• 2D Hexagonal Boron Nitride (2D-hBN) Explored as a Potential Electrocatalyst for the Oxygen Reduction Reaction

      Khan, Aamar F.; Brownson, Dale A. C.; Ji, Xiaobo; Smith, Graham C.; Banks, Craig E.; Manchester Metropolitan University (Khan, Brownson, Banks); University of Chester (Smith); Central South University Changsha (Ji) (Wiley, 2016-09-28)
      Crystalline 2D hexagonal Boron Nitride (2D-hBN) is explored as a potential electrocatalyst towards the oxygen reduction reaction (ORR) when electrically wired via a drop-casting approach upon a range of carbon based electrode surfaces; namely, glassy carbon (GC), boron-doped diamond (BDD), and screen-printed graphitic electrodes (SPEs). We consider the ORR in acidic conditions and critically evaluate the performance of unmodified and 2D-hBN modified electrodes, implementing coverage studies (commonly neglected in the literature) in order to ascertain the true impact of this novel nanomaterial. The behaviour of 2D-hBN towards the ORR is shown to be highly dependent upon both the underlying carbon substrate and the coverage/mass utilised. 2D-hBN modified SPEs are found to exhibit the most beneficial response towards the ORR, reducing the peak potential by ca. 0.28 V when compared to an unmodified/bare SPE. Such improvements at this supporting substrate are inferred due to favourable 2D-hBN interaction with ridged surfaces exposing a high proportion of edge regions/sites, where conversely, we show that relatively smooth substrate surfaces (such as GC) are less conducive towards successful 2D-hBN immobilisation. In this paper, we reveal for the first time (in the specific case of using a rough supporting substrate) that 2D-hBN gives rise to beneficial electrochemical behaviour towards the ORR. Unfortunately, this material is not considered an electrocatalyst for use within fuel cells given that the estimated number of electrons transferred during the ORR ranges between 1.90–2.45 for different coverages, indicating that the ORR at 2D-hBN predominantly produces hydrogen peroxide. 2D-hBN does however have potential and should be explored further by those designing, fabricating and consequently electrochemically testing modified electrocatalysts towards the ORR.
    • 2D Hexagonal Boron Nitride (2D-hBN) Explored for the Electrochemical Sensing of Dopamine

      Khan, Aamar F.; Brownson, Dale A. C.; Randviir, Edward P.; Smith, Graham C.; Banks, Craig E.; Manchester Metropolitan University (Khan, Brownson, Randviir, Banks); University of Chester (Smith) (American Chemical Society, 2016-09-23)
      Crystalline 2D hexagonal boron nitride (2D-hBN) nanosheets are explored as a potential electrocatalyst toward the electroanalytical sensing of dopamine (DA). The 2D-hBN nanosheets are electrically wired via a drop-casting modi fication process onto a range of commercially available carbon supporting electrodes, including glassy carbon (GC), boron-doped diamond (BDD), and screen-printed graphitic electrodes (SPEs). 2D-hBN has not previously been explored toward the electrochemical detection/electrochemical sensing of DA. We critically evaluate the potential electrocatalytic performance of 2D-hBN modified electrodes, the effect of supporting carbon electrode platforms, and the effect of “mass coverage” (which is commonly neglected in the 2D material literature) toward the detection of DA. The response of 2D-hBN modified electrodes is found to be largely dependent upon the interaction between 2D-hBN and the underlying supporting electrode material. For example, in the case of SPEs, modification with 2D-hBN (324 ng) improves the electrochemical response, decreasing the electrochemical oxidation potential of DA by ∼ 90 mV compared to an unmodified SPE. Conversely, modification of a GC electrode with 2D-hBN (324 ng) resulted in an increased oxidation potential of DA by ∼ 80 mV when compared to the unmodified electrode. We explore the underlying mechanisms of the aforementioned examples and infer that electrode surface interactions and roughness factors are critical considerations. 2D-hBN is utilized toward the sensing of DA in the presence of the common interferents ascorbic acid (AA) and uric acid (UA). 2D-hBN is found to be an effective electrocatalyst in the simultaneous detection of DA and UA at both pH 5.0 and 7.4. The peak separations/resolution between DA and UA increases by ∼ 70 and 50 mV (at pH 5.0 and 7.4, respectively, when utilizing 108 ng of 2D-hBN) compared to unmodified SPEs, with a particularly favorable response evident in pH 5.0, giving rise to a significant increase in the peak current of DA. The limit of detection (3σ) is found to correspond to 0.65 μM for DA in the presence of UA. However, it is not possible to deconvolute the simultaneous detection of DA and AA. The observed electrocatalytic effect at 2D-hBN has not previously been reported in the literature when supported upon carbon or any other electrode. We provide valuable insights into the modifier −substrate interactions of this material, essential for those designing, fabricating, and consequently performing electrochemical experiments utilizing 2D-hBN and related 2D materials.
    • 2D Molybdenum Disulphide (2D-MoS2) Modified Electrodes Explored Towards the Oxygen Reduction Reaction

      Rowley-Neale, Samuel J.; Fearn, Jamie; Brownson, Dale A. C.; Smith, Graham C.; Ji, Xiaobo; Banks, Craig E.; Manchester Metropolitan University (Rowley-Neale, Fearn, Brownson, Banks); University of Chester (Smith); Central South University Changsha (Ji) (Royal Society of Chemistry, 2016-07-11)
      Two-dimensional molybdenum disulphide nanosheets (2D-MoS2)have proven to be an effective lectro- catalyst, with particular attention being focused on their use towards increasing the efficiency of the reac-tions associated with hydrogen fuel cells. Whilst the majority of research has focused on the Hydrogen Evolution Reaction (HER), herein we explore the use of 2D-MoS2 as a potential electrocatalyst for the much less researched Oxygen Reduction Reaction (ORR). We stray from literature conventions and perform experiments in 0.1 M H2SO4 acidic electrolyte for the first time, evaluating the electrochemical performance of the ORR with 2D-MoS2 electrically wired/immobilised upon several carbon based elec-trodes (namely; Boron Doped Diamond (BDD), Edge Plane Pyrolytic Graphite (EPPG), Glassy Carbon (GC) and Screen-Printed Electrodes (SPE)) whilst exploring a range of 2D-MoS2 coverages/masses. Conse-quently, the findings of this study are highly applicable to real world fuel cell applications. We show that significant improvements in ORR activity can be achieved through the careful selection of the under-lying/supporting carbon materials that electrically wire the 2D-MoS2and utilisation of an optimal mass of 2D-MoS2. The ORR onset is observed to be reduced to ca.+0.10 V for EPPG, GC and SPEs at 2D-MoS2 (1524 ng cm−2 modification), which is far closer to Pt at +0.46 V compared to bare/unmodified EPPG, GC and SPE counterparts. This report is the first to demonstrate such beneficial electrochemical responses in acidic conditions using a 2D-MoS2 based electrocatalyst material on a carbon-based substrate (SPEs in this case). Investigation of the beneficial reaction mechanism reveals the ORR to occur via a 4 electron process in specific conditions; elsewhere a 2 electron process is observed. This work offers valuable insights for those wishing to design, fabricate and/or electrochemically test 2D-nanosheet materials towards the ORR
    • 2D nanosheet molybdenum disulphide (MoS2) modified electrodes explored towards the hydrogen evolution reaction

      Rowley-Neale, Samuel J.; Brownson, Dale A. C.; Smith, Graham C.; Satwell, David A. G.; Kelly, Peter J.; Banks, Craig E.; Faculty of Science and Engineering, Manchester Metropolitain University, Manchester M 5GD, UK (Rowley-Neale, Brownson, Satwell, Kelly & Banks); Department of Natural Sciences, University of Chester, Thornton Science Park, Chester CH2 4NU (Smith) (Royal Society of Chemistry, 2015-10-06)
      We explore the use of two-dimensional (2D) MoS2 nanosheets as an electro-catalyst for the Hydrogen Evolution Reaction (HER). Using four commonly employed commercially available carbon based electrode support materials, namely edge plane pyrolytic graphite (EPPG), glassy carbon (GC), boron-doped diamond (BDD) and screen-printed graphite electrodes (SPE), we critically evaluate the reported electro-catalytic performance of unmodified and MoS2 modified electrodes towards the HER. Surprisingly, current literature focuses almost exclusively on the use of GC as an underling support electrode upon which HER materials are immobilised. 2D MoS2 nanosheet modified electrodes are found to exhibit a coverage dependant electrocatalytic effect towards the HER. Modification of the supporting electrode surface with an optimal mass of 2D MoS2 nanosheets results in a lowering of the HER onset potential by ca. 0.33, 0.57, 0.29 and 0.31 V at EPPG, GC, SPE and BDD electrodes compared to their unmodified counterparts respectively. The lowering of the HER onset potential is associated with each supporting electrodes individual electron transfer kinetics/properties. The effect of MoS2 coverage is also explored. We reveal that its ability to catalyse the HER is dependent on the mass deposited until a critical mass of 2D MoS2 nanosheets is achieved, after which its electrocatalytic benefits and/or surface stability curtail. The active surface site density and turn over frequency for the 2D MoS2 nanosheets is determined, characterised and found to be dependent on both the coverage of 2D MoS2 nanosheets and the underlying/supporting substrate. This work is essential for those designing, fabricating and consequently electrochemically testing 2D nanosheet materials for the HER.
    • 3D printed graphene based energy storage devices

      Foster, Christopher W.; Down, Michael P.; Zhang, Yan; Ji, Xiaobo; Rowley-Neale, Samuel J.; Smith, Graham C.; Kelly, Peter J.; Banks, Craig E.; Manchester Metropolitan University; University of Chester; Central South University Changsha (Springer Nature, 2017-03-03)
      3D printing technology provides a unique platform for rapid prototyping of numerous applications due to its ability to produce low cost 3D printed platforms. Herein, a graphene-based polylactic acid filament (graphene/PLA) has been 3D printed to fabricate a range of 3D disc electrode (3DE) configurations using a conventional RepRap fused deposition moulding (FDM) 3D printer, which requires no further modification/ex-situ curing step. To provide proof-of-concept, these 3D printed electrode architectures are characterised both electrochemically and physicochemically and are advantageously applied as freestanding anodes within Li-ion batteries and as solid-state supercapacitors. These freestanding anodes neglect the requirement for a current collector, thus offering a simplistic and cheaper alternative to traditional Li-ion based setups. Additionally, the ability of these devices’ to electrochemically produce hydrogen via the hydrogen evolution reaction (HER) as an alternative to currently utilised platinum based electrodes (with in electrolysers) is also performed. The 3DE demonstrates an unexpectedly high catalytic activity towards the HER (−0.46 V vs. SCE) upon the 1000th cycle, such potential is the closest observed to the desired value of platinum at (−0.25 V vs. SCE). We subsequently suggest that 3D printing of graphene-based conductive filaments allows for the simple fabrication of energy storage devices with bespoke and conceptual designs to be realised.
    • A Numerical Feasibility Study of Kinetic Energy Harvesting from Lower Limb Prosthetics

      Jia, Yu; orcid: 0000-0001-9640-1666; email: yu.jia.gb@ieee.org; Wei, Xueyong; orcid: 0000-0002-6443-4727; email: seanwei@mail.xjtu.edu.cn; Pu, Jie; email: 1821721@chester.ac.uk; Xie, Pengheng; email: 1821700@chester.ac.uk; Wen, Tao; orcid: 0000-0002-3216-6967; email: t.wen@chester.ac.uk; Wang, Congsi; email: congsiwang@163.com; Lian, Peiyuan; email: lian100fen@126.com; Xue, Song; email: sxue@xidian.edu.cn; Shi, Yu; orcid: 0000-0003-3891-7175; email: y.shi@chester.ac.uk (MDPI, 2019-10-10)
      With the advancement trend of lower limb prosthetics headed towards bionics (active ankle and knee) and smart prosthetics (gait and condition monitoring), there is an increasing integration of various sensors (micro-electromechanical system (MEMS) accelerometers, gyroscopes, magnetometers, strain gauges, pressure sensors, etc.), microcontrollers and wireless systems, and power drives including motors and actuators. All of these active elements require electrical power. However, inclusion of a heavy and bulky battery risks to undo the lightweight advancements achieved by the strong and flexible composite materials in the past decades. Kinetic energy harvesting holds the promise to recharge a small on-board battery in order to sustain the active systems without sacrificing weight and size. However, careful design is required in order not to over-burden the user from parasitic effects. This paper presents a feasibility study using measured gait data and numerical simulation in order to predict the available recoverable power. The numerical simulations suggest that, depending on the axis, up to 10s mW average electrical power is recoverable for a walking gait and up to 100s mW average electrical power is achievable during a running gait. This takes into account parasitic losses and only capturing a fraction of the gait cycle to not adversely burden the user. The predicted recoverable power levels are ample to self-sustain wireless communication and smart sensing functionalities to support smart prosthetics, as well as extend the battery life for active actuators in bionic systems. The results here serve as a theoretical foundation to design and develop towards regenerative smart bionic prosthetics.
    • Acclimation of Microalgae to Wastewater Environments Involves Increased Oxidative Stress Tolerance Activity

      Osundeko, Olumayowa; Dean, Andrew P.; Davies, Helena; Pittman, Jon K.; University of Chester (Oxford Academic, 2014-09-16)
      A wastewater environment can be particularly toxic to eukaryotic microalgae. Microalgae can adapt to these conditions but the specific mechanisms that allow strains to tolerate wastewater environments are unclear. Furthermore, it is unknown whether the ability to acclimate microalgae to tolerate wastewater is an innate or species-specific characteristic. Six different species of microalgae (Chlamydomonas debaryana, Chlorella luteoviridis, Chlorella vulgaris, Desmodesmus intermedius, Hindakia tetrachotoma, Parachlorella kessleri) that had never previously been exposed to wastewater conditions were acclimated over an eight week period in secondary-treated municipal wastewater. With the exception of C. debaryana, acclimation to wastewater resulted in significantly higher growth rate and biomass productivity. With the exception of C. vulgaris, total chlorophyll content was significantly increased in all acclimated strains, while all acclimated strains showed significantly increased photosynthetic activity. The ability of strains to acclimate was species-specific, with two species, C. luteoviridis and P. kessleri, able to acclimate more efficiently to the stress than C. debaryana and D. intermedius. Metabolic fingerprinting of the acclimated and non-acclimated microalgae using Fourier transform infrared spectroscopy was able to differentiate strains on the basis of metabolic responses to the stress. In particular, strains exhibiting greater stress response and altered accumulation of lipids and carbohydrates could be distinguished. The acclimation to wastewater tolerance was correlated with higher accumulation of carotenoid pigments and increased ascorbate peroxidase activity.
    • Active Power and DC Voltage Coordinative Control for Cascaded DC–AC Converter With Bidirectional Power Application

      Tian, Yanjun; Chen, Zhe; Deng, Fujin; Sun, Xiaofeng; Hu, Yanting; University of Chester (IEEE, 2015-10)
      Two stage-cascaded converters are widely used in dc–ac hybrid systems to achieve the bidirectional power transmission. The topology of dual active bridge cascaded with inverter DABCI) is commonly used in this application. This paper proposes a coordinative control method for DABCI and it is able to reduce the dc-link voltage fluctuation between the DAB and inverter, then reduce the stress on the switching devices, as well as improve the system dynamic performance. In the proposed control method, the DAB and inverter are coordinated to control the dc-link voltage and the power, and this responsibility sharing control can effectively suppress the impact of the power variation on the dc-link voltage, without sacrificing stability. The proposed control method is also effective for DABCI in unidirectional power transmission. The effectiveness of the propose control has been validated by both simulations and experiments.
    • Adapting Jake Knapp’s Design Sprint Approach for AR/VR Applications in Digital Heritage

      Southall, Helen; Marmion, Maeve; Davies, Andrew; University of Chester (Springer Nature, 2019-04-21)
      Modern digital devices offer huge potential for the delivery of engaging heritage experiences to visitors, offering a better visitor experience, higher visitor numbers, and opportunities for increased tourism income. However, all software development entails risk, including the risk of developing a product which few will want, or be able, to use. Identifying user experience priorities and problems at an early stage is therefore extremely important. This chapter describes work in progress on a shortened version of Jake Knapp’s Design Sprint approach, and its application to designing VR/AR solutions for a specific heritage case study.
    • Addendum to the article: On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the Half-Line

      Antonopoulou, Dimitra; Kamvissis, Spyridon (IOPSCIENCE Published jointly with the London Mathematical Society, 2016-08-31)
      We present a short note on the extension of the results of [1] to the case of non-zero initial data. More specifically, the defocusing cubic NLS equation is considered on the half-line with decaying (in time) Dirichlet data and sufficiently smooth and decaying (in space) initial data. We prove that for this case also, and for a large class of decaying Dirichlet data, the Neumann data are sufficiently decaying so that the Fokas unified method for the solution of defocusing NLS is applicable.
    • Addressing problems of student retention and achievement with the help of a Virtual Learning Environment (VLE)

      Scott, Tony; University College Chester (Subject Centre for Information and Computer Sciences, Higher Education Academy, 2004)
      This article discussed methods taken during 2002-2003 to improve retention and achievement in the Introduction to Software Design module. They include e-mail feedback, study guides, and use of the college's VLE.
    • Aerosol Chemistry Resolved by Mass Spectrometry: Linking Field Measurements of Cloud Condensation Nuclei Activity to Organic Aerosol Composition

      Vogel, Alexander; Schneider, Johannes; Mueller-Tautges, Christina; Phillips, Gavin J.; Poehlker, Mira L.; Rose, Diana; Zuth, Christoph; Makkonen, Ulla; Hakola, Hannele; Crowley, John N.; et al. (American Chemical Society, 2016-10-06)
      Aerosol hygroscopic properties were linked to its chemical composition by using complementary online mass spectrometric techniques in a comprehensive chemical characterization study at a rural mountaintop station in central Germany in August 2012. In particular, atmospheric pressure chemical ionization mass spectrometry ((−)APCI-MS) provided measurements of organic acids, organosulfates, and nitrooxy-organosulfates in the particle phase at 1 min time resolution. Offline analysis of filter samples enabled us to determine the molecular composition of signals appearing in the online (−)APCI-MS spectra. Aerosol mass spectrometry (AMS) provided quantitative measurements of total submicrometer organics, nitrate, sulfate, and ammonium. Inorganic sulfate measurements were achieved by semionline ion chromatography and were compared to the AMS total sulfate mass. We found that up to 40% of the total sulfate mass fraction can be covalently bonded to organic molecules. This finding is supported by both on- and offline soft ionization techniques, which confirmed the presence of several organosulfates and nitrooxy-organosulfates in the particle phase. The chemical composition analysis was compared to hygroscopicity measurements derived from a cloud condensation nuclei counter. We observed that the hygroscopicity parameter (κ) that is derived from organic mass fractions determined by AMS measurements may overestimate the observed κ up to 0.2 if a high fraction of sulfate is bonded to organic molecules and little photochemical aging is exhibited.
    • Aging and Cholesterol Metabolism

      Mc Auley, Mark T.; University of Chester (Springer, 2019-07-30)
      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.
    • Aging and computational systems biology

      Mooney, Kathleen M.; Morgan, Amy; Mc Auley, Mark T.; Edgehill University, University of Chester (John Wiley & Sons, 2016-01-29)
      Aging research is undergoing a paradigm shift, which has led to new and innovative methods of exploring this complex phenomenon. The systems biology approach endeavors to understand biological systems in a holistic manner, by taking account of intrinsic interactions, while also attempting to account for the impact of external inputs, such as diet. A key technique employed in systems biology is computational modeling, which involves mathematically describing and simulating the dynamics of biological systems. Although a large number of computational models have been developed in recent years, these models have focused on various discrete components of the aging process, and to date no model has succeeded in completely representing the full scope of aging. Combining existing models or developing new models may help to address this need and in so doing could help achieve an improved understanding of the intrinsic mechanisms which underpin aging.
    • Aging and condensed phase chemistry affects the hygroscopicity of ambient SOA

      Vogel, Alexander; Müller-Tautges, Christina; Krueger, Mira; Rose, Diana; Schneider, Johannes; Phillips, Gavin J.; Makkonen, Ulla; Hakola, Hannele; Crowley, John N.; Poeschl, Ulrich; et al. (European Aerosol Assembly, 2015-09)
      Secondary inorganic and organic aerosol particles are ubiquitous constituents in the atmosphere. They are largely produced through the photo-oxidation of gaseous precursor molecules, such as SO2, NOx and VOCs, from both anthropogenic and natural sources. Once grown to atmospherically relevant sizes, they can act as cloud condensation nuclei (CCN) and thus affect earth’s climate (IPCC, 2013). However, their chemical composition can vary considerably over their atmospheric lifetime (up to one week) as a result of which, their physico-chemical properties may change significantly due to chemical transformation processes (Jimenez et al., 2009). One of these properties is hygroscopicity, which largely depends on the chemical composition. Linking both, measured chemical composition and hygroscopicity helps to advance our current understanding of the hygroscopicity parametrisation. In this work we investigated how photochemical aging of the organic aerosol fraction and chemical reactions between inorganic and organic compounds can affect the hygroscopicity parameter κ (Petters and Kreidenweis, 2007). The measurements were conducted at the semi-rural Taunus Observatory/ Germany during summer 2012. An extensive suite of particle phase characterizing instrumentation was applied for the detailed composition analysis of submicron aerosol: We used online atmospheric pressure chemical ionization mass spectrometry (APCI-MS) (Vogel et al., 2013), aerosol mass spectrometry (AMS), and filter sampling for laboratory based analysis using ultrahigh performance liquid chromatography coupled to electrospray ionization ultrahigh resolution (OrbitrapTM) mass spectrometry (UHPLC/ESI-UHRMS). The AMS allows quantification of total organics, sulfate and nitrate, whereas the APCI-MS can identify single organic species (organic acids, organosulfates, nitrooxy-organosulfates), both at a high measurement frequencies (< 1 minute). The UHPLC/ESI-UHRMS analysis of filter samples provides vital information helping to understand the complex online spectra of the APCI-MS by the unambiguous determination of the elemental composition of different organic compounds. Furthermore, we used a MARGA (Monitor for Aerosols and Gases in Ambient Air) to measure the concentration of purely inorganic sulfate in PM10. Finally a CCN counter coupled to a differential mobility analyser (DMA) and to a condensation particle counter (CPC) was used to measure size-resolved CCN efficiency spectra and to derive the hygroscopicity parameter κ. We determined the κ-value of the ambient aerosol from size resolved chemical composition measurements by the AMS and compared it to the measured values of the CCN efficiency spectra. The relative evolution of the aerosol aging was determined by measuring the ratio of two biogenic acids: the aging product 1,2,3-methyl-butane-tricarboxylic acid (MBTCA) and the first generation oxidation product pinic acid by the online APCI-MS. The occurrence of organosulfates and nitrooxy-organosulfates was observed by the ultrahigh resolution MS analysis and the online APCI-MS. Comparison of the total sulfate concentration measured by the AMS with the sulfate measurements by the MARGA allowed for the determination of the fraction of sulfate which is bonded to organic molecules. We observed that photochemical aging and the formation of (hydrophobic) nitrooxy-organosulfates is responsible for the observed bias between the predicted and measured κ-value.
    • Airlift Bioreactor for Biological Applications with Microbubble Mediated Transport Processes

      Al-Mashhadani, Mahmood K. H.; Wilkinson, Stephen J.; Zimmerman, William B.; University of Chester (Elsevier, 2015/06)
      Airlift bioreactors can provide an attractive alternative to stirred tanks, particularly for bioprocesses with gaseous reactants or products. Frequently, however, they are susceptible to being limited by gas-liquid mass transfer and by poor mixing of the liquid phase, particularly when they are operating at high cell densities. In this work we use CFD modelling to show that microbubbles generated by fluidic oscillation can provide an effective, low energy means of achieving high interfacial area for mass transfer and improved liquid circulation for mixing. The results show that when the diameter of the microbubbles exceeded 200 μm, the “downcomer” region, which is equivalent to about 60 % of overall volume of the reactor, is free from gas bubbles. The results also demonstrate that the use of microbubbles not only increases surface area to volume ratio, but also increases mixing efficiency through increasing the liquid velocity circulation around the draft tube. In addition, the depth of downward penetration of the microbubbles into the downcomer increases with decreasing bubbles size due to a greater downward drag force compared to the buoyancy force. The simulated results indicate that the volume of dead zone increases as the height of diffuser location is increased. We therefore hypothesise that poor gas bubble distribution due to the improper location of the diffuser may have a markedly deleterious effect on the performance of the bioreactor used in this work.
    • An algorithm for the numerical solution of two-sided space-fractional partial differential equations.

      Ford, Neville J.; Pal, Kamal; Yan, Yubin; University of Chester (de Gruyter, 2015-08-20)
      We introduce an algorithm for solving two-sided space-fractional partial differential equations. The space-fractional derivatives we consider here are left-handed and right-handed Riemann–Liouville fractional derivatives which are expressed by using Hadamard finite-part integrals. We approximate the Hadamard finite-part integrals by using piecewise quadratic interpolation polynomials and obtain a numerical approximation of the space-fractional derivative with convergence order
    • An algorithm to detect small solutions in linear delay differential equations

      Ford, Neville J.; Lumb, Patricia M. (Elsevier, 2006-08-15)
      This preprint discusses an algorithm that provides a simple reliable mechanism for the detection of small solutions in linear delay differential equations.
    • Algorithms for the fractional calculus: A selection of numerical methods

      Diethelm, Kai; Ford, Neville J.; Freed, Alan D.; Luchko, Yury (Elsevier Science, 2005-02)
      This article discusses how numerical algorithms can help engineers work with fractional models in an efficient way.
    • An Altered Four Circulant Construction for Self-Dual Codes from Group Rings and New Extremal Binary Self-dual Codes I

      Gildea, Joe; Kaya, Abidin; Yildiz, Bahattin; University of Chester; Sampoerna University; Northern Arizona University (Elsevier, 2019-08-07)
      We introduce an altered version of the four circulant construction over group rings for self-dual codes. We consider this construction over the binary field, the rings F2 + uF2 and F4 + uF4; using groups of order 4 and 8. Through these constructions and their extensions, we find binary self-dual codes of lengths 16, 32, 48, 64 and 68, many of which are extremal. In particular, we find forty new extremal binary self-dual codes of length 68, including twelve new codes with \gamma=5 in W68,2, which is the first instance of such a value in the literature.