共查询到10条相似文献,搜索用时 171 毫秒
1.
IntroductionEady’smodelisanimportantexampleof 3_dimensionalcontinuouslystratifiledquasi_geostrophicmotion[1].Recently ,someresultsofnonlinearstabilityforEady’smodelwereobtained[2 ,3],wheretheresultofRef.[3 ]istheimprovementofRef.[2 ] ,suchthattheresultisthebestinsomesense[4 ].Inthispaper,theresultofRef.[3 ]isimprovedbyestablishinganenhancedPoincar啨typeintegralinequality .ThenewresultshowsthatthenecessaryandsufficientlinearstabilityconditionforEady’smodelisalsothesu… 相似文献
2.
Stability analysis of nonplanar free vibrations of a cantilever beam is made by using the nonlinear normal mode concept. Assuming
nonplanar motion of the beam, we introduce a nonlinear two-degree-of-freedom model by using Galerkin’s method based on the
first mode in each direction. The system turns out to have two normal modes. Using Synge’s stability concept, we examine the
stability of each mode. In order to check the validity of the stability criterion obtained analytically, we plot a Poincaré
map of the motions neighboring on each mode obtained numerically. It is found that the maps agree with the stability criterion
obtained analytically. 相似文献
3.
Instabilities associated with 2:1 and 4:1 resonances of two models for the parametric forcing of a strictly nonlinear oscillator
are analyzed. The first model involves a nonlinear Mathieu equation and the second one is described by a 2 degree of freedom
Hamiltonian system in which the forcing is introduced by the coupling. Using averaging with elliptic functions, the threshold
of the overlapping phenomenon between the resonance bands 2:1 and 4:1 (Chirikov’s overlap criterion) is determined for both
models, offering an approximation for the transition from local to global chaos. The analytical results are compared to numerical
simulations obtained by examining the Poincaré section of the two systems. 相似文献
4.
Dmitry Khavinson Mihai Putinar Harold S. Shapiro 《Archive for Rational Mechanics and Analysis》2007,185(1):143-184
One of the earliest attempts to rigorously prove the solvability of Dirichlet’s boundary value problem was based on seeking
the solution in the form of a “potential of double layer”, and this leads to an integral equation whose kernel is (in general)
both singular and non-symmetric. C. Neumann succeeded with this approach for smoothly bounded convex domains, and H. Poincaré,
by a tremendous tour de force, showed how to push through the analysis for domains with sufficiently smooth boundaries but
no hypothesis of convexity. In this work he was (according to his own account) guided by consideration of a variational problem
involving the partition of energy of an electrostatic field induced by charges placed on the boundary of a domain, more precisely
the charge distributions which render stationary the energy of the field inside the domain divided by the energy of the field
outside the domain. Unfortunately, a rigorous treatment of this problem was not possible with the tools available at that
time (as Poincaré was well aware). So far as we know, the only one to propose a rigorous treatment of Poincaré’s problem was
T. Carleman (in the two-dimensional case) in his doctoral dissertation. Thanks to later developments (especially concerning
Sobolev spaces, and spectral theory of operators on Hilbert space) we can now give a complete, general and rigorous account
of Poincaré’s variational problem, and that is the main object of the present paper. As a by-product, we refine some technical
aspects in the theory of symmetrizable operators and prove in any number of dimensions the basic properties of the analogue
of the planar Bergman–Schiffer singular integral equation. We interpret Poincaré’s variational principle as a non-selfadjoint
eigenvalue problem for the angle operator between two distinct pairs of subspaces of potentials. We also prove a series of
novel spectral analysis facts (some of them conjectured by Poincaré) related to the Poincaré–Neumann integral operator. 相似文献
5.
A new method of formulating dyadic Green‘s functions in lossless , reciprocal and unbounded chiral medium was presented. Based on Helmholtz theorem and the nondivergence and irrotational splitting of dyadic Dirac delta-function was this method, the electrical vector dyadic Green‘s function equation was first decomposed into the nondivergence electrical vector dyadic Green‘s function equation and irrotational electrical vector dyadic Green‘s function equation, and then Fourier‘s transformation was used to derive the expressions of the non-divergence and irrotational component of the spectral domain electrical dyadic Green‘s function in chiral media. It can avoid having to use the wavefield decomposition method and dyadic Green‘s function eigenfunction expansion technique that this method is used to derive the dyadic Green‘s functions in chiral media. 相似文献
6.
On the basis of the nonlinear stability theorem in the context of Arnol’s second theorem for the generalized Phillips model, nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated. By choosing appropriate artificial stable basic flows, the upper bounds on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model are obtained, which are analytic completely and without the limitation of infinitesimal initial disturbance. 相似文献
7.
Daniel Matthes Ansgar Jüngel Giuseppe Toscani 《Archive for Rational Mechanics and Analysis》2011,199(2):563-596
We study families of convex Sobolev inequalities, which arise as entropy–dissipation relations for certain linear Fokker–Planck
equations. Extending the ideas recently developed by the first two authors, a refinement of the Bakry–émery method is established,
which allows us to prove non-trivial inequalities even in situations where the classical Bakry–émery criterion fails. The
main application of our theory concerns the linearized fast diffusion equation in dimensions d ≧ 1, which admits a Poincaré, but no logarithmic Sobolev inequality. We calculate bounds on the constants in the interpolating
convex Sobolev inequalities, and prove that these bounds are sharp on a specified range. In dimension d = 1, our estimates improve the corresponding results that can be obtained by the measure-theoretic techniques of Barthe and
Roberto. As a by-product, we give a short and elementary alternative proof of the sharp spectral gap inequality first obtained
by Denzler and McCann. In further applications of our method, we prove convex Sobolev inequalities for a mean field model
for the redistribution of wealth in a simple market economy, and the Lasota model for blood cell production. 相似文献
8.
1 IntroductionandHypothesesInrecentyears,withthedevelopmentofnonlinearsciencesandthedeepstudyofchaoticphenomena,thebifurcationproblemsofhomoclinicloopsforhigherdimensionalsystemswerestudiedextensivelyandalotofresultswereobtained (seeRefs.[1~ 8] ) .Especially ,Refs.[3 ,4]discussedthehomoclinicloopbifurcationswithcodimension 2 .Refs.[5,6]consideredthedegeneratedhomoclinicbifurcations.Inthispaper,westudythebifurcationsoftwistedhomoclinicloopsandthestabilityinhigherdimensionalspace .Considerth… 相似文献
9.
A new lattice model of traffic flow based on Nagatani’s model is proposed by taking the effect of driver’s memory into account.
The linear stability condition of the extended model is obtained by using the linear stability theory. The analytical results
show that the stabile area of the new model is larger than that of the original lattice hydrodynamic model by adjusting the
driver’s memory intensity parameter p of the past information in the system. The modified KdV equation near the critical point is derived to describe the traffic
jam by nonlinear analysis, and the phase space could be divided into three regions: the stability region, the metastable region,
and the unstable region, respectively. Numerical simulation also shows that our model can stabilize the traffic flow by considering
the information of driver’s memory. 相似文献
10.
Vincent Girinon 《Journal of Mathematical Fluid Mechanics》2011,13(3):309-339
Following the ideas developed in Girinon (Annales de l’Institut Poincaré. Analyse Non Linéaire 26:2025–2053, 2009), we prove
the existence of a weak solution to Navier–Stokes equations describing the isentropic flow of a gas in a bounded region, W ì R3{\Omega\subset \mathbf{R}^{3}} , with nonhomogeneous Dirichlet boundary conditions on ∂Ω. 相似文献