(Saturday, 4/7/2018)
Room: Foyer
Purpose: Mapping the magnetic force-equivalent vector field from measurements made in a 3D space using a gaussmeter. This method can be implemented for use in delivery of superparamagnetic iron oxide nanoparticles (SPION), providing precision targeting of nanomedicine; as well as potential secondary applications in mapping force field lines in MRI rooms.
Methods: We demonstrate computation of the force equivalent vector field by applying a simplified Maxwell stress tensor to a 3D magnetic field space (setting electric fields to zero). From the generalized force equation of a purely magnetic field, we apply the tensor and compute the forward derivative to arrive at the equivalent force. We use a next-next nearest neighbor (NNNN) method to compute the gradient from one point in space to its 8 N-N nearest neighbors. This method increases computational efficiency and allows multidirectional computation of the derivative by comparing the change in magnetic field across all directions. Demonstration of the method is performed by constructing a simulated magnetic field in a 3D space and applying the calculations to the sample field.
Results: For a sample 5x5x5 magnetic field that grows isotropically, the 8 NNNN force equivalent field is found and plotted with magnitude and direction. The calculation produced appropriate results with equivalent force vectors increasing in directions with increasing gradients.
Conclusion: This work provides the underlying work for computing force fields in any space where the step size between measurements is known, and can be generalized to any arbitrary time-invariant electromagnetic fields. While the work here demonstrates this method applied to a full 3D field, the input fields can be 1D or 2D, and the outputs can be manipulated to show field planes along the full 3D space.
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