Multiphysics and Thermodynamic Formulations for Equilibrium and Non-equilibrium Interactions: Non-linear Finite Elements Applied to Multi-coupled Active Materials

[EN] Combining several theories this paper presents a general multiphysics framework applied to the study of coupled and active materials, considering mechanical, electric, magnetic and thermal fields. The framework is based on thermodynamic equilibrium and non-equilibrium interactions, both linked by a two-temperature model. The multi-coupled governing equations are obtained from energy, momentum and entropy balances; the total energy is the sum of thermal, mechanical and electromagnetic parts. The momentum balance considers mechanical plus electromagnetic balances; for the latter the Abraham rep- resentation using the Maxwell stress tensor is formulated. This tensor is manipulated to automatically fulfill the angular momentum balance. The entropy balance is for- mulated using the classical Gibbs equation for equilibrium interactions and non-equilibrium thermodynamics. For the non-linear finite element formulations, this equation requires the transformation of thermoelectric coupling and conductivities into tensorial form. The two-way thermoe- lastic Biot term introduces damping: thermomechanical, pyromagnetic and pyroelectric converse electromagnetic dynamic interactions. Ponderomotrix and electromagnetic forces are also considered. The governing equations are converted into a variational formulation with the resulting four-field, multi-coupled formalism implemented and val- idated with two custom-made finite elements in the research code FEAP. Standard first-order isoparametric eight-node elements with seven degrees of freedom (dof) per node (three displacements, voltage and magnetic scalar potentials plus two temperatures) are used. Non-linearities and dynamics are solved with Newton-Raphson and New- mark-b algorithms, respectively. Results of thermoelectric, thermoelastic, thermomagnetic, piezoelectric, piezomag- netic, pyroelectric, pyromagnetic and galvanomagnetic interactions are presented, including non-linear depen- dency on temperature and some second-order interactions.This research was partially supported by grants CSD2008-00037 Canfranc Underground Physics, Polytechnic University of Valencia under programs PAID 02-11-1828 and 05-10-2674. The first author used the grant Generalitat Valenciana BEST/2014/232 for the completion of this work.Pérez-Aparicio, JL.; Palma, R.; Taylor, R. (2016). Multiphysics and Thermodynamic Formulations for Equilibrium and Non-equilibrium Interactions: Non-linear Finite Elements Applied to Multi-coupled Active Materials. Archives of Computational Methods in Engineering. 23:535-583. https://doi.org/10.1007/s11831-015-9149-9S53558323Abraham M (1910) Sull’elettrodinamica di Minkowski. 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Candidate Gene Screen in the Red Flour Beetle Tribolium Reveals Six3 as Ancient Regulator of Anterior Median Head and Central Complex Development

Several highly conserved genes play a role in anterior neural plate patterning of vertebrates and in head and brain patterning of insects. However, head involution in Drosophila has impeded a systematic identification of genes required for insect head formation. Therefore, we use the red flour beetle Tribolium castaneum in order to comprehensively test the function of orthologs of vertebrate neural plate patterning genes for a function in insect head development. RNAi analysis reveals that most of these genes are indeed required for insect head capsule patterning, and we also identified several genes that had not been implicated in this process before. Furthermore, we show that Tc-six3/optix acts upstream of Tc-wingless, Tc-orthodenticle1, and Tc-eyeless to control anterior median development. Finally, we demonstrate that Tc-six3/optix is the first gene known to be required for the embryonic formation of the central complex, a midline-spanning brain part connected to the neuroendocrine pars intercerebralis. These functions are very likely conserved among bilaterians since vertebrate six3 is required for neuroendocrine and median brain development with certain mutations leading to holoprosencephaly