Now showing items 527-546 of 626

• #### Space-Time Discontinuous Galerkin Methods for the '\eps'-dependent Stochastic Allen-Cahn Equation with mild noise

We consider the $\eps$-dependent stochastic Allen-Cahn equation with mild space- time noise posed on a bounded domain of R^2. The positive parameter $\eps$ is a measure for the inner layers width that are generated during evolution. This equation, when the noise depends only on time, has been proposed by Funaki in [15]. The noise although smooth becomes white on the sharp interface limit as $\eps$ tends to zero. We construct a nonlinear dG scheme with space-time finite elements of general type which are discontinuous in time. Existence of a unique discrete solution is proven by application of Brouwer's Theorem. We first derive abstract error estimates and then for the case of piece-wise polynomial finite elements we prove an error in expectation of optimal order. All the appearing constants are estimated in terms of the parameter $\eps$. Finally, we present a linear approximation of the nonlinear scheme for which we prove existence of solution and optimal error in expectation in piece-wise linear finite element spaces. The novelty of this work is based on the use of a finite element formulation in space and in time in 2+1-dimensional subdomains for a nonlinear parabolic problem. In addition, this problem involves noise. These type of schemes avoid any Runge-Kutta type discretization for the evolutionary variable and seem to be very effective when applied to equations of such a difficulty.
• #### Spatial discretization for stochastic semilinear subdiffusion driven by integrated multiplicative space-time white noise

Spatial discretization of the stochastic semilinear subdiffusion driven by integrated multiplicative space-time white noise is considered. The spatial discretization scheme discussed in Gy\"ongy \cite{gyo_space} and Anton et al. \cite{antcohque} for stochastic quasi-linear parabolic partial differential equations driven by multiplicative space-time noise is extended to the stochastic subdiffusion. The nonlinear terms $f$ and $\sigma$ satisfy the global Lipschitz conditions and the linear growth conditions. The space derivative and the integrated multiplicative space-time white noise are discretized by using finite difference methods. Based on the approximations of the Green functions which are expressed with the Mittag-Leffler functions, the optimal spatial convergence rates of the proposed numerical method are proved uniformly in space under the suitable smoothness assumptions of the initial values.
• #### Spreadsheet tools to estimate the thermal transmittance and thermal conductivities of gas spaces of an Insulated Glazing Unit

An Insulated Glazing unit (IGU) is constructed with two or more layers of glass panes sealed together by gas spaces in-between. IGUs are prevalent in windows, doors and rooflights, primarily due to their improved thermal resistance. Today, most IGUs are either two or three layered. Adding further layers of glass improves thermal insulation but with the penalty of increased cost and weight. Low emissivity (Low-e) film coatings, when deposited on the glass panes, reduce long-wavelength radiative heat losses. Furthermore, filling the gas spaces with the inert gases (e.g. Argon, Krypton, Xenon and SF6), further reduce conduction and natural convection across the gap. In summary, higher thermal insulation performance of an IGU can be achieved with gas fillings and Low-e coatings on glass. This report discusses spreadsheets that have been developed, capable of estimating the thermal transmittance values of IGU, as per BS EN 673. The spreadsheet tools also have the ability to estimate the thermal conductivity of the gas spaces between the panes of IGU.
• #### SrFe12O19 based ceramics with ultra-low dielectric loss in the millimetre-wave band

Non-reciprocal devices such as isolators and circulators, based mainly on ferromagnetic materials, require extremely low dielectric loss in order for strict power-link budgets to be met for millimetre (mm)-wave and terahertz (THz) systems. The dielectric loss of commercial SrFe12O19 hexaferrite was significantly reduced to below 0.002 in the 75 - 170 GHz band by thermal annealing. While the overall concentration of Fe2+ and oxygen vacancy defects is relatively low in the solid, their concentration at the surface is significantly higher, allowing for a surface sensitive technique such as XPS to monitor the Fe3+/Fe2+ redox reaction. Oxidation of Fe2+ and a decrease in oxygen vacancies is found at the surface on annealing, which is reflected in the bulk sample by a small change in unit cell volume. The significant decrease in dielectric loss property can be attributed to the decreased concentration of charged defects such as Fe2+ and oxygen vacancies through annealing process, which demonstrated that thermal annealing could be effective in improving the dielectric performance of ferromagnetic materials for various applications.
• #### Stability analysis of a continuous model of mutualism with delay dynamics

In this paper we introduce delay dynamics to a coupled system of ordinary differential equations which represent two interacting species exhibiting facultative mutualistic behaviour. The delays are represen- tative of the beneficial effects of the indirect, interspecies interactions not being realised immediately. We show that the system with delay possesses a continuous solution, which is unique. Furthermore we show that, for suitably-behaved, positive initial functions that this unique solution is bounded and remains positive, i.e. both of the components representing the two species remain greater than zero. We show that the system has a positive equilibrium point and prove that this point is asymptotically stable for positive solutions and that this stability property is not conditional upon the delays.
• #### Stability of a numerical method for a fractional telegraph equation

In this paper, we introduce a numerical method for solving the time-space fractional telegraph equations. The numerical method is based on a quadrature formula approach and a stability condition for the numerical method is obtained. Two numerical examples are given and the stability regions are plotted.

• #### Stabilizing a mathematical model of plant species interaction

In this paper, we will consider how to stabilize a mathematical model of plant species interaction which is modelled by using Lotka-Volterra system. We first identify the unstable steady states of the system, then we use the feedback control based on the solutions of the Riccati equation to stabilize the linearized system. We further stabilize the nonlinear system by using the feedback controller obtained in the stabilization of the linearized system. We introduce the backward Euler method to approximate the feedback control nonlinear system and obtain the error estimates. Four numerical examples are given which come from the application areas.
• #### The status of hydrogen technologies in the UK: A multi-disciplinary review

Hydrogen has the potential to offer deep decarbonisation across a range of global heavy-emitting sectors. To have an impact on the global energy system, hydrogen technologies must be deployed with greater urgency. This review article facilitates the much needed, multi-disciplinary discussion around hydrogen. In doing so, the paper outlines recent advancements, prevailing challenges and areas of future research concerning hydrogen technologies, policy, regulation and social considerations in a UK setting. Findings suggest that hydrogen will play a significant role in decarbonising several UK sectors whilst simultaneously addressing challenges faced by alternative low-carbon technologies. Optimal production, delivery and storage systems must be developed to accommodate perceived future demand. Whilst this will be largely dictated by scale, efficiency, cost and technological maturity, significant improvements in existing policies and regulation will also be critical. The future role of hydrogen in the UK’s decarbonisation strategy is not clearly defined. In comparison to alternative low- carbon technologies, policy and regulatory support for hydrogen has been minimal. Whilst there is growing evidence concerning the public perception of hydrogen in UK homes, additional research is required given its many potential applications. The findings detailed in this article support the urgency for further multi- disciplinary collaborative research.
• #### Stigmergic Interoperability for Autonomic Systems: Managing Complex Interactions in Multi-Manager Scenarios

The success of autonomic computing has led to its popular use in many application domains, leading to scenarios where multiple autonomic managers (AMs) coexist, but without adequate support for interoperability. This is evident, for example, in the increasing number of large datacentres with multiple managers which are independently designed. The increase in scale and size coupled with heterogeneity of services and platforms means that more AMs could be integrated to manage the arising complexity. This has led to the need for interoperability between AMs. Interoperability deals with how to manage multi-manager scenarios, to govern complex coexistence of managers and to arbitrate when conflicts arise. This paper presents an architecture-based stigmergic interoperability solution. The solution presented in this paper is based on the Trustworthy Autonomic Architecture (TAArch) and uses stigmergy (the means of indirect communication via the operating environment) to achieve indirect coordination among coexisting agents. Usually, in stigmergy-based coordination, agents may be aware of the existence of other agents. In the approach presented here in, agents (autonomic managers) do not need to be aware of the existence of others. Their design assumes that they are operating in 'isolation' and they simply respond to changes in the environment. Experimental results with a datacentre multi-manager scenario are used to analyse the proposed approach.
• #### Strecker degradation of amino acids promoted by a camphor-derived sulfonamide

A camphor-derived sulfonimine with a conjugated carbonyl group, oxoimine 1 (O2SNC10H13O), reacts with amino acids (glycine, L-alanine, L-phenylalanine, L-leucine) to form a compound O2SNC10H13NC10H14NSO2 (2) which was characterized by spectroscopic means (MS and NMR) and supported by DFT calculations. The product, a single diastereoisomer, contains two oxoimine units connected by a –N= bridge, and thus has a structural analogy to the colored product Ruhemann´s purple obtained by the ninhydrin reaction with amino acids. A plausible reaction mechanism that involves zwitterions, a Strecker degradation of an intermediate imine and water-catalyzed tautomerizations was developed by means of DFT calculations on potential transition states.
• #### Structural speciation in chemical reactivity profiling of binary-ternary systems of Ni(II) with iminodialcohol and aromatic chelators

The importance of structural speciation in the control of chemical reactivity in Ni(II) binary-ternary systems, involving (O,O,N)-containing substrates (1,1’-iminodi-2-propanol), and aromatic chelators (2,2’-bipyridine, 1,10-phenanthroline), prompted the systematic synthesis of new crystalline materials characterized by elemental analysis, FT-IR, UV-Visible, Luminescence, TGA, magnetic susceptibility, and X-ray crystallography. The structures contain mononuclear octahedral assemblies, the lattice architecture of which exemplifies reaction conditions under which conformational variants and solvent-associated lattice-imposed complexes are assembled. Transformations between complex species denote their association with reactivity pathways, suggesting alternate synthetic methodologies for their isolation. Theoretical work (Hirshfeld, Electrostatic Potential, DFT) signifies the impact of crystal structure on energy profiles of the generated species. The arisen physicochemical profiles of all compounds portray a well-configured interwoven network of pathways, projecting strong connection between structural speciation and Ni(II) reactivity patterns in organic-solvent media. The collective results provide well-defined parameterized profiles, poised to influence the synthesis of new Ni(II)-iminodialcohol materials with specified structural-magneto-optical properties.
• #### Structure and dielectric properties of double A-site doped bismuth sodium titanate relaxor ferroelectrics for high power energy storage applications

The structural and dielectric properties of barium/strontium substituted Bi0.5Na0.5TiO3 were examined in compositions of general formula (Ba0.4Sr0.6TiO3)x(Bi0.5Na0.5TiO3)1-x. An average classic cubic perovskite structure is maintained from x = 0.5 to 1.0. The temperature dependence of dielectric properties of studied compositions shows relaxor-ferroelectric behaviour attributed to the existence of polar nano-regions. Ferroelectric measurements under variable temperature demonstrated two transitions from normal ferroelectric to relaxor-ferroelectric and relaxor-ferroelectric to paraelectric, at the dipole freezing temperature, Tf, and temperature of maximum permittivity, Tm, respectively. The obtained value of Tf coincides with the onset of linear thermal expansion of the cubic unit cell parameter obtained from high resolution powder neutron diffraction data. Careful analysis of the neutron diffraction data revealed no significant change in the average cubic structure from -263 to 150 C. However, changes in the Gaussian variance component of the neutron peak shape, reveal three distinct regions with transitions at about -100 and 100 C corresponding to the beginning and end of the dielectric dispersion seen in the permittivity and loss spectra. This variation in the Gaussian variance parameter is attributed to the activity of the polar nano-regions. The composition (Ba0.4Sr0.6)0.5(Bi0.5Na0.5)0.5TiO3 was found to exhibit the maximum recoverable energy storage density, with a value of 1.618 J cm-3 and 76.9% storage efficiency at a field of 17 kV mm-1.
• #### Studies of black diamond as an antibacterial surface for gram negative bacteria: the interplay between chemical and mechanical bactericidal activity

‘Black silicon’ (bSi) samples with surfaces covered in nanoneedles of length ~5 μm were fabricated using a plasma etching process and then coated with a conformal uniform layer of diamond using hot filament chemical vapour deposition to produce ‘black diamond’ (bD) nanostructures. The diamond needles were then chemically terminated with H, O, NH2 or F using plasma treatment, and the hydrophilicity of the resulting surfaces were assessed using water droplet contact-angle measurements, and scaled in the order O > H ≈NH2 >F, with the F-terminated surface being superhydrophobic. The effectiveness of these differently terminated bD needles in killing the Gram-negative bacterium E. coli was semiquantified by Live/Dead staining and fluorescence microscopy, and visualised by environmental scanning electron microscopy. The total number of adhered bacteria was consistent for all the nanostructured bD surfaces at around 50% of the value for the flat diamond control. This, combined with a chemical bactericidal effect of 20–30%, shows that the nanostructured bD surfaces supported significantly fewer viable E. coli than flat surfaces. Moreover, the bD surfaces were particularly effective at preventing the establishment of bacterial aggregates – a precursor to biofilm formation. The percentage of dead bacteria also decreased as a function of hydrophilicity. These results are consistent with a predominantly mechanical mechanism for bacteria death based on the stretching and disruption of the cell membrane, combined with an additional effect from the chemical nature of the surface.
• #### Studies of black silicon and black diamond as materials for antibacterial surfaces

‘Black silicon’ (bSi) samples with surfaces covered in nanoneedles of varying length, areal density and sharpness, have been fabricated using a plasma etching process. These nanostructures were then coated with a conformal uniform layer of diamond using hot filament chemical vapour deposition to produce ‘black diamond’ (bD) surfaces. The effectiveness of these bSi and bD surfaces in killing Gram-negative (E. coli) and Gram-positive (S. gordonii) bacteria was investigated by culturing the bacteria on the surfaces for a set time and then measuring the live-to-dead ratio. All the nanostructured surfaces killed E. coli at a significantly higher rate than the respective flat Si or diamond control samples. The length of the needles was found to be less important than their separation, i.e. areal density. This is consistent with a model for mechanical bacteria death based on the stretching and disruption of the cell membrane, enhanced by the cells motility on the surfaces. In contrast, S. gordonii were unaffected by the nanostructured surfaces, possibly due to their smaller size, thicker cell membrane and/or their lack of motility.
• #### Superfast solution of linear convolutional Volterra equations using QTT approximation

This article address a linear fractional differential equation and develop effective solution methods using algorithms for the inversion of triangular Toeplitz matrices and the recently proposed QTT format. The inverses of such matrices can be computed by the divide and conquer and modified Bini’s algorithms, for which we present the versions with the QTT approximation. We also present an efficient formula for the shift of vectors given in QTT format, which is used in the divide and conquer algorithm. As a result, we reduce the complexity of inversion from the fast Fourier level O(nlogn) to the speed of superfast Fourier transform, i.e., O(log^2n). The results of the paper are illustrated by numerical examples.