When one cup of a co-axial viscometer oscillates, the measured moment on the another (stationary) cup shows a phase lag, partly due to the inertial effect of the fluid within the gap between the two cups. Such an effe...When one cup of a co-axial viscometer oscillates, the measured moment on the another (stationary) cup shows a phase lag, partly due to the inertial effect of the fluid within the gap between the two cups. Such an effect was illustrated by a new exact solution of Navier-Stokes equation, which was derived herein by a scheme of reducing it to a two-point boundary value problem for ordinary differential equations. The numerical results indicate that, as the Womersley number or the dimensionless gap width increases, the fluid velocity profile within the gap gradually deviates from the linear one and transits to that of the boundary layer type, with the result that the moment decreases in the magnitude and lags behind in the phase. With the advantage of high accuracy and excellent stability, the scheme proposed here can be easily extended to solve other linear periodic problems.展开更多
We present a method by which to determine the bulk viscosity of water from pulse duration measurements of stimulated Brillouin scattering （SBS）. Beginning from a common model of Brillouin scattering, the bulk viscos...We present a method by which to determine the bulk viscosity of water from pulse duration measurements of stimulated Brillouin scattering （SBS）. Beginning from a common model of Brillouin scattering, the bulk viscosity is shown to play an important role in Brillouin linewidth determination. Pulse durations of SBS back-reflected optical pulses are measured over the temperature range of 5-40℃. SBS linewidths are de- termined via Fourier transformation of the time-domain results, and the bulk viscosity of water is measured and derived from the obtained values. Our results show that the proposed method for measurement of pulse durations is an effective approach for determining bulk viscosity. The method can be easily extended to determine bulk viscosities of other Newtonian liquids.展开更多
This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, w...This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.展开更多
文摘When one cup of a co-axial viscometer oscillates, the measured moment on the another (stationary) cup shows a phase lag, partly due to the inertial effect of the fluid within the gap between the two cups. Such an effect was illustrated by a new exact solution of Navier-Stokes equation, which was derived herein by a scheme of reducing it to a two-point boundary value problem for ordinary differential equations. The numerical results indicate that, as the Womersley number or the dimensionless gap width increases, the fluid velocity profile within the gap gradually deviates from the linear one and transits to that of the boundary layer type, with the result that the moment decreases in the magnitude and lags behind in the phase. With the advantage of high accuracy and excellent stability, the scheme proposed here can be easily extended to solve other linear periodic problems.
基金supported by the National Natural Sci-ence Foundation of China under Grants Nos.41206084 and 61177096
文摘We present a method by which to determine the bulk viscosity of water from pulse duration measurements of stimulated Brillouin scattering （SBS）. Beginning from a common model of Brillouin scattering, the bulk viscosity is shown to play an important role in Brillouin linewidth determination. Pulse durations of SBS back-reflected optical pulses are measured over the temperature range of 5-40℃. SBS linewidths are de- termined via Fourier transformation of the time-domain results, and the bulk viscosity of water is measured and derived from the obtained values. Our results show that the proposed method for measurement of pulse durations is an effective approach for determining bulk viscosity. The method can be easily extended to determine bulk viscosities of other Newtonian liquids.
文摘This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.
