scholarly journals Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas

2018 ◽  
Vol 84 (4) ◽  
Author(s):  
I. H. Hutchinson
Keyword(s):  
Stability Boundary ◽  
Low Frequency ◽  
Transverse Mode ◽  
Momentum Conservation ◽  
Particle Simulation ◽  
Equilibrium Potential ◽  
Electron Hole ◽  
The Stability ◽  
Particle Force ◽  
Electron Focusing

The stability of an initially one-dimensional electron hole to perturbations varying sinusoidally transverse to its trapping direction is analysed in detail. It is shown that the expected low-frequency eigenmode of the linearized Vlasov–Poisson system consists of a shift mode, proportional to the gradient of the equilibrium potential. The resulting dispersion relation is that the total jetting force exerted by a perturbed hole on the particles balances the electric restoring tension of the hole. The tension is quantitatively small and can often be ignored. The particle force is expressed as integrals of equilibrium parameters over the hole and is shown at low frequency to be exactly equal to what has recently been found (by different analysis) to express ‘kinematic’ hole momentum conservation. The mechanism of instability has nothing to do with the previously hypothesized transverse electron focusing. The unmagnetized growth rate$\unicode[STIX]{x1D6FE}(k)$is found numerically and is in excellent agreement with recent kinematic estimates. Magnetic field stabilization of the transverse mode is also evaluated. The resulting stability boundary for Maxwellian holes is in reasonable agreement with previously published criteria based on particle simulation. It arises from a change of trapped force sign across the resonance between bounce and cyclotron frequencies.

Nonlinear Analysis of Hysteretic Modulation-Based Sliding Mode Controlled Quadratic Buck–Boost Converter

2018 ◽  
Vol 28 (02) ◽  
pp. 1950025 ◽  
Author(s):  
Muppala Kumar Kavitha ◽  
Anbukumar Kavitha
Keyword(s):  
Hopf Bifurcation ◽  
Phase Portrait ◽  
Sliding Mode ◽  
Stability Boundary ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Input Voltage ◽  
Boost Converter ◽  
Complex Conjugate ◽  
The Stability

In this paper, the dynamics of hysteresis current-controlled quadratic buck-boost converter is investigated in detail. The system model is derived based on the sliding mode approach and also in its dimensionless form for algebraic brevity. The stability of the system is disclosed with the aid of the movement of eigenvalues. Onset of Hopf bifurcation is identified when the complex conjugate eigenvalue pair crosses the imaginary axis of the complex plane. The stability boundary is drawn to benefit the power electronics engineer for a stable and reliable design. The computer simulation of the switched model is performed using MATLAB/Simulink software to uncover the sequential occurrence of nonlinear behavior exhibited due to Hopf bifurcation for variation in control parameters and the input voltage. The phase portrait disclosing the subtle periodicity is plotted at different operating points to elicit that the stable period-1 attractor bifurcates to the quasi-periodic orbit and finally to a limit cycle. The precise dynamic of the phase portrait is also captured using the Poincare section. Experimental outputs are presented for confirming the low-frequency bifurcation scenario witnessed in the simulated and analytical results.

scholarly journals Nonlinear analysis of low-frequency combustion instabilities in liquid rocket engines

2019 ◽  
Author(s):  
M. Leonardi ◽  
F. Di Matteo ◽  
J. Steelant ◽  
F. Nasuti ◽  
M. Onofri
Keyword(s):  
Characteristic Frequency ◽  
Stability Boundary ◽  
Time Lag ◽  
Low Frequency ◽  
Fuel Injector ◽  
Combustion Instabilities ◽  
Variable Time ◽  
Lag Model ◽  
Double Time ◽  
The Stability

Low-frequency combustion instabilities are here studied taking advantage of the software EcosimPro. A specific module has been implemented based on the double time lag model and the coupling of combustion chamber and feed line oscillations were investigated by using a complete set of nonlinear equations. The characteristic time lags have been identified following two approaches: (i) a constant time lag approach; and (ii) a variable time lag approach based on correlations available in open literature. To prove the module capabilities, an experimental setup was reproduced and a stability map was generated, comparing the obtained results with literature data from both experiments and a linear double time lag model. The stability boundaries obtained with the chugging module are in good agreement with those obtained in open literature and the first characteristic frequency of the engine is well predicted. Furthermore, the model proves its capability in reconstructing the reversal in the slope of the stability boundary at low fuel injector pressure drops and in detecting the high-frequency content typically observed in presence of multimode oscillations. However, in the calculations, the higher frequency does not dominate the instabilities, that is, in the unstable regime, the model diverges with a frequency equal to the first characteristic frequency. In the last part of the paper, the variable time lag approach is used to investigate a portion of the aforementioned stability map. Thanks to the semiempirical correlations, the present authors managed to improve the prediction of the first characteristic frequency, whereas the stability boundary does not change significantly and remains comparable with the one predicted by the constant double time lag approach.

APPROXIMATE ROTATIONAL SOLUTIONS OF PENDULUM UNDER COMBINED VERTICAL AND HORIZONTAL EXCITATION

2012 ◽  
Vol 22 (05) ◽  
pp. 1250100 ◽  
Author(s):  
EKATERINA PAVLOVSKAIA ◽  
BRYAN HORTON ◽  
MARIAN WIERCIGROCH ◽  
STEFANO LENCI ◽  
GIUSEPPE REGA
Keyword(s):  
Stability Boundary ◽  
Low Frequency ◽  
Horizontal Component ◽  
Minor Effect ◽  
Solution Existence ◽  
Good Correspondence ◽  
Analytical Approximations ◽  
The Stability ◽  
A Minor ◽  
The Solution Existence

A pendulum excited by the combination of vertical and horizontal forcing at the pivot point was considered and the period-1 rotational motion was studied. Analytical approximations of period-1 rotations and their stability boundary on the excitation parameters (ω, p)-plane are derived using asymptotic analysis for the pendulum excited elliptically and along a tilted axis. It was assumed that the damping is small and the frequency of the base excitation is relatively high. The accuracy of the approximations was examined for different values of the parameters e and κ controlling the shape of excitation, and it was found that using the second and third order approximations ensures a good correspondence between analytical and numerical results in the majority of cases. Basins of attractions of the coexisting solutions were constructed numerically to evaluate the robustness of the obtained rotational solutions. It was found that the horizontal component of excitation has a larger effect on the shift in position of the saddle node bifurcations for the elliptically excited case than for the pendulum excited along a tilted axis. For the elliptically excited pendulum with pivot rotating in the same direction as the pendulum the stability boundary is shifted downwards providing a larger region of the solution existence. When the pendulum and the pivot rotate in opposite directions, the boundary is shifted upwards significantly limiting the region of the solution existence. In contrast, for the pendulum excited along the tilted axis, the direction of the rotation has a minor effect for low frequency values and the addition of the horizontal component always results in a larger region of the solution existence.

Resonance in a mathematical model of baroreflex control: arterial blood pressure waves accompanying postural stress

2005 ◽  
Vol 288 (6) ◽  
pp. R1637-R1648 ◽  
Author(s):  
Peter E. Hammer ◽  
J. Philip Saul
Keyword(s):  
Blood Pressure ◽  
Mathematical Model ◽  
Blood Volume ◽  
Low Frequency ◽  
Pressure Waves ◽  
Central Blood Volume ◽  
Arterial Baroreflex ◽  
Arterial Blood ◽  
Gain Margin ◽  
The Stability

A mathematical model of the arterial baroreflex was developed and used to assess the stability of the reflex and its potential role in producing the low-frequency arterial blood pressure oscillations called Mayer waves that are commonly seen in humans and animals in response to decreased central blood volume. The model consists of an arrangement of discrete-time filters derived from published physiological studies, which is reduced to a numerical expression for the baroreflex open-loop frequency response. Model stability was assessed for two states: normal and decreased central blood volume. The state of decreased central blood volume was simulated by decreasing baroreflex parasympathetic heart rate gain and by increasing baroreflex sympathetic vaso/venomotor gains as occurs with the unloading of cardiopulmonary baroreceptors. For the normal state, the feedback system was stable by the Nyquist criterion (gain margin = 0.6), but in the hypovolemic state, the gain margin was small (0.07), and the closed-loop frequency response exhibited a sharp peak (gain of 11) at 0.07 Hz, the same frequency as that observed for arterial pressure fluctuations in a group of healthy standing subjects. These findings support the theory that stresses affecting central blood volume, including upright posture, can reduce the stability of the normally stable arterial baroreflex feedback, leading to resonance and low-frequency blood pressure waves.

scholarly journals Evolution of a narrow-band spectrum of random surface gravity waves

2003 ◽  
Vol 478 ◽  
pp. 1-10 ◽  
Author(s):  
KRISTIAN B. DYSTHE ◽  
KARSTEN TRULSEN ◽  
HARALD E. KROGSTAD ◽  
HERVÉ SOCQUET-JUGLARD
Keyword(s):  
Three Dimensional ◽  
Low Frequency ◽  
Three Dimensions ◽  
Band Spectrum ◽  
Nls Equation ◽  
Random Surface ◽  
Narrow Bandwidth ◽  
Quasi Stationary State ◽  
The Stability ◽  
Three Dimensional Simulations

Numerical simulations of the evolution of gravity wave spectra of fairly narrow bandwidth have been performed both for two and three dimensions. Simulations using the nonlinear Schrödinger (NLS) equation approximately verify the stability criteria of Alber (1978) in the two-dimensional but not in the three-dimensional case. Using a modified NLS equation (Trulsen et al. 2000) the spectra ‘relax’ towards a quasi-stationary state on a timescale (ε2ω0)−1. In this state the low-frequency face is steepened and the spectral peak is downshifted. The three-dimensional simulations show a power-law behaviour ω−4 on the high-frequency side of the (angularly integrated) spectrum.

Tertiary solutions and their stability in rotating plane Couette flow

1998 ◽  
Vol 358 ◽  
pp. 357-378 ◽  
Author(s):  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Stability Boundary ◽  
Streamwise Vortex ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Plane Couette Flow ◽  
Streamwise Direction ◽  
The Stability ◽  
Oscillatory Instabilities

The stability of nonlinear tertiary solutions in rotating plane Couette flow is examined numerically. It is found that the tertiary flows, which bifurcate from two-dimensional streamwise vortex flows, are stable within a certain range of the rotation rate when the Reynolds number is relatively small. The stability boundary is determined by perturbations which are subharmonic in the streamwise direction. As the Reynolds number is increased, the rotation range for the stable tertiary motions is destroyed gradually by oscillatory instabilities. We expect that the tertiary flow is overtaken by time-dependent motions for large Reynolds numbers. The results are compared with the recent experimental observation by Tillmark & Alfredsson (1996).

FABRICATION OF NANOPOROUS CHITOSAN MEMBRANES

NANO ◽  
2010 ◽  
Vol 05 (01) ◽  
pp. 53-60 ◽  
Author(s):  
XIAOLIANG WANG ◽  
XIANG LI ◽  
ELEANOR STRIDE ◽  
MOHAN EDIRISINGHE
Keyword(s):  
Low Frequency ◽  
Drug Carriers ◽  
Structural Features ◽  
Wound Dressings ◽  
Ftir Analysis ◽  
Tissue Engineering Scaffolds ◽  
Nanoscale Structures ◽  
Low Frequency Ultrasound ◽  
Chitosan Membranes ◽  
The Stability

Naturally derived biopolymers have been widely used for biomedical applications such as drug carriers, wound dressings, and tissue engineering scaffolds. Chitosan is a typical polysaccharide of great interest due to its biocompatibility and film-formability. Chitosan membranes with controllable porous structures also have significant potential in membrane chromatography. Thus, the processing of membranes with porous nanoscale structures is of great importance, but it is also challenging and this has limited the application of these membranes to date. In this study, with the aid of a carefully selected surfactant, polyethyleneglycol stearate-40, chitosan membranes with a well controlled nanoscale structure were successfully prepared. Additional control over the membrane structure was obtained by exposing the suspension to high intensity, low frequency ultrasound. It was found that the concentration of chitosan/surfactant ratio and the ultrasound exposure conditions affect the structural features of the membranes. The stability of nanopores in the membrane was improved by intensive ultrasonication. Furthermore, the stability of the blended suspensions and the intermolecular interactions between chitosan and the surfactant were investigated using scanning electron microscope and Fourier transform infrared spectroscopy (FTIR) analysis, respectively. Hydrogen bonds and possible reaction sites for molecular interactions in the two polymers were also confirmed by FTIR analysis.

Nonstationary Response of a Two-Degrees-of-Freedom Nonlinear Ship Model Under Modulated Excitation

1995 ◽  
Author(s):  
Ruigui Pan ◽  
Huw G. Davies
Keyword(s):  
Degrees Of Freedom ◽  
Stability Boundary ◽  
Period Doubling ◽  
Approximate Solutions ◽  
Loss Of Stability ◽  
Two Degrees Of Freedom ◽  
Ship Model ◽  
Nonstationary Response ◽  
Period 2 ◽  
The Stability

Abstract Nonstationary response of a two-degrees-of-freedom system with quadratic coupling under a time varying modulated amplitude sinusoidal excitation is studied. The nonlinearly coupled pitch and roll ship model is based on Nayfeh, Mook and Marshall’s work for the case of stationary excitation. The ship model has a 2:1 internal resonance and is excited near the resonance of the pitch mode. The modulated excitation (F0 + F1 cos ωt) cosQt is used to model a narrow band sea-wave excitation. The response demonstrates a variety of bifurcations, loss of stability, and chaos phenomena that are not present in the stationary case. We consider here the periodically modulated response. Chaotic response of the system is discussed in a separate paper. Several approximate solutions, under both small and large modulating amplitudes F1, are obtained and compared with the exact one. The stability of an exact solution with one mode having zero amplitude is studied. Loss of stability in this case involves either a rapid transition from one of two stable (in the stationary sense) branches to another, or a period doubling bifurcation. From Floquet theory, various stability boundary diagrams are obtained in F1 and F0 parameter space which can be used to predict the various transition phenomena and the period-2 bifurcations. The study shows that both the modulation parameters F1 and ω (the modulating frequency) have great effect on the stability boundaries. Because of the modulation, the stable area is greatly expanded, and the stationary bifurcation point can be exceeded without loss of stability. Decreasing ω can make the stability boundary very complicated. For very small ω the response can make periodic transitions between the two (pseudo) stable solutions.

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