Introduction: The limitation of the 2 order diffusion tensor model in the representation of voxels containing more than one dominant fiber direction have led to the development of more advanced representations. Here the focus is especially on higher order diffusion tensor models [1,2]. These more advanced diffusion models require datasets which provide diffusion information for a larger number ...

In this paper, the magnetic properties of carbon based material, graphene is studied, which is generated by laser ablation in cryogenic media. Transmission electron microscopy (TEM) and alternating gradient force magnetometer (AGFM) are applied to investigate the graphene morphology and magnetic properties, respectively. The graphene synthesized by the laser ablation method exhibits diamagnetic...

In diffusion tensor imaging (DTI) an effective diffusion tensor in each voxel is measured by using a set of diffusion-weighted images (DWIs) in which diffusion gradients are applied in a multiplicity of oblique directions. However, to estimate the diffusion tensor accurately, one must account for the effects of all imaging and diffusion gradient pulses on each signal echo, which are embodied in...

This paper proposes a geometric approach for comparing tensor-valued images (tensor fields) that is based on the idea of matching intrinsically low-dimensional shapes embedded in a higher-dimensional ambient space. More specifically, instead of regarding the tensor fields as tensor-valued functions defined on a given (image) domain, we consider their image graphs. These tensorial image graphs c...

We show that the only shrinking gradient solitons with vanishing Weyl tensor are quotients of the standard ones Sn, S × R, and Rn. This gives a new proof of the Hamilton-Ivey-Perel’man classification of 3dimensional shrinking gradient solitons. We also show that gradient solitons with constant scalar curvature and suitably decaying Weyl tensor when noncompact are quotients of Hn, H × R, Rn, S ×...

In this paper we propose a new operator which combines advantages of monogenic scale-space and Gaussian scale-space, of the monogenic signal and the structure tensor. The gradient energy tensor (GET) defined in this paper is based on Gaussian derivatives up to third order using different scales. These filters are commonly available, separable, and have an optimal uncertainty. The response of th...

In boundary element analysis, first order function derivatives, e.g., boundary potential gradient or stress tensor, can be accurately computed by evaluating the hypersingular integral equation for these quantities. However, this approach requires a complete integration over the boundary and is therefore computationally quite expensive. Herein it is shown that this method can be significantly si...

We prove analytic criteria for the existence of finite-time attracting and repelling material surfaces and lines in threedimensional unsteady flows. The longest lived such structures define coherent structures in a Lagrangian sense. Our existence criteria involve the invariants of the velocity gradient tensor along fluid trajectories. An alternative approach to coherent structures is shown to l...

In the permanent magnet linear synchronous motor (PMLSM), force ripple is harmful, useless and disturbing. The force ripple is basically composed of two components: detent force and mutual force ripple. This force is influenced by the geometric parameters of the permanent magnet (PM) motors; such as width, thickness and length of the magnet poles, length and thickness of the rotor and stato...