A high velocity accessory for friction force microscopy measurements for velocities up to the mm/s range was developed for a commercial stand-alone atomic force microscope (AFM). The accessory consists of a shear piezo element, which rapidly displaces the sample in the lateral direction, perpendicular to the main axis of the AFM cantilever. Friction forces, which are acquired via conventional optical beam deflection detection, can thus be measured as a function of velocity and load in controlled environment (0–40% relative humidity and 0–40°C). Using the accessory, a broad range of velocities up to several mm/s can be accessed independent of the lateral scan size up to a maximum scan size of 1000nm. The velocity dependence of friction forces and coefficients was measured on organic [poly(methylmethacrylate)], as well as inorganic [oxidized Si(100)] samples to demonstrate the feasibility and underline the importance of high velocity nanotribology using this accessory.
In this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. Potential problems related to the generalization of transmission-line equations with the use of FO derivatives are presented. It is demonstrated that some formulations of FO derivatives have limited applicability in the circuit theory. Out of the most popular approaches considered in this paper, only the Grünwald–Letnikov and Marchaud definitions (which are actually equivalent) satisfy the semigroup property and are naturally representable in the phasor domain. The generalization of this concept, i.e., the two-sided fractional Ortigueira–Machado derivative, satisfies the semigroup property, but its phasor representation is less natural. Other ideas (including the Riemann–Liouville and Caputo derivatives—with a finite or an infinite base point) seem to have limited applicability.
Abstract-This paper presents an implementation of the FDTDcompatible Green's function on a heterogeneous parallel processing system.The developed implementation simultaneously utilizes computational power of the central processing unit (CPU) and the graphics processing unit (GPU) to the computational tasks best suited for each architecture. Recently, closed-form expression for this discrete Green's function (DGF) was derived, which facilitates its applications in the FDTD simulations of radiation and scattering problems. Unfortunately, implementation of the new DGF formula in software requires a multiple precision arithmetic and may cause long runtimes. Therefore, an acceleration of the DGF computations on a CPU-GPU heterogeneous parallel processing system was developed using the multiple precision arithmetic and the OpenMP and CUDA parallel programming interfaces. The method avoids drawbacks of the CPUand GPU-only accelerated implementations of the DGF, i.e., long runtime on the CPU and significant overhead of the GPU initialization respectively for long and short length of the DGF waveform. As a result, the sevenfold speedup was obtained relative to the reference DGF implementation on a multicore CPU thus applicability of the DGF in FDTD simulations was significantly improved.
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