Photosynthesis-dependent biosynthesis of medium chain-length fatty acids and alcohols

Cyanobacteria can directly channel atmospheric CO2 into a wide range of versatile carbon products such as fatty acids and fatty alcohols with applications including fuel, cosmetics, and health products. Works on alcohol production in cyanobacteria have so far focused on either long (C12-C18) or short (C2-C4) chain-length products. In the present work, we report the first synthetic pathway for 1-octanol (C8) biosynthesis in Synechocystis sp. PCC 6803, employing a carboxylic acid reductase and C8-preferring fatty acyl-ACP thioesterase. The first engineered strain produced 1-octanol but exhibited poor productivity and cellular health issues. We therefore proceeded to systematically optimize the strain and cultivation conditions in order to understand what the limiting factors were. The identification of optimal promoters and ribosomal binding sites, in combination with isopropyl myristate solvent overlay, resulted in a combined (C8-OH and C10-OH) titer of more than 100 mg/L (a 25-fold improvement relative to the first engineered strain) and a restoration of cellular health. Additionally, more than 905 mg/L 1-octanol was produced when the strain expressing sfp (phosphopantetheinyl transferase) and car (carboxylic acid reductase) was fed with octanoic acid. A combination of feeding experiments and protein quantification indicated that the supply of octanoic acid from the introduced thioesterase, and possibly also native fatty acid synthesis pathway, were the main bottlenecks of the pathway

Alternating strain regimes for failure propagation in flexural systems

We consider both analytical and numerical studies of a steady-state fracture process inside a discrete mass-beam structure, composed of periodically placed masses connected by Euler-Bernoulli beams. A fault inside the structure is assumed to propagate with a constant speed and this occurs as a result of the action of a remote sinusoidal, mechanical load. The established regime of fracture corresponds to the case of an alternating generalised strain regime. The model is reduced to a Wiener-Hopf equation and its solution is presented. We determine the minimum feeding wave energy required for the steady-state fracture process to occur. In addition, we identify the dynamic features of the structure during the steady-state fracture regime. A transient analysis of this problem is also presented, where the existence of steady-state fracture regimes, revealed by the analytical model, are verified and the associated transient features of this process are discussed

Localization in semi-infinite herringbone waveguides

The paper includes novel results for the scattering and localization of a time-harmonic flexural wave by a semi-infinite herringbone waveguide of rigid pins embedded within an elastic Kirchhoff plate. The analytical model takes into account the orientation and spacing of the constituent parts of the herringbone system, and incorporates dipole approximations for the case of closely spaced pins. Illustrative examples are provided, together with the predictive theoretical analysis of the localized waveforms

Wave polarization and dynamic degeneracy in a chiral elastic lattice

This paper addresses fundamental questions arising in the theory of Bloch–Floquet waves in chiral elastic lattice systems. This area has received a significant attention in the context of ‘topologically protected’ waveforms. Although practical applications of chiral elastic lattices are widely appreciated, especially in problems of controlling low-frequency vibrations, wave polarization and filtering, the fundamental questions of the relationship of these lattices to classical waveforms associated with longitudinal and shear waves retain a substantial scope for further development. The notion of chirality is introduced into the systematic analysis of dispersive elastic waves in a doubly-periodic lattice. Important quantitative characteristics of the dynamic response of the lattice, such as lattice flux and lattice circulation, are used in the analysis along with the novel concept of ‘vortex waveforms’ that characterize the dynamic response of the chiral system. We note that the continuum concepts of pressure and shear waves do not apply for waves in a lattice, especially in the case when the wavelength is comparable with the size of the elementary cell of the periodic structure. Special critical regimes are highlighted when vortex waveforms become dominant. Analytical findings are accompanied by illustrative numerical simulations

Wave Characterisation in a Dynamic Elastic Lattice: Lattice Flux and Circulation

A novel characterisation of dispersive waves in a vector elastic lattice is presented in the context of wave polarisation. This proves to be especially important in analysis of dynamic anisotropy and standing waves trapped within the lattice. The operators of lattice flux and lattice circulation provide the required quantitative description, especially in cases of intermediate and high frequency dynamic regimes. Dispersion diagrams are conventionally considered as the ultimate characteristics of dynamic properties of waves in periodic systems. Generally, a waveform in a lattice can be thought of as a combination of pressure-like and shear-like waves. However, a direct analogy with waves in the continuum is not always obvious. We show a coherent way to characterise lattice waveforms in terms of so-called lattice flux and lattice circulation. In the long wavelength limit, this leads to well-known interpretations of pressure and shear waves. For the cases when the wavelength is comparable with the size of the lattice cell, new features are revealed which involve special directions along which either lattice flux or lattice circulation is zero. The cases of high frequency and wavelength comparable to the size of the elementary cell are considered, including dynamic anisotropy and dynamic neutrality in structured solids

Singular perturbations and cloaking illusions for elastic waves in membranes and Kirchhoff plates

A perturbation approach is used for analysis of a near-cloak in shielding a finite scatterer from an incident flexural wave. The effect of the boundary conditions on the interior surface of the cloaking layer is analysed in detail, based on the explicit analytical solutions of a wave propagation problem for a membrane as well as a Kirchhoff flexural plate. It is shown that the Dirichlet boundary condition on the interior contour of the cloak significantly reduces the cloaking action in the membrane case, and it also makes cloaking impossible for flexural waves in a Kirchhoff plate

Gyro-elastic beams for the vibration reduction of long flexural systems

The paper presents a model of a chiral multi-structure incorporating gyro-elastic beams. Floquet–Bloch waves in periodic chiral systems are investigated in detail, with the emphasis on localization and the formation of standing waves. It is found that gyricity leads to low-frequency standing modes and generation of stop-bands. A design of an earthquake protection system is offered here, as an interesting application of vibration isolation. Theoretical results are accompanied by numerical simulations in the time-harmonic regime

Controlling Flexural Waves in Semi-Infinite Platonic Crystals with Resonator-Type Scatterers

We address the scattering and transmission of a plane flexural wave through a semi-infinite array of point scatterers/resonators, which take a variety of physically interesting forms. The mathematical model accounts for several classes of point defects, including mass-spring resonators attached to the top surface of the flexural plate and their limiting case of concentrated point masses. We also analyse the special case of resonators attached to opposite faces of the plate. The problem is reduced to a functional equation of the Wiener–Hopf type, whose kernel varies with the type of scatterer considered. A novel approach, which stems from the direct connection between the kernel function of the semi-infinite system and the quasi-periodic Green's functions for corresponding infinite systems, is used to identify special frequency regimes. We thereby demonstrate dynamically anisotropic wave effects in semi-infinite platonic crystals, with particular attention paid to designing systems that exhibit dynamic neutrality (perfect transmission) and localisation close to the structured interface

“Deflecting elastic prism” and unidirectional localisation for waves in chiral elastic systems

For the first time, a design of a “deflecting elastic prism” is proposed and implemented for waves in a chiral medium. A novel model of an elastic lattice connected to a non-uniform system of gyroscopic spinners is designed to create a unidirectional wave pattern, which can be diverted by modifying the arrangement of the spinners within the medium. This important feature of the gyro-system is exploited to send a wave from a point of the lattice to any other point in the lattice plane, in such a way that the wave amplitude is not significantly reduced along the path. We envisage that the proposed model could be very useful in physical and engineering applications related to directional control of elastic waves

Flexural vibration systems with gyroscopic spinners

In this paper, we study the spectral properties of a finite system of flexural elements connected by gyroscopic spinners. We determine how the eigenfrequencies and eigenmodes of the system depend on the gyricity of the spinners. In addition, we present a transient numerical simulation that shows how a gyroscopic spinner attached to the end of a hinged beam can be used as a ‘stabilizer’, reducing the displacements of the beam. We also discuss the dispersive properties of an infinite periodic system of beams with gyroscopic spinners at the junctions. In particular, we investigate how the band-gaps of the structure can be tuned by varying the gyricity of the spinners