Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

Candidate radial-inflow turbines and high-density working fluids for geothermal power systems

Optimisation of Organic Rankine Cycle (ORCs) for binary-cycle geothermal applications could play a major role in determining the competitiveness of low to moderate temperature geothermal resources. Part of this optimisation process is matching cycles to a given resource such that power output can be maximised. Two major and largely interrelated components of the cycle are the working fluid and the turbine. Both components need careful consideration: the selection of working fluid and appropriate operating conditions as well as optimisation of the turbine design for those conditions will determine the amount of power that can be extracted from a resource. In this paper, we present the rationale for the use of radial-inflow turbines for ORC applications and the preliminary design of several radial-inflow machines based on a number of promising ORC systems that use five different working fluids: R134a, R143a, R236fa, R245fa and n-Pentane. Preliminary meanline analysis lead to the generation of turbine designs for the various cycles with similar efficiencies (77%) but large differences in dimensions (139–289 mm rotor diameter). The highest performing cycle, based on R134a, was found to produce 33% more net power from a 150 °C resource flowing at 10 kg/s than the lowest performing cycle, based on n-Pentane.

Candidate radial-inflow turbines and high-density working fluids for geothermal power systems

Optimisation of Organic Rankine Cycles (ORCs) for binary-cycle geothermal applications could play a major role in the competitiveness of low to moderate temperature geothermal resources. Part of this optimisation process is matching cycles to a given resource such that power output can be maximised. Two major and largely interrelated components of the cycle are the working fluid and the turbine. Both components need careful consideration. Due to the temperature differences in geothermal resources a one-size-fits-all approach to surface power infrastructure is not appropriate. Furthermore, the traditional use of steam as a working fluid does not seem practical due to the low temperatures of many resources. A variety of organic fluids with low boiling points may be utilised as ORC working fluids in binary power cycle loops. Due to differences in thermodynamic properties, certain fluids are able to extract more heat from a given resource than others over certain temperature and pressure ranges. This enables the tailoring of power cycle infrastructure to best match the geothermal resource through careful selection of the working fluid and turbine design optimisation to yield the optimum overall cycle performance. This paper presents the rationale for the use of radial-inflow turbines for ORC applications and the preliminary design of several radial-inflow turbines based on a selection of promising ORC cycles using five different high-density working fluids: R134a, R143a, R236fa, R245fa and n-Pentane at sub- or trans-critical conditions. Numerous studies published compare a variety of working fluids for various ORC configurations. However, there is little information specifically pertaining to the design and implementation of ORCs using realistic radial turbine designs in terms of pressure ratios, inlet pressure, rotor size and rotational speed. Preliminary 1D analysis leads to the generation of turbine designs for the various cycles with similar efficiencies (77%) but large differences in dimensions (139289 mm rotor diameter). The highest performing cycle (R134a) was found to produce 33% more net power from a 150°C resource flowing at 10 kg/s than the lowest performing cycle (n-Pentane).

Thermo-magnetic convection of paramagnetic fluids with non-instantaneous heating

The unsteady boundary-layer development for thermomagnetic convection of paramagnetic fluids inside a square cavity has been considered in this study. The cavity is placed in a microgravity condition (no gravitation acceleration) and under a uniform magnetic field which acts vertically. A ramp temperature boundary condition is applied on left vertical side wall of the cavity where the temperature initially increases with time up to some specific time and maintain constant thereafter. A distinct magnetic convection boundary layer is developed adjacent to the left vertical wall due to the effect of the magnetic body force generated on the paramagnetic fluid. An improved scaling analysis has been performed using triple-layer integral method and verified by numerical simulations. The Prandtl number has been chosen greater than unity varied over 5-100. Moreover, the effect of various values of the magnetic parameter and magnetic Rayleigh number on the fluid flow and heat transfer has been shown.

Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.

Mid- and near-infrared spectroscopic investigation of homogeneous cation distribution in MgxZnyAl(x+y)/2-layered double hydroxide (LDH)

In this report, a detailed FTIR fitting analysis was used to recognize Mg, Zn and Al homogeneous distribution in MgxZnyAl(x+y)/2-Layered double hydroxide (LDH) hydroxyl layer. In detail, OH-Mg2Al:OH-Mg3 ratios decreased from 95.2:4.8 (MIR) and 94.2:5.8 (NIR) to 58.9:41.1 (MIR) and 61.8:38.2 (NIR), when Mg:Al increased from 2.2:1.0 to 4.1:1.0 in MgAl-LDHs. These fitting results were similar with theoretical calculations of 94.3:5.7 and 59.0:41.0. In a further analysis of MgxZnyAl(x+y)/2-LDHs, OH bonded Zn2Mg, Zn2Al, MgZnAl, Mg2Al and Mg2Zn peaks were identified at 3420, 3430, 3445–3450, 3454 and 3545 cm-1, respectively. With the decrease of Mg:Zn from 3:1 to 1:3, metal-hydroxyl bands changed from OH-Mg2Al and MgZnAl (with a ratio of 49.4:50.6) to OH-MgZnAl and Zn2Al (with a ratio of 55.0:45.0). They were also similar with theoretical calculations of 47.6:52.4 and 54.6:45.4. As a result, these results show that there is an ordered cation distribution in MgxZnyAl(x+y)/2-LDH, and FTIR is feasible in recognizing this structure.

Magnetic convection heat transfer in an open-ended enclosure filled with paramagnetic fluids

Numerical simulations of thermomagnetic convection of paramagnetic fluids placed in a micro-gravity condition (g ≈ 0) and under a uniform vertical gradient magnetic field in an open ended square enclosure with ramp heating temperature condition applied on a vertical wall is investigated in this study. In presence of the strong magnetic gradient field thermal convection of the paramagnetic fluid might take place even in a zero-gravity environment as a direct consequence of temperature differences occurring within the fluid. The thermal boundary layer develops adjacent to the hot wall as soon as the ramp temperature condition is applied on it. There are two scenarios can be observed based on the ramp heating time. The steady state of the thermal boundary layer can be reached before the ramp time is finished or vice versa. If the ramp time is larger than the quasi-steady time then the thermal boundary layer is in a quasi-steady mode with convection balancing conduction after the quasi-steady time. Further increase of the heat input simply accelerates the flow to maintain the proper thermal balance. Finally, the boundary layer becomes completely steady state when the ramp time is finished. Effects of magnetic Rayleigh number, Prandtl number and paramagnetic fluid parameter on the flow pattern and heat transfer are presented.

Magnetic convection heat transfer in an open ended enclosure filled with paramagnetic fluids

Numerical simulations of thermomagnetic convection of paramagnetic fluids placed in a micro-gravity condition (g nearly 0) and under a uniform vertical gradient magnetic field in an open ended square enclosure with ramp heating temperature condition applied on a vertical wall is investigated in this study. In presence of the strong magnetic gradient field thermal convection of the paramagnetic fluid might take place even in a zero-gravity environment as a direct consequence of temperature differences occurring within the fluid. The thermal boundary layer develops adjacent to the hot wall as soon as the ramp temperature condition is applied on it. There are two scenario that can be observed based on the ramp heating time. The steady state of the thermal boundary layer can be reached before the ramp time is finished or vice versa. If the ramp time is larger than the quasi-steady time then the thermal boundary layer is in a quasi-steady mode with convection balancing conduction after the quasi-steady time. Further increase of the heat input simply accelerates the flow to maintain the proper thermal balance. Finally, the boundary layer becomes completely steady state when the ramp time is finished. Effects of magnetic Rayleigh number, Prandtl number and paramagnetic fluid parameter on the flow pattern and heat transfer are presented.

Crushed tablets : does the administration of food vehicles and thickened fluids to aid medication swallowing alter drug release?

Purpose. To evaluate the influence of co-administered vehicles on in vitro dissolution in simulated gastric fluid of crushed immediate release tablets as an indicator for potential drug bioavailability compromise. Methods. Release and dissolution of crushed amlodipine, atenolol, carbamazepine and warfarin tablets were tested with six foods and drinks that are frequently used in the clinical setting as mixers for crushed medications (water, orange juice, honey, yoghurt, strawberry jam and water thickened with Easythick powder) in comparison to whole tablets. Five commercial thickening agents (Easythick Advanced, Janbak F, Karicare, Nutilis, Viscaid) at three thickness levels were tested for their effect on the dissolution of crushed atenolol tablets. Results. Atenolol dissolution was unaffected by mixing crushed tablets with thin fluids or food mixers in comparison to whole tablets or crushed tablets in water, but amlodipine was delayed by mixing with jam. Mixing crushed warfarin and carbamazepine tablets with honey, jam or yoghurt caused them to resemble the slow dissolution of whole tablets rather than the faster dissolution of crushed tablets in water or orange juice. Crushing and mixing any of the four medications with thickened water caused a significant delay in dissolution. When tested with atenolol, all types of thickening agents at the greatest thickness significantly restricted dissolution, and products that are primarily based on xanthan gum also delayed dissolution at the intermediate thickness level. Conclusions. Dissolution testing, while simplistic, is a widely used and accepted method for comparing drug release from different formulations as an indicator for in vivo bioavailability. Thickened fluids have the potential to retard drug dissolution when used at the thickest levels. These findings highlight potential clinical implications of the addition of these agents to medications for the purpose of dose delivery and indicate that further investigation of thickened fluids and their potential to influence therapeutic outcomes is warranted.

Homogeneous bent functions of degree n in 2n variables do not exist for n>3

We prove that homogeneous bent functions f:GF(2)^2n --> GF(2) of degree n do not exist for n>3. Consequently homogeneous bent functions must have degree 3.

The eight variable homogeneous degree three bent functions

We determine the affine equivalence classes of the eight variable degree three homogeneous bent functions using a new algorithm. Our algorithm applies to general bent functions and can systematically determine the automorphism groups. We provide a partial verification of the enumeration of eight variable degree three homogeneous bent functions obtained by Meng et al. We determine the affine equivalence classes of these functions.

One-step homogeneous C-reactive protein assay for saliva

Background: Cardiovascular disease is the leading cause of death in the world. Human C-reactive protein (CRP) has been used in the risk assessment of coronary events. Human saliva mirrors the body's health and well-being and is non-invasive, easy to collect and ideal for third world countries as well as for large patient screening. The aim was to establish a saliva CRP reference range and to demonstrate the clinical utility of salivary CRP levels in assessing the coronary events in a primary health care setting. Methods: We have used a homogeneous bead based assay to detect CRP levels in human saliva. We have developed a rapid 15 min (vs 90 min), sequential, one-step assay to detect CRP in saliva. Saliva was collected from healthy volunteers (n = 55, ages 20-70 years) as well as from cardiac patients (n = 28, ages 43-86 years). Results: The assay incubation time was optimised from 90 min to 15 mm and generated a positive correlation (n = 29, range 10-2189 pg/mL, r2 = 0.94; Passing Bablok slope 0.885. Intercept 0, p>0.10), meaning we could decrease the incubation time and produce equivalent results with confidence. The mean CRP level in the saliva of healthy human volunteers was 285 pg/mL and in cardiac patients was 1680 pg/mL (p<0.01). Analysis of CRP concentrations in paired serum and saliva samples from cardiac patients gave a positive correlation (r2 = 0.84, p<0.001) and the salivary CRP concentration capable of distinguishing healthy from diseased patients. Conclusions: The results suggest that this minimally invasive, rapid and sensitive assay will be useful in large patient screening studies for risk assessment of coronary events. (C) 2011 Elsevier B.V. All rights reserved.

Delivering crushed tablets using thickened fluids : is drug diffusion into gastric fluids restricted?

Solid medications are often crushed and mixed with food or thickened water to aid drug delivery for those who cannot or prefer not to swallow whole tablets or capsules. Dysphagic patients have the added problem of being unable to safely swallow thin fluids so water thickened with polysaccharides is used to deliver crushed medications and ensure safe swallowing. It is postulated that these polysaccharide systems may restrict drug release by reducing the diffusion of the drug into gastric fluids. METHODS By using a vertical diffusion cell separated with a synthetic membrane, the diffusion of a model drug (atenolol) was studied from a donor system containing the drug dispersed into thickened water with xanthan gum (concentration range from 0.005%-2.2%) into a receptor system containing simulated gastric fluid (SGF) at 37°C. The amount of drug transferred was measured over 8 hours and diffusion coefficients estimated using the Higuchi model approach. RESULTS Atenolol diffusion decreased with increasing xanthan gum concentration up to 1.0%, above which diffusion remained around 300 μ2s-1. The rheological measurements captured the influence of the structure and conformation of the polysaccharide in water on the movement and availability of the drug in SGF. DISCUSSION Dose form administration for dysphagic patients’ needs special attention from general practitioners, pharmacist and patients. Improving drug release of crushed tablets from thickening agents requires a reduction in the diffusion pathway (e.g. by decreasing drop size radius). This approach could make the drug available in SGF in a short time without compromising the mechanical aspects of thickening agents that guarantee safe swallowing.