In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular...In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green's integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.展开更多
A new method of nonlinear analysis is established by combining phase space reconstruction and data reduction sub-frequency band wavelet. This method is applied to two types of chaotic dynamic systems(Lorenz and Rssler...A new method of nonlinear analysis is established by combining phase space reconstruction and data reduction sub-frequency band wavelet. This method is applied to two types of chaotic dynamic systems(Lorenz and Rssler) to examine the anti-noise ability for complex systems. Results show that the nonlinear dynamic system analysis method resists noise and reveals the internal dynamics of a weak signal from noise pollution. On this basis, the vertical upward gas–liquid two-phase flow in a 2 mm × 0.81 mm small rectangular channel is investigated. The frequency and energy distributions of the main oscillation mode are revealed by analyzing the time–frequency spectra of the pressure signals of different flow patterns. The positive power spectral density of singular-value frequency entropy and the damping ratio are extracted to characterize the evolution of flow patterns and achieve accurate recognition of different vertical upward gas–liquid flow patterns(bubbly flow:100%, slug flow: 92%, churn flow: 96%, annular flow: 100%). The proposed analysis method will enrich the dynamics theory of multi-phase flow in small channel.展开更多
In this paper, the flow fields of underexpanded impinging jet issued from rectangular nozzles of aspect ratio 1, 3 and 5 are numerically and experimentally studied. Two dimensional temperature and pressure distributio...In this paper, the flow fields of underexpanded impinging jet issued from rectangular nozzles of aspect ratio 1, 3 and 5 are numerically and experimentally studied. Two dimensional temperature and pressure distributions are measured by using infrared camera and the combination of a pressure scanning device and a stepping motor, respectively. The variation of the stagnation pressure on the impinging plate reveals that a hysteretic phenomenon exists during the increasing and decreasing of the pressure ratio for the aspect ratio of 3.0 and 5.0. It is also found that the nozzle of aspect ratio 1.0 caused the largest total pressure loss Pc /p0= 0.27 at the pressure ratio of Po /p0 = 6.5, where Pc is the stagnation center pressure on the wall, P0 the upstream stagnation pressure, Pb the ambient pressure. The other two nozzles showed that the pressure loss Pc / P0 =0.52 and 0.55 were achieved by the nozzles of the aspect ratio 3,0 and 5.0, respectively. The comparison between the calculations and experiments is fairly good, showing the three dimensional streamlines and structures of the shock waves in the jets. However, the hysteresis of the pressure variations observed in the experiments between the pressure ratio of 3.5 and 4.5 cannot be confirmed in the calculations.展开更多
The investigation of the interplay between geometry and nonlinearity may open the road to the control of extreme waves. We study three-dimensional localization and dispersive shocks in a bent cigar shaped potential by...The investigation of the interplay between geometry and nonlinearity may open the road to the control of extreme waves. We study three-dimensional localization and dispersive shocks in a bent cigar shaped potential by the nonlinear Schro¨ dinger equation. At high bending and high nonlinearity, topological trapping is frustrated by the generation of curved wave-breaking. Four-dimensional parallel simulations confirm the theoretical model. This work may contribute to novel devices based on geometrically constrained highly nonlinear dynamics and tests and analogs of fundamental physical theories in curved space.展开更多
The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays expo...The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.展开更多
In this paper we described our study of the behaviors of field emitters driven by square-wave voltages. We observed phenomena under pulsed voltages that generally do not manifest themselves under direct-current voltag...In this paper we described our study of the behaviors of field emitters driven by square-wave voltages. We observed phenomena under pulsed voltages that generally do not manifest themselves under direct-current voltages. We interpreted these phenomena with the cathode and anode combined treated as equivalent to a resistor and a condenser in series connection. First,because of the delay caused by the charging process of the condenser, the waveform of the voltage across the cathode-anode gap was remarkably distorted. Second, the resistor led to considerable attenuation in field emission, which was clearly observable within each pulse and became more dramatic with increasing repetition frequency of the pulses. Furthermore, the field emission currents under direct-current voltages were lower than those under pulsed voltages. This disparity is attributed to rising resistance in the circuit with rising temperature. We also discussed the restrictions that the waveform distortion and current attenuation could impose on potential field emitter applications.展开更多
The twin impulse wave leads to very complicated flow fields, such as Mach stem, spherical waves, and vortex ring. The twin impulse wave discharged from the exits of the two tubes placed in parallel is investigated to ...The twin impulse wave leads to very complicated flow fields, such as Mach stem, spherical waves, and vortex ring. The twin impulse wave discharged from the exits of the two tubes placed in parallel is investigated to understand the detailed flow physics associated with the twin impulse wave, compared with those in a single impulse wave. In the current study, the merging phenomena and propagation characteristics of the impulse waves are investigated using a shock tube experiment and by numerical computations. The Harten-Yee''s total variation diminishing (TVD) scheme is used to solve the unsteady two-dimensional compressible Euler equations. The Mach number Ms of incident shock wave is changed below 1.5 and the distance between two-parallel tubes, L/d, is changed from 1.2 to 4.0. In the shock tube experiment, the twin impulse waves are visualized by a Schlieren optical system for the purpose of validation of computational work. The results obtained show that on the symmetric axis between two-parallel tubes, the peak pressure produced by the twin impulse waves and its location strongly depend upon the distance between two-parallel tubes, L/d and the incident shock Mach number, Ms. The predicted Schlieren images represent the measured twin-impulse wave with a good accuracy.展开更多
基金Partially Supported by the Department of Science and Technology Through a Research Grant to RG(No.SR/FTP/MS-020/2010)
文摘In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green's integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.
基金Supported by the National Natural Science Foundation of China(51406031)
文摘A new method of nonlinear analysis is established by combining phase space reconstruction and data reduction sub-frequency band wavelet. This method is applied to two types of chaotic dynamic systems(Lorenz and Rssler) to examine the anti-noise ability for complex systems. Results show that the nonlinear dynamic system analysis method resists noise and reveals the internal dynamics of a weak signal from noise pollution. On this basis, the vertical upward gas–liquid two-phase flow in a 2 mm × 0.81 mm small rectangular channel is investigated. The frequency and energy distributions of the main oscillation mode are revealed by analyzing the time–frequency spectra of the pressure signals of different flow patterns. The positive power spectral density of singular-value frequency entropy and the damping ratio are extracted to characterize the evolution of flow patterns and achieve accurate recognition of different vertical upward gas–liquid flow patterns(bubbly flow:100%, slug flow: 92%, churn flow: 96%, annular flow: 100%). The proposed analysis method will enrich the dynamics theory of multi-phase flow in small channel.
文摘In this paper, the flow fields of underexpanded impinging jet issued from rectangular nozzles of aspect ratio 1, 3 and 5 are numerically and experimentally studied. Two dimensional temperature and pressure distributions are measured by using infrared camera and the combination of a pressure scanning device and a stepping motor, respectively. The variation of the stagnation pressure on the impinging plate reveals that a hysteretic phenomenon exists during the increasing and decreasing of the pressure ratio for the aspect ratio of 3.0 and 5.0. It is also found that the nozzle of aspect ratio 1.0 caused the largest total pressure loss Pc /p0= 0.27 at the pressure ratio of Po /p0 = 6.5, where Pc is the stagnation center pressure on the wall, P0 the upstream stagnation pressure, Pb the ambient pressure. The other two nozzles showed that the pressure loss Pc / P0 =0.52 and 0.55 were achieved by the nozzles of the aspect ratio 3,0 and 5.0, respectively. The comparison between the calculations and experiments is fairly good, showing the three dimensional streamlines and structures of the shock waves in the jets. However, the hysteresis of the pressure variations observed in the experiments between the pressure ratio of 3.5 and 4.5 cannot be confirmed in the calculations.
基金the support of a grant from the John Templeton Foundation(58277)support by the European Research Council Grant ERC-POC-2014 Vanguard(664782)
文摘The investigation of the interplay between geometry and nonlinearity may open the road to the control of extreme waves. We study three-dimensional localization and dispersive shocks in a bent cigar shaped potential by the nonlinear Schro¨ dinger equation. At high bending and high nonlinearity, topological trapping is frustrated by the generation of curved wave-breaking. Four-dimensional parallel simulations confirm the theoretical model. This work may contribute to novel devices based on geometrically constrained highly nonlinear dynamics and tests and analogs of fundamental physical theories in curved space.
基金Project supported by the National Natural Science Foundation of China(No.60174008).
文摘The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.
基金supported by the Ministry of Science and Technology of China(Grant No.2013CB933604)
文摘In this paper we described our study of the behaviors of field emitters driven by square-wave voltages. We observed phenomena under pulsed voltages that generally do not manifest themselves under direct-current voltages. We interpreted these phenomena with the cathode and anode combined treated as equivalent to a resistor and a condenser in series connection. First,because of the delay caused by the charging process of the condenser, the waveform of the voltage across the cathode-anode gap was remarkably distorted. Second, the resistor led to considerable attenuation in field emission, which was clearly observable within each pulse and became more dramatic with increasing repetition frequency of the pulses. Furthermore, the field emission currents under direct-current voltages were lower than those under pulsed voltages. This disparity is attributed to rising resistance in the circuit with rising temperature. We also discussed the restrictions that the waveform distortion and current attenuation could impose on potential field emitter applications.
文摘The twin impulse wave leads to very complicated flow fields, such as Mach stem, spherical waves, and vortex ring. The twin impulse wave discharged from the exits of the two tubes placed in parallel is investigated to understand the detailed flow physics associated with the twin impulse wave, compared with those in a single impulse wave. In the current study, the merging phenomena and propagation characteristics of the impulse waves are investigated using a shock tube experiment and by numerical computations. The Harten-Yee''s total variation diminishing (TVD) scheme is used to solve the unsteady two-dimensional compressible Euler equations. The Mach number Ms of incident shock wave is changed below 1.5 and the distance between two-parallel tubes, L/d, is changed from 1.2 to 4.0. In the shock tube experiment, the twin impulse waves are visualized by a Schlieren optical system for the purpose of validation of computational work. The results obtained show that on the symmetric axis between two-parallel tubes, the peak pressure produced by the twin impulse waves and its location strongly depend upon the distance between two-parallel tubes, L/d and the incident shock Mach number, Ms. The predicted Schlieren images represent the measured twin-impulse wave with a good accuracy.