Now showing items 1-20 of 32

• #### Aging and Cholesterol Metabolism

The role cholesterol metabolism has to play in health span is clear, and monitoring the parameters of cholesterol metabolism is key to aging successfully. The aim of this chapter is to provide a brief overview of the mechanisms which regulate cholesterol in the body, secondly to discuss how aging effects cholesterol metabolism, and thirdly to unveil how systems biology is leading to an improved understanding of the intersection between aging and the dysregulation of cholesterol metabolism.
• #### Angus I. Kirkland and Sarah J. Haigh (Eds.): Nanocharacterization, 2nd ed.

Book review of NanoCharacterisation, second edition, Editors Angus I. Kirkland and Sarah J. Haigh. Published by Royal Society of Chemistry ISBN: 978-1-84973-805-7
• #### Delamination Detection via Reconstructed Frequency Response Function of Composite Structures

Online damage detection technologies could reduce the weight of structures by allowing the use of less conservative margins of safety. They are also associated with high economical benefits by implementing a condition-based maintenance system. This paper presented a damage detection and location technique based on the dynamic response of glass fibre composite laminate structures (frequency response function). Glass fibre composite laminate plates of 200×200×2.64 mm, which had a predefined delamination, were excited using stationary random vibration waves of 500 Hz band-limited noise input at ≈1.5 g. The response of the structure was captured via Micro-ElectroMechanical System (MEMS) accelerometer to detect damage. The frequency response function requires data from damaged structures only, assuming that healthy structures are homogeneous and smooth. The frequency response of the composite structure was then reconstructed and fitted using the least-squares rational function method. Delamination as small as 20 mm was detected using global changes in the natural frequencies of the structure, the delamination was also located with greater degree of accuracy due to local changes of frequency response of the structure. It was concluded that environmental vibration waves (stationary random vibration waves) can be utilised to monitor damage and health of composite structures effectively.
• #### Detailed error analysis for a fractional Adams method

This preprint discusses a method for a numerical solution of a nonlinear fractional differential equation, which can be seen as a generalisation of the Adams–Bashforth–Moulton scheme.
• #### Detailed error analysis for a fractional adams method with graded meshes

We consider a fractional Adams method for solving the nonlinear fractional differential equation $\, ^{C}_{0}D^{\alpha}_{t} y(t) = f(t, y(t)), \, \alpha >0$, equipped with the initial conditions $y^{(k)} (0) = y_{0}^{(k)}, k=0, 1, \dots, \lceil \alpha \rceil -1$. Here $\alpha$ may be an arbitrary positive number and $\lceil \alpha \rceil$ denotes the smallest integer no less than $\alpha$ and the differential operator is the Caputo derivative. Under the assumption $\, ^{C}_{0}D^{\alpha}_{t} y \in C^{2}[0, T]$, Diethelm et al. \cite[Theorem 3.2]{dieforfre} introduced a fractional Adams method with the uniform meshes $t_{n}= T (n/N), n=0, 1, 2, \dots, N$ and proved that this method has the optimal convergence order uniformly in $t_{n}$, that is $O(N^{-2})$ if $\alpha > 1$ and $O(N^{-1-\alpha})$ if $\alpha \leq 1$. They also showed that if $\, ^{C}_{0}D^{\alpha}_{t} y(t) \notin C^{2}[0, T]$, the optimal convergence order of this method cannot be obtained with the uniform meshes. However, it is well known that for $y \in C^{m} [0, T]$ for some $m \in \mathbb{N}$ and $0 < \alpha 1$, we show that the optimal convergence order of this method can be recovered uniformly in $t_{n}$ even if $\, ^{C}_{0}D^{\alpha}_{t} y$ behaves as $t^{\sigma}, 0< \sigma <1$. Numerical examples are given to show that the numerical results are consistent with the theoretical results.
• #### Dielectric and Double Debye Parameters of Artificial Normal Skin and Melanoma

The aim of this study is to characterise the artificial normal skin and melanoma by testing samples with different fibroblast and metastatic melanoma cell densities using terahertz (THz) time-domain spectroscopy (TDS) attenuated total reflection (ATR) technique. Results show that melanoma samples have higher refractive index and absorption coefficient than artificial normal skin with the same fibroblast density in the frequency range between 0.4 and 1.6 THz, and this contrast increases with frequency. It is primarily because that the melanoma samples have higher water content than artificial normal skin, and the main reason to melanoma containing more water is that tumour cells degrade the contraction of the collagen lattice. In addition, complex refractive index and permittivity of the melanoma samples have larger variations than that of normal skin samples. For example, the refractive index of artificial normal skin at 0.5 THz increases 4.3% while that of melanoma samples increases 8.7% when the cell density rises from 0.1 to 1 M/ml. It indicates that cellular response of fibroblast and melanoma cells to THz radiation is significantly different. Furthermore, the extracted double Debye (DD) model parameters demonstrate that the static permittivity at low frequency and slow relaxation time can be reliable classifiers to differentiate melanoma from healthy skin regardless of the cell density. This study helps understand the complex response of skin tissues to THz radiation and the origin of the contrast between normal skin and cancerous tissues.
• #### Double Bordered Constructions of Self-Dual Codes from Group Rings over Frobenius Rings

In this work, we describe a double bordered construction of self-dual codes from group rings. We show that this construction is effective for groups of order 2p where p is odd, over the rings F2 + uF2 and F4 + uF4. We demonstrate the importance of this new construction by finding many new binary self-dual codes of lengths 64, 68 and 80; the new codes and their corresponding weight enumerators are listed in several tables
• #### Dynamics of shadow system of a singular Gierer-Meinhardt system on an evolving domain

The main purpose of the current paper is to contribute towards the comprehension of the dynamics of the shadow system of a singular Gierer-Meinhardt model on an isotropically evolving domain. In the case where the inhibitor's response to the activator's growth is rather weak, then the shadow system of the Gierer-Meinhardt model is reduced to a single though non-local equation whose dynamics is thoroughly investigated throughout the manuscript. The main focus is on the derivation of blow-up results for this non-local equation, which can be interpreted as instability patterns of the shadow system. In particular, a diffusion-driven instability (DDI), or Turing instability, in the neighbourhood of a constant stationary solution, which then is destabilised via diffusion-driven blow-up, is observed. The latter indicates the formation of some unstable patterns, whilst some stability results of global-in-time solutions towards non-constant steady states guarantee the occurrence of some stable patterns. Most of the theoretical results are verified numerically, whilst the numerical approach is also used to exhibit the dynamics of the shadow system when analytical methods fail.
• #### Edge-based nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic flux-correction schemes

For the case of approximation of convection–diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.
• #### Efficacy of a virtual environment for training ball passing skills in rugby

We have designed a configurable virtual environment to train rugby ball passing skills. Seeking to validate the system’s ability to correctly aid training, two experiments were performed. Ten participants took part in ball passing activities, which were used to compare the combinations of different user positions relative to the physical screen, the use of stereoscopic presentation and the use of a floor screen to extend the field of view of the virtual scene. Conversely to what was expected, the results indicate that the participants did not respond well to simulated target distances, and only the users physical distance from the screen had an effect on the distance thrown.
• #### Evolutionary Robot Swarm Cooperative Retrieval

In nature bees and leaf-cutter ants communicate to improve cooperation during food retrieval. This research aims to model communication in a swarm of auton-omous robots. When food is identified robot communication is emitted within a limited range. Other robots within the range receive the communication and learn of the location and size of the food source. The simulation revealed that commu-nication improved the rate of cooperative food retrieval tasks. However a counter-productive chain reaction can occur when robots repeat communications from other robots causing cooperation errors. This can lead to a large number of robots travelling towards the same food source at the same time. The food becomes de-pleted, before some robots have arrived. Several robots continue to communicate food presence, before arriving at the food source to find it gone. Nature-inspired communication can enhance swarm behaviour without requiring a central control-ler and may be useful in autonomous drones or vehicles.
• #### Existence of time periodic solutions for a class of non-resonant discrete wave equations

In this paper, a class of discrete wave equations with Dirichlet boundary conditions are obtained by using the center-difference method. For any positive integers m and T, when the existence of time mT-periodic solutions is considered, a strongly indefinite discrete system needs to be established. By using a variant generalized weak linking theorem, a non-resonant superlinear (or superquadratic) result is obtained and the Ambrosetti-Rabinowitz condition is improved. Such a method cannot be used for the corresponding continuous wave equations or the continuous Hamiltonian systems; however, it is valid for some general discrete Hamiltonian systems.
• #### Fractional boundary value problems: Analysis and numerical methods

This journal article discusses nonlinear boundary value problems.
• #### G-Codes, self-dual G-Codes and reversible G-Codes over the Ring Bj,k

In this work, we study a new family of rings, Bj,k, whose base field is the finite field Fpr . We study the structure of this family of rings and show that each member of the family is a commutative Frobenius ring. We define a Gray map for the new family of rings, study G-codes, self-dual G-codes, and reversible G-codes over this family. In particular, we show that the projection of a G-code over Bj,k to a code over Bl,m is also a G-code and the image under the Gray map of a self-dual G-code is also a self-dual G-code when the characteristic of the base field is 2. Moreover, we show that the image of a reversible G-code under the Gray map is also a reversible G2j+k-code. The Gray images of these codes are shown to have a rich automorphism group which arises from the algebraic structure of the rings and the groups. Finally, we show that quasi-G codes, which are the images of G-codes under the Gray map, are also Gs-codes for some s.
• #### Group Rings, G-Codes and Constructions of Self-Dual and Formally Self-Dual Codes

We describe G-codes, which are codes that are ideals in a group ring, where the ring is a finite commutative Frobenius ring and G is an arbitrary finite group. We prove that the dual of a G-code is also a G-code. We give constructions of self-dual and formally self-dual codes in this setting and we improve the existing construction given in [13] by showing that one of the conditions given in the theorem is unnecessary and, moreover, it restricts the number of self-dual codes obtained by the construction. We show that several of the standard constructions of self-dual codes are found within our general framework. We prove that our constructed codes must have an automorphism group that contains G as a subgroup. We also prove that a common construction technique for producing self-dual codes cannot produce the putative [72, 36, 16] Type II code. Additionally, we show precisely which groups can be used to construct the extremal Type II codes over length 24 and 48. We define quasi-G codes and give a construction of these codes.
• #### Higher order numerical methods for solving fractional differential equations

In this paper we introduce higher order numerical methods for solving fractional differential equations. We use two approaches to this problem. The first approach is based on a direct discretisation of the fractional differential operator: we obtain a numerical method for solving a linear fractional differential equation with order 0 < α < 1. The order of convergence of the numerical method is O(h^(3−α)). Our second approach is based on discretisation of the integral form of the fractional differential equation and we obtain a fractional Adams-type method for a nonlinear fractional differential equation of any order α >0. The order of convergence of the numerical method is O(h^3) for α ≥ 1 and O(h^(1+2α)) for 0 < α ≤ 1 for sufficiently smooth solutions. Numerical examples are given to show that the numerical results are consistent with the theoretical results.
• #### Impact Damage Characteristics of Carbon Fibre Metal Laminates: Experiments and Simulation

In this work, the impact response of carbon fibre metal laminates (FMLs) was experimentally and numerically studied with an improved design of the fibre composite lay-up for optimal mechanical properties and damage resistance. Two different stacking sequences (Carall 3–3/2–0.5 and Carall 5–3/2–0.5) were designed and characterised. Damage at relatively low energy impact energies (≤30 J) was investigated using Ultrasonic C-scanning and X–ray Computed Tomography (X-RCT). A 3D finite element model was developed to simulate the impact induced damage in both metal and composite layers using Abaqus/Explicit. Cohesive zone elements were introduced to capture delamination occurring between carbon fibre/epoxy plies and debonding at the interfaces between aluminium and the composite layers. Carall 5–3/2–0.5 was found to absorb more energy elastically, which indicates better resistance to damage. A good agreement is obtained between the numerically predicted results and experimental measurements in terms of force and absorbed energy during impact where the damage modes such as delamination was well simulated when compared to non-destructive techniques (NDT).
• #### Interface Cohesive Elements to Model Matrix Crack Evolution in Composite Laminates

In this paper, the transverse matrix (resin) cracking developed in multidirectional composite laminates loaded in tension was numerically investigated by a finite element (FE) model implemented in the commercially available software Abaqus/Explicit 6.10. A theoretical solution using the equivalent constraint model (ECM) of the damaged laminate developed by Soutis et al. was employed to describe matrix cracking evolution and compared to the proposed numerical approach. In the numerical model, interface cohesive elements were inserted between neighbouring finite elements that run parallel to fibre orientation in each lamina to simulate matrix cracking with the assumption of equally spaced cracks (based on experimental measurements and observations). The stress based traction-separation law was introduced to simulate initiation of matrix cracking and propagation under mixed-mode loading. The numerically predicted crack density was found to depend on the mesh size of the model and the material fracture parameters defined for the cohesive elements. Numerical predictions of matrix crack density as a function of applied stress are in a good agreement to experimentally measured and theoretically (ECM) obtained values, but some further refinement will be required in near future work.
• #### Interventional radiology virtual simulator for liver biopsy

Training in Interventional Radiology currently uses the apprenticeship model, where clinical and technical skills of invasive procedures are learnt during practice in patients. This apprenticeship training method is increasingly limited by regulatory restrictions on working hours, concerns over patient risk through trainees' inexperience and the variable exposure to case mix and emergencies during training. To address this, we have developed a computer-based simulation of visceral needle puncture procedures. Methods A real-time framework has been built that includes: segmentation, physically based modelling, haptics rendering, pseudo-ultrasound generation and the concept of a physical mannequin. It is the result of a close collaboration between different universities, involving computer scientists, clinicians, clinical engineers and occupational psychologists. Results The technical implementation of the framework is a robust and real-time simulation environment combining a physical platform and an immersive computerized virtual environment. The face, content and construct validation have been previously assessed, showing the reliability and effectiveness of this framework, as well as its potential for teaching visceral needle puncture. Conclusion A simulator for ultrasound-guided liver biopsy has been developed. It includes functionalities and metrics extracted from cognitive task analysis. This framework can be useful during training, particularly given the known difficulties in gaining significant practice of core skills in patients.
• #### Modelling low velocity impact induced damage in composite laminates

The paper presents recent progress on modelling low velocity impact induced damage in fibre reinforced composite laminates. It is important to understand the mechanisms of barely visible impact damage (BVID) and how it affects structural performance. To reduce labour intensive testing, the development of finite element (FE) techniques for simulating impact damage becomes essential and recent effort by the composites research community is reviewed in this work. The FE predicted damage initiation and propagation can be validated by Non Destructive Techniques (NDT) that gives confidence to the developed numerical damage models. A reliable damage simulation can assist the design process to optimise laminate configurations, reduce weight and improve performance of components and structures used in aircraft construction.