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

Off-line simulation inspires insight: a neurodynamics approach to efficient robot task learning

There is currently an increasing demand for robots able to acquire the sequential organization of tasks from social learning interactions with ordinary people. Interactive learning-by-demonstration and communication is a promising research topic in current robotics research. However, the efficient acquisition of generalized task representations that allow the robot to adapt to different users and contexts is a major challenge. In this paper, we present a dynamic neural field (DNF) model that is inspired by the hypothesis that the nervous system uses the off-line re-activation of initial memory traces to incrementally incorporate new information into structured knowledge. To achieve this, the model combines fast activation-based learning to robustly represent sequential information from single task demonstrations with slower, weight-based learning during internal simulations to establish longer-term associations between neural populations representing individual subtasks. The efficiency of the learning process is tested in an assembly paradigm in which the humanoid robot ARoS learns to construct a toy vehicle from its parts. User demonstrations with different serial orders together with the correction of initial prediction errors allow the robot to acquire generalized task knowledge about possible serial orders and the longer term dependencies between subgoals in very few social learning interactions. This success is shown in a joint action scenario in which ARoS uses the newly acquired assembly plan to construct the toy together with a human partner.

Quantum field theory approach to the optical conductivity of strained and deformed graphene

The computation of the optical conductivity of strained and deformed graphene is discussed within the framework of quantum field theory in curved spaces. The analytical solutions of the Dirac equation in an arbitrary static background geometry for one dimensional periodic deformations are computed, together with the corresponding Dirac propagator. Analytical expressions are given for the optical conductivity of strained and deformed graphene associated with both intra and interbrand transitions. The special case of small deformations is discussed and the result compared to the prediction of the tight-binding model.

Correction of the initial conditions

"Series title: Springerbriefs in applied sciences and technology, ISSN 2191-530X"

A multi–physics approach applied to masonry structures with non–hydraulic lime mortars

Tese de Doutoramento em Engenharia Civil (área de especialização em Engenharia de Estruturas).