Pulse dynamics and stability in optical fibers in the presence of both self-steepening and quintic nonlinear effects are analyzed. Propagating profiles of the quintic derivative nonlinear Schr¨odinger model are i...Pulse dynamics and stability in optical fibers in the presence of both self-steepening and quintic nonlinear effects are analyzed. Propagating profiles of the quintic derivative nonlinear Schr¨odinger model are isolated via two invariants of motion. The resulting canonical equation admits exact periodic propagating patterns in terms of the Jacobi elliptic functions, and solitary pulses are recovered in the long wave limit, i.e. degenerate cases of periodic profiles where each pulse is widely separated from the adjacent ones. Two families of such exact wave profiles are identified. The first one has a precise constraint concerning the magnitude of self-steepening and quintic nonlinear effects, while the second one permits more freedom. The reduction to the well established temporal soliton in an optical fiber waveguide in the absence of self-steepening and quintic nonlinearity is demonstrated explicitly. Numerical simulations are performed to identify regimes of parameter values where robust propagation patterns exist.展开更多
Intracranial aneurysm can lead to hemorrhagic stroke upon rupture. Deployment of flow diverters can restrict the blood flow into aneurysm and mitigate the rupture risk. Computational fluid dynamics（CFD） and ultrason...Intracranial aneurysm can lead to hemorrhagic stroke upon rupture. Deployment of flow diverters can restrict the blood flow into aneurysm and mitigate the rupture risk. Computational fluid dynamics（CFD） and ultrasonography with pulse-wave and color Doppler ultrasound measurements were employed jointly to investigate the complex flow pattern in cerebral aneurysms, both before and after the deployment of flow diverters. Patient-specific configurations of both bifurcation and side-wall aneurysms were selected. The effect of downstream flow resistance was investigated by adjusting the volume flow rate and pressure at the outlet vessels computationally and experimentally. Velocity profiles in the aneurysm measured from ultrasonography showed good agreement with those from computer simulations. The discrepancy in velocity between the computational and experimental sets of data is less than 10%. The downstream resistance can alter the volume flux into a bifurcation aneurysm with a flow diverter deployed by 236%, while the corresponding value of a side-wall aneurysm is negligible. The vorticity of the aneurysmal flow was reduced by more than 80% in both cases after stenting. This study demonstrated that careful investigation of downstream flow resistance of a bifurcation aneurysm is essential to provide an accurate assessment of the aneurysmal flow dynamics after flow diverter deployment.展开更多
基金Support for this project has been provided by the Research Grants Council General Research Fund contract HKU 711713E
文摘Pulse dynamics and stability in optical fibers in the presence of both self-steepening and quintic nonlinear effects are analyzed. Propagating profiles of the quintic derivative nonlinear Schr¨odinger model are isolated via two invariants of motion. The resulting canonical equation admits exact periodic propagating patterns in terms of the Jacobi elliptic functions, and solitary pulses are recovered in the long wave limit, i.e. degenerate cases of periodic profiles where each pulse is widely separated from the adjacent ones. Two families of such exact wave profiles are identified. The first one has a precise constraint concerning the magnitude of self-steepening and quintic nonlinear effects, while the second one permits more freedom. The reduction to the well established temporal soliton in an optical fiber waveguide in the absence of self-steepening and quintic nonlinearity is demonstrated explicitly. Numerical simulations are performed to identify regimes of parameter values where robust propagation patterns exist.
基金provided by the Seed Funding Program for Basic Research of The University of Hong KongInnovation and Technology Fund (ITS/150/15) of the Government of the Hong Kong Special Administrative Region
文摘Intracranial aneurysm can lead to hemorrhagic stroke upon rupture. Deployment of flow diverters can restrict the blood flow into aneurysm and mitigate the rupture risk. Computational fluid dynamics（CFD） and ultrasonography with pulse-wave and color Doppler ultrasound measurements were employed jointly to investigate the complex flow pattern in cerebral aneurysms, both before and after the deployment of flow diverters. Patient-specific configurations of both bifurcation and side-wall aneurysms were selected. The effect of downstream flow resistance was investigated by adjusting the volume flow rate and pressure at the outlet vessels computationally and experimentally. Velocity profiles in the aneurysm measured from ultrasonography showed good agreement with those from computer simulations. The discrepancy in velocity between the computational and experimental sets of data is less than 10%. The downstream resistance can alter the volume flux into a bifurcation aneurysm with a flow diverter deployed by 236%, while the corresponding value of a side-wall aneurysm is negligible. The vorticity of the aneurysmal flow was reduced by more than 80% in both cases after stenting. This study demonstrated that careful investigation of downstream flow resistance of a bifurcation aneurysm is essential to provide an accurate assessment of the aneurysmal flow dynamics after flow diverter deployment.
