Geometric and Topological Aspects of Soft & Active Matter

Topological and geometric ideas are now a mainstay of condensed matter physics, underlying much of our understanding of conventional materials in terms of defects and geometric frustration in ordered media, and protected edge states in topological insulators. In this thesis, I will argue that such an approach successfully identifies the relevant physics in metamaterials and living matter as well, even when traditional techniques fail. I begin with the problem of kirigami mechanics, i.e., designing a pattern of holes in a thin elastic sheet to engineer a specific mechanical response. Using an electrostatic analogy, I show that holes act as sources of geometric incompatibility, a feature that can fruitfully guide design principles for kirigami metamaterials. Next I consider nonequilibrium active matter composed of self-driven interacting units that exhibit large scale collective and emergent behaviour, as commonly seen in living systems. By focusing on active liquid crystals in two dimensions, with both polar and nematic orientational order, I show how broken time-reversal symmetry due to the active drive allows polar flocks on a curved surface to support topologically protected sound modes. In an active nematic, activity instead causes topological disclinations to become spontaneously motile, driving defect unbinding to organize novel phases of defect order and chaos. In all three cases, geometric and topological ideas enable the relevant degrees of freedom to be identified, allowing complex phenomena to be treated in a tractable fashion, with novel and surprising consequences along the way

Simulations of dynamics and motility in active fluids

Active fluids are ubiquitous in nature, spanning both microscopic and macroscopic length scales. They belong to an interesting new class of nonequilibrium systems in physics. In contrast with externally driven materials, active fluids are intrinsically forced out of equilibrium by their constituent active particles, which consume energy from the environment, using it to engage in nonequilibrium activities, such as motility and replication. Two of the most prevalent examples of active particles are bacteria and actomyosin complexes. In both cases, we observe rich collective behaviour giving rise to, respectively, the multicellular organisation of bacterial colonies and the intracellular structure in eukaryotes. A hydrodynamic description can be used to model the behaviour of active fluids. This approach is based on the fact that the active particles exert stresses on the surrounding fluid as they move through it. Within the hydrodynamic framework, we can study many interesting nonequilibrium phenomena, including hydrodynamic instabilities and spontaneous symmetry breaking. These provide an explanation for macroscopic motility patterns in active systems. In our work, we use a hybrid lattice Boltzmann method to simulate a range of motile states and their chiral characteristics. We start by studying the dynamics of an active fluid enclosed in a droplet with imposed orientational anchoring at the interface. Our results show that when the anchoring is strong enough, active extensile and contractile stresses lead to spontaneous droplet rotation. In contrast, if the anchoring is weak, the droplet instead translates. The signature of the observed rotating states is a significant deformation of the droplet shape, distinguishing it from the rotation of spiral defects, which has been previously reported. Moreover, the sense of rotation is selected via spontaneous symmetry breaking, so that the droplet is equally likely to start rotating clockwise or anticlockwise, acquiring a random chirality. Most biological active particles are also microscopically chiral themselves. Thus, active processes must involve chiral interactions at the microscale. We address this feature by considering a chiral active stress originating from a collection of active torque dipoles. We find that the active chiral stresses drive a nonequilibrium transition to a self-assembled cholesteric phase in both active fluids and dry active systems. This spontaneously twisted phase shares many of the characteristics of equilibrium cholesterics, including the formation of layered and fingering patterns, and the existence on non-singular defects. If the activity is suciently high, chiral active stresses are capable of untwisting an equilibrium cholesteric configuration (which is thermodynamically favoured). Finally, we look at active fluids with both achiral (extensile, contractile) and chiral active stresses. We observe that contractile activity suppresses the spontaneous twist, while extensile activity enhances it. We also show the existence of a pitchsplay instability in these systems, leading to a bend deformation of cholesteric layers

Active matter: from collective self-propelled rods to cell-like particles

Active matter comprises systems with sustained energy uptake and dissipation of its constituents. This applies to systems across many scales. We study ensembles of self-propelled rods (SPRs) in periodic boundaries and in confinement to mimic the collective behavior and dynamics of bacteria, and active filaments. Our models describe active systems that allow the propulsion to adapt to its environment. While SPRs with density-dependent slowing down partially capture the behavior observed for bacteria, SPRs in ring-like confinements can be considered as a minimal, soft matter model for cell motility. Phoretic microswimmers and genetically modified E. coli show density-dependent reduced propulsion.This motivates the investigation of the collective behavior and dynamics of SPRs with density-dependent propulsion force. The density-dependent slowing down enhances polar ordering and cluster formation, and induces rod perpendicularity at cluster borders. As a model of cellular motility due to cytoskeletal activity, SPRs inside mobile, rigid circular confinement are considered, which build complex self-propelled rings. The rod self-organization gives rise to complex motility patterns, such as run-and-tumble and run-and-circle motion. Motility patterns observed for self-propelled rigid rings are also observed for motile cells. Taking a further step towards a more realistic modeling of cell motility, we study SPRs inside mobile, deformable rings. In addition to ring motility, also ring deformability plays a crucial role in SPR alignment and cluster formation. Here, pulling forces at the back of the rings are crucial to recovering cell-like shapes and motion. While our models do not take into account biochemical aspects of biological systems, they allow the identification of crucial mechanical aspects, and help to test different underlying mechanisms to interpret microscopic observations

Fibre properties affecting the softness of wool and other keratins

The emerging market for next-to-skin knitwear requires wool to satisfy the consumer’s tactile requirements for softness. The role of the fibre’s surface and physical properties on fibre and fabric softness was examined. The fibre’s cuticle properties were found to have a greater influence on softness than the fibre’s mechanical properties

Serological studies of avian infectious bronchitis virus

Imperial Users onl

The optimisation of brass instruments to include wall vibration effects

This thesis focuses on the design optimisation of a brass instrument. The bore profile of such an instrument is known to be the primary influence on the sound of the instrument as it directly controls the shape of the air-column contained within the instruments' walls. It has long been claimed, however, that other factors, such as the wall material and wall vibrations, are also significant, although to a lesser degree. In recent years, it has been proven that wall vibrations do indeed have an audible effect on the sound (Moore et al 2005, Kausel et al 2007, Nachtmann et al 2007, Kausel, Zietlow and Moore 2010). This effect corresponds to a relative increase in the power of upper harmonics of the sound spectrum when vibrations are greatest, and relative increase in the power of the lower harmonics, in particular the fundamental, when vibrations are at their least. The result is a timbral difference where a greater relative power in the upper harmonics results in a 'brighter' sound, and where the opposite results in a 'darker' sound. Studies have also found that the degree of the wall vibration is increased when the resonant frequencies of the air-column and those of the instruments' structure align. It is this principle that this work is based on. The primary objective of this work was to devise a suitable approach for incorporating the wall vibration effect into an optimisation method to investigate the optimum designs for two scenarios: maximum wall vibration and minimum wall vibration. It was also of interest to investigate if there were any design characteristics for each scenario. Two analysis methods were investigated for their suitability, namely free and forced vibration using finite element analysis (FEA). Different approaches to defining the design variables were explored and the suitability of different optimisation algorithms was investigated. The free vibration approach was found to be inadequate for this application due to the inherent omission of valuable magnitude information. The forced vibration approach was found to be more successful, although it was not possible to align a resonance with each frequency of interest