The Experts below are selected from a list of 10149 Experts worldwide ranked by ideXlab platform
Anna Lisa Varri - One of the best experts on this subject based on the ideXlab platform.
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l 1 weinberg s weakly Damped Mode in an n body Model of a spherical stellar system
Monthly Notices of the Royal Astronomical Society, 2020Co-Authors: Douglas C Heggie, Anna Lisa Varri, Philip G BreenAbstract:Spherical stellar systems such as King Models, in which the distribution function is a decreasing function of energy and depends on no other invariant, are stable in the sense of collisionless dynamics. But Weinberg showed, by a clever application of the matrix method of linear stability, that they may be nearly unstable, in the sense of possessing {\sl weakly} Damped Modes of oscillation. He also demonstrated the presence of such a Mode in an $N$-body Model by endowing it with initial conditions generated from his perturbative solution. In the present paper we provide evidence for the presence of this same Mode in $N$-body simulations of the King $W_0 = 5$ Model, in which the initial conditions are generated by the usual Monte Carlo sampling of the King distribution function. It is shown that the oscillation of the density centre correlates with variations in the structure of the system out to a radius of about 1 virial radius, but anticorrelates with variations beyond that radius. Though the oscillations appear to be continually reexcited (presumably by the motions of the particles) we show by calculation of power spectra that Weinberg's estimate of the period (strictly, $2\pi$ divided by the real part of the eigenfrequency) lies within the range where the power is largest. In addition, however, the power spectrum displays another very prominent feature at shorter periods, around 5 crossing times.
Luc Mongeau - One of the best experts on this subject based on the ideXlab platform.
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dual driver standing wave tube acoustic impedance matching with robust repetitive control
IEEE Transactions on Control Systems and Technology, 2004Co-Authors: Yaoyu Li, George T C Chiu, Luc MongeauAbstract:In some acoustic applications, it may be desirable to make a shorter standing wave tube operate like a longer tube at the same driving frequency. The basic idea is to reduce the length of a long tube, and replace the removed section with a secondary driver. The problem is then to match the acoustic impedance at the boundary where the secondary driver is installed to that of the original system. Two control formulations were investigated for this problem: a two-input-two-output (TITO) and a single-input-single-output (SISO) formulation. The TITO formulation directly tracks the two acoustic variables associated with the desired acoustic impedance, while the SISO formulation minimizes the impedance matching error. The desired impedance containing a very lightly Damped Mode is embedded in the augmented plant for feedback control design. In addition to the balance realization method, the Schur method was used for Model reduction for the high-order plant. Since the standing wave tubes are driven by tonal signals, repetitive control was incorporated into the control frameworks to achieve the desired performance. Good performance of impedance matching was obtained for both formulations. The SISO formulation yielded slightly wider bandwidth of good impedance matching than the TITO. The TITO formulation offered additional control to individual signals related to the acoustic impedance of interest.
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dual driver standing wave tube acoustic impedance matching with robust repetitive control
American Control Conference, 2002Co-Authors: Yaoyu Li, George T C Chiu, Luc MongeauAbstract:In many applications of acoustic standing wave tubes, for instance thermoacoustic heat pumping systems, it is desirable to make a shorter tube operate like a longer standing wave tube at the same driving frequency. The basic idea here is to reduce the physical length of the tube, and replace the removed section with a secondary driver. The problem is then to match the acoustic impedance at the boundary where the secondary driver is installed to that of the original system. A two-input-two-output (TITO) formulation directly tracks the two acoustic variables related to the impedance, while a SISO formulation minimizes the impedance matching error. The desired impedance containing a very lightly Damped Mode is embedded in the augmented plant for feedback control design. In addition to the balance realization method, the Schur method was used in Model reduction for the high-order non-minimum phase plants. Since the standing wave tubes are driven by tonal signals, repetitive control was incorporated into the control frameworks to achieve the desired performance. Good impedance matching performance was obtained for both formulations. The formulations are compared.
Yaoyu Li - One of the best experts on this subject based on the ideXlab platform.
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dual driver standing wave tube acoustic impedance matching with robust repetitive control
IEEE Transactions on Control Systems and Technology, 2004Co-Authors: Yaoyu Li, George T C Chiu, Luc MongeauAbstract:In some acoustic applications, it may be desirable to make a shorter standing wave tube operate like a longer tube at the same driving frequency. The basic idea is to reduce the length of a long tube, and replace the removed section with a secondary driver. The problem is then to match the acoustic impedance at the boundary where the secondary driver is installed to that of the original system. Two control formulations were investigated for this problem: a two-input-two-output (TITO) and a single-input-single-output (SISO) formulation. The TITO formulation directly tracks the two acoustic variables associated with the desired acoustic impedance, while the SISO formulation minimizes the impedance matching error. The desired impedance containing a very lightly Damped Mode is embedded in the augmented plant for feedback control design. In addition to the balance realization method, the Schur method was used for Model reduction for the high-order plant. Since the standing wave tubes are driven by tonal signals, repetitive control was incorporated into the control frameworks to achieve the desired performance. Good performance of impedance matching was obtained for both formulations. The SISO formulation yielded slightly wider bandwidth of good impedance matching than the TITO. The TITO formulation offered additional control to individual signals related to the acoustic impedance of interest.
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dual driver standing wave tube acoustic impedance matching with robust repetitive control
American Control Conference, 2002Co-Authors: Yaoyu Li, George T C Chiu, Luc MongeauAbstract:In many applications of acoustic standing wave tubes, for instance thermoacoustic heat pumping systems, it is desirable to make a shorter tube operate like a longer standing wave tube at the same driving frequency. The basic idea here is to reduce the physical length of the tube, and replace the removed section with a secondary driver. The problem is then to match the acoustic impedance at the boundary where the secondary driver is installed to that of the original system. A two-input-two-output (TITO) formulation directly tracks the two acoustic variables related to the impedance, while a SISO formulation minimizes the impedance matching error. The desired impedance containing a very lightly Damped Mode is embedded in the augmented plant for feedback control design. In addition to the balance realization method, the Schur method was used in Model reduction for the high-order non-minimum phase plants. Since the standing wave tubes are driven by tonal signals, repetitive control was incorporated into the control frameworks to achieve the desired performance. Good impedance matching performance was obtained for both formulations. The formulations are compared.
Qian Wang - One of the best experts on this subject based on the ideXlab platform.
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excitation of nonlinear ion acoustic waves in ch plasmas
Physics of Plasmas, 2016Co-Authors: Q S Feng, C Y Zheng, Z J Liu, C Z Xiao, Qian WangAbstract:Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number kλDe increases, the linear Landau damping of the fast Mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of Ti/Te<0.2 in which the fast Mode is weakly Damped Mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with kλDe increasing. When kλDe is not large, such as kλDe=0.1,0.3,0.5, the nonlinear IAW can be excited by the driver with the linear frequency of the Modes. However, when kλDe is large, such as kλDe=0.7, the linear frequency cannot be applied to exciting the nonlinear IAW, while the frequenc...
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excitation of nonlinear ion acoustic waves in ch plasmas
arXiv: Plasma Physics, 2016Co-Authors: Q S Feng, C Y Zheng, Z J Liu, C Z Xiao, Qian WangAbstract:Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number $ k\lambda_{De} $ increases, the linear Landau damping of the fast Mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of $ T_i/T_e < 0.2 $ in which the fast Mode is weakly Damped Mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with $k\lambda_{De}$ increasing. When $k\lambda_{De}$ is not large, such as $k\lambda_{De}=0.1, 0.3, 0.5$, the nonlinear IAW can be excited by the driver with the linear frequency of the Modes. However, when $k\lambda_{De}$ is large, such as $k\lambda_{De}=0.7$, the linear frequency can not be applied to exciting the nonlinear IAW, while the frequency calculated by the dispersion relation with no damping can be applied to exciting the nonlinear IAW.
C Y Zheng - One of the best experts on this subject based on the ideXlab platform.
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excitation of nonlinear ion acoustic waves in ch plasmas
Physics of Plasmas, 2016Co-Authors: Q S Feng, C Y Zheng, Z J Liu, C Z Xiao, Qian WangAbstract:Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number kλDe increases, the linear Landau damping of the fast Mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of Ti/Te<0.2 in which the fast Mode is weakly Damped Mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with kλDe increasing. When kλDe is not large, such as kλDe=0.1,0.3,0.5, the nonlinear IAW can be excited by the driver with the linear frequency of the Modes. However, when kλDe is large, such as kλDe=0.7, the linear frequency cannot be applied to exciting the nonlinear IAW, while the frequenc...
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excitation of nonlinear ion acoustic waves in ch plasmas
arXiv: Plasma Physics, 2016Co-Authors: Q S Feng, C Y Zheng, Z J Liu, C Z Xiao, Qian WangAbstract:Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number $ k\lambda_{De} $ increases, the linear Landau damping of the fast Mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of $ T_i/T_e < 0.2 $ in which the fast Mode is weakly Damped Mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with $k\lambda_{De}$ increasing. When $k\lambda_{De}$ is not large, such as $k\lambda_{De}=0.1, 0.3, 0.5$, the nonlinear IAW can be excited by the driver with the linear frequency of the Modes. However, when $k\lambda_{De}$ is large, such as $k\lambda_{De}=0.7$, the linear frequency can not be applied to exciting the nonlinear IAW, while the frequency calculated by the dispersion relation with no damping can be applied to exciting the nonlinear IAW.
