<div>Segmented material systems have been shown to provide advantages over monolithic materials including the potential for combinations of properties such as strength, toughness, and ductility that are not otherwise attainable. One such class of segmented system is that of topologically interlocked material (TIM) systems. These are material systems consisting of one or more repeating unit blocks assembled in a planar configuration. When coupled with a bounding frame, this plate-like structure can withstand transverse loads without the use of adhesive or fasteners between blocks.</div><div><br></div><div>One method of generating TIM systems is to start with a 2D tiling and project each edge of the tiles at alternating angles from the tile normal. This work examines 18 unique configurations of TIM systems generated from the Archimedean and the Laves tilings. These systems are constructed as segmented plates having approximately the same number of building blocks and with equivalent overall dimensions so that the effect of the segmentation patterns on the load response of the TIM system can be investigated. Finite element models were utilized to simulate both displacement controlled loading and body force loading of each configuration with various coefficients of friction. The load responses were recorded and the characteristics of chirality and reciprocity of the load response were observed.</div><div><br></div><div>The TIM system configurations in this study resulted in a wide variety of performance. Their range of properties is presented, and a mechanism for strength in a TIM system is postulated. The findings of this work enable the material design space to be expanded by facilitating the creation of material systems with a greater range of properties than is possible with monolithic materials.</div>

Requirements for increased operating efficiencies mean that future generations of aero-engines will need to operate at temperatures beyond the capabilities of current nickel-base superalloys. As a result, new alloy compositions for turbine disc applications are being developed. Optimising these alloy compositions requires balancing directly competing requirements. Increased Cr contents are needed to provide environmental resistance and increased concentrations of other refractory metals to improve solid solution strengthening. However, these elements compromise the alloyâs long-term microstructural stability by promoting the formation of topologically close-packed (TCP) phases, which are deleterious to alloy performance. High $\gamma^\prime$ volume fractions, which are needed to provide high-temperature strength, exacerbate the problem by increasing the concentration of these elements in the $\gamma$ phase. Therefore, an understanding of TCP formation and the compositional limits of stability is vital in the design of new alloys. This thesis presents a combination of fundamental studies of TCP phase formation in model alloys and microstructural assessment of the thermal stability of developmental alloy compositions. Knowledge of the effect of individual elements on thermal stability is important to enable the development of optimised alloy compositions. As a result, the first fundamental study investigated the effect of Co content on thermal stability. An unexpected transition in $\sigma$ precipitation behaviour after 500 hours at 800°C was observed between 12 and 16 at.\% Co. It is proposed that this behaviour may be due to the effect of Co on the $\gamma$/$\gamma^\prime$ partitioning behaviour of other elements. Preliminary results from further fundamental studies investigating the effect of the Mo/W ratio and B content on thermal stability are also presented. Decreasing the Mo/W ratio was found to reduce the quantity of $\sigma$ precipitation and promote the precipitation of a W-rich phase. B additions were found to promote the precipitation of the M$_3$B$_2$ phase. Thermodynamic predictions are frequently used to inform alloy design as an alternative to time-consuming and costly experiments. However, the accuracy of solvus temperature predictions for TCP phases has not been thoroughly considered. In this work, it was found that differential scanning calorimetry could be used as a means of measuring $\sigma$ solvus temperature in a series of alloys designed to be sufficiently unstable with respect to $\sigma$ precipitation. Comparison of experimental results with thermodynamic solvus temperature predictions revealed a significant underprediction of the $\sigma$ solvus temperatures for all of the studied alloys. This can inform our use of such predictions during alloy design. The ability to quantify the amount of TCP precipitation that occurs is extremely important when assessing the thermal stability of alloys. A new method was applied to the problem of TCP quantification, involving synchrotron X-ray diffraction of solid aged samples. This was an attempt to avoid some of the problems identified with the commonly used quantification method, which involves electrolytic extraction of minor phases, and assess the accuracy of the results produced by this method. Samples of a currently used commercial alloy, RR1000, were investigated following ageing for up to 5000 hours at 800°C, revealing the evolution of phases at this temperature. The presence of extremely low quantities of minor phases was successfully detected in the solid samples using this method. However, these quantities were too low for this to be a reliable method of quantification for commercial alloys. In parallel with these fundamental and technique-based studies, the thermal stability of a number of candidate alloys, which were developed during the design of a next-generation disc alloy by Rolls-Royce, was assessed. The alloys were characterised following a variety of thermal exposure temperatures and durations, which were determined by industrial needs at the time. Various minor phases were identified depending on the alloy compositions, including the TCP phases, $\sigma$ and $\mu$, as well as MC and M$_{23}$C$_6$ carbides and M$_3$B$_2$ borides.

A closed, orientable, splitting surface in an oriented 3-manifold is a topologically minimal surface of index n if its associated disk complex is (n-2)-connected but not (n-1)-connected. A critical surface is a topologically minimal surface of index 2. In this thesis, we use an equivalent combinatorial definition of critical surfaces to construct the first known critical bridge spheres for nontrivial links.

In recent years, there has been an upsurge in interest in three-dimensional theories of gravity. In particular, two theories of massive gravity in three dimensions hold strong promise in the search for fully consistent theories of quantum gravity, an understanding of which will shed light on the problems of quantum gravity in four dimensions. One of these theories is the “old” third-order theory of topologically massive gravity (TMG) and the other one is a “new” fourth-order theory of massive gravity (NMG). Despite this increase in research activity, the problem of finding and classifying solutions of TMG and NMG remains a wide open area of research. In this thesis, we provide explicit new solutions of massive gravity in three dimensions and suggest future directions of research. These solutions belong to the Kundt class of spacetimes. A systematic analysis of the Kundt solutions with constant scalar polynomial curvature invariants provides a glimpse of the structure of the spaces of solutions of the two theories of massive gravity. We also find explicit solutions of topologically massive gravity whose scalar polynomial curvature invariants are not all constant, and these are the first such solutions. A number of properties of Kundt solutions of TMG and NMG, such as an identification of solutions which lie at the intersection of the full nonlinear and linearized theories, are also derived. / text

Within every human cell, approximately two meters of DNA must be compacted into a nucleus with a diameter of around ten micrometers. Alongside this daunting storage problem, the 3D organisation of the genome also helps determine which genes are up- or down-regulated, which in turn effects the functionality of the cell itself. While the organisational structure of the genome can be revealed using experimental techniques such as chromosome conformation capture and its high-throughput variant Hi-C, the mechanisms driving this organisation are still unclear. The first two results chapters of this thesis use molecular dynamics simulations to investigate the effect of a potential organisational mechanisms for DNA known as the "bridging-induced attraction". This mechanism involves multivalent DNA-binding proteins bridging genomically distant regions of DNA, which in turn promotes further binding of proteins and compaction of the DNA. In chapter 2 (the first results chapter) we look at a model where proteins can bind non-specifically to DNA, leading to cluster formation for suitable protein-DNA interaction strengths. We also show the effects of protein concentration on the DNA, with a collapse from a swollen to a globular phase observed for suitably high protein concentrations. Chapter 3 develops this model further, using genomic data from the ENCODE project to simulate the "specific binding" of proteins to either active (euchromatin) or inactive (heterochromatin) regions. We were then able to compare contact maps for specific simulated chromosomes with the experimental Hi-C data, with our model reproducing well the topologically associated domains (TADs) seen in Hi-C contact maps. In chapter 4 of the thesis we use numerical methods to study a model for the coupling between DNA topology (in particular, supercoiling in DNA and chromatin) and transcription in a genome. We present details of this model, where supercoiling flux is induced by gene transcription, and can diffuse along the DNA. The probability of transcription is also related to supercoiling, as regions of DNA which are negatively supercoiled have a greater likelihood of being transcribed. By changing the magnitude of supercoiling flux, we see a transition between a regime where transcription is random and a regime where transcription is highly correlated. We also find that divergent gene pairs show increased transcriptional activity, along with transcriptional waves and bursts in the highly correlated regime { all these features are associated with genomes of living organisms.

The aim of this thesis was to identify topologically protected states in the materials SnTe and Fe3Sn2. Such states are currently receiving a large amount of interest due to their applications for spintronic devices. Recently SnTe was discovered to be a crystalline topological insulator, a state of matter where its surface is highly conducting while the bulk remains insulating. However detection of these surface states is difficult using transport measurements, since the bulk is not totally insulating but still contains a large number of free carriers. SnTe undergoes a rhombohedral structural distortion on cooling caused by a soft transverse optic phonon, with the exact Tc strongly dependent on the carrier concentration. The distortion acts to lower crystal symmetry removing some of the symmetries that protect the surface state. Single crystal samples displaying the structural transition were grown and investigated using inelastic X-ray scattering to measure the phonon softening previously reported by other authors. The soft phonon was seen to recover again after distortion indicative of a 2nd order ferroelectric transition. This is the first reported discovery of the recovery showing the distortion is ferroelectric in nature. Shubnikov de Haas quantum oscillations were measured to study the Fermi surface under ambient and high hydrostatic pressure conditions. A distortion of the Fermi surface caused by the structural transition was evident, resulting in 4 distinct oscillation frequencies. However at applied pressures above 6 kbar, the transition was suppressed and only 1 oscillation measured. A two component Hall response also becomes apparent under high pressure. The possible origin of this and its relation to possible surface states is discussed. The anomalous Hall effect was also measured in the ferromagnet Fe3Sn2 which has a bilayer Kagome structure. Previous measurements on polycrystalline Fe3Sn2 suggested a non-collinear spin rotation from the spins pointing along the c-axis at high temperature to lying in the a-b plane below 80 K. A spin glass phase is then expected below 80 K. Single crystal magnetisation measurements carried out in this thesis show the spins are in the a-b plane at high temperatures and begin to display a ferromagnetic component along the c-axis approaching 80 K. The difference is accounted for by considering the demagnetising factor in the plate shaped single crystals. For this temperature range an applied field along the c-direction however rotates the moments towards c. At intermediate fields there are strong features evident in both the anomalous Hall effect and magnetoresistance. These features may be due to a topological Hall effect caused by a non-collinear spin structure. The possible existence of Skyrmion excitations was also recently discussed theoretically in Fe3Sn2. Our data is more suggestive of static Skyrmions known to cause topological Hall effects in MnSi.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第19991号 / 工博第4235号 / 新制||工||1655(附属図書館) / 33087 / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 北村 隆行, 教授 田畑 修, 教授 鈴木 基史 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

<p dir="ltr">This thesis focuses on the study of wave propagation in architected material systems. Specifically of interest is wave propagation in topologically interlocking material (TIM) systems made of tetrahedra and bio-inspired blocks. TIM systems are assemblies of composed of blocks in which the block geometry constrains blocks in place. Individual blocks can only be removed by disassembling the system. This interlocking of block geometry allows these systems to bear loads without the need for adhesives. Overall, load bearing is affected by block geometry, contact interaction, and assembly architecture. Wavefronts and wave velocities are computed using an explicit finite element code. Wave propagation is investigated first in a row of interlocking tetrahedra, then in 3D planar TIM systems of tetrahedra and bio-inspired scutoid blocks.</p><p dir="ltr">The propagation of linear traveling waves through a row of interlocking tetrahedra is demonstrated by the use of finite element simulations. The wave velocity was found to be independent of wave amplitude for ideal contact conditions but dependent on impact velocity for an exponential pressure-overclosure relationship between surfaces. For a frictionless, constant contact stiffness model, the effective wave velocity is about 50% of the 1D material wave speed. In the presence of friction, the wave velocity increases to about 80% of the 1D material wave speed. The wave velocity is attributed to wave-guiding set by the geometry of the tetrahedra. The wave velocity is further modulated by the rocking motion of the tetrahedra about an axis perpendicular to the wave propagation direction. The rocking motion is affected by friction and is reduced as friction is increased. Experimental results on wave propagation in a row of 3D-printed triangular prisms demonstrate pulse-like voltage versus time wave responses. With rough and tacky surfaces, the velocity of the linear traveling waves is measured as approximately 20% the 1D material wave speed. For smooth and low friction surface conditions, significantly higher wave velocities are measured. Similarly, reducing the number of contact surfaces by fusing pairs of building blocks also results in higher measured wave velocities. Experiments on rectangular prisms lack the wave-guiding geometry and provide a reference configuration. Finite element models are used to gain detailed insight into the wave propagation process. Wave-guide models are defined to predict wave speeds based on the effective path of wave propagation. The proposed models closely predict measured and computed wave speeds for the tetrahedra and triangular prisms.</p><p dir="ltr">Scutoids are prism-like shapes containing lateral vertices between two parallel polygonal surfaces. With the lateral vertices at the midplane, scutoid blocks can be periodically and densely packed. Scutoid-based planar arrays are demonstrated to behave mechanically as TIM systems. Under quasi-static transverse loads, assembly properties (stiffness, strength, toughness) match or exceed those of the corresponding tetrahedra-based TIM systems. The scutoid-based TIM systems have unique chiral characteristics. Chirality is attributed to the combination of building block and assembly symmetry. Chirality leads to asymmetric internal load transfer patterns resulting in unbalanced in-plane reaction forces and reaction moments. Experiments confirm the computational findings. Under transverse indentation, these systems have nonlinear force-displacement responses and measurable torque responses.</p><p dir="ltr">Wave propagation following transverse impact on planar arrays of interlocking tetrahedra and scutoids is investigated. Unique wave speed and wavefront development are demonstrated to occur in these systems. The 1D material wave speed emerges as the limiting wave speed of the TIM systems, rather than the dilatational wave speed. In tetrahedra assemblies, waves propagate with a velocity of approximately 25% of the 1D material wave speed. The wave velocity is attributed to wave-guiding from the interlocking tetrahedra geometry. Tetrahedra are not perfectly space-filling and block-to-block interactions are not limited to one direction. In the scutoid assemblies, waves propagate at velocities between 80% and 90% of the 1D material wave speed. These velocities are along directions associated with dominant load paths. The wave velocities in the scutoid-based TIM systems approach the 1D material wave speed as the contact surfaces are substantially orthogonal to the assembly surface. In comparison to monolithic plates, wavefronts develop with significant spatial non-uniformity. Wave patterns exhibit the symmetry or asymmetry also observed in the quasi-static response. Overall, contact surface orientation, block geometry, and assembly architecture affect wave velocity and wavefront development.</p>

Yes / Mammalian genomes contain several dozens of large (>0.5 Mbp) lineage-specific gene loci harbouring functionally related genes. However, spatial chromatin folding, organization of the enhancer-promoter networks and their relevance to Topologically Associating Domains (TADs) in these loci remain poorly understood. TADs are principle units of the genome folding and represents the DNA regions within which DNA interacts more frequently and less frequently across the TAD boundary. Here, we used Chromatin Conformation Capture Carbon Copy (5C) technology to characterize spatial chromatin interaction network in the 3.1 Mb Epidermal Differentiation Complex (EDC) locus harbouring 61 functionally related genes that show lineage-specific activation during terminal keratinocyte differentiation in the epidermis. 5C data validated by 3D-FISH demonstrate that the EDC locus is organized into several TADs showing distinct lineage-specific chromatin interaction networks based on their transcription activity and the gene-rich or gene-poor status. Correlation of the 5C results with genome-wide studies for enhancer-specific histone modifications (H3K4me1 and H3K27ac) revealed that the majority of spatial chromatin interactions that involves the gene-rich TADs at the EDC locus in keratinocytes include both intra- and inter-TAD interaction networks, connecting gene promoters and enhancers. Compared to thymocytes in which the EDC locus is mostly transcriptionally inactive, these interactions were found to be keratinocyte-specific. In keratinocytes, the promoter-enhancer anchoring regions in the gene-rich transcriptionally active TADs are enriched for the binding of chromatin architectural proteins CTCF, Rad21 and chromatin remodeler Brg1. In contrast to gene-rich TADs, gene-poor TADs show preferential spatial contacts with each other, do not contain active enhancers and show decreased binding of CTCF, Rad21 and Brg1 in keratinocytes. Thus, spatial interactions between gene promoters and enhancers at the multi-TAD EDC locus in skin epithelial cells are cell type-specific and involve extensive contacts within TADs as well as between different gene-rich TADs, forming the framework for lineage-specific transcription. / This study was supported by the grants 5R01AR064580 and 1RO1AR071727 to VAB, TKS and AAS, as well as by the grants from MRC (MR/ M010015/1) and BBSRC (BB/K010050/1) to VAB.

<p>A topologically interlocked material (TIM) system belongs to a class of architectured materials and is known to perform outstanding mechanical properties such as stiffness, strength, and toughness. TIM systems are assemblies of polyhedral or building blocks, where individual elements constrain each other on inclined sides of building blocks. This thesis first focuses on developing novel designs of TIM plates composed of building blocks that interact with each other. The resulting TIM systems can be characterized concerning their periodicity and symmetry. Consequently, this study investigates how the proposed geometric features enhance mechanical properties and contribute to emerging properties. Specifically, four research questions provide a clear direction and framework for the investigation. For efficient analysis, finite element calculations are employed, and physical validation methods are used to verify them.</p> <p>The first research question is how the mechanical properties of aperiodic systems differ from those of periodic systems. Aperiodic systems offer diverse possibilities in terms of forms and arrangements. In this thesis, aperiodicity is further divided into two aspects: disrupting symmetry and preserving symmetry. In the approach that disrupts symmetry, the shapes of the tiles are randomly generated. An aperiodic system does not necessarily possess inherently superior or inferior mechanical properties compared to a periodic system. However, the flexibility of aperiodic systems allows for numerous forms and arrangements, presenting promising alternatives to identify factors or patterns that contribute to improved mechanical performance. To simplify these complex configurations, network theory is employed.</p> <p>Each building and its contact interfaces are represented as nodes and links. By utilizing network theory, a focused analysis of the links is conducted, enabling a comprehensive understanding of force propagation across TIM systems. The quantification of the significance of each link assists in reinforcing critical links while potentially sacrificing less critical ones.</p> <p>This approach not only simplifies the research problem but also facilitates the creation of customized design systems by adjusting the links.</p> <p>The other approach to achieve aperiodicity while preserving symmetry utilizes quasicrystal structures. This is based on another research question: What are the benefits of creating TIM systems with quasi-crystal tilting? Quasi-crystals possess a unique characteristic of maintaining 5-fold rotational symmetry while breaking away from periodic patterns observed in traditional systems. The arrangement of elements in quasi-crystal structures extends in a non-repetitive pattern from the center outward, offering a multitude of potential possibilities for TIM systems. By incorporating quasi-crystal tiling, TIM systems are expected to open up exceptional mechanical properties and unconventional behaviors.</p> <p>The third research question investigates whether the influence on mechanical performance varies based on the symmetry level of TIM systems. Despite using identical unit blocks, the arrangement of an assembly can lead to different levels of symmetry. Furthermore, it is possible to modify the symmetry of the unit block, thereby impacting the overall symmetry of the assembly. To achieve this, the symmetry of a unit block is adjusted by modifying the angles of side faces, transitioning from larger angles to smaller angles or vice versa. This modification introduces directionality (rotational symmetry) to the unit block and creates a greater variety of symmetry levels depending on the arrangements of these blocks. By implementing a broader range of symmetry levels that conventional TIM systems cannot achieve, this research aims to investigate the relationship between these symmetries and mechanical properties.</p> <p>The fourth research question is about what emerging properties could be present in TIM systems. While the primary application of TIMs is to enhance the damage tolerance of brittle materials against an external load, there have been ongoing attempts to research emerging properties like negative stiffness, sound absorption, and chirality. Chirality, in particular, serves as a valuable geometric property to describe a circulation of force propagation. Generally, the ability of TIM systems to carry transverse loads is explained through equivalent Mises truss along x− and y − axis. However, chirality enables the representation of not only axial force paths but also circulations of forces within TIM systems. In addition, a rich variety of geometric patches are observed in quasi-crystal structures. In crystal structures, a limited number of patches are repetitively arranged, resulting in a restricted range of properties. However, quasi-crystals like Penrose are non-periodic and possess a greater capacity to generate diverse patches, allowing for the selection of various mechanical properties.</p>