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31.
A solute transport through a porous medium is examined provided that the fluid leaving the porous sample returns back in a continuous way. The porous medium is thus included into a closed hydrodynamic circuit. This cycling process is suggested as an experimental tool to determine porous medium parameters describing transport. In the present paper the mathematical theory of this method is developed. For the advective type of transport with solute retention and degradation in porous medium, the system of transport equations in a closed circuit is transformed to a delay differential equation. The exact analytical solution to this equation is obtained. The solute concentration manifests both the oscillatory and monotonous behaviors depending on system parameters. The number of oscillation splashes is shown to be always finite. The maximum/minimum points are determined as solutions of a polynomial equation whose degree depends on the unknown solution itself. The cyclic methods to determine porous medium parameters as porosity and retention rate are developed. 相似文献
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IntroductionThestabilityoftheintervalmatrixanduncertainsystemwithtimedelayhavebeenconsideredbyresearchersinthepapers [1 -1 3 ] .Thestabilityandαexponentialstabilityofthefollowingintervaldynamicalsystemwithsingletimedelay x(t) =N[P ,Q]x(t) +N[C ,D]x(t-τ)havebeenconsi… 相似文献
35.
Michael C. Mackey Irina G. Nechaeva 《Journal of Dynamics and Differential Equations》1994,6(3):395-426
We study the stability of linear stochastic differential delay equations in the presence of additive or multiplicative white and colored noise. Using a stochastic analog of the second Liapunov method, sufficient conditions for mean square and stochastic stability are derived. 相似文献
36.
Cargo Pendulation Reduction of Ship-Mounted Cranes 总被引:4,自引:0,他引:4
Ship-mounted cranes are used to transfer cargo from large container ships to smaller lighters when deep-water ports are not
available. The wave-induced motion of the crane ship can produce large pendulations of the cargo being hoisted and cause operations
to be suspended. In this work, we show that it is possible to reduce these pendulations significantly by controlling the slew
and luff angles of the boom. Such a control can be achieved with the heavy equipment that is already part of the crane so
that retrofitting existing cranes would require a small effort. Moreover, the control is superimposed on the commands of the
operator transparently. The successful control strategy is based on delayed feedback of the angles of the cargo-hoisting cable
in and out of the plane of the boom and crane tower. Its effectiveness is demonstrated in a fully nonlinear three-dimensional
computer simulation and in an experiment with a 1/24th-scale model of a T-ACS (The Auxiliary Crane Ship) crane mounted on
a platform moving with three degrees of freedom. The results demonstrate that the pendulations can be significantly reduced,
and therefore the range of sea conditions in which cargo-transfer operations can take place can be greatly expanded. 相似文献
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Fractal modeling of the rugged crack geometry is considered for the stable and dynamic fracture mechanics characterizing the morphology of a fracture surface and the influence of its growth. It is shown that the fractal dimension has a strong influence on the rising of the R-curve in brittle materials. For the unstable Griffith–Mott’s approach or dynamical crack growth the fractal dimension has a strong influence on the velocity limit of the crack growth. It is also shown that the limit of crack velocity lowers with increasing surface ruggedness (higher fractal dimension D = 2 − H) explaining the intangibility of the Rayleigh wave velocity by the cracks. 相似文献
39.
Hans-Otto Walther 《Journal of Dynamics and Differential Equations》2007,19(3):593-622
Automatic soft landing is modeled by a differential equation with state-dependent delay. It is shown that in the model soft
landing occurs for an open set of initial data, which is determined by means of a smooth invariant manifold.
相似文献
40.
对线性系统模态控制及其时滞补偿进行研究。模态控制分控制全部模态和控制有限模态两种情况 ,时滞补偿采用移相补偿。最后结合算例对两种控制模态下的控制效果和控制有限模态时的时滞补偿进行了数值计算和结果对比 相似文献