Thermal and Laser Properties of Nd:YVO4 Crystal

Nd:YVO₄ crystal has been grown by Czochralski method. The data of thermal expansion and specific heat have been measured. The thermal expansion coefficients along a- and c-axis are a₁ = 2.2 x 10^-6 /K, and a₃ = 8.4 x 10^-6 /K respectively. The specific heat is 24.6 cal/mol x K at 330 K. The large anisotropy along c- and a-axis of thermal expansion coefficients is explained by the structure of YVO₄ crystal. 921 mW output laser at 1.06 mikrom has been obtained with a 3 mm x 3 mm x 1mm crystal sample when pumped by 1840 mW cw laser diode, and the slope efficiency is 55.5%.     

NMR imaging as a new tool for rheology

Examples of NMR imaging used to study the evolution of microstructure and flow velocities in sheared, highly filled suspensions are described. Fast NMR imaging methods were used to freeze the motion in a falling-ball experiment, allowing us to monitor the local concentrations of suspended particles and ball position during the course of the experiment The migration of particles induced by shear and concentration gradients was followed in a Couette cell. Flow imaging methods were developed and applied to a Newtonian fluid and a non-Newtonian suspension flowing in an axisymmetric pipe contraction.     

Data-driven linear complexity low-rank approximation of general kernel matrices: A geometric approach

A general, rectangular kernel matrix may be defined as $K_{ij}=\kappa (x_i,y_j)$ where $\kappa (x,y)$ is a kernel function and where $X={\{x_i\}}_{i=1}^m$ and $Y={\{y_i\}}_{i=1}^n$ are two sets of points. In this paper, we seek a low-rank approximation to a kernel matrix where the sets of points $X$ and $Y$ are large and are arbitrarily distributed, such as away from each other, “intermingled”, identical, and so forth. Such rectangular kernel matrices may arise, for example, in Gaussian process regression where $X$ corresponds to the training data and $Y$ corresponds to the test data. In this case, the points are often high-dimensional. Since the point sets are large, we must exploit the fact that the matrix arises from a kernel function, and avoid forming the matrix, and thus ruling out most algebraic techniques. In particular, we seek methods that can scale linearly or nearly linearly with respect to the size of data for a fixed approximation rank. The main idea in this paper is to geometrically select appropriate subsets of points to construct a low rank approximation. An analysis in this paper guides how this selection should be performed.