An atomistic investigation of nanometric cutting process using a multi-tip single crystal diamond tool

In recent years great efforts are being made for the design and fabrication of periodic nanostructures used in emerging nano-products, such as plasmonic lens, nano-grating and high density hard disk etc. In our previous research work, a deterministic fabrication approach to cost-effectively manufacturing nano gratings over large area has been developed through single point diamond turning by using a multi-tip nano-scale single crystal diamond tool fabricated by FIB (Focus Ion Beam). However, the machining mechanism and technical limits of this approach i.e. the minimum dimension of nanostructures that can be obtained has not known yet. Due to the limitation of real-time detect equipment as well as the high research cost, it is difficult to obtain a quick answer through experimental work. On the other hand molecular dynamics (MD) simulation provides a cost-effective solution for this problem. Based on the merit offered by the large-scale molecular dynamics simulation method and new progresses made in high performance computing (HPC) technique, this paper proposes a new MD model for nanometric cutting process using a multi-tip single crystal diamond (SCD) tools to machine single crystal copper workpieces. By using centrosymmetry parameter (CSP) method and combining it with the dislocation nucleation and propagation theory, the machining mechanism and generation of nanostructures are studied through MD simulation. In order to reveal the dependence of the depth of cut on the integrality of generated nanostructures, a number of MD simulations have been carried out under depth of cut varying from 0.5, 1.0, 1.5, 2.0, and 3.0nm. The simulation results show that the depth of cut has significant influence on the integrality of the machined nanostructured surfaces and cutting force. A concept of maximum depth of cut to obtain high precision nanostructured surfaces in a single cutting pass is proposed based on analysis of the dimensional accuracy of the integrality machined nanostructures. In all simulations the cutting forces fluctuate around a constant value after chip formation

Multi-consensus Decentralized Accelerated Gradient Descent

This paper considers the decentralized optimization problem, which has applications in large scale machine learning, sensor networks, and control theory. We propose a novel algorithm that can achieve near optimal communication complexity, matching the known lower bound up to a logarithmic factor of the condition number of the problem. Our theoretical results give affirmative answers to the open problem on whether there exists an algorithm that can achieve a communication complexity (nearly) matching the lower bound depending on the global condition number instead of the local one. Moreover, the proposed algorithm achieves the optimal computation complexity matching the lower bound up to universal constants. Furthermore, to achieve a linear convergence rate, our algorithm \emph{doesn't} require the individual functions to be (strongly) convex. Our method relies on a novel combination of known techniques including Nesterov's accelerated gradient descent, multi-consensus and gradient-tracking. The analysis is new, and may be applied to other related problems. Empirical studies demonstrate the effectiveness of our method for machine learning applications

Single machine scheduling with job-dependent machine deterioration

We consider the single machine scheduling problem with job-dependent machine deterioration. In the problem, we are given a single machine with an initial non-negative maintenance level, and a set of jobs each with a non-preemptive processing time and a machine deterioration. Such a machine deterioration quantifies the decrement in the machine maintenance level after processing the job. To avoid machine breakdown, one should guarantee a non-negative maintenance level at any time point; and whenever necessary, a maintenance activity must be allocated for restoring the machine maintenance level. The goal of the problem is to schedule the jobs and the maintenance activities such that the total completion time of jobs is minimized. There are two variants of maintenance activities: in the partial maintenance case each activity can be allocated to increase the machine maintenance level to any level not exceeding the maximum; in the full maintenance case every activity must be allocated to increase the machine maintenance level to the maximum. In a recent work, the problem in the full maintenance case has been proven NP-hard; several special cases of the problem in the partial maintenance case were shown solvable in polynomial time, but the complexity of the general problem is left open. In this paper we first prove that the problem in the partial maintenance case is NP-hard, thus settling the open problem; we then design a $2$-approximation algorithm.Comment: 15 page

Investigation of a scale-up manufacturing approach for nanostructures by using a nanoscale multi-tip diamond tool

Increasing interest in commercializing functional nanostructured devices heightens the need for cost-effective manufacturing approaches for nanostructures. This paper presents an investigation of a scale-up manufacturing approach for nanostructures through diamond turning using a nanoscale multi-tip diamond tool (four tip tool with tip width of 150 nm) fabricated by focused ion beam (FIB). The manufacturing capacity of this new technique is evaluated through a series of cutting trials on copper substrates under different cutting conditions (depth of cut 100–500 nm, spindle speed 12–120 rpm). The machined surface roughness and nanostructure patterns are measured by using a white light interferometer and a scanning electron microscope, respectively. Results show that the form accuracy and integrity of the machined nanostructures were degraded with the increase of the depth of cut and the cutting speed. The burr and the structure damage are two major machining defects. High precision nano-grooves (form error of bottom width < 6.7 %) was achieved when a small depth of cut of 100 nm was used (spindle speed = 12 rpm). Initial tool wear was found at both the clearance cutting edge and the side edges of tool tips after a cutting distance of 2.5 km. Moreover, the nanometric cutting process was emulated by molecular dynamic (MD) simulations. The research findings obtained from MD simulation reveal the underlying mechanism for machining defects and the initialization of tool wear observed in experiments