The thermo-electric effect of magnetite and the mechanism of geo-electric abnormalities during earthquakes

The thermo-electric coefficients of twenty-six magnetite samples, formed either by magmatism or metamorphism, were tested by the thermo-electric instrument BHET -06. Results showed that the coef- ficient is of a constant value of about -0.05 mV/℃. It is emphasized that because every magnetite grain was tested randomly, the coefficient is independent of the crystallographic direction. This fact means the thermal voltage generated from a single magnetite crystal can be accumulated, and as a result a new thermo-electric field can arise when a gradient thermal field exists and is active within the earth＇s crust. Because magnetite is widespread in the earth＇s crust （generally appearing more in the middle-lower crust）, there is more-thanrandom probability that the additional thermo-electric field can be generated when certain thermal conditions are fulfilled. We, therefore, used the thermo-electric effect of magnetite to study the mechanism responsible for the presence of abnormal geo-electric fields during earthquake formation and occurrence, because gradient thermal fields always exist before earthquakes. The possible presence of additional thermo-electric fields was calculated under theoretical seismological conditions, using the following calculation formula：E= - 0.159（σ×△T×Ф×ρ2×[[（h^2 - 2x^2）cos α ＋ 3hxsin α]/ρ1 （h^2 ＋x^2）^5/2）. In the above formula, σ is thermo-electric coefficient of magnetite, △T is the temperature difference acting on it, Ф is a sectional area on a block of magnetite vertically perpendicular to the direction of the thermal current, ρ1 and ρ2 are the respective resistivities of magnetite and the crust, and h, α, and x, respectively, h is the depth of embedded magnetite block. α means the angle created by the horizontal line and ligature of the two poles of magnetite block, and x is the distance from observation point to projective center point of the magnetite block on earth surface. According to simulations calculated with this formula, additional thermo-electric field intensity may reach as high as n to n × 10^2 mV/km. This field is strong enough to cause obvious anomalies in the background geo-electric field, and can be easy probed by earthquake monitoring equipment. Therefore, we hypothesize that geo-electric abnormalities which occur during earthquakes may be caused by the thermo-electric effect of magnetite.

Thermo-Electric Motions and Structures Generated by Static Magnetic Fields During the Solidification of Metallic Alloys

Thermo-electric currents in the presence of static magnetic fields generate significant electromagnetic forces(TEM forces).The thermo-electric currents are due to the Seebeck effect when temperature gradients exist in the material. Those forces may produce various phenomena like pumping,stirring in liquid metals as well as solid motions,stresses in the solid metal.Those effects may be encountered especially during the solidification of metallic materials because of the existence of significant temperature gradients.In liquid metals the application of a static magnetic field enhances TEM convection at moderate intensity but also damps it when it is strong enough.This means that there exists a maximum of the convection which occurs when the Hartmann layers are comparable to the considered length scale.However,the smaller the length scales are(for example when primary or secondary dendrite arm spacings are considered),the higher the magnetic field strength which is needed to damp the TEM convection.So far,many solidification experiments on various types of alloys(e.g.,Sn-Pb,Al-Cu,Al-Si,Al-Ni etc.)have been carried out.The experiments have shown that TEM convection occurs both in the liquid bulk but also in the deep mushy zone.TEM convection may strongly influence the meso-macrosegregation patterns,the solidification structures and the grain boundaries leading to the striking grain boundary structure of the mushy zone.The flow pattern and accordingly the segregations may be controlled by changing the orientation of the applied magnetic field,i.e.,axial or transverse.We have shown that very high magnetic field strengths,up to 16 T,are needed to damp the TEM convection.Heuristic numerical and analytical investigations show that the TEM force density is very important in the liquid,but can be even more important in the solid.Indeed,for high Hartmann number,the electric currents are confined in a small skin layer near the solid boundaries leading to a decay of the flow.However,the situation is different in the solid,since the force is still important and is not confined.This is confirmed experimentally,since the solidified structures are subject to a much greater rate of dislocations and twinning effects.Furthermore,the TEM forces on the solid promote the appearance of direct Columnar-to-Equiaxed Transitions thanks to the possible enhanced fragmentation of the dendrites.Such mechanisms have been recently partly observed by X-ray in situ observations,where channel formation effects as well as detachment of grains along with horizontal motions were observed.

Modelling Thermo-Electro-Mechanical Effects in Orthotropic Cardiac Tissue

In this paper we introduce a new mathematical model for the active contraction of cardiac muscle,featuring different thermo-electric and nonlinear conductivity properties.The passive hyperelastic response of the tissue is described by an orthotropic exponential model,whereas the ionic activity dictates active contraction in-corporated through the concept of orthotropic active strain.We use a fully incompressible formulation,and the generated strain modifies directly the conductivity mechanisms in the medium through the pull-back transformation.We also investigate the influence of thermo-electric effects in the onset of multiphysics emergent spatiotem-poral dynamics,using nonlinear diffusion.It turns out that these ingredients have a key role in reproducing pathological chaotic dynamics such as ventricular fibrillation during inflammatory events,for instance.The specific structure of the governing equations suggests to cast the problem in mixed-primal form and we write it in terms of Kirchhoff stress,displacements,solid pressure,dimensionless electric potential,activation generation,and ionic variables.We also advance a new mixed-primal finite element method for its numerical approximation,and we use it to explore the properties of the model and to assess the importance of coupling terms,by means of a few computational experiments in 3D.