Red shift and broadening of backward harmonic radiation from electron oscillations driven by femtosecond laser pulse

The characteristics of backward harmonic radiation due to electron oscillations driven by a linearly polarized fs laser pulse are analysed considering a single electron model. The spectral distributions of the electron's backward harmonic radiation are investigated in detail for different parameters of the driver laser pulse. Higher order harmonic radiations are possible for a sufficiently intense driving laser pulse. We have shown that for a realistic pulsed photon beam, the spectrum of the radiation is red shifted as well as broadened because of changes in the longitudinal velocity of the electrons during the laser pulse. These effects are more pronounced at higher laser intensities giving rise to higher order harmonics that eventually leads to a continuous spectrum. Numerical simulations have further shown that by increasing the laser pulse width the broadening of the high harmonic radiations can be controlled.

Experimental Investigations on Interaction of Two Drops by Thermocapillary-Buoyancy Migration

Experiments were performed, in a terrestrial environment, to study the migration and interaction of two drops with different diameters in matrix liquid under temperature gradient field. Pure soybean oil and silicon oil were used as matrix liquid and the drop liquid, respectively. The information on the motions of two drops was recorded by CCD camera system in the experiments to analyze the trajectories and velocities of the drops. Our experiments showed that, upon two drops approaching each other, the influence of the larger drop on the motion of the smaller one became significant. Meanwhile the smaller drop had a little influence on the larger one all the time. The oscillation of migration velocities of both drops was observed as they were approaching. For a short period the smaller drop even moved backward when it became side by side with the larger one during the migration. Although our experimental results on the behavior of two drops are basically consistent with the theoretical predictions, there are also apparent differences. 2006 Elsevier Ltd. All rights reserved. Keywords: Thermocapillary migration; Drop; Interaction; Oscillation 1. Introduction A bubble or drop will move when placed in another fluid with temperature gradient. This motion happens as a consequence of the variation of interfacial tension with temperature. Such a phenomenon is already known as Marangoni migration problem. With the development of microgravity science, bubble dynamics and droplet dynamics became a hot point problem of research because this investigation is very important for basic research as well as for applications in reduced gravity environment, such as space material science, chemical engineering and so on. Young et al. first investigated the thermocapillary migration of

Oxyhydrogen combustion and detonation driven shock tube

The performance of combustion driver ignited by multi-spark plugs distributed along axial direction has been analysed and tested. An improved ignition method with three circumferential equidistributed ignitors at main diaphragm has been presented, by which the produced incident shock waves have higher repeatability, and better steadiness in the pressure, temperature and velocity fields of flow behind the incident shock, and thus meets the requirements of aerodynamic experiment. The attachment of a damping section at the end of the driver can eliminate the high reflection pressure produced by detonation wave, and the backward detonation driver can be employed to generate high enthalpy and high density test flow. The incident shock wave produced by this method is well repeated and with weak attenuation. The reflection wave caused by the contracted section at the main diaphragm will weaken the unfavorable effect of rarefaction wave behind the detonation wave, which indicates that the forward detonation driver can be applied in the practice. For incident shock wave of identical strength, the initial pressure of the forward detonation driver is about 1 order of magnitude lower than that of backward detonation.

An analysis of subgrid-resolved scale interactions with use of results from direct numerical simulations

Subgrid nonlinear interaction and energy transfer are analyzed using direct numerical simulations of isotropic turbulence. Influences of cutoff wave number at different ranges of scale on the energetics and dynamics have been investigated. It is observed that subgrid-subgrid interaction dominates the turbulent dynamics when cut-off wave number locates in the energy-containing range while resolved-subgrid interaction dominates if it is in the dissipation range; By decomposing the subgrid energy transfer and nonlinear interaction into 'forward' and 'backward' groups according to the sign of triadic interaction, we find that individually each group has very large contribution, but the net of them is much smaller, implying that tremendous cancellation happens between these two groups.

Optimal bounded control of first-passage failure of quasi-integrable Hamiltonian systems with wide-band random excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged It$\ddot{\rm o}$ equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.

Experimental Investigation Of Particle Velocity Distributions In Windblown Sand Movement

With the PDPA (Phase Doppler Particle Analyzer) measurement technology, the probability distributions of particle impact and lift-off velocities on bed surface and the particle velocity distributions at different heights are detected in a wind tunnel. The results show that the probability distribution of impact and lift-off velocities of sand grains can be expressed by a log-normal function, and that of impact and lift-off angles complies with an exponential function. The mean impact angle is between 28 degrees and 39 degrees, and the mean lift-off angle ranges from 30 degrees to 44 degrees. The mean lift-off velocity is 0.81-0.9 times the mean impact velocity. The proportion of backward-impacting particles is 0.05-0.11, and that of backward-entrained particles ranges from 0.04 to 0.13. The probability distribution of particle horizontal velocity at 4 mm height is positive skew, the horizontal velocity of particles at 20 mm height varies widely, and the variation of the particle horizontal velocity at 80 mm height is less than that at 20 mm height. The probability distribution of particle vertical velocity at different heights can be described as a normal function.

First-passage failure of quasi-integrable Hamiltonian systems

The first-passage failure of quasi-integrable Hamiltonian si-stems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.

First-passage time of Duffing oscillator under combined harmonic and white-noise excitations

The first-passage time of Duffing oscillator under combined harmonic and white-noise excitations is studied. The equation of motion of the system is first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. Numerical results for two resonant cases with several sets of parameter values are obtained and the analytical results are verified by using those from digital simulation.

Optimal bounded control of first-passage failure of strongly non-linear oscillators under combined harmonic and white-noise excitations

A procedure for designing the optimal bounded control of strongly non-linear oscillators under combined harmonic and white-noise excitations for minimizing their first-passage failure is proposed. First, a stochastic averaging method for strongly non-linear oscillators under combined harmonic and white-noise excitations using generalized harmonic functions is introduced. Then, the dynamical programming equations and their boundary and final time conditions for the control problems of maximizing reliability and of maximizing mean first-passage time are formulated from the averaged Ito equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraint. Finally, the conditional reliability function, the conditional probability density and mean of the first-passage time of the optimally controlled system are obtained from solving the backward Kolmogorov equation and Pontryagin equation. An example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation. (C) 2003 Elsevier Ltd. All rights reserved.

An optimal theory for an expansion of flow quantities to capture the flow structures

An optimal theory on how database analysis to capture the flow structures has been developed in this paper, which include the POD method as its special case. By means of the remainder minimization method in the Sobolev space, for more general optimal conditions the new theory has the potential to overcome an inherent limitation of the POD method, i.e., it cannot be used to the situations in which the optimal condition is other than the inner product global one. As an example, using the new theory, the database of a two-dimensional flow over a backward-facing step is analyzed in detail, with velocity and vorticity bases.

后台阶下游床面冲刷过程数值模拟研究

以床面瞬时剪应力作为泥沙起动及输运的水动力机制,建立了结构物周围复杂流场下床面局部冲刷的数学模型。并应用大涡模拟方法对后台阶下游三维湍流流动进行数值模拟,得到台阶下游床面瞬时剪应力的分布规律。为了确定床面瞬时剪应力与泥沙上扬通量的关系,先应用数学模型对不同模型参数下,冲刷开始后5分钟时台阶下游床面形状进行试算。通过试算与实验结果的比较,确定床面瞬时剪应力与泥沙上扬通量关系中需要的模型参数。进一步对冲刷开始后30分钟内台阶下游床面演化规律进行模拟,模拟结果与实验结果相符合。