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.

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.

Interparticle distance-temperature-strain rate equivalence for the brittle-tough transition in polymer blends

From the angle of energy transformation an equation was obtained for the brittle transition in polymer blends. The effects of interparticle distance, temperature and strain rate on the brittle-tough transition in polymer blends were characterized by this equation. The calculations show that, for this transition: (1) increasing temperature and decreasing interparticle distance are equivalent and the shift factor increases with increasing temperature; (2) decreasing strain rate and decreasing interparticle distance have equivalent effects on the transition; (3) the strain rate must be optimum in order to find the brittle-tough transition phenomena for a given temperature region. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.

Oscillatory instability of Rayleigh-Marangoni-Bénard convection in two-layer liquid systems

The oscillatory behaviour of the Rayleigh-Marangoni-Bénard convective instability (R-M-B instability) regarding two combinations of two-layer fluid systems has been investigated theoretically and numerically. For the two-layer system of Silicone oil (10cSt) over Fluorinert (FC70), both linear instability analysis and 2D numerical simulation show that the instability of the system depends strongly on the depth ratio Hr = H1/H2 of the two-layer liquid. The oscillatory regime at the onset of R-M-B convection enlarges with reducing Γ = Ra/Ma values. In the two-layer system of Silicone oil (2cSt) over water, it loses its stability and onsets to steady convection at first, then the steady convection bifurcates to oscillatory convection with increasing Rayleigh number Ra. This behaviour was found through numerical simulation above the onset of steady convection in the case of r = 2.9, ε=(Ra-Ruc)/Rac = 1.0, and Hr = 0.5. Our findings are different from the previous study of the Rayleigh-Benard instability and show the strong effects of the thermocapillary force at the interface on the time-dependent oscillations at or after the onset of convection. We propose a secondary oscillatory instability mechanism to explain the experimental observation of Degen et al. [Phys. Rev. E, 57 (1998), 6647-6659].

Information Preservation Modeling of Rayleigh-Benard Transition from Thermal Conduction to Convection

Onset and evolution of the Rayleigh-Benard (R-B) convection are investigated using the Information Preservation (IP) method. The information velocity and temperature are updated using the Octant Flux Splitting (OFS) model developed by Masters & Ye based on the Maxwell transport equation suggested by Sun & Boyd. Statistical noise inherent in particle approaches such as the direct simulation Monte Carlo (DSMC) method is effectively reduced by the IP method, and therefore the evolutions from an initial quiescent fluid to a final steady state are shown clearly. An interesting phenomenon is observed: when the Rayleigh number (Ra) exceeds its critical value, there exists an obvious incubation stage. During the incubation stage, the vortex structure clearly appears and evolves, whereas the Nusselt number (Nu) of the lower plate is close to unity. After the incubation stage, the vortex velocity and Nu rapidly increase, and the flow field quickly reaches a steady, convective state. A relation of Nu to Ra given by IP agrees with those given by DSMC, the classical theory and experimental data.

Monte Carlo Simulation Of Thermal Fluctuations Below The Onset Of Rayleigh-Benard Convection

The density fluctuations below the onset of convection in the Rayleigh-Benard problem are studied with the direct simulation Monte Carlo method. The particle simulation results clearly show the connection between the static correlation functions of fluctuations below the critical Rayleigh number and the flow patterns above the onset of convection for small Knudsen number flows (Kn=0.01 and Kn=0.005). Furthermore, the physical nature for no convection in the Rayleigh-Benard problem under large Knudsen number conditions (Kn>0.028) is explained based on the dynamics of fluctuations.

Mechanical and thermal structure of a cylindrical plume in the earth's mantle

A mantle plume is understood as a hot, narrow, upwelling flow in the earth's mantle and accompanied by an efficient transfer of mass and energy from deep to upper layer of the earth. The cylindrical plume in earth's mantle plays an important role in explaining the origin of the surface hot spots and linear island chains. From the basic hydrodynamical equations, the detailed mechanical and thermal structure of a cylindrical plume of Newtouian fluids with temperature and pressure-dependent viscosity are given in the present paper. For two sets of rheological parameters the radial profiles of upward velocity, temperature and viscosity in the plume and radiuses of the plume at various depths have been calculated.

Experimental Study on Bénard-Marangoni Convection in Double Immiscible Liquid Layer

An experimental investigation of Bénard-Marangoni convection has been performed in double immiscible liquid layers of rectangular configuration on the ground. The two kinds of liquid are 10cst silicon oil and FC-70 respectively. The size of rectangular chamber is 100mm×40mm in horizontal cross-section. The evolution processes of convection are observed in the differential thickness ratio of two liquid layers. The critical temperature difference was measured via the detections of fluid convection by a particle image velocimetry (PIV) in the vertical cross-section of the liquid layer. The critical temperature difference or the critical Marangoni number was given. And the influence of the thickness ratio of two liquid layers on the convection instability was discussed. The evolution processes of patterns and temperature distributions on the interface are displayed by using thermal liquid crystal. The velocity distributions on the interface were also obtained. In comparison with the thermocapillary effect, the effect of buoyancy convection will relatively increase when the depth of the liquid layer increases. Because of the coupling of buoyancy and thermocapillary effect, the convection instability is much more complex than that in the microgravity environment. And the critical convection depends on the change of the thickness of liquid layers and also the change of thickness ratio of two liquid layers.

Rayleigh-Marangoni-Bénard Convective Instability

The Rayleigh-Marangoni-Benard convective instability (R-M-B instability) and flow patterns in the two-layer system of silicon oil 10cSt and Fluorinert FC70 liquids are studied theoretically and experimentally. Both linear instability analysis and 2D numerical simulation (A=L/H=10) were performed to study the influence of thermocapillary force on the convective instability of the two-layer system. Time-dependent oscillations arising at the onset of convection were investigated in a larger various range of two-layer depth ratios (Hr=H1/H2) from 0.2 to 5.0 for different total depth less than 12mm. Our results are different from the previous study on the Rayleig-B閚ard instability and show the strong effects of thermocapillary force at the interface on the time-dependent oscillations at the onset of instability convection. Primary experimental results of the critical instability parameters and the convective structure in the R-M-B convection have been obtained by using the digital particle image velocimetry (DPIV) system, and a good agreement in comparison with the results of numerical simulation was obtained.

Si based quantum cascade structure: from energy band structures design to materials growth

In this paper, we propose an n-type vertical transition bound-to-continuum Ge/SiGe quantum cascade structure utilizing electronic quantum wells in the L and Gamma valleys of the Ge layers. The optical transition levels are located in the quantum wells in the L valley. The Gamma-L intervalley scattering is used to depopulate the lower level and inject the electrons into the upper level. We also show that high quality Si1-yGey pseudosubstrate is obtained by thermal annealing of Si1-xGex/Ge/Si structure. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Thermal effects on Rayleigh-Marangoni-Benard instability in a system of superposed fluid and porous layers

Thermal effects of the heat transfer at free surface (represented by Biot number) on the Rayleigh-Marangoni-Benard instability in a system of liquid-porous layers with top free surface are investigated numerically. The results indicate that this thermal effect can evidently lead to the mode transition of convection, which is overlooked in previous works. (C) 2010 Elsevier Ltd. All rights reserved.

Instability of Two-Layer Rayleigh-Benard Convection with Interfacial Thermocapillary Effect

The linear instability analysis of the Rayleigh-Allarangoni-Benard convection in a two-layer system of silicon oil 10cS and fluorinert FC70 liquids are performed in a larger range of two-layer depth ratios H, from 0.2 to 5.0 for different total depth H less than or equal to 12 mm. Our results are different from the previous study on the Rayleigh-Benard instability and show strong effects of thermocapillary force at the interface on the time-dependent oscillations arising from the onset of instability convection.

A New Ignition Criterion Based Upon a Critical Thermal Energy Density

It has long been known that various ignition criteria of energetic materials have been limited in applicability to small regions. In order to explore the physical nature of ignition, we calculated how much thermal energy per unit mass of energetic materials was absorbed under different external stimuli. Hence, data of several typical sensitivity tests were analyzed by order of magnitude estimation. Then a new concept on critical thermal energy density was formulated. Meanwhile, the chemical nature of ignition was probed into by chemical kinetics.