We report our experimental finding that there exists an oscillation of magnetic anisotropy with varying Cr sublayer thickness along the direction normal to the easy axis in Fe/Cr/Fe trilayers, where the easy axis is induced along a certain direction in the film plane by applying an external field during film deposition. Interestingly enough, the squareness of the hysteresis loop measured along ...

We consider strips of Ising spins at criticality. For strips of width N sites, subdominant (additive) finite-size corrections to scaling are assumed to be of the form a(k)/N(k) for the free energy, and b(k)/N(k) for inverse correlation length, with integer values of k. We investigate the set {a(k),b(k)} (k≥2) by exact evaluation and numerical transfer-matrix diagonalization techniques, and thei...

The evolution of strain and development of material anisotropy in models of Earth’s mantle flow convey important information about how to interpret the geometric relationship between observation of seismic anisotropy and the actual mantle flow field. By combining feature extraction techniques such as path line integration and tensor accumulation, we compute time-varying strain vector fields tha...

We study the (analytic) finite-size corrections in the Ising model on the strip with free, fixed (++), and mixed boundary conditions. For fixed (++) boundary conditions, the spins are fixed to the same values on two sides of the strip. We find that subdominant finite-size corrections to scaling should be to the form a(p)/N(2p-1) for the free energy f(N) and b(p)/N(2p-1) for inverse correlation ...

This paper provides a converse Liapunov theorem for uniformly locally exponentially stable, locally Lipschitz, non-linear, time-varying, possibly non-smooth systems that admit Carathéodory solutions. The main result proves that a critical point of such a system is uniformly locally exponentially stable if and only if the system admits a local (possibly non-smooth, timevarying) Liapunov function.

This paper details the derivation of rotationally invariant scalar measures from higher-rank diffusion tensors (DTs) and functions defined on a unit sphere. This was accomplished with the use of an expression that generalizes the evaluation of the trace operator to tensors of arbitrary rank, and even to functions whose domains are the unit sphere. It is shown that the mean diffusivity is invari...

Cerebral cortical development involves complex changes in cellular architecture and connectivity that occur at regionally varying rates. Using diffusion tensor magnetic resonance imaging (DTI) to analyze cortical microstructure, previous studies have shown that cortical maturation is associated with a progressive decline in water diffusion anisotropy. We applied high-resolution DTI to fixed pos...

Shear-wave splitting (SWS) analyses are essential in understanding the structure and dynamics of the Earth’s deep interior. While splitting measurements have excellent horizontal resolution relative to other anisotropy-measuring techniques, their vertical resolution is low due to the steep incidence angle of the seismic phases used by the analyses. Here, using synthetic and real data, we presen...

White matter microstructure and volume show synchronous developmental patterns in children. White matter volume increases considerably during development. Fractional anisotropy, a measure for white matter microstructural directionality, also increases with age. Development of white matter volume and development of white matter microstructure seem to go hand in hand. The extent to which the same...