173 research outputs found
Tailored Topological Edge Waves via Chiral Hierarchical Metamaterials
Precise manipulation of the direction and re-direction of vibrational wave
energy is a key demand in wave physics and engineering. We consider the
paradigm of a finite frame-like structure and the requirement to channel energy
away from critical regions, leaving them vibration-free, and redirect energy
along edges towards energy concentrators for damping or energy harvesting. We
design an exemplar frame metamaterial, combining two distinct areas of wave
physics. Firstly, topological edge states taking an unconventional tetrachiral
lattice. We control these highly localised protected edge states leveraging a
hierarchy of scales through the addition of micro-resonators that impose
tuneable symmetry breaking and reconfigurable mass. This allows us to achieve
precise positional control in the macro-scale frame lattice, thereby opening
opportunities for robust signal transport and vibration control. Experiments,
theory, simulation are all utilised to provide a comprehensive analysis and
interpretation of the physics
Erratum: Elastic orbital angular momentum [Phys. Rev. Lett. 128, 064301 (2022)]
Corrected 13 July 2022
Preface. Bifurcations and Pattern Formation in Biological Applications
In the preface we present a short overview of articles included in the issue "Bifurcations and pattern formation in biological applications" of the journal Mathematical Modelling of Natural Phenomena
Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth
Cell-scale degradation of peritumoural extracellular matrix fibre network and its role within tissue-scale cancer invasion
Local cancer invasion of tissue is a complex, multiscale process which plays
an essential role in tumour progression. Occurring over many different temporal
and spatial scales, the first stage of invasion is the secretion of matrix
degrading enzymes (MDEs) by the cancer cells that consequently degrade the
surrounding extracellular matrix (ECM). This process is vital for creating
space in which the cancer cells can progress and it is driven by the activities
of specific matrix metalloproteinases (MMPs). In this paper, we consider the
key role of two MMPs by developing further the novel two-part multiscale model
introduced in [33] to better relate at micro-scale the two micro-scale
activities that were considered there, namely, the micro-dynamics concerning
the continuous rearrangement of the naturally oriented ECM fibres within the
bulk of the tumour and MDEs proteolytic micro-dynamics that take place in an
appropriate cell-scale neighbourhood of the tumour boundary. Focussing
primarily on the activities of the membrane-tethered MT1-MMP and the soluble
MMP-2 with the fibrous ECM phase, in this work we investigate the MT1-MMP/MMP-2
cascade and its overall effect on tumour progression. To that end, we will
propose a new multiscale modelling framework by considering the degradation of
the ECM fibres not only to take place at macro-scale in the bulk of the tumour
but also explicitly in the micro-scale neighbourhood of the tumour interface as
a consequence of the interactions with molecular fluxes of MDEs that exercise
their spatial dynamics at the invasive edge of the tumour
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