scholarly journals A New Signal Representation Using Complex Conjugate Pair Sums

2019 ◽  
Vol 26 (2) ◽  
pp. 252-256 ◽  
Author(s):  
Basheeruddin Shah Shaik ◽  
Vijay Kumar Chakka ◽  
Arikatla Satyanarayana Reddy
Keyword(s):  
Complex Conjugate ◽  
Signal Representation ◽  
Conjugate Pair ◽  
Complex Conjugate Pair

Nonlinear evolution of the elliptical instability: an example of inertial wave breakdown

1999 ◽  
Vol 396 ◽  
pp. 73-108 ◽  
Author(s):  
D. M. MASON ◽  
R. R. KERSWELL
Keyword(s):  
Finite Amplitude ◽  
Complex Conjugate ◽  
Small Scale ◽  
Conjugate Pair ◽  
Weakly Nonlinear ◽  
Elliptical Instability ◽  
Elliptical Flow ◽  
Complex Conjugate Pair ◽  
Generic Instability ◽  
Secondary Instabilities

A direct numerical simulation is presented of an elliptical instability observed in the laboratory within an elliptically distorted, rapidly rotating, fluid-filled cylinder (Malkus 1989). Generically, the instability manifests itself as the pairwise resonance of two different inertial modes with the underlying elliptical flow. We study in detail the simplest ‘subharmonic’ form of the instability where the waves are a complex conjugate pair and which at weakly supercritical elliptical distortion should ultimately saturate at some finite amplitude (Waleffe 1989; Kerswell 1992). Such states have yet to be experimentally identified since the flow invariably breaks down to small-scale disorder. Evidence is presented here to support the argument that such weakly nonlinear states are never seen because they are either unstable to secondary instabilities at observable amplitudes or neighbouring competitor elliptical instabilities grow to ultimately disrupt them. The former scenario confirms earlier work (Kerswell 1999) which highlights the generic instability of inertial waves even at very small amplitudes. The latter represents a first numerical demonstration of two competing elliptical instabilities co-existing in a bounded system.

On the onset of instability by oscillatory modes in hydromagnetic Couette flow

1967 ◽  
Vol 301 (1467) ◽  
pp. 451-471 ◽  
Keyword(s):  
Couette Flow ◽  
Hartmann Number ◽  
Outer Wall ◽  
Angular Speed ◽  
Complex Conjugate ◽  
Neutral Stability ◽  
Narrow Gap ◽  
Conjugate Pair ◽  
Average Value ◽  
Complex Conjugate Pair

The transition of the onset of instability from stationary modes to oscillatory modes for an incompressible, conducting Couette flow between two coaxial, perfectly conducting, non-permeable, rotating cylinders under the influence of an axially applied magnetic field is considered. Results for three cases are reported. These pertain to flow between (1) a rotating inner wall with a stationary outer wall, (2) counterrotating walls, and (3) corotating walls. It is found that, for high values of the Hartmann number, there may exist some range of convective wavenumbers for which neither of the two lowest modes of axisymmetrical disturbances will become stationary. Within this range, the neutral stability curve is determined by a complex-conjugate pair of oscillatory axisymmetrical modes of equal stability. The oscillatory modes may, in fact, become more critical than the stationary modes. It is demonstrated that the approximation of replacing the angular speed by its average value, combined with the assumption of a narrow gap between the cylindrical walls, eliminates the oscillatory axisymmetrical modes.

Poles and Zeros of a Bandpass Filter Obtained by Transformation of a Lowpass Filter

1979 ◽  
Vol 16 (1) ◽  
pp. 39-41
Author(s):  
S. C. Duttaroy
Keyword(s):  
Bandpass Filter ◽  
Damping Ratio ◽  
Complex Conjugate ◽  
Lowpass Filter ◽  
Transformed Roots ◽  
Conjugate Pair ◽  
Complex Conjugate Pair ◽  
Poles And Zeros ◽  
Explicit Expressions

The standard lowpass to bandpass transformation is shown to transform a complex conjugate pair of roots (poles or zeros) to two such pairs having equal damping ratio. Explicit expressions are given for the locations of the transformed roots; these should be useful in active R.C. bandpass realizations.

scholarly journals On Complex Conjugate Pair Sums and Complex Conjugate Subspaces

2019 ◽  
Vol 26 (9) ◽  
pp. 1403-1407
Author(s):  
Shaik Basheeruddin Shah ◽  
Vijay Kumar Chakka ◽  
Arikatla Satyanarayana Reddy
Keyword(s):  
Complex Conjugate ◽  
Conjugate Pair ◽  
Complex Conjugate Pair

QUARK-GLUON VERTEX AND STRUCTURE OF MESONS AND DIQUARKS

1994 ◽  
Vol 09 (38) ◽  
pp. 3551-3563 ◽  
Author(s):  
S.J. STAINSBY ◽  
R.T. CAHILL
Keyword(s):  
Form Factors ◽  
Quark Propagator ◽  
The Other ◽  
Analytic Structure ◽  
Complex Conjugate ◽  
Branch Points ◽  
Conjugate Pair ◽  
Gluon Vertex ◽  
Scalar Diquark ◽  
Complex Conjugate Pair

Two quark propagators with different analytic structure are employed in Bethe-Salpeter type equations for the pion and scalar diquark form factors. One of the quark propagators has been calculated with the inclusion of a trivial (bare) quark-gluon vertex and, as a consequence, contains a complex conjugate pair of logarithmic branch points. The other quark propagator is obtained using a non-trivial (dressed) vertex ansatz and is entire, with an essential singularity at infinity. The effects of these different quark propagators on the BSE solutions are compared.

scholarly journals Coquaternionic Quantum Dynamics for Two-level Systems

10.14311/1394 ◽  
2011 ◽  
Vol 51 (4) ◽  
Author(s):  
D. C. Brody ◽  
E. M. Graefe
Keyword(s):  
State Space ◽  
Time Evolution ◽  
Quantum Dynamics ◽  
Complex Conjugate ◽  
Conjugate Pair ◽  
Open Orbit ◽  
Energy Eigenvalues ◽  
Complex Conjugate Pair ◽  
Two Level Systems ◽  
Different Characteristics

The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionic quantum theory are investigated. It is shown that the time evolution exhibits three different characteristics, depending on the values of the parameters of the Hamiltonian. When energy eigenvalues are real, the evolution is either isomorphic to that of a complex Hermitian theory on a spherical state space, or else it remains unitary along an open orbit on a hyperbolic state space. When energy eigenvalues form a complex conjugate pair, the orbit of the time evolution closes again even though the state space is hyperbolic.

scholarly journals Simulink and Simelectronics based Position Control of a Coupled Mass-Spring Damper Mechanical System

2018 ◽  
Vol 8 (5) ◽  
pp. 3636
Author(s):  
Oyetola O. K. ◽  
Olaluwoye O. O.
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Position Control ◽  
Lagrange Equation ◽  
Complex Conjugate ◽  
Conjugate Pair ◽  
Modeling And Control ◽  
Position Errors ◽  
Result Analysis ◽  
Mass Spring

This paper presents the use of Simelectronics Program for modeling and control of a two degrees-of freedom coupled mass-spring-damper mechanical system.The aims of this paper are to establish a mathematical model that represents the dynamic behaviour of a coupled mass-spring damper system and effectively control the mass position using both Simulink and Simelectronics.The mathematical model is derived based on the augmented Lagrange equation and to simulate the dynamic accurately a PD controller is implemented to compensate for the oscillation sustained by the system as a result of the complex conjugate pair poles near to the imaginary axis.The input force has been subjected to an obstacle to mimic actual challenges and to validate the mathematical model a Simulink and Simelectronics models were developed, consequently, the results of the models were compared. According to the result analysis, the controller tracked the position errors and stabilized the positions to zero within a settling time of 6.5sec and significantly reduced the overshoot by 99.5% and 99. 7% in Simulink and Simelectronics respectively. Furthermore, it is found that Simelectronics model proved to be capable having advantages of simplicity, less time-intense and requires no mathematical model over the Simulink approach.

On a Fire Fighter’s Problem

2019 ◽  
Vol 30 (02) ◽  
pp. 231-246 ◽  
Author(s):  
Rolf Klein ◽  
Elmar Langetepe ◽  
Barbara Schwarzwald ◽  
Christos Levcopoulos ◽  
Andrzej Lingas
Keyword(s):  
Golden Ratio ◽  
Complex Function ◽  
Logarithmic Spiral ◽  
Fire Fighter ◽  
Cyclic Order ◽  
Complex Conjugate ◽  
Conjugate Pair ◽  
Complex Argument ◽  
Real Functions ◽  
Unit Speed

Suppose that a circular fire spreads in the plane at unit speed. A single fire fighter can build a barrier at speed [Formula: see text]. How large must [Formula: see text] be to ensure that the fire can be contained, and how should the fire fighter proceed? We contribute two results. First, we analyze the natural curve [Formula: see text] that develops when the fighter keeps building, at speed [Formula: see text], a barrier along the boundary of the expanding fire. We prove that the behavior of this spiralling curve is governed by a complex function [Formula: see text], where [Formula: see text] and [Formula: see text] are real functions of [Formula: see text]. For [Formula: see text] all zeroes are complex conjugate pairs. If [Formula: see text] denotes the complex argument of the conjugate pair nearest to the origin then, by residue calculus, the fire fighter needs [Formula: see text] rounds before the fire is contained. As [Formula: see text] decreases towards [Formula: see text] these two zeroes merge into a real one, so that argument [Formula: see text] goes to 0. Thus, curve [Formula: see text] does not contain the fire if the fighter moves at speed [Formula: see text]. (That speed [Formula: see text] is sufficient for containing the fire has been proposed before by Bressan et al. [6], who constructed a sequence of logarithmic spiral segments that stay strictly away from the fire.) Second, we show that for any curve that visits the four coordinate half-axes in cyclic order, and in increasing distances from the origin the fire can not be contained if the speed [Formula: see text] is less than 1.618…, the golden ratio.

Application of Bifurcation Theory to Subsynchronous Resonance in Power Systems

1998 ◽  
Vol 08 (01) ◽  
pp. 157-172 ◽  
Author(s):  
Ali H. Nayfeh ◽  
Ahmad M. Harb ◽  
Char-Ming Chin ◽  
Anan M. A. Hamdan ◽  
Lamine Mili
Keyword(s):  
Hopf Bifurcation ◽  
Power Systems ◽  
Power System ◽  
Limit Cycle ◽  
System Modeling ◽  
Complex Conjugate ◽  
Conjugate Pair ◽  
Subsynchronous Resonance ◽  
Basin Boundary ◽  
Compensation Level

A bifurcation analysis is used to investigate the complex dynamics of a heavily loaded single-machine-infinite-busbar power system modeling the characteristics of the BOARDMAN generator with respect to the rest of the North-Western American Power System. The system has five mechanical and two electrical modes. The results show that, as the compensation level increases, the operating condition loses stability with a complex conjugate pair of eigenvalues of the Jacobian matrix crossing transversely from the left- to the right-half of the complex plane, signifying a Hopf bifurcation. As a result, the power system oscillates subsynchronously with a small limit-cycle attractor. As the compensation level increases, the limit cycle grows and then loses stability in a secondary Hopf bifurcation, resulting in the creation of a two-period quasiperiodic subsynchronous oscillation, a two-torus attractor. On further increases of the compensation level, the quasiperiodic attractor collides with its basin boundary, resulting in the destruction of the attractor and its basin boundary in a bluesky catastrophe. Consequently, there are no bounded motions. The results show that adding damper windings may induce subsynchronous resonance.

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