Efficient QR Decomposition Using Low Complexity Column-wise Givens Rotation (CGR)

QR decomposition (QRD) is a widely used Numerical Linear Algebra (NLA) kernel with applications ranging from SONAR beamforming to wireless MIMO receivers. In this paper, we propose a novel Givens Rotation (GR) based QRD (GR QRD) where we reduce the computational complexity of GR and exploit higher degree of parallelism. This low complexity Column-wise GR (CGR) can annihilate multiple elements of a column of a matrix simultaneously. The algorithm is first realized on a Two-Dimensional (2 D) systolic array and then implemented on REDEFINE which is a Coarse Grained run-time Reconfigurable Architecture (CGRA). We benchmark the proposed implementation against state-of-the-art implementations to report better throughput, convergence and scalability.

Partial rotation of the isopropyl group in the solid state: single-crystal-to-single-crystal phase transformation in a carvacrol derivative

A hitherto unseen rotation of the isopropyl group in the solid state, predicted to be forbidden based on theoretical investigations, is reported. This C-C rotation observed during the temperature dependent single-crystal-to-single-crystal transformation is attributed to the concomitant changes in molecular structure and intermolecular packing.

Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container

In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subjec

Rotation Numbers Of Invariant Manifolds Around Unstable Periodic Orbits For The Diamagnetic Kepler Problem

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic orbits in a phase space are taken as an object of comparison. The rotation numbers are determined from the definition and connected with symbolic sequences encoding the periodic orbits in a reduced Poincare section. Only symbolic codes with inverse ordering in the forward mapping can contribute to the rotation of invariant manifolds around the periodic orbits. By using symbolic ordering, the reduced Poincare section is constricted along stable manifolds and a topological template, which preserves the ordering of forward sequences and can be used to extract the rotation numbers, is established. The rotation numbers computed from the topological template are the same as those computed from their original definition.

Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.

Adiabatic compression of plasma with purely toroidal rotation

A variational method is developed to find approximate solutions to the generalized Grad-Shafranov equations for an adiabatic compression of the plasma with toroidal rotation, via the expansion in Fourier series in poloidal angle of the flux surface coordinates. The numerical results, which are carried out by the present method and by the usual two-dimensional method for a static equilibrium state, agree well.

Variational method for adiabatic compression of plasma with poloidal and toroidal rotation

A variational method is developed for adiabatic compression of plasma with both poloidal and toroidal rotation.

参数激励圆柱形容器中的非线性Faraday波

在柱坐标系下，通过奇异摄动理论的多尺度展开法求解势流方程，研究了垂直强迫激励圆柱形容器中的单一模式水表面驻波模式．假设流体是无粘、不可压且运动是无旋的，在忽略了表面张力的影响下，用两变量时间展开法得到一个具有立方项以及底部驱动项影响的非线性振幅方程．对上述方程进行了数值计算，计算的结果显示了在不同驱动振幅和驱动频率下，会激发不同自由水表面驻波模式，从等高线的图像来看，和以往的实验结果相当吻合．