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By applying the locally optimal rotation method to deal with the lowest eigenvalue of a Hessian matrix, we have efficiently incorporated the hyperdynamics method into the ab initio scheme. In the present method, we only need to calculate the first derivative of the potential and several more force calls in each molecular dynamics (MD) step, which makes hyperdynamics simulation applicable in ab initio MD simulations. With this implementation, we are able to simulate defect diffusion in silicon with boost factors up to 105. We utilized both direct MD and the hyperdynamics method to investigate diffusion of lithium atoms and silicon vacancies in silicon. We identified the complex diffusion process. The obtained diffusion coefficients of Li atoms and Si vacancies are in good agreement with the direct MD results. [ABSTRACT FROM AUTHOR]

Transition states are fundamental to understanding the reaction dynamics qualitatively in chemical physics. To date various methods of first principle location of the transition states have been developed. In the absence of the knowledge of the final structure, the softest-mode following method climbs up to a transition state without calculating the Hessian matrix. One weakness of this kind of approaches is that the number of rotations to determine the softest mode is usually unpredictable. In this paper, we propose a locally optimal search direction finding algorithm, namely LOR, which is an extension of the traditional conjugate gradient method without additional calculations of the forces. We also show that the translation of forces improves the numerical stability. Experiments for the Baker test system show that the proposed algorithm is much faster than the original dimer conjugate gradient method. [ABSTRACT FROM AUTHOR]

The rotational accuracy of a machine tool spindle has critical influence upon the geometric shape and surface roughness of finished workpiece. The rotational performance of the rolling element bearings is a main factor which affects the spindle accuracy, especially in the ultra-precision machining. In this paper, a new method is developed to measure the rotational accuracy of rolling element bearings of machine tool spindles. Variable and measurable axial preload is applied to seat the rolling elements in the bearing races, which is used to simulate the operating conditions. A high-precision (radial error is less than 300 nm) and high-stiffness (radial stiffness is 600 N/μm) hydrostatic reference spindle is adopted to rotate the inner race of the test bearing. To prevent the outer race from rotating, a 2-degrees of freedom flexure hinge mechanism (2-DOF FHM) is designed. Correction factors by using stiffness analysis are adopted to eliminate the influences of 2-DOF FHM in the radial direction. Two capacitive displacement sensors with nano-resolution (the highest resolution is 9 nm) are used to measure the radial error motion of the rolling element bearing, without separating the profile error as the traditional rotational accuracy metrology of the spindle. Finally, experimental measurements are performed at different spindle speeds (100-4000 rpm) and axial preloads (75-780 N). Synchronous and asynchronous error motion values are evaluated to demonstrate the feasibility and repeatability of the developed method and instrument.