidating the origin of these desirable properties. Whilst achieving the physical characterisation of the domain structures is relatively uncomplicated, the elucidation of structures at the interface presents a significant experimental challenge. In this work, we combine atomic force microscopy (AFM) with an IR laser (AFM-IR) and thermal cantilever probes (nanoTA) to gain insights into the chemical heterogeneity and extent of mixing within the blend structure for the first time. The AFM-IR and nanoTA measurements show that domains in the blend are compositionally different from those of the pure PEEK and PBI polymers, with significant variations observed in a transition region several microns wide in proximity to domain boundary. This strongly points to physical mixing of the two components on a molecular scale at the interface. The versatility intrinsic to the combined methodology employed in this work provides nano- and microscale chemical information that can be used to understand the link between properties of different length scales across a wide range of materials.

Boundary element methods for the wave equation based on hierarchical matrices and adaptive cross approximation

Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices have to be computed for a large number of time steps or frequencies. In this article, we propose a new approximation scheme for the Convolution Quadrature Method powered BEM, which we apply to scattering problems governed by the wave equation. We use $${\mathscr {H}}^2$$ H 2 -matrix compression in the spatial domain and employ an adaptive cross approximation algorithm in the frequency domain. In this way, the storage and computational costs are reduced significantly, while the accuracy of the method is preserved.

Numerical and Experimental Investigation of the Performance of Dynamic Wing for Augmenting Ship Propulsion in Head and Quartering Seas

Flapping-foil thrusters arranged at the bow of the ship are examined for the exploitation of energy from wave motions by direct conversion to useful propulsive power, offering at the same time dynamic stability and reduction of added wave resistance. In the present work, the system consisting of the ship and an actively controlled wing located in front of its bow is examined in irregular waves. Frequency-domain seakeeping analysis is used for the estimation of ship-foil responses and compared against experimental measurements of a ferry model in head waves tested at the National Technical University of Athens (NTUA) towing tank. Next, to exploit the information concerning the responses from the verified seakeeping model, a detailed time-domain analysis of the loads acting on the foil, both in head and quartering seas, is presented, as obtained by means of a cost-effective time-domain boundary element method (BEM) solver validated by a higher fidelity RANSE finite volume solver. The results demonstrate the good performance of the examined system and will further support the development of the system at a larger model scale and the optimal design at full scale for specific ship types.

Joint estimation of Robin coefficient and domain boundary for the Poisson problem

We consider the problem of simultaneously inferring the heterogeneous coefficient field for a Robin boundary condition on an inaccessible part of the boundary along with the shape of the boundary for the Poisson problem. Such a problem arises in, for example, corrosion detection, and thermal parameter estimation. We carry out both linearised uncertainty quantification, based on a local Gaussian approximation, and full exploration of the joint posterior using Markov chain Monte Carlo (MCMC) sampling. By exploiting a known invariance property of the Poisson problem, we are able to circumvent the need to re-mesh as the shape of the boundary changes. The linearised uncertainty analysis presented here relies on a local linearisation of the parameter-to-observable map, with respect to both the Robin coefficient and the boundary shape, evaluated at the maximum a posteriori (MAP) estimates. Computation of the MAP estimate is carried out using the Gauss-Newton method. On the other hand, to explore the full joint posterior we use the Metropolis-adjusted Langevin algorithm (MALA), which requires the gradient of the log-posterior. We thus derive both the Fréchet derivative of the solution to the Poisson problem with respect to the Robin coefficient and the boundary shape, and the gradient of the log-posterior, which is efficiently computed using the so-called adjoint approach. The performance of the approach is demonstrated via several numerical experiments with simulated data.

DomBpred: protein domain boundary predictor using inter-residue distance and domain-residue level clustering

Domain boundary prediction is one of the most important problems in the study of protein structure and function, especially for large proteins. At present, most domain boundary prediction methods have low accuracy and limitations in dealing with multi-domain proteins. In this study, we develop a sequence-based protein domain boundary predictor, named DomBpred. In DomBpred, the input sequence is firstly classified as either a single-domain protein or a multi-domain protein through a designed effective sequence metric based on a constructed single-domain sequence library. For the multi-domain protein, a domain-residue level clustering algorithm inspired by Ising model is proposed to cluster the spatially close residues according inter-residue distance. The unclassified residues and the residues at the edge of the cluster are then tuned by the secondary structure to form potential cut points. Finally, a domain boundary scoring function is proposed to recursively evaluate the potential cut points to generate the domain boundary. DomBpred is tested on a large-scale test set of FUpred comprising 2549 proteins. Experimental results show that DomBpred better performs than the state-of-the-art methods in classifying whether protein sequences are composed by single or multiple domains, and the Matthew's correlation coefficient is 0.882. Moreover, on 849 multi-domain proteins, the domain boundary distance and normalised domain overlap scores of DomBpred are 0.523 and 0.824, respectively, which are 5.0% and 4.2% higher than those of the best comparison method, respectively. Comparison with other methods on the given test set shows that DomBpred outperforms most state-of-the-art sequence-based methods and even achieves better results than the top-level template-based method.

Pattern forming systems coupling linear bulk diffusion to dynamically active membranes or cells

Some analytical and numerical results are presented for pattern formation properties associated with novel types of reaction–diffusion (RD) systems that involve the coupling of bulk diffusion in the interior of a multi-dimensional spatial domain to nonlinear processes that occur either on the domain boundary or within localized compartments that are confined within the domain. The class of bulk-membrane system considered herein is derived from an asymptotic analysis in the limit of small thickness of a thin domain that surrounds the bulk medium. When the bulk domain is a two-dimensional disk, a weakly nonlinear analysis is used to characterize Turing and Hopf bifurcations that can arise from the linearization around a radially symmetric, but spatially non-uniform, steady-state of the bulk-membrane system. In a singularly perturbed limit, the existence and linear stability of localized membrane-bound spike patterns is analysed for a Gierer–Meinhardt activator-inhibitor model that includes bulk coupling. Finally, the emergence of collective intracellular oscillations is studied for a class of PDE-ODE bulk-cell model in a bounded two-dimensional domain that contains spatially localized, but dynamically active, circular cells that are coupled through a linear bulk diffusion field. Applications of such coupled bulk-membrane or bulk-cell systems to some biological systems are outlined, and some open problems in this area are discussed. This article is part of the theme issue ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.

Numerical Simulation for the Evolution of Internal Solitary Waves Propagating over Slope Topography

In this study, the propagation and evolution characteristics of internal solitary waves on slope topography in stratified fluids were investigated. A numerical model of internal solitary wave propagation based on the nonlinear potential flow theory using the multi-domain boundary element method was developed and validated. The numerical model was used to calculate the propagation process of internal solitary waves on the topography with different slope parameters, including height and angle, and the influence of slope parameters, initial amplitude, and densities jump of two-layer fluid on the evolution of internal solitary waves is discussed. It was found that the wave amplitude first increased while climbing the slope and then decreased after passing over the slope shoulder based on the calculation results, and the wave amplitude reached a maximum at the shoulder of the slope. A larger height and angle of the slope can induce larger maximum wave amplitude and more obvious tail wave characteristics. The wave amplitude gradually decreased, and a periodic tail wave was generated when propagating on the plateau after passing the slope. Both frequency and height of the tail wave were affected by the geometric parameters of the slope bottom; however, the initial amplitude of the internal solitary wave only affects the tail wave height, but not the frequency of the tail wave.