scholarly journals Frequency Locking by External Forcing in Systems with Rotational Symmetry

2012 ◽  
Vol 11 (3) ◽  
pp. 771-800 ◽  
Author(s):  
Lutz Recke ◽  
Anatoly Samoilenko ◽  
Viktor Tkachenko ◽  
Serhiy Yanchuk
Keyword(s):  
Rotational Symmetry ◽  
External Forcing ◽  
Frequency Locking

Phase-reduction analysis of periodic thermoacoustic oscillations in a Rijke tube

2021 ◽  
Vol 933 ◽  
Author(s):  
Calum S. Skene ◽  
Kunihiko Taira
Keyword(s):  
Optimal Placement ◽  
External Forcing ◽  
Frequency Locking ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
Phase Dynamics ◽  
Sustained Oscillations ◽  
Phase Reduction ◽  
Efficient Route ◽  
Thermoacoustic Oscillations

Phase-reduction analysis captures the linear phase dynamics with respect to a limit cycle subjected to weak external forcing. We apply this technique to study the phase dynamics of the self-sustained oscillations produced by a Rijke tube undergoing thermoacoustic instability. Through the phase-reduction formulation, we are able to reduce these dynamics to a scalar equation for the phase, which allows us to efficiently determine the synchronisation properties of the system. For the thermoacoustic system, we find the conditions for which $m:n$ frequency locking occurs, which sheds light on the mechanisms behind asynchronous and synchronous quenching. We also reveal the optimal placement of pressure actuators that provide the most efficient route to synchronisation.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

Frequency locking using cascaded fibre Bragg gratings in OFDM systems

1996 ◽  
Vol 32 (12) ◽  
pp. 1120 ◽  
Author(s):  
C.S. Park ◽  
G.Y. Lyu ◽  
D.H. Lee
Keyword(s):  
Bragg Gratings ◽  
Ofdm Systems ◽  
Frequency Locking ◽  
Fibre Bragg Gratings

scholarly journals An 18.8–33.9 GHz, 2.26 mW Current-Reuse Injection-Locked Frequency Divider for Radar Sensor Applications

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2551
Author(s):  
Kwang-Il Oh ◽  
Goo-Han Ko ◽  
Jeong-Geun Kim ◽  
Donghyun Baek
Keyword(s):  
Supply Voltage ◽  
Cmos Technology ◽  
Frequency Divider ◽  
Oxide Semiconductor ◽  
Center Frequency ◽  
Radar Sensor ◽  
Frequency Locking ◽  
Current Reuse ◽  
Sensor Applications ◽  
Locking Range

An 18.8–33.9 GHz, 2.26 mW current-reuse (CR) injection-locked frequency divider (ILFD) for radar sensor applications is presented in this paper. A fourth-order resonator is designed using a transformer with a distributed inductor for wideband operating of the ILFD. The CR core is employed to reduce the power consumption compared to conventional cross-coupled pair ILFDs. The targeted input center frequency is 24 GHz for radar application. The self-oscillated frequency of the proposed CR-ILFD is 14.08 GHz. The input frequency locking range is from 18.8 to 33.8 GHz (57%) at an injection power of 0 dBm without a capacitor bank or varactors. The proposed CR-ILFD consumes 2.26 mW of power from a 1 V supply voltage. The entire die size is 0.75 mm × 0.45 mm. This CR-ILFD is implemented in a 65 nm complementary metal-oxide semiconductor (CMOS) technology.

scholarly journals On Time Scales of Intrinsic Oscillations in the Climate System

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 459
Author(s):  
Anastasios A. Tsonis ◽  
Geli Wang ◽  
Wenxu Lu ◽  
Sergey Kravtsov ◽  
Christopher Essex ◽  
...  
Keyword(s):  
Low Frequency ◽  
Milankovitch Cycles ◽  
Data Sets ◽  
External Forcing ◽  
Natural Oscillations ◽  
Climatic Oscillations ◽  
Slow Feature Analysis ◽  
Limited Length ◽  
Past Data ◽  
Cumulative Evidence

Proxy temperature data records featuring local time series, regional averages from areas all around the globe, as well as global averages, are analyzed using the Slow Feature Analysis (SFA) method. As explained in the paper, SFA is much more effective than the traditional Fourier analysis in identifying slow-varying (low-frequency) signals in data sets of a limited length. We find the existence of a striking gap from ~1000 to about ~20,000 years, which separates intrinsic climatic oscillations with periods ranging from ~ 60 years to ~1000 years, from the longer time-scale periodicities (20,000 yr +) involving external forcing associated with Milankovitch cycles. The absence of natural oscillations with periods within the gap is consistent with cumulative evidence based on past data analyses, as well as with earlier theoretical and modeling studies.

scholarly journals On the Reconstruction of the Center of a Projection by Distances and Incidence Relations

2020 ◽  
Author(s):  
András Pongrácz ◽  
Csaba Vincze
Keyword(s):  
Algebraic Surface ◽  
Basic Problem ◽  
Rotational Symmetry ◽  
Image Plane ◽  
Equivalent Condition ◽  
Central Projection ◽  
Profile Curve ◽  
Reconstruction Process ◽  
Restricted Area ◽  
Photographic Images

AbstractUp to an orientation-preserving symmetry, photographic images are produced by a central projection of a restricted area in the space into the image plane. To obtain reliable information about physical objects and the environment through the process of recording is the basic problem of photogrammetry. We present a reconstruction process based on distances from the center of projection and incidence relations among the points to be projected. For any triplet of collinear points in the space, we construct a surface of revolution containing the center of the projection. It is a generalized conic that can be represented as an algebraic surface. The rotational symmetry allows us to restrict the investigations to the defining polynomial of the profile curve in the image plane. An equivalent condition for the boundedness is given in terms of the input parameters, and it is shown that the defining polynomial of the profile curve is irreducible.

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