Geometrical and Graphical Representations Analysis of Lissajous Figures in Rotor Dynamic System

Al-Khazali, Hisham A. H.; Askari, Mohama R.

doi:10.9790/3021-0205971978

Cited by 49 publications

(27 citation statements)

References 4 publications

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“…In order to quantify the hysteric response of the different models, the amplitude and phase delay are calculated from the hysteresis loop using Lissajous graphic method . Figure shows an example of a Lissajous figure, where A is the velocity amplitude and C is the zero crossing height.…”

Section: Verification Methodsmentioning

confidence: 99%

New dynamic‐inflow engineering models based on linear and nonlinear actuator disc vortex models

Tavernier

Ferreira

et al. 2019

Wind Energy

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Two new engineering models are presented for the aerodynamic induction of a wind turbine under dynamic thrust. The models are developed using the differential form of Duhamel integrals of indicial responses of actuator disc type vortex models. The time constants of the indicial functions are obtained by the indicial responses of a linear and a nonlinear actuator disc model. The new dynamic‐inflow engineering models are verified against the results of a Computational Fluid Dynamics (CFD) model and compared against the dynamic‐inflow engineering models of Pitt‐Peters, Øye, and Energy Research Center of the Netherlands (ECN), for several load cases. Comparisons of all models show that two time constants are necessary to predict the dynamic induction. The amplitude and phase delay of the velocity distribution shows a strong radial dependency. Verifying the models against results from the CFD model shows that the model based on the linear actuator disc vortex model predicts a similar performance as the Øye model. The model based on the nonlinear actuator disc vortex model predicts the dynamic induction better than the other models concerning both phase delay and amplitude, especially at high load.

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Section: Verification Methodsmentioning

confidence: 99%

New dynamic‐inflow engineering models based on linear and nonlinear actuator disc vortex models

Tavernier

Ferreira

et al. 2019

Wind Energy

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“…In both cases we plot the square root of the quantum variance, or the standard deviation δJ, versus average current J as the interaction strength varies. We find two distinct classes of the δJ-J Lissajous curve [20][21][22]: (1) A one-to-one correspondence between δJ and J in the absence of interactions except possible isolated points due to energy degeneracy and (2) a loop or more complicated patterns in the presence of interactions. The Lissajous loop thus establishes a multi-valued relation between δJ and J for interacting many-body systems.…”

mentioning

confidence: 99%

Many-body multivaluedness of particle-current variance in closed and open cold-atom systems

et al. 2018

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The quantum variance of an observable is a fundamental quantity in quantum mechanics, and the variance provides additional information other than the average itself. By examining the relation between the particlecurrent variance (δJ) 2 and the average current J in both closed and open interacting fermionic systems, we show the emergence of a multi-valued Lissajous curve between δJ and J due to interactions. As a closed system we considered the persistent current in a benzene-like lattice enclosing an effective magnetic flux and solved it by exact diagonalization. For the open system, the steady-state current flowing through a few lattice sites coupled to two particle reservoirs was investigated using a Lindblad equation. In both cases, interactions open a loop and change the topology of the corresponding δJ-J Lissajous curve, showing that this effect is model-independent. We finally discuss how the predicted phenomena can be observed in ultracold atoms, thus offering an alternative way of probing the dynamics of many-body systems.Quantum fluctuations of the current flowing in a system provide more information than the average current itself [1][2][3]. This fact has been demonstrated in several experimental and theoretical studies ranging from quantum dots [4] to nanoscale systems [5,6], to name a few. In all those studies, two-time correlations of current are measured (or calculated) away from the average current, and from their spectrum one can infer the type of physical processes at play [2]. On the other hand, equal-time density fluctuations at different spatial locations have been measured in ultracold atoms [7], revealing spatial correlations in quantum gases.However, one could also study quantum variance of the current, a property of fundamental importance in quantum mechanics because of the uncertainty principle [8]. This equal-time, equal-space quantity has been less explored, presumably because of experimental difficulty in measuring it in a current-carrying system. Emergence of cold atoms [9][10][11] as new model systems to study a host of phenomena otherwise difficult to probe using traditional solid-state materials, makes this transport property readily accessible experimentally [12]. It is then natural to ask what information the variance would reveal, and how that information might be useful in characterizing the many-body dynamics.In this paper, having in mind cold-atom systems as possible experimental verification of our predictions, we study the quantum variance, (δJ) 2 , of current flowing in a fermionic many-body system, and relate this quantity to the average current, J. We consider two experimentally realizable situations: the persistent current of a periodic system and the steady-state limit of the current in an open system. The latter case is more amenable to an easier experimental realization in ultracold atoms [13,14].In order to solve the many-body problem exactly (hence beyond mean field), we have considered, as a closed system, a benzene-like ring lattice with a static magnetic flux to...

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“…Figure 1c shows the time evolution of excitation DI(t)( dotted red line) and the response of the interface position, DX(t)(full blue line), obtained after image processing of movie S1, the details of which are given in Figure S1 and S2 of the Supporting Information. [22,23] Now,w et urn to the energetic aspects of the problem. First, the HS/LS interface performs periodic oscillations (the same applies for the HS fraction / DX(t)) at the excitation frequency (n = 0.1 Hz), with ad elay Dt % 5s.T he maximum velocity measured for the front propagation (which depends on temperature) was approximately 10 mms À1 and corresponded to the "natural" growth of the HS phase under the usual warming experiment at 0.2 Kmin À1 .S econd, ag lobal drift of the average interface position (black curve of Figure 1c)a ppears in the beginning of the process before reaching an ew stationary value around 40 sl ater.…”

mentioning

confidence: 99%

Reversible Control by Light of the High‐Spin Low‐Spin Elastic Interface inside the Bistable Region of a Robust Spin‐Transition Single Crystal

Garrot

Slimani

et al. 2016

Angew Chem Int Ed

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By using a weak modulated laser intensity we have succeeded in reversibly controlling the dynamics of the spin-crossover (SC) single crystal [{Fe(NCSe)(py)2 }2 (m-bpypz)] inside the thermal hysteresis. The experiment could be repeated several times with a reproducible response of the high-spin low-spin interface and without crystal damage. In-depth investigations as a function of the amplitude and frequency of the excitation brought to light the existence of a cut-off frequency ca. 1.5 Hz. The results not only document the applicability of SC materials as actuators, memory devices, or switches, but also open a new avenue for the reversible photo-control of the spin transition inside the thermal hysteresis.

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Geometrical and Graphical Representations Analysis of Lissajous Figures in Rotor Dynamic System

Cited by 49 publications

References 4 publications

New dynamic‐inflow engineering models based on linear and nonlinear actuator disc vortex models

New dynamic‐inflow engineering models based on linear and nonlinear actuator disc vortex models

Many-body multivaluedness of particle-current variance in closed and open cold-atom systems

Reversible Control by Light of the High‐Spin Low‐Spin Elastic Interface inside the Bistable Region of a Robust Spin‐Transition Single Crystal

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