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11.
We discuss the parametrization of real finite-gap solutions of an integrable equation by frequency and wavenumber vectors. This parametrization underlies perturbation and averaging theories for the finite-gap solutions. Out of the framework of integrable equations, the parametrization gives a convenient coordinate system on the corresponding manifold of Riemann curves. 相似文献
12.
With the advent of medium and large gamma detector arrays, it is now possible to look at nuclear structure at high rotational
forces. The role of pairing correlations and their eventual breakdown, along with the shell effects have showed us the interesting
physics for nuclei at high spins — superdeformation, shape co-existence, yrast traps, alignments and their dramatic effects
on nuclear structure and so on. Nuclear structure studies have recently become even more exciting, due to efforts and possibilities
to reach nuclei far off from the stability valley. Coupling of gamma ray arrays with ‘filters’, like neutron wall, charged
particle detector array, gamma ray total energy and multiplicity castles, conversion electron spectrometers etc gives a great
handle to study nuclei produced online with ‘low’ cross-sections. Recently we studied, nuclei in mass region 80 using an array
of 8 germanium detectors in conjunction with the recoil mass analyser, HIRA at the Nuclear Science Centre and, most unexpectedly
came across the phenomenon of identical bands, with two quasi-particle difference. The discovery of magnetic rotation is another
highlight. Our study of light In nucleus, 107In brought us face to face with the ‘dipole’ bands. I plan to discuss some of
these aspects. There is also an immensely important development — that of the ‘radioactive ion beams’. The availability of
RIB, will probably very dramatically influence our ‘conventional’ concept of nuclear structure. The exotic shapes of these
exotic nuclei and some of their expected properties will also be touched upon. 相似文献
13.
We study questions related to the orientability of the infinite-dimensional moduli spaces formed by solutions of elliptic
equations for mappings of manifolds. The principal result states that the first Stiefel–Whitney class of such a moduli space
is given by the ℤ2-spectral flow of the families of linearised operators. Under an additional compactness hypotheses, we develop elements of
Morse–Bott theory and express the algebraic number of solutions of a non-homogeneous equation with a generic right-hand side
in terms of the Euler characteristic of the space of solutions corresponding to the homogeneous equation. The applications
of this include estimates for the number of homotopic maps with prescribed tension field and for the number of the perturbed
pseudoholomorphic tori, sharpening some known results.
Mathematics Subject Classifications (2000): 35J05, 58B15, 58E05, 58E20, 53D45 相似文献
14.
The paper deals with infinite-dimensional random dynamical systems. Under the condition that the system in question is of mixing type and possesses a random compact attracting set, we show that the support of the unique invariant measure is the minimal random point attractor. The results obtained apply to the randomly forced 2D Navier–Stokes system. 相似文献
15.
We study a class of dissipative nonlinear PDE's forced by a random force ηomega(
t
,
x
), with the space variable x varying in a bounded domain. The class contains the 2D Navier–Stokes equations (under periodic or Dirichlet boundary conditions),
and the forces we consider are those common in statistical hydrodynamics: they are random fields smooth in t and stationary, short-correlated in time t. In this paper, we confine ourselves to “kick forces” of the form
where the η
k
's are smooth bounded identically distributed random fields. The equation in question defines a Markov chain in an appropriately
chosen phase space (a subset of a function space) that contains the zero function and is invariant for the (random) flow of
the equation. Concerning this Markov chain, we prove the following main result (see Theorem 2.2): The Markov chain has a unique invariant measure. To prove this theorem, we present a construction assigning, to any invariant measure, a Gibbs measure for a 1D system with
compact phase space and apply a version of Ruelle–Perron–Frobenius uniqueness theorem to the corresponding Gibbs system. We
also discuss ergodic properties of the invariant measure and corresponding properties of the original randomly forced PDE.
Received: 24 January 2000 / Accepted: 17 February 2000 相似文献
16.
17.
We study space-periodic 2D Navier–Stokes equations perturbed by an unbounded random kick-force. It is assumed that Fourier coefficients of the kicks are independent random variables all of whose moments are bounded and that the distributions of the first N
0 coefficients (where N
0 is a sufficiently large integer) have positive densities against the Lebesgue measure. We treat the equation as a random dynamical system in the space of square integrable divergence-free vector fields. We prove that this dynamical system has a unique stationary measure and study its ergodic properties. 相似文献
18.
The mobility of dislocations in the over-barrier motion in different metals (Al, Cu, Fe, Mo) has been investigated using the molecular dynamics method. The phonon drag coefficients have been calculated as a function of the pressure and temperature. The results obtained are in good agreement with the experimental data and theoretical estimates. For face-centered cubic metals, the main mechanism of dislocation drag is the phonon scattering. For body-centered cubic metals, the contribution of the radiation friction becomes significant at room temperature. It has been found that there is a correlation between the temperature dependences of the phonon drag coefficient and the lattice constant. The dependences of the phonon drag coefficient on the pressure have been calculated. In contrast to the other metals, iron is characterized by a sharp increase in the phonon drag coefficient with an increase in the pressure at low temperatures due to the α-∈ phase transition. 相似文献
19.
We treat the nonlinear Klein-Gordon (NKG) equation as the Sine-Gordon (SG) equation, perturbed by a higher order term. It
is proved that most small-amplitude finite-gap solutions of the SG equation, which satisfy either Dirichlet or Neumann boundary
conditions, persist in the NKG equation and jointly form partial central manifolds, which are “Lipschitz manifolds with holes”.
Our proof is based on an analysis of the finite-gap solutions of the boundary problems for SG equation by means of the Schottky
uniformization approach, and an application of an infinite-dimensional KAM-theory.
The first author was supported by the Alexander von Humbold Foundation and the Sonder-forschungsbereich 288. 相似文献
20.
Summary We give a complete classification of the small-amplitude finite-gap solutions of the sine-Gordon (SG) equation on an interval under Dirichlet or Neumann boundary conditions. Our classification is based on an analysis of the finite-gap solutions of the boundary problems for the SG equation by means of the Schottky uniformization approach.On leave from IPPI, Moscow, Russia 相似文献