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.

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

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

Modeling microbes: New methods for integrated metabolic and regulatory network reconstruction

PhD Thesis in Bioengineering

A relational algebra approach to ETL modeling

The MAP-i Doctoral Programme in Informatics, of the Universities of Minho, Aveiro and Porto

High strain rate constitutive modeling forhistorical structures subjected to blast loading

Doctoral Thesis Civil Engineering

Fused deposition modeling with polypropylene

This paper addresses the potential of polypropylene (PP) as a candidate for fused deposition modeling (FDM)-based 3D printing technique. The entire filament production chain is evaluated, starting with the PP pellets, filament production by extrusion and test samples printing. This strategy enables a true comparison between parts printed with parts manufactured by compression molding, using the same grade of raw material. Printed samples were mechanically characterized and the influence of filament orientation, layer thickness, infill degree and material was assessed. Regarding the latter, two grades of PP were evaluated: a glass-fiber reinforced and a neat, non-reinforced, one. The results showed the potential of the FDM to compete with conventional techniques, especially for the production of small series of parts/components; also, it was showed that this technique allows the production of parts with adequate mechanical performance and, therefore, does not need to be restricted to the production of mockups and prototypes.

[Editorial] Current challenges in modeling cellular metabolism

The authors would like to thank the financial support from the NovoNordiskFoundation.

Evaluation of the DPMFoam solver

[Extrat] Multiphase flows are relevant in several industrial processes, thus the availability of accurate numerical modeling tools, able to support the design of products and processes, is of much significance. OpenFOAM version 2.3.x comprises a multiphase flow solver able to couple Eulerian and Lagrangian phases using the discrete particles method (DPM), the DPMFoam. In this work the DPMFoam solver is assessed by comparing its predictions with analytical results and experimental and simulated data available in the literature. They are results from Goldschmidt’s [1] and Hoomans’s [2] theses and the analytical Ergun equation. The goal was to define accuracy and performance of DPMFoam in general scientific or commercial applications. Obtained results demonstrate a good agreement with the reference simulation data and is within reasonable deviations from the experimental values. (...)

Modeling separator membranes physical characteristics for optimized lithium ion battery performance

The effect of varying separator membrane physical parameters such as degree of porosity, tortuosity and thickness, on battery delivered capacity was studied in order to optimize performance of lithium-ion batteries. This was achieved by a theoretical mathematical model relating the Bruggeman coefficient with the degree of porosity and tortuosity. The inclusion of the separator membrane in the simulation model of the battery system does not affect the delivered capacity of the battery. The ionic conductivity of the separator and consequently the delivered capacity values obtained at different discharge rates depends on the value of the Bruggeman coefficient, which is related with the degree of porosity and tortuosity of the membrane. Independently of scan rate, the optimal value of the degree of porosity is above 50% and the separator thickness should range between 1 μm at 32 μm for improved battery performance.

Population Dynamics Modeling of Arapaima gigas

Pirarucu (Arapaima gigas) has been of the most important natural fishing resources of the Amazon region. Due to its economic importance, and the necessity to preserve the species hand, field research concerning the habits and behavior of the pirarucu has been increasing for the last 20 years. The aim of this paper is to present a mathematical model for the pirarucu population dynamics considering the species peculiarities, particularly the male parental care over the offspring. The solution of the dynamical systems indicates three possible equilibrium points for the population. The first corresponds to extinction; the third corresponds to a stable population close to the environmental carrying capacity. The second corresponds to an unstable equilibrium located between extinction and full use of the carrying capacity. It is shown that lack of males’ parental care closes the gap between the point corresponding to the unstable equilibrium and the point of stable non-trivial equilibrium. If guarding failure reaches a critical point the two points coincide and the population tends irreversibly to extinction. If some event tends to destabilize the population equilibrium, as for instance inadequate parental care, the model responds in such a way as to restore the trajectory towards the stable equilibrium point avoiding the route to extinction. The parameters introduced to solve the system of equations are partially derived from limited but reliable field data collected at the Mamirauá Sustainable Development Reserve (MSDR) in the Brazilian Amazonian Region.

Numerical modeling and assessment of the thermal environment in an industrial premise of automotive components

Dissertação de mestrado em Engenharia Industrial

Influence of the hip joint modeling approaches on the kinematics of human gait

The influence of the hip joint formulation on the kinematic response of the model of human gait is investigated throughout this work. To accomplish this goal, the fundamental issues of the modeling process of a planar hip joint under the framework of multibody systems are revisited. In particular, the formulations for the ideal, dry, and lubricated revolute joints are described and utilized for the interaction of femur head inside acetabulum or the hip bone. In this process, the main kinematic and dynamic aspects of hip joints are analyzed. In a simple manner, the forces that are generated during human gait, for both dry and lubricated hip joint models, are computed in terms of the system’s state variables and subsequently introduced into the dynamics equations of motion of the multibody system as external generalized forces. Moreover, a human multibody model is considered, which incorporates the different approaches for the hip articulation, namely ideal joint, dry, and lubricated models. Finally, several computational simulations based on different approaches are performed, and the main results presented and compared to identify differences among the methodologies and procedures adopted in this work. The input conditions to the models correspond to the experimental data capture from an adult male during normal gait. In general, the obtained results in terms of positions do not differ significantly when the different hip joint models are considered. In sharp contrast, the velocity and acceleration plotted vary significantly. The effect of the hip joint modeling approach is clearly measurable and visible in terms of peaks and oscillations of the velocities and accelerations. In general, with the dry hip model, intra-joint force peaks can be observed, which can be associated with the multiple impacts between the femur head and the cup. In turn, when the lubricant is present, the system’s response tends to be smoother due to the damping effects of the synovial fluid.

A integração de técnicas BIM (Building Information Modeling) no projeto e na construção de estruturas de madeira

Dissertação de mestrado integrado em Engenharia Civil

A integração do Building Information Modeling (BIM) num projeto de reabilitação

Dissertação de mestrado integrado em Engenharia Civil