A mathematical model for the energy stored in green roofs

A simple mathematical model to estimate the energy stored in a green roof is developed. Analytical solutions are derived corresponding to extensive (shallow) and intensive (deep) substrates. Results are presented for the surface temperature and energy stored in both green roofs and concrete during a typical day. Within the restrictions of the model assumptions the analytical solution demonstrates that both energy and surface temperature vary linearly with fractional leaf coverage, albedo and irradiance, while the effect of evaporation rate and convective heat transfer is non-linear. It is shown that a typical green roof is significantly cooler and stores less energy than a concrete one even when the concrete has a high albedo coating. Evaporation of even a few millimetres per day from the soil layer can reduce the stored energy by a factor of more than three when compared to an equivalent thickness concrete roof

Contaminant Removal by Adsorption

We develop a mathematical model for filtration in a cylindrical column packed with a porous material. The base model involves coupling an advection-diffusion equation to a sink term which represents the sorption and is appropriate when trace quantities are removed from the fluid. This is then extended to include the variation of velocity and pressure, which is appropriate for the removal of significant quantities, and leads to a system of five coupled equations. For the case of CO2 removal we are able to reduce the complexity of the equations and to derive an analytical expression for the breakthrough curve. This expression is then verified against experimental data for the adsorption of CO2 from gas and antibiotics from water. Finally, we show how the work may be modified to deal with certain extraction processes, where a clean fluid is used to remove material from the porous matrix, such as lanolin from wool

Modelling mass transfer from a packed bed by fluid extraction

A mathematical model describing the erosion or leaching of a solid material by a flowing fluid in a column is developed. This involves an advection-diffusion equation coupled to a linear kinetic reaction describing the mass transfer between the solid and fluid. Two specific cases are analysed, the first where the extracted material has the same saturation solubility and rate of mass transfer throughout the process, the second where the solubility switches after a certain amount of erosion. In the first case there are only two model unknowns, the solubility and mass transfer coefficient, in the second there is a third unknown, the second solubility. Exploiting the fact that erosion is a slow process (relative to the flow rate) a perturbation solution based on the smallness of the amount removed is developed to describe the concentration and radius throughout the column. From this an analytical expression for the extracted fraction is obtained. The extracted fraction has a large linear section which results in a simple calculation to estimate the initial solubility from a very few or even a single data point. The remaining unknowns may also be easily calculated from the formula and later data points. A numerical solution, using finite differences, is developed to verify the perturbation solution. The analytical solution is also verified against experimental data for the removal of lanolin from wool fibres with a supercritical CO2/ethanol solvent. Values for the mass transfer rate and two solubilities are obtained for different pressures and shown to provide excellent agreement with a series of experimental results for the extracted fraction

An analytical investigation into solute transport and sorption via intra-particle diffusion in the dual-porosity limit

We develop a mathematical model for adsorption based on averaging the flow around, and diffusion inside, adsorbent particles in a column. The model involves three coupled partial differential equations for the contaminant concentration both in the carrier fluid and within the particle as well as the adsorption rate. The adsorption rate is modelled using the Sips equation, which is suitable for describing both physical and chemical adsorption mechanisms. Non-dimensionalisation is used to determine the controlling parameter groups as well as to determine negligible terms and so reduce the system complexity. The inclusion of intra-particle diffusion introduces new dimensionless parameters to those found in standard works, including a form of internal Damk\"ohler number and a new characteristic time scale. We provide a numerical method for the full model and show how in certain situations a travelling wave approach can be utilized to find analytical solutions. The model is validated against available experimental data for the removal of Mercury(II) and CO$_\text{2}$. The results show excellent agreement with measurements of column outlet contaminant concentration and provide insights into the underlying chemical reactions.Comment: 36 pages, 10 figures, 8 table

An exact algorithm for the static rebalancing problem arising in bicycle sharing systems

Bicycle sharing systems can significantly reduce traffic, pollution, and the need for parking spaces in city centers. One of the keys to success for a bicycle sharing system is the efficiency of rebalancing operations, where the number of bicycles in each station has to be restored to its target value by a truck through pickup and delivery operations. The Static Bicycle Rebalancing Problem aims to determine a minimum cost sequence of stations to be visited by a single vehicle as well as the amount of bicycles to be collected or delivered at each station. Multiple visits to a station are allowed, as well as using stations as temporary storage. This paper presents an exact algorithm for the problem and results of computational tests on benchmark instances from the literature. The computational experiments show that instances with up to 60 stations can be solved to optimality within 2 hours of computing time

Wider implications of video-assisted thoracic surgery versus open approach for lung metastasectomy

Lung metastasectomy is considered a safe and potentially curative procedure despite there is not a strong evidence that metastasectomy prolongs long-term survival in patients with lung metastases. Moreover, the debate is open regarding the best approach for lung metastasectomy, video-assisted thoracic surgery versus open approach. A systematic review of literature to clarify what is the best approach to prolong survival in patients with lung metastases was performed. Our study confirms that overall survival is equivalent for video-assisted thoracic surgery and thoracotomy, therefore the ‘gold standard’ surgical treatment for lung metastases remains a point of debate. The choice of the surgical approach still depends more on the single center or surgeon practice than on strong scientific evidence. A prospective randomized trial could clarify the question

Business cycles, international trade and capital flows: Evidence from Latin America

This paper adopts a flexible framework to assess both short- and long-run business cycle linkages between six Latin American (LA) countries and the four largest economies in the world (namely the US, the Euro area, Japan and China) over the period 1980:I-2011:IV. The result indicate that within the LA region there are considerable differences between countries, success stories coexisting with extremely vulnerable economies. They also show that the LA region as a whole is largely dependent on external developments, especially in the years after the great recession of 2008 and 2009. The trade channel appears to be the most important source of business cycle comovement, whilst capital flows are found to have a limited role, especially in the very short run

Response to growth hormone in patients with RNPC3 mutations

Peer reviewe

Polyethylene Glycol 35 as a perfusate additive for mitochondrial and glycocalyx protection in HOPE liver preservation

Organ transplantation is a multifactorial process in which proper graft preservation is a mandatory step for the success of the transplantation. Hypothermic preservation of abdominal organs is mostly based on the use of several commercial solutions, including UW, Celsior, HTK and IGL-1. The presence of the oncotic agents HES (in UW) and PEG35 (in IGL-1) characterize both solution compositions, while HTK and Celsior do not contain any type of oncotic agent. Polyethylene glycols (PEGs) are non-immunogenic, non-toxic and water-soluble polymers, which present a combination of properties of particular interest in the clinical context of ischemia-reperfusion injury (IRI): they limit edema and nitric oxide induction and modulate immunogenicity. Besides static cold storage (SCS), there are other strategies to preserve the organ, such as the use of machine perfusion (MP) in dynamic preservation strategies, which increase graft function and survival as compared to the conventional static hypothermic preservation. Here we report some considerations about using PEG35 as a component of perfusates for MP strategies (such as hypothermic oxygenated perfusion, HOPE) and its benefits for liver graft preservation. Improved liver preservation is closely related to mitochondria integrity, making this organelle a good target to increase graft viability, especially in marginal organs (e.g., steatotic livers). The final goal is to increase the pool of suitable organs, and thereby shorten patient waiting lists, a crucial problem in liver transplantation