Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Fractional bioheat equation

In this work we develop a new mathematical model for the Pennes’ bioheat equation assuming a fractional time derivative of single order. A numerical method for the solu- tion of such equations is proposed, and, the suitability of the new model for modelling real physical problems is studied and discussed

A multi-criteria decision support system for a routing problem in waste collection

Autor proof

The non-emergency patient transport modelled as a team orienteering problem

This work presents an improved model to solve the non-emergency patients transport (NEPT) service issues given the new rules recently established in Portugal. The model follows the same principle of the Team Orienteering Problem by selecting the patients to be included in the routes attending the maximum reduction in costs when compared with individual transportation. This model establishes the best sets of patients to be transported together. The model was implemented in AMPL and a compact formulation was solved using NEOS Server. A heuristic procedure based on iteratively solving Orienteering Problems is presented, and this heuristic provides good results in terms of accuracy and computation time. Euclidean instances as well as asymmetric real data gathered from Google maps were used, and the model has a promising performance mainly with asymmetric cost matrices.

A taxonomy for the flexible job shop scheduling problem

This chapter aims at developing a taxonomic framework to classify the studies on the flexible job shop scheduling problem (FJSP). The FJSP is a generalization of the classical job shop scheduling problem (JSP), which is one of the oldest NP-hard problems. Although various solution methodologies have been developed to obtain good solutions in reasonable time for FSJPs with different objective functions and constraints, no study which systematically reviews the FJSP literature has been encountered. In the proposed taxonomy, the type of study, type of problem, objective, methodology, data characteristics, and benchmarking are the main categories. In order to verify the proposed taxonomy, a variety of papers from the literature are classified. Using this classification, several inferences are drawn and gaps in the FJSP literature are specified. With the proposed taxonomy, the aim is to develop a framework for a broad view of the FJSP literature and construct a basis for future studies.

A decision support system for a waste collection vehicle routing problem

The selective collection of municipal solid waste for recycling is a very complex and expensive process, where a major issue is to perform cost-efficient waste collection routes. Despite the abundance of commercially available software for fleet management, they often lack the capability to deal properly with sequencing problems and dynamic revision of plans and schedules during process execution. Our approach to achieve better solutions for the waste collection process is to model it as a vehicle routing problem, more specifically as a team orienteering problem where capacity constraints on the vehicles are considered, as well as time windows for the waste collection points and for the vehicles. The final model is called capacitated team orienteering problem with double time windows (CTOPdTW).We developed a genetic algorithm to solve routing problems in waste collection modelled as a CTOPdTW. The results achieved suggest possible reductions of logistic costs in selective waste collection.

Fractional pennes' bioheat equation: theoretical and numerical studies

In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.

Methodology for real-time adaptation of tunnels support using the observational method

The observational method in tunnel engineering allows the evaluation in real time of the actual conditions of the ground and to take measures if its behavior deviates considerably from predictions. However, it lacks a consistent and structured methodology to use the monitoring data to adapt the support system in real time. The definition of limit criteria above which adaptation is required are not defined and complex inverse analysis procedures (Rechea et al. 2008, Levasseur et al. 2010, Zentar et al. 2001, Lecampion et al. 2002, Finno and Calvello 2005, Goh 1999, Cui and Pan 2012, Deng et al. 2010, Mathew and Lehane 2013, Sharifzadeh et al. 2012, 2013) may be needed to consistently analyze the problem. In this paper a methodology for the real time adaptation of the support systems during tunneling is presented. In a first step limit criteria for displacements and stresses are proposed. The methodology uses graphics that are constructed during the project stage based on parametric calculations to assist in the process and when these graphics are not available, since it is not possible to predict every possible scenario, inverse analysis calculations are carried out. The methodology is applied to the “Bois de Peu” tunnel which is composed by two tubes with over 500 m long. High uncertainty levels existed concerning the heterogeneity of the soil and consequently in the geomechanical design parameters. The methodology was applied in four sections and the results focus on two of them. It is shown that the methodology has potential to be applied in real cases contributing for a consistent approach of a real time adaptation of the support system and highlight the importance of the existence of good quality and specific monitoring data to improve the inverse analysis procedure.

Assessing the application of polypropylene multifilament yarns in brain phantoms

The currently available clinical imaging methods do not provide highly detailed information about location and severity of axonal injury or the expected recovery time of patients with traumatic brain injury [1]. High-Definition Fiber Tractography (HDFT) is a novel imaging modality that allows visualizing and quantifying, directly, the degree of axons damage, predicting functional deficits due to traumatic axonal injury and loss of cortical projections. This imaging modality is based on diffusion technology [2]. The inexistence of a phantom able to mimic properly the human brain hinders the possibility of testing, calibrating and validating these medical imaging techniques. Most research done in this area fails in key points, such as the size limit reproduced of the brain fibers and the quick and easy reproducibility of phantoms [3]. For that reason, it is necessary to develop similar structures matching the micron scale of axon tubes. Flexible textiles can play an important role since they allow producing controlled packing densities and crossing structures that match closely the human crossing patterns of the brain. To build a brain phantom, several parameters must be taken into account in what concerns to the materials selection, like hydrophobicity, density and fiber diameter, since these factors influence directly the values of fractional anisotropy. Fiber cross-section shape is other important parameter. Earlier studies showed that synthetic fibrous materials are a good choice for building a brain phantom [4]. The present work is integrated in a broader project that aims to develop a brain phantom made by fibrous materials to validate and calibrate HDFT. Due to the similarity between thousands of hollow multifilaments in a fibrous arrangement, like a yarn, and the axons, low twist polypropylene multifilament yarns were selected for this development. In this sense, extruded hollow filaments were analysed in scanning electron microscope to characterize their main dimensions and shape. In order to approximate the dimensional scale to human axons, five types of polypropylene yarns with different linear density (denier) were used, aiming to understand the effect of linear density on the filament inner and outer areas. Moreover, in order to achieve the required dimensions, the polypropylene filaments cross-section was diminished in a drawing stage of a filament extrusion line. Subsequently, tensile tests were performed to characterize the mechanical behaviour of hollow filaments and to evaluate the differences between stretched and non-stretched filaments. In general, an increase of the linear density causes the increase in the size of the filament cross section. With the increase of structure orientation of filaments, induced by stretching, breaking tenacity increases and elongation at break decreases. The production of hollow fibers, with the required characteristics, is one of the key steps to create a brain phantom that properly mimics the human brain that may be used for the validation and calibration of HDFT, an imaging approach that is expected to contribute significantly to the areas of brain related research.

Titanium oxide adhesion layer for high temperature annealed Si/Si3N4/TiOx/Pt/LiCoO2 battery structures

This work describes the influence of a high annealing temperature of about 700C on the Si(substrate)/Si3N4/TiOx/Pt/LiCoO2 multilayer system for the fabrication of all-solid-state lithium ion thin film microbatteries. Such microbatteries typically utilize lithium cobalt oxide (LiCoO2) as cathode material with a platinum (Pt) current collector. Silicon nitride (Si3N4) is used to act as a barrier against Li diffusion into the substrate. For a good adherence between Si3N4 and Pt, commonly titanium (Ti) is used as intermediate layer. However, to achieve crystalline LiCoO2 the multilayer system has to be annealed at high temperature. This post-treatment initiates Ti diffusion into the Pt-collector and an oxidation to TiOx, leading to volume expansion and adhesion failures. To solve this adhesion problem, we introduce titanium oxide (TiOx) as an adhesion layer, avoiding the diffusion during the annealing process. LiCoO2, Pt and Si3N4 layers were deposited by magnetron sputtering and the TiOx layer by thermal oxidation of Ti layers deposited by e-beam technique. Asdeposited and annealed multilayer systems using various TiOx layer thicknesses were studied by scanning electron microscopy (SEM) and time-of-flight secondary ion mass spectrometry (ToF-SIMS) and x-ray photoelectron spectroscopy (XPS). The results revealed that an annealing process at temperature of 700C leads to different interactions of Ti atoms between the layers, for various TiOx layer thicknesses (25–45 nm).

Predicting pre-triage waiting time in a maternity emergency room through data mining

An unsuitable patient flow as well as prolonged waiting lists in the emergency room of a maternity unit, regarding gynecology and obstetrics care, can affect the mother and child’s health, leading to adverse events and consequences regarding their safety and satisfaction. Predicting the patients’ waiting time in the emergency room is a means to avoid this problem. This study aims to predict the pre-triage waiting time in the emergency care of gynecology and obstetrics of Centro Materno Infantil do Norte (CMIN), the maternal and perinatal care unit of Centro Hospitalar of Oporto, situated in the north of Portugal. Data mining techniques were induced using information collected from the information systems and technologies available in CMIN. The models developed presented good results reaching accuracy and specificity values of approximately 74% and 94%, respectively. Additionally, the number of patients and triage professionals working in the emergency room, as well as some temporal variables were identified as direct enhancers to the pre-triage waiting time. The imp lementation of the attained knowledge in the decision support system and business intelligence platform, deployed in CMIN, leads to the optimization of the patient flow through the emergency room and improving the quality of services.

The application of the equivalent annulus width concept in thermal diffusion separations

The equivalent annulus width concept is used to characterize a small commercial thermogravitational hermal diffusion column and its validity checked experimentally by separating batchwise in the column mixtures of n-heptanebenzene with different initial concentrations. The equation of Ruppell and Coull was used to analyse the data in the short separation times range and determine the equivalent annulus width. Good agreement was obtained between the experimental and predicted time-separation curves when using the equivalent annulus width value and on averaged value of the thermal diffusion constant. A new method is presented for the simultaneous determination of the equivalent annulus width and the thermal diffusion constant of a binary mixture from a single set of experimental data.

Single molecule simulation of diffusion and enzyme kinetics

This work presents a molecular-scale agent-based model for the simulation of enzymatic reactions at experimentally measured concentrations. The model incorporates stochasticity and spatial dependence, using diffusing and reacting particles with physical dimensions. We developed strategies to adjust and validate the enzymatic rates and diffusion coefficients to the information required by the computational agents, i.e., collision efficiency, interaction logic between agents, the time scale associated with interactions (e.g., kinetics), and agent velocity. Also, we tested the impact of molecular location (a source of biological noise) in the speed at which the reactions take place. Simulations were conducted for experimental data on the 2-hydroxymuconate tautomerase (EC 5.3.2.6, UniProt ID Q01468) and the Steroid Delta-isomerase (EC 5.3.3.1, UniProt ID P07445). Obtained results demonstrate that our approach is in accordance to existing experimental data and long-term biophysical and biochemical assumptions.