The van der Pol (VDP) equation is a nonlinear differential equation, and it is also the mathematical model for an audion circuit. It has given much attention by researchers and has been widely used in many fields. In ...
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The van der Pol (VDP) equation is a nonlinear differential equation, and it is also the mathematical model for an audion circuit. It has given much attention by researchers and has been widely used in many fields. In this paper, using the noted Poincare-Bendixson theorem, we propose a new proof of the existence of closed trajectory in the van der Pol oscillator when damping value is positive (/spl mu/>0). By comparison, we find that, our method is natural and simple.
The Department of Energy (DOE) Distributed Power Program (DPP) is conducting work to complete, validate in the field, and support the development of a national interconnection standard for distributed energy resources...
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The Department of Energy (DOE) Distributed Power Program (DPP) is conducting work to complete, validate in the field, and support the development of a national interconnection standard for distributed energy resources (DER), and to address the institutional and regulatory barriers affecting the commercial adoption of DER systems. This work includes support for the IEEE interconnection standard development process, including P1547 Standard for Interconnecting Distributed Resources with Electric Power Systems, P1589 Standard for Conformance Test Procedures for Equipment Interconnecting Distributed Resources with Electric Power Systems, and the P1608 Application Guide. Work is also in progress on system integration research and development (R&D) on the interface and integration of control of DER with local energy systems. Additional efforts are supporting DER's role in providing high-reliability power for industry, evaluating innovative concepts for DER applications, and exploring effective interface and control technologies for intelligent autonomous interconnection systems. This paper summarizes (1) the current status of the IEEE interconnection standards and application guides in support of DER and (2) the R&D in progress at the National Renewable Energy Laboratory (NREL) for interconnection and system integration and application of distributed energy resources.
The design and optimization of a high-speed, low-voltage CMOS flash analog to digital converter (ADC) is presented. The optimization procedures used during the design give the needed specifications of the different bu...
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The design and optimization of a high-speed, low-voltage CMOS flash analog to digital converter (ADC) is presented. The optimization procedures used during the design give the needed specifications of the different building blocks. The used analog power supply is only 1.8V. The maximum sampling speed is 1.3GHz, SNDR@133kHz is 33,2dB. SNDR@500MHz is 32dB. The total power consumption of the converter at full speed is 600µW and the total active area is only 0.13 mm 2 . The ADC is implemented in a 0.25 µm pure digital CMOS technology.
As distributed energy resource (DER) projects grow in popularity, there has been little focus on their potential to influence the dynamic stability of a transmission system. If implemented in large enough numbers, DER...
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As distributed energy resource (DER) projects grow in popularity, there has been little focus on their potential to influence the dynamic stability of a transmission system. If implemented in large enough numbers, DER equipment may feasibly be leveraged to provide ancillary services such as spinning reserve, system inertia, or system stabilization. To determine the potential impacts of DER on future transmission grid stability, dynamic models of DER load combinations were created, reduced in order, and scattered throughout central and southem Califomia within an existing Western Systems Coordinating Council (WSCC) dynamic model. Evaluation of the composite WSCC-DER dynamic model allows correlations to be drawn between various DER properties and the transmission grid stability. Key findings show that increasing DER inertia tends to destabilize the transmission system. The cause of this counterintuitive relationship requires further study but likely is related to the high impedance separating the DER from the transmission grid.
The working principle of nuclear analytical methods (NAMs) is not influenced by the chemical bond. Consequently, they are independent counterparts to the well-known chemical procedures. NAMs obey fundamental laws or c...
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The working principle of nuclear analytical methods (NAMs) is not influenced by the chemical bond. Consequently, they are independent counterparts to the well-known chemical procedures. NAMs obey fundamental laws or can be described and understood thoroughly. This qualifies them as candidates for reference methods. Although following similar nuclear reaction schemes, they comprise bulk analyzing capability (neutron and photon activation analysis) as well as detection power in surface near regions of solids lion beam techniques). Prominent features of NAMs are sensitivity, selectivity, multielement determination and linearity of the calibration function covering a concentration range of several orders of magnitude. Moreover, ion beam techniques allow depth profiling with nm-resolution in several cases while the ion microprobe additionally offers a lateral resolution in the mum-scale. As NAMs require expensive apparatus (nuclear reactor, accelerator in radioactive control areas) their availability is restricted to a small number of suitably equipped institutes. However, they are able to solve complex analytical tasks, take part in key comparisons and play an essential role in the certification of reference materials.
The van der Pol equation [1] corresponds to a non-linear oscillatory system that has both input and output sources of energy. This equation is given by the expression where μ is a non-negative parameter. For the case...
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The van der Pol equation [1] corresponds to a non-linear oscillatory system that has both input and output sources of energy. This equation is given by the expression where μ is a non-negative parameter. For the case where no input in energy exists, equation (1) reduces to This equation can be appropriately called the "unplugged" van der Pol equation and all of its solutions are expected to oscillate with decreasing amplitude to zero. The approach to zero of its solutions can be shown by using an energy argument [2]. Writing equation (2) in system form gives Multiplying the first equation by 2x, the second equation by 2y, and adding yields the result Since the right-hand side of equation (4) is non-positive for all values of x and y, it follows that [2] It is of interest to note that elementary methods of numerical integration, applied to the unplugged van der Pol equation (2), do not give results that are consistent with equation (5). In fact, the use of the forward Euler method leads to a scheme for which the fixed-point (x,y)=(0,0) is always unstable [3]. Thus, the dynamics of the discrete equations are inconsistent with those of the original differential equation (2). The main purpose of this paper is to show that a dynamically consistent finite-difference scheme can be constructed for the unplugged van der Pol equation using the non-standard procedures investigated by Mickens [4,5]. Further, this scheme requires a restriction on the step-size that depends on the initial conditions and the damping parameter μ.
Sea surface temperatures (SST) as derived from the Pathfinder sea surface temperature data set and the Along-Track Scanning Radiometer on-board the European Remote Sensing satellite provide a unique opportunity for co...
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Sea surface temperatures (SST) as derived from the Pathfinder sea surface temperature data set and the Along-Track Scanning Radiometer on-board the European Remote Sensing satellite provide a unique opportunity for comparing two independent SST data sets. Previous comparisons (Vazquez-Cuervo and Sumgaysay, 2001) with the ATSR-l instrument on-board the ERS-1 platform indicated that biases on the order of 1 degree are possible. A significant percentage of this bias appears to be attributable to cloud contamination in either the Pathfinder or ATSR data sets. We continue the comparisons, but with the ATSR-2 data.
For the short-distance and high-speed optical interconnection light source, 850 nm vertical cavity surface emitting lasers (VCSELs) are very attractive. VCSELs are expected to be used with a high frequency modulation ...
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For the short-distance and high-speed optical interconnection light source, 850 nm vertical cavity surface emitting lasers (VCSELs) are very attractive. VCSELs are expected to be used with a high frequency modulation over 10 Gbps. In this study, we fabricated 850 nm oxide confined VCSELs, and measured 10 Gbps operations for both VCSELs confirmed on carrier and TO-can.
This paper investigates a multi-mode oscillations in a four fully-interconnected van der Pol oscillators. In particular, we focus our attention to the asymmetric system where non-resonant double and triple modes, bifu...
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ISBN:
(纸本)0780366859
This paper investigates a multi-mode oscillations in a four fully-interconnected van der Pol oscillators. In particular, we focus our attention to the asymmetric system where non-resonant double and triple modes, bifurcated from a 3-fold degenerate mode, can exist. As a result, we found that a certain non-resonant double mode cannot be synchronized even if its component frequencies are very close.
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