A comparsion of force sensors for atomic force microscopy based on quartz tuning forks and length extensional resonators

The force sensor is key to the performance of atomic force microscopy (AFM). Nowadays, most AFMs use micro-machined force sensors made from silicon, but piezoelectric quartz sensors are applied at an increasing rate, mainly in vacuum. These self sensing force sensors allow a relatively easy upgrade of a scanning tunneling microscope to a combined scanning tunneling/atomic force microscope. Two fundamentally different types of quartz sensors have achieved atomic resolution: the 'needle sensor' that is based on a length extensional resonator and the 'qPlus sensor' that is based on a tuning fork. Here, we calculate and measure the noise characteristics of these sensors. We find four noise sources: deflection detector noise, thermal noise, oscillator noise and thermal drift noise. We calculate the effect of these noise sources as a factor of sensor stiffness, bandwidth and oscillation amplitude. We find that for self sensing quartz sensors, the deflection detector noise is independent of sensor stiffness, while the remaining three noise sources increase strongly with sensor stiffness. Deflection detector noise increases with bandwidth to the power of 1.5, while thermal noise and oscillator noise are proportional to the square root of the bandwidth. Thermal drift noise, however, is inversely proportional to bandwidth. The first three noise sources are inversely proportional to amplitude while thermal drift noise is independent of the amplitude. Thus, we show that the earlier finding that quoted optimal signal-to-noise ratio for oscillation amplitudes similar to the range of the forces is still correct when considering all four frequency noise contributions. Finally, we suggest how the signal-to-noise ratio of the sensors can be further improved and briefly discuss the challenges of mounting tips.Comment: 40 pages, 14 figure

Hierarchical and Frequency-Aware Model Predictive Control for Bare-Metal Cloud Applications

Bare-metal cloud provides a dedicated set of physical machines (PMs) and enables both PMs and virtual machines (VMs) on the PMs to be scaled in/out dynamically. However, to increase efficiency of the resources and reduce violations of service level agreements (SLAs), resources need to be scaled quickly to adapt to workload changes, which results in high reconfiguration overhead, especially for the PMs. This paper proposes a hierarchical and frequency-aware auto-scaling based on Model Predictive Control, which enable us to achieve an optimal balance between resource efficiency and overhead. Moreover, when performing high-frequency resource control, the proposed technique improves the timing of reconfigurations for the PMs without increasing the number of them, while it increases the reallocations for the VMs to adjust the redundant capacity among the applications; this process improves the resource efficiency. Through trace-based numerical simulations, we demonstrate that when the control frequency is increased to 16 times per hour, the VM insufficiency causing SLA violations is reduced to a minimum of 0.1% per application without increasing the VM pool capacity

Thermally Assisted Penetration and Exclusion of Single Vortex in Mesoscopic Superconductors

A single vortex overcoming the surface barrier in a mesoscopic superconductor with lateral dimensions of several coherence lengths and thickness of several nanometers provides an ideal platform to study thermal activation of a single vortex. In the presence of thermal fluctuations, there is non-zero probability for vortex penetration into or exclusion from the superconductor even when the surface barrier does not vanish. We consider the thermal activation of a single vortex in a mesoscopic superconducting disk of circular shape. To obtain statistics for the penetration and exclusion magnetic fields, slow and periodic magnetic fields are applied to the superconductor. We calculate the distribution of the penetration and exclusion fields from the thermal activation rate. This distribution can also be measured experimentally, which allows for a quantitative comparison.Comment: 7 pages, 4 figure