Phase noise analysis of a mechanical autonomous impact oscillator with a MEMS resonator

In this paper, phase noise analysis of a mechanical autonomous impact oscillator with a MEMS resonator is performed. Since the circuit considered belongs to the class of hybrid systems, methods based on the variational model for the evaluation of either phase noise or steady state solutions cannot be directly applied. As a matter of fact, the monodromy matrix is not defined at impact events in these systems. By introducing saltation matrices, this limit is overcome and the aforementioned methods are extended. In particular, the unified theory developed by Demir is used to analyze the phase noise after evaluating the asymptotically stable periodic solution of the system by resorting to the shooting method. Numerical results are presented to show how noise sources affect the phase noise performances. © 2011 IEEE.

Periodic window arising in the parameter space of an impact oscillator

In the bi-dimensional parameter space of an impact-pair system, shrimp-shaped periodic windows are embedded in chaotic regions. We show that a weak periodic forcing generates new periodic windows near the unperturbed one with its shape and periodicity. Thus, the new periodic windows are parameter range extensions for which the controlled periodic oscillations substitute the chaotic oscillations. We identify periodic and chaotic attractors by their largest Lyapunov exponents. (C) 2010 Elsevier B.V. All rights reserved.

Design and fabrication of a nonlinear micro impact oscillator

In this paper we describe the design and fabrication of a mechanical autonomous impact oscillator with a MEMS resonator as the frequency control element. The design has been developed with scalability to large 2-D arrays of coupled oscillators in mind. The dynamic behaviour of the impact oscillator was numerically studied and it was found that the geometry nonlinearity has an effect on the static pull-in voltage and equilibrium position. The external driving power can alter the frequency of the impact oscillator. The autonomous nature of the oscillator simplifies the complexity of the drive circuitry and is essential for large 2-D arrays.

Nonlinear dynamics of atomic force microscopy with intermittent contact

When the atomic force microscopy (AFM) in tapping mode is in intermittent contact with a soft substrate, the contact time can be a significant portion of a cycle, resulting in invalidity of the impact oscillator model, where the contact time is assumed to be infinitely small. Furthermore, we demonstrate that the AFM intermittent contact with soft substrate can induce the motion of higher modes in the AFM dynamic response. Traditional ways of modeling AFM (one degree of freedom (DOF) system or single mode analysis) are shown to have serious mistakes when applied to this kind of problem. A more reasonable displacement criterion on contact is proposed, where the contact time is a function of the mechanical properties of AFM and substrate, driving frequencies/amplitude, initial conditions, etc. Multi-modal analysis is presented and mode coupling is also shown. (c) 2006 Published by Elsevier Ltd.

Self-similarities of periodic structures for a discrete model of a two-gene system

We report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps. (C) 2012 Elsevier B.V. All rights reserved.

Dynamic method of stiffness identification in impacting systems for percussive drilling applications

Peer reviewed

Within-Die Gate Delay Variability Measurement using Re-configurable Ring Oscillator

We report a circuit technique to measure the on-chip delay of an individual logic gate (both inverting and non-inverting) in its unmodified form using digitally reconfigurable ring oscillator (RO). Solving a system of linear equations with different configuration setting of the RO gives delay of an individual gate. Experimental results from a test chip in 65nm process node show the feasibility of measuring the delay of an individual inverter to within 1pS accuracy. Delay measurements of different nominally identical inverters in close physical proximity show variations of up to 26% indicating the large impact of local or within-die variations.

Within-Die Gate Delay Variability Measurement Using Reconfigurable Ring Oscillator

We report the design and characterization of a circuit technique to measure the on-chip delay of an individual logic gate (both inverting and noninverting) in its unmodified form. The test circuit comprises of digitally reconfigurable ring oscillator (RO). The gate under test is embedded in each stage of the ring oscillator. A system of linear equations is then formed with different configuration settings of the RO, relating the individual gate delay to the measured period of the RO, whose solution gives the delay of the individual gates. Experimental results from a test chip in 65-nm process node show the feasibility of measuring the delay of an individual inverter to within 1 ps accuracy. Delay measurements of different nominally identicall inverters in close physical proximity show variations of up to 28% indicating the large impact of local variations. As a demonstration of this technique, we have studied delay variation with poly-pitch, length of diffusion (LOD) and different orientations of layout in silicon. The proposed technique is quite suitable for early process characterization, monitoring mature process in manufacturing and correlating model-to-hardware.

Electron impact excitation of Ar XVII

Energies for the lowest 49 levels among the 1s(2) and 1snl (n = 2-5) configurations of Ar XVII have been calculated using the GRASP code of Dyall et al. (1989, Comput. Phys. Comm., 55, 424). Additionally, radiative rates, oscillator strengths, and line strengths are calculated for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels. Furthermore, collision strengths have also been calculated for all the 1176 transitions among the above 49 levels using the Dirac Atomic R-matrix Code (DARC) of Norrington & Grant (2005, Comput. Phys. Commun., in preparation), over a wide energy range up to 580 Ryd. Resonances have been resolved in the threshold region, and effective collision strengths have been obtained over a wide temperature range up to log T-e = 7.2 K. Comparisons are made with the limited results available in the literature, and the accuracy of the data is assessed. Our energy levels are estimated to be accurate to better than 0.1%, whereas results for other parameters are probably accurate to better than 20%.

Electron impact excitation of Fe XIII

Energy levels and radiative rates for transitions among the lowest 97 fine-structure levels belonging to the (1s(2) 2s(2) 2p(6)) 3 s(2) 3p(2), 3s3p(3), 3s(2) 3p3d, 3p(4), 3s3p(2) 3d and 3s(2) 3d(2) configurations of Fe XIII have been calculated using the fully relativistic GRASP code. Additionally, collision strengths for transitions among these levels have been computed using the Dirac Atomic R-matrix Code (DARC) of Norrington & Grant (2004). Radiative rates and oscillator strengths are tabulated for all allowed transitions among the 97 fine-structure levels, while collision strengths are reported for some transitions at a few energies above thresholds. Comparisons are made with the available results, and the accuracy of the data is assessed.

Radiative rates and electron impact excitation rates for H-like Ar XVIII

Aims. In this paper we report on calculations for energy levels, radiative rates, collision strengths, and effective collision strengths for
transitions among the lowest 25 levels of the n ≤ 5 configurations of H-like Ar xviii.
Methods. The general-purpose relativistic atomic structure package (grasp) andDirac atomic R-matrix code (darc) are adopted for
the calculations.
Results. Radiative rates, oscillator strengths, and line strengths are reported for all electric dipole (E1), magnetic dipole (M1), electric
quadrupole (E2), and magnetic quadrupole (M2) transitions among the 25 levels. Furthermore, collision strengths and effective
collision strengths are listed for all 300 transitions among the above 25 levels over a wide energy (temperature) range up to 800 Ryd
(107.4 K).

Electron impact excitation of S-like iron

Energy levels and radiative rates for transitions among the lowest 48 fine-structure levels belonging to the (1s(2) 2s(2) 2p (6)) 3s (2)3p (4) , 3s3p(5), 3s (2)3p (3) 3d and 3p(6) configurations of Fe xi have been calculated using the fully relativistic grasp code. Additionally, collision strengths for transitions among these levels have also been computed using the Dirac Atomic R-matrix Code (darc) of Norrington & Grant. Radiative rates and oscillator strengths are tabulated for all allowed transitions among the 48 fine-structure levels, while collision strengths are reported at three energies above thresholds, i.e. 8, 16 and 24 Ryd for a few representative transitions. Furthermore, excitation rates have been calculated in a wide electron temperature range below 5 x 10(6) K, and the contribution of resonances has been included in the threshold regions. Comparisons are made with the earlier available theoretical and experimental rates, and it is concluded that the experimental rates are overestimated by up to a factor of 2.

Energy levels, radiative rates, and electron impact excitation rates for transitions in OVII

Aims.
In this paper we report calculations for energy levels, radiative rates, and electron impact excitation rates for transitions in O vii.
Methods.
The grasp (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative
rates. For determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code (darc) and the
flexible atomic code (fac) are used.
Results.
Oscillator strengths, radiative rates, and line strengths are reported for all E1, E2, M1, and M2 transitions among the lowest
49 levels of O vii. Collision strengths have been averaged over a Maxwellian velocity distribution, and the resulting effective collision
strengths are reported over a wide temperature range below 2 × 106 K. Additionally, lifetimes are also listed for all levels.
Key words.

Radiative rates and electron impact excitation rates for H-like Fe XXVI

Aims. In this paper we report on calculations for energy levels, radiative rates, collision strengths, and effective collision strengths for transitions among the lowest 25 levels of the n $\le$ 5 configurations of H-like Fe XXVI.
Methods. The general-purpose relativistic atomic structure package (GRASP) and Dirac atomic R-matrix code (DARC) are adopted for the calculations.
Results. Radiative rates, oscillator strengths, and line strengths are reported for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among the 25 levels. Furthermore, collision strengths and effective collision strengths are reported for all the 300 transitions among the above 25 levels over a wide energy (temperature) range up to 1500 Ryd (107.7 K). Comparisons are made with earlier available results and the accuracy of the data is assessed.

Effective collision strengths for electron-impact excitation of S X

Effective collision strengths computed by the R-matrix method are presented for the electron-impact excitation of nitrogen-like S X. The total wave function used in the expansion includes the lowest 11 eigenstates of S X which arise from the 2s(2)2p(3), 2s2p(4), 2p(5) and 2s(2)2p(2)3s configurations. These 11 LS target states correspond to 22 fine-structure levels, giving 231 possible transitions. All the effective collision strengths for these transitions are tabulated in the range log T(K) = 4.6 to log T(K) = 6.7. The energy level values and oscillator strengths for allowed transitions are also tabulated. The effective collision strengths were calculated by averaging the electron collision strengths over a Maxwellian distribution of velocities. The present effective collision strengths are the only results currently available for these fine-structure transition rates. (C) 2000 Academic Press.