Ac dc module

To characterize the electric field distribution in aluminum foils at the initial stage of anodization, we exploited the ACDC module (simple resistor) from COMSOL Multiphysics (5.1 version) for simulation. The geometrical features of surface-patterned aluminum foils exploited in simulation were set according to the experimental observation. Quadruple and sextuple unit cells with periodic boundary conditions were exploited for calculation, corresponding to the experimental nanoconcaves of tetragonal and hexagonal arrangements, respectively. A voltage difference was applied between the top surface and bottom of the aluminum foil to simulate the external AV.

The fingerprint sensing signals, i.e., the mutual capacitance and capacitance difference values at the sensing nodes, for different sensor patterns were calculated by using the electrostatic modeling capabilities of COMSOL’s AC/DC module. The fingerprint sensor was modeled with a 24 × 44 electrode array, including an active region consisting of a 12 Tx × 32 Rx electrode array and six grounded dummy electrodes on the borders of each side of the active region. A fingerprint template with a constant pitch was included in the model. The mutual capacitance between the Tx and Rx electrodes at each node in the active region was calculated. The materials of each layer in the model and their characteristics are listed in Table 2.Table 2

Thicknesses and dielectric constants of the constituent layers used in the simulation

Layer	Material	Thickness (μm)	Dielectric constant (at 1 MHz, 25 °C)
Ridge	Human tissue	400	50
Valley	Air	59	1
Cover	Schott D263T glass	100	7.7
OCA	3 M CEF series (acrylic)	15	3.65
Insulating/passivation layer	Dongwoo Fine-Chem DNI-LT09	1	3.5
Substrate	Corning Eagle XG glass	700	5.27

Since the wavelength of the electric field in the different layers is much larger than the dimensions of the electrodes, a quasi-static electrical conduction model was applied to solve for the electric field in the saline solution (15 (link), 44 ). The finite element simulation using the 3D AC/DC module of COMSOL Multiphysics was then performed for impedance measurements in the model. After obtaining the solution for the electric potential, boundary integration was used to determine electric current and consequently obtaining the electric impedance. With the AC/DC module of COMSOL it is possible to obtain the solution for the electric impedance at different frequencies. Simulations were repeated for frequencies exponentially distributed from 10 Hz to 1 MHz, to characterize the frequency response and the bioimpe-dance readings were recorded (46 ). The whole process was performed for different models with different number of surface electrodes (28 , 32 (link), 44 and 48 ) as well as different ground and terminal electrode dimensions (r_terminal = 1, 2, 2.5 mm and r_ground = 0.5, 1 mm).
Finally, to find the optimized electrode configuration for the measurement set-up, the contribution of the different parts of the model, especially the venous segment, to the impedance measured between the surface and the ground electrode (total impedance) was computed.

For the magnetostatic problem, the AC/DC Module in COMSOL was used. For the three protocols studied, two geometrically different NdFeB magnets were used (Figure 3). The remanence magnetization value was the same for all magnets, equal to ${\mu }_0 M=1.2$
T, and the vector direction was such in all protocols that the reference plane was yz (Figure 3) and the origin was the center mass point of the magnet. Specifically, the magnetic flux density component vectors for all three protocols were: $${{\rm B}}_x=0 T\hspace{1em}{{\rm B}}_y=0.771 T\hspace{1em}\hspace{1em}{{\rm B}}_z=0.919 T$$
The relative magnetic permeability of the magnets was set to ${\mu }_r=1.05$ . In addition, the equations were solved in an air-filled space, where the relative magnetic permeability was considered equal to 1. The presence of tissues in this space (assumed later) did not change the value of the magnetic permeability, since human tissues do not have magnetic properties.
Magnetic insulation was assumed at the boundaries of the computational domain used for the solution of the magnetostatic problem (the domain was much larger than the nose/nasopharynx model).

The electromagnetic model is based on the COMSOL AC/DC module, and it is based on Maxwell equations, as shown in Equation (4): $\{\begin{array}{c}\nabla \cdot B=0\\ J=\nabla \times H\\ \nabla \times E=-\frac{\partial B}{\partial t}\end{array}$
where B is the magnetic flux density, J is the current density, H is the magnetic field strength, E is the electric field strength, and t represent time.
Figure 3 shows a schematic diagram of the electromagnetic model, which is a two-dimensional axisymmetric graph. Figure 3b is a diagram with mesh generation in simulation, the thickness of the superconducting layer is magnified 10 times to accelerate the simulation. About mesh generation in superconducting layer, 20 grids in z direction and 1 grid in r direction are generated.
In order to simplify the model and speed up the calculation, $B_{\parallel }$ (Equation (2)) is the average of parallel magnetic field in one turn, and $B_{\perp }$ (Equation (2)) is the average of vertical magnetic field in one turn. Differences in current density at different points are ignored for the same turn. The electromagnetic model is used to calculate the I_YBCO and I_shunt when the total current is determined.
The specifications of the SFCL model are shown in Table 1.