The purpose of this thesis is to explore the methods to solve the tensor completion problem. Inspired by the matrix completion problem, the tensor completion problem is formulated as an unconstrained nonlinear optimization problem, which finds three factors that give a low-rank approximation. Various of iterative methods, including the gradient-based methods, stochastic gradient descent method ...

where E,, E, and If,, H, represent electric and magnetic components measured along two orthogonal axes (in this paper, for simplicity, to be north and east, respectively). The elements ;,, comprise the magnetotelluric impedance tensor, and they are generally complex due to phase differences between the electric and magnetic fields. All quantities in equation (I ) are frequency dependent. For th...

In this paper, the Hartree-Fock method has been formulated to investigate some of the ground state properties of quasi-one-dimensional interacting electron gas in the presence of the magnetic field. The bare coulomb interaction between electrons has been assumed. For this system, we have also computed some of its thermodynamic and magnetic properties such as the energy, pressure, incompressibil...

The dips of boundaries in faults and caldera walls play an important role in understanding their formation mechanisms. The fault dip is a particularly important parameter in numerical simulations for hazard map creation as the fault dip affects estimations of the area of disaster occurrence. In this study, I introduce a technique for estimating the fault dip using the eigenvector of the observe...

A mean-field Fokker-Planck equation approach to the dynamics of ferrofluids in the presence of a magnetic field and velocity gradients is proposed that incorporates magnetic dipole-dipole interactions of the colloidal particles. The model allows to study the combined effect of a magnetic field and dipolar interactions on the viscosity of the ferrofluid. It is found that dipolar interactions lea...

Diffusion tensor magnetic resonance imaging (DTI) is useful for studying the microstructural changes in the spinal cord following traumatic injury; however, image quality is generally poor due to the small size of the spinal cord, physiological motion and susceptibility artifacts. Self-navigated, interleaved, variable-density spiral diffusion tensor imaging (SNAILS-DTI) is a distinctive pulse s...