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1.
Destabilization of deep-water risers by a heaving platform   总被引:2,自引:0,他引:2  
Offshore gas and oil fields are being discovered and exploited nowadays in water depths of more than 2000 m. In order to convey the hydrocarbon to the sea level, a steel slender pipe is installed between wellhead at the sea bed and floating platform. If used in deep waters, these pipes are commonly referred to as deep-water risers. The heave (vertical motion) of a floating platform induces a fluctuation in time of the axial tension of the riser. A possible and undesirable phenomenon is the excitation of a transverse riser vibration caused by this fluctuation. Owing to this fluctuation, the governing equation of transverse motion of the riser is a nonlinear partial differential equation containing a time-dependent coefficient. As a first step, this equation is linearized around the straight equilibrium, and stability of this equilibrium is investigated using the Galerkin method and the Floquet theory. Then, the dynamic equilibrium is studied that the riser reaches if its straight equilibrium is unstable. This is done using a numerical time-domain technique. Two qualitatively different mechanisms of stability loss are distinguished, discussed and exemplified. The first is classical parametric resonance that occurs solely due to periodic time variation of the axial tension. The second mechanism occurs if the amplitude of vibration of the platform is large enough to change tension into compression in a segment of the riser for a part of the vibration cycle. It is shown that the second mechanism can cause dangerously large dynamic stresses in the riser.  相似文献   

2.
F. Vodák 《Physica A》1979,97(2):463-465
The balance equation of the specific area of a discontinuity surface is derived and the effect of this balance on the formulation of the hypothesis of local equilibrium is discussed.  相似文献   

3.
W. Maass 《Annalen der Physik》1972,483(3):205-210
For the linearized BOLTZMANN equation and a class of “modifications” of the linearized BOLTZMANN equation (including the usual BOLTZMANN equation) exponential-asymptotic stability of the total equilibrium is proved with respect to some boundary and existence assumptions which seem to be physically reasonable. Of course, this structural stability is important if BOLTZMANN 's equation has to be considered under the influence of “perturbations” or if it is substituted by model equations.  相似文献   

4.
Kinetic methods are used to derive the transport equations, virial equation, dynamic equilibrium condition, and the equation of the envelope of an axially symmetric paraxial relativistic electron beam propagating in an Ohmic plasma channel during the evolution of resistive firehose instability. The equation of the beam envelope is generalized by taking this instability into account.  相似文献   

5.
We associate to the plane incompressible Euler equation with periodic conditions the corresponding Hopf equation, as an equation for measures on the space of solenoidal distributions. We define equilibrium states as the solutions of the stationary Hopf equation. We find a class of equilibrium states which corresponds to a class of infinitely divisible distributions, and investigate the properties of gaussian and poissonian states. Equilibrium dynamics for a class of poissonian states is constructed by means of the Onsager vortex equations.Research partially supported by C.N.R., G.N.F.M.  相似文献   

6.
An impurity particle coupling to its host fluid via inelastic hard sphere collisions is considered. It is shown that the exact equation for its distribution function can be mapped onto that for an impurity with elastic collisions and an effective mass. The application of this result to the Enskog-Lorentz kinetic equation leads to several conclusions: (1) every solution in the elastic case is equivalent to a class of solutions in the granular case; (2) for an equilibrium host fluid the granular impurity approaches equilibrium at a different temperature, with a dominant diffusive mode at long times; (3) for a granular host fluid in its scaling state, the granular impurity approaches the corresponding scaling solution.  相似文献   

7.
Several ad hoc models describe inelastic nucleon-nucleus and nucleus-nucleus collisions at high energy. Why do they work and how are they related? We investigate this question by studying an exactly soluble model. It is based on Glauber's multiple scattering approach. The following results are derived and discussed: (1) The inclusive cross section for the observation of one nucleon is the space integral of a Wigner transform. (2) The Wigner transform obeys a classical transport equation. (3) The equation is equivalent to the Boltzmann equation at high energy. (4) The interpenetration of two nuclei is viewed as a diffusion phenomenon governed by a Fokker-Planck equation. (5) Hydrodynamic equations are shown to yield approximate solutions to the transport equation. (6) A kind of thermal equilibrium is quickly reached in a nuclear collision process. (7) The equilibrium equation of state corresponds to an ideal gas with two degrees of freedom.  相似文献   

8.
The nonlinear Langevin equation for a system of Coulomb particles with random processes, which are functionals of the velocity distribution function of such particles, has been derived and analyzed. It is shown by direct numerical solutions that this equation correctly describes the collisional relaxation of such a system even in the case of anomalous deviation of the initial velocity distribution of particles from the equilibrium distribution. The equation can be conveniently used in the Monte Carlo methods and in “particle-in-cell” methods.  相似文献   

9.
A kinetic equation is derived for the two-time phase space correlation function in a dilute classical electron gas in equilibrium. The derivation is based on a density expansion of the correlation function and the resummation of the most divergent terms in each order in the density. It is formally analogous to the ring summation used in the kinetic theory of neutral fluids. The kinetic equation obtained is consistent to first order in the plasma parameter and is the generalization of the linearized Balescu-Guersey-Lenard operator to describe spatially inhomogeneous equilibrium fluctuations. The importance of consistently treating static correlations when deriving a kinetic equation for an electron gas is stressed. A systematic derivation as described here is needed for a further generalization to a kinetic equation that includes mode-coupling effects. This will be presented in a future paper.  相似文献   

10.
Density waves analogous to second sound are studied in a gas of magnons. Quasiparticle interaction is considered for both equilibrium and non equilibrium thermodynamics. The non equilibrium theory is based on a Boltzmann equation for magnon-magnon scattering. Contrary to the total energy and magnetization, (quasi)-momentum is not strictly conserved. In the hydrodynamic regime, the transport equation is reduced to a set of two coupled equations for the magnetization and the local temperature. For low temperatures these have diffusive and propagating solutions while for high temperatures, where momentum is dissipated by Umklapp processes, the solutions are only diffusive. The magnetization response function and the corresponding spectral function are discussed for various wavenumbers and temperatures.  相似文献   

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