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1.
A Maximum Principle Applied to Quasi-Geostrophic Equations 总被引:16,自引:7,他引:9
We study the initial value problem for dissipative 2D Quasi-geostrophic equations proving local existence, global results for small initial data in the super-critical case, decay of Lp-norms and asymptotic behavior of viscosity solution in the critical case. Our proofs are based on a maximum principle valid for more general flows.Partially supported by BFM2002-02269 grant.Partially supported by BFM2002-02042 grant. 相似文献
2.
The invariantsJ
K,k
of a framed knotK coloured by the irreducibleSU(2)
q
-module of dimensionk are studied as a function ofk by means of the universalR-matrix. It is shown that whenJ
K,k
is written as a power series inh withq=e
h
, the coefficient ofh
d
is an odd polynomial ink of degree at most 2d+1. This coefficient is a Vassiliev invariant ofK. In the second part of the paper it is shown that ask varies, these invariants span ad-dimensional subspace of the space of all Vassiliev invariants of degreed for framed knots. The analogous questions for unframed knots are also studied.Partially supported by NSF Grant DMS-9123657 相似文献
3.
We introduce a class of stochastic models of particles on the cubic lattice ℤ
d
with velocities and study the hydrodynamical limit on the diffusive spacetime scale. Assuming special initial conditions
corresponding to the incompressible regime, we prove that in dimensiond≧3 there is a law of large numbers for the empirical density and the rescaled empirical velocity field. Moreover the limit
fields satisfy the corresponding incompressible Navier-Stokes equations, with viscosity matrices characterized by a variational
formula, formally equivalent to the Green-Kubo formula.
Partially supported by GNFM-CNR and MURST.
Partially supported by GNFM-CNR, INFN and MURST.
Partially supported by U.S. National Science Foundation grant 9403462 and David and Lucile Packard Foundation Fellowship. 相似文献
4.
Alfred Wünsche 《Annalen der Physik》1992,504(3):181-197
The eigenvalue problem for arbitrary linear combinations kα + μα? of a boson annihilation operator α and a boson creation operator α? is solved. It is shown that these operators possess nondegenerate eigenstates to arbitrary complex eigenvalues. The expansion of these eigenstates into the basic set of number states | n >, (n = 0, 1, 2, …), is found. The eigenstates are normalizable and are therefore states of a Hilbert space for | ζ | < 1 with ζ ? μ/k and represent in this case squeezed coherent states of minimal uncertainty product. They can be considered as states of a rigged Hilbert space for | ζ | ? 1. A completeness relation for these states is derived that generalizes the completeness relation for the coherent states | α 〉. Furthermore, it is shown that there exists a dual orthogonality in the entire set of these states and a connected dual completeness of the eigenstates on widely arbitrary paths over the complex plane of eigenvalues. This duality goes over into a selfduality of the eigenstates of the hermitian operators kα + k* α? to real eigenvalues. The usually as nonexistent considered eigenstates of the boson creation operator α? are obtained by a limiting procedure. They belong to the most singular case among the considered general class of eigenstates with ζ ? μ/k as a parameter. 相似文献
5.
László?Erd?s Benjamin?Schlein Horng-Tzer?Yau 《Communications in Mathematical Physics》2009,287(2):641-655
We consider N × N Hermitian random matrices with independent identical distributed entries. The matrix is normalized so that the average spacing
between consecutive eigenvalues is of order 1/N. Under suitable assumptions on the distribution of the single matrix element, we prove that, away from the spectral edges,
the density of eigenvalues concentrates around the Wigner semicircle law on energy scales . Up to the logarithmic factor, this is the smallest energy scale for which the semicircle law may be valid. We also prove
that for all eigenvalues away from the spectral edges, the ℓ
∞-norm of the corresponding eigenvectors is of order O(N
−1/2), modulo logarithmic corrections. The upper bound O(N
−1/2) implies that every eigenvector is completely delocalized, i.e., the maximum size of the components of the eigenvector is
of the same order as their average size.
In the Appendix, we include a lemma by J. Bourgain which removes one of our assumptions on the distribution of the matrix
elements.
Supported by Sofja-Kovalevskaya Award of the Humboldt Foundation. On leave from Cambridge University, UK.
Partially supported by NSF grant DMS-0602038. 相似文献
6.
We show that for an odd prime r>3 and an integer g>1, in the projective representation given by the SO(3) Witten-Reshitikhin-Turaev theory at an rth root of unity, the image of the mapping class group of a surface of genus g is dense.
Partially supported by NSF DMS 0100537 and DMS 0354772.
Partially supported by NSF EIA 0130388, and DMS 0354772, and ARO. 相似文献
7.
Lisa C. Jeffrey 《Communications in Mathematical Physics》1992,147(3):563-604
We derive explicit formulas for the Chern-Simons-Witten invariants of lens spaces and torus bundles overS
1, for arbitrary values of the levelk. Most of our results are for the groupG=SU(2), though some are for more general compact groups. We explicitly exhibit agreement of the limiting values of these formulas ask with the semiclassical approximation predicted by the Chern-Simons path integral.Partially supported by an NSF Graduate FellowshipAddress as of September 1, 1991: School of Natural Science, Institute for Advanced Study, Princeton, NJ 08540; USA 相似文献
8.
《The European Physical Journal C - Particles and Fields》2005,39(3):311-329
New results are reported on inclusive charged particle production inK
+
p,π
+
p andpp collisions at 250 GeV/c. Inclusive longitudinal and transverse momentum spectra of positively and negatively charged particles
are presented. Scaling in the fragmentation regions and scaling violation in the central c.m. region is investigated in detail.
The topological pseudo-rapidity densities are shown to scale in the c.m. energy range from 22 to 900 GeV.
Partially funded by the German Federal Minister for Research and Technology (BMFT) under the contract number 053AC41P
Partially supported by grants from CPBP 01.06 and 01.09 相似文献
9.
In this paper we considered several formally determined problems in two dimensions. There are no global identifiability results for these problems. However, we can recover an important feature of these functions, namely their singularities. More precisely, we prove that one can determine the location and strength of singularities of anL
compactly supported potential by knowing the associated scattering amplitude at a fixed energy. Also we prove that one can determine the location and strength of the singularities of the sound speed of a medium by making measurements just on the boundary of the medium.Partially supported by NSF grant DMS-9123742Partially supported by NSF grant DMS-9100178 相似文献
10.
The partition functions of quantum Yang-Mills theory have an expansion in powers of the coupling constant; the leading order term in this expansion is called the semiclassical approximation. We study the semiclassical approximation for Yang-Mills theory on a compact Riemannian 4-manifold using geometric techniques, and do explicit calculations for the case when the manifold is the 4-sphere. This involves calculating the Riemannian measure and certain functional determinants on the moduli space of self-dual connections. The main result is that the contribution to the semiclassical partition functions coming from thek=1 connections on the 4-sphere isfinite andcalculable. We also discuss a renormalization procedure in which the radius of the 4-sphere is allowed to tend to infinity.Partially supported by N.S.F. grant DMS-8905211Partially supported by N.S.F. grant DMS-8802885 相似文献
11.
We construct a cellular space which has as a continuous limit the Euclidean spaceR
N
. We consider quantum mechanics on this cellular space and we examine in particular an harmonic oscillator and a free particle on the cellularR
1,R
2 respectively. In both cases we find that the energy spectrum is bounded from above.Partially supported by CEC Science project No SC1-CT91-0729 相似文献
12.
S. Brajamani P. S. Mazumdar S. K. Chowdhury Sukanya Sur 《International Journal of Theoretical Physics》1991,30(4):487-493
The ground state and first few excited energy levels of the generalized anharmonic oscillator defined by the HamiltonianH=–d
2/dx
2+x
2+x
2k (k=3, 4,...) have been calculated by employing the method of quantum normal form, which is the quantum mechanical analogue of the classical Birkhoff-Gustavson normal form. The present energy eigenvalues are consistent with other tabulations of the energy levels. 相似文献
13.
It is proved that a nucleus of chargeZ can bind at mostZ+O(Z
a) electrons, witha=47/56.Partially supported by a NSF grant at Princeton UniversitySupported by a Sloan Foundation Dissertation Fellowship at Princeton University 相似文献
14.
We study the motion of a tagged particle in a one-dimensional lattice gas with nearest-neighbor asymmetric jumps, withp (respectively,q),p > q, the probability to jump to the right (left). It was shown in Ref. 6 that the fluctuations in the position of the tagged particle behave normally; (X)2Dt. Here we compute explicitly the diffusion coefficient. We findD=(1-)(p-q). where is the gas density. The result confirms some recent conjectures based on theoretical arguments and computer experiments.Partially supported by NSF grant No. DMR81-14726.Partially supported by CNR.Partially supported by CNPq, grant No. 201682-83. 相似文献
15.
In this paper we study the topology of
, the moduli spaces ofSU(2) monopoles associated with the Yang-Mills-Higgs and Bogomol'nyi equations, and (m)
k
, non-linear models from quantum field theory. Beautiful work of Donaldson [18, 19], Hitchin [24, 25] and Taubes [37, 39, 40] shows that gauge equivalence classes of monopoles correspond to based rational self-maps of the Riemann sphere. Similarly, the non-linear models we consider here are based harmonic maps from the Riemann sphere to complex projectivem space. In seminal work, Segal [35] studied (m)
k
, the space of based rational maps from the Riemann sphere to complex projectivem space of a fixed degreek. Any element of (m)
k
is clearly an element of
k
2
CP(m), the space of all based continuous maps from the Riemann sphere to complex projectivem space of a fixed degreek, and this assignment gives rise to the natural inclusion of (m)
k
in
k
2
CP(m). Segal showed that these natural inclusions are homotopy equivalences through dimensionk(2m – 1). As the topology of the two-fold loop space 2
CP(m) is well understood, Segal's result gives a very efficient way to explicitly determine the low dimensional topology of (m)
k
. Thus iterated loop spaces have much to say about the topology of monopoles and non-linear models.Partially supported by NSF grant DMS-8508950Partially supported by NSF grant DMS-8701539 相似文献
16.
Aldo Procacci Benedetto Scoppola Victor Gerasimov 《Communications in Mathematical Physics》2003,235(2):215-231
Given an infinite graph 𝔾 quasi-transitive and amenable with maximum degree Δ, we show that reduced ground state degeneracy
per site W
r
(𝔾, q) of the q-state antiferromagnetic Potts model at zero temperature on 𝔾 is analytic in the variable 1/q, whenever |2Δe
3
/q|<1. This result proves, in an even stronger formulation, a conjecture originally sketched in [12] and explicitly formulated
in [16 and 19], based on which a sufficient condition for W
r
(𝔾, q) to be analytic at 1/q=0 is that 𝔾 is a regular lattice.
Received: 16 January 2002 / Accepted: 17 October 2002 Published online: 18 February 2003
RID="*"
ID="*" Partially supported by CNPq (Brazil)
RID="**"
ID="**" Partially supported by CNR, G.N.F.M. (Italy)
Communicated by H. Spohn 相似文献
17.
Without using product representations or elaborate comparisons of zeros we prove the two key properties of the Bessel function ratioJ
p+1
j
p+1,1
x/J
p
j
p,1
x that we used to prove the Payne-Pólya-Weinberger conjecture. In these new proofs we use only differential equations and the Rayleigh-Ritz method for estimating lowest eigenvalues. The new proofs admit generalization to other related problems where our previous proofs fail.Partially supported by FONDECYT (Chile) project number 1238-90 相似文献
18.
The rotation number for almost periodic potentials 总被引:10,自引:2,他引:8
We define and analyze the rotation number for the almost periodic Schrödinger operatorL= –d
2/dx
2+q(x). We use the rotation number to discuss (i) the spectrum ofL; (ii) its relation to the Korteweg-de Vries equation.Partially supported by the National Science Foundation under Grant NSF-MCS 77-01986 相似文献
19.
We study resonances associated to Schrödinger operators with compactly supported potentials on ℝd, d≥3, odd. We consider potentials depending holomorphically on a parameter For certain such families, for all z except those in a pluripolar set, the associated resonance–counting function has order of growth d.Partially supported by NSF grant DMS 0088922. 相似文献
20.
The high-velocity distribution of a two-dimensional dilute gas of Maxwell molecules under uniform shear flow is studied. First
we analyze the shear-rate dependence of the eigenvalues governing the time evolution of the velocity moments derived from
the Boltzmann equation. As in the three-dimensional case discussed by us previously, all the moments of degreek⩾4 diverge for shear rates larger than a critical valuea
c
(k)
, which behaves for largek asa
c
(k)
∼k
−1. This divergence is consistent with an algebraic tail of the formf(V) ∼V
−4-σ(a), where σ is a decreasing function of the shear rate. This expectation is confirmed by a Monte Carlo simulation of the Boltzmann
equation far from equilibrium. 相似文献