共查询到20条相似文献,搜索用时 31 毫秒
1.
A mixed spectral and finite difference model to study finite amplitude baroclinic waves in a differentially heated rotating annulus is presented. The model consists of the full Navier-Stokes equations and the heat equation. The field variables f = f(r, φ z; t) are decomposed into zonally averaged components fo(r, z; t) and eddy components f(r, φ, z; t), the latter being periodic in f and represented in terms of Fourier series. The unknowns fo(r, z; t) and fc, s(r, z; t), which are Fourier amplitudes of f′(r, φ, z; t) are governed by two-dimensional primitive equations with the addition of source terms. These equations are solved semi-implicitly by the alternating direction implicit method on variable grids.A simplified model with two Fourier components which permits self-interaction of the chosen wave and the interaction of the wave and the mean fields had been used to repeat a computation done by G. P. Williams, who used a fully three-dimensional finite difference algorithm. We can reproduce almost all of Williams' results in 1/20 of the computing time with the present model. It only requires 1/30 the additional computer storage of Williams' finite difference model over the axisymmetric problem.The potential of the present model for investigation of multiwave interaction as well as the advantages and disadvantages of the two different approaches is discussed. 相似文献
2.
3.
I.S. Osad'ko 《Optics Communications》2010,283(23):4671-4675
A single two-level molecule driven by CW-laser field and a photomultiplier tube (PMT) are considered as two parts of the united dynamical system connected with each other by photons of molecular fluorescence. Each PMT is characterized by a rate α of photo-effect and by a rate β of PMT recovery. A theory for the photon distribution function wN(t) and for the photoelectric pulse distribution function fn(t) for such a system is built up. If times 1/ α and 1/ β characterizing PMT are much shorter as compared to the average time interval 1/ k between two successively emitted photons of fluorescence, the photon and the photoelectron distribution functions coincide with each other, i.e. fn(t) ≅ wN(t). A relation between wN(t) and fn(t) is studied in detail for the case in which PMT works slower as compared to the rate k of photon emission, i.e. at 1/ α, 1/ β ≥ 1/ k. 相似文献
4.
A system of N particles $\xi ^N = x_1 ,\upsilon_1,...,x_N ,\upsilon _N )$ interacting self-consistently with one wave Z = A exp(iφ) is considered. Given initial data (Z (N)(0), ξ N (0)), it evolves according to Hamiltonian dynamics to (Z (N)(t), ξ N (t)). In the limit N → ∞, this generates a Vlasov-like kinetic equation for the distribution function f(x, v, t), abbreviated as f(t), coupled to the envelope equation for Z: initial data (Z (∞)(0), f(0)) evolve to (Z (∞)(t), f(t)). The solution (Z, f) exists and is unique for any initial data with finite energy. Moreover, for any time T>0, given a sequence of initial data with N particles distributed so that the particle distribution f N(0) → f(0) weakly and with Z (N)(0) → Z(0) as N → ∞, the states generated by the Hamiltonian dynamics at all times 0 ≤ t ≤ T are such that (Z (N)(t), f N(t)) converges weakly to (Z (∞)(t), f(t)). 相似文献
5.
Francesco Calogero 《Journal of Nonlinear Mathematical Physics》2018,25(3):433-441
We use previous results concerning the time evolution of the zeros xn(t) of time-dependent polynomials pN (z;t) or entire functions F(z;t) of the complex variable z, in order to identify lots of nonlinearly-coupled, finite or infinite, systems of Ordinary Differential Equations the solutions of which feature remarkable Diophantine properties. 相似文献
6.
In this paper, we study the asymptotic behavior of solutions of semilinear abstract differential equations (*) u′(t) = Au(t) + t
n
f(t, u(t)), where A is the generator of a C
0-semigroup (or group) T(·), f(·, x) ∈ A for each x ∈ X, A is the class of almost periodic, almost automorphic or Levitan almost periodic Banach space valued functions ϕ: ℝ → X and n ∈ {0, 1, 2, ...}. We investigate the linear case when T(·)x is almost periodic for each x ∈ X; and the semilinear case when T(·) is an asymptotically stable C
0-semigroup, n = 0 and f(·, x) satisfies a Lipschitz condition. Also, in the linear case, we investigate (*) when ϕ belongs to a Stepanov class S
p-A defined similarly to the case of S
p-almost periodic functions. Under certain conditions, we show that the solutions of (*) belong to A
u:= A ∩ BUC(ℝ, X) if n = 0 and to t
n
A
u ⊕ w
n
C
0 (ℝ, X) if n ∈ ℕ, where w
n(t) = (1 + |t|)n. The results are new for the case n ∈ ℕ and extend many recent ones in the case n = 0.
Dedicated to the memory of B. M. Levitan 相似文献
7.
J. Fischer 《Communications in Mathematical Physics》1973,30(3):249-260
The properties of the scattering amplitude allow to define a functionf(z) satisfying the following conditions:
- f(z) is holomorphic in a simply connected domain , which can be mapped conformally onto the unit disk;
- |Imf(z)| is bounded by some constantM in ;
- |Ref(z)| is known not to exceed some constantm on a certain part Γ1 of the boundary Γ of ;f(z) is continuously extensible onto Γ.
8.
We study the behavior of 〈σ0x(t)σnx(0)〉 and 〈σ0y(t)σny(0)〉 for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t → ∞ and n → ∞with , , or where z is fixed of order one. In this latter region the general Painlevé V solution is shown to reduce to a Painlevé II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values. 相似文献
9.
An explicit form for the charmed quark fragmentation function DCc(z) into hadrons has been obtained with the help of the “reciprocity relation” and the c-quark distribution function in charmed mesons (the function calculated in terms of the Kuti-Weisskopf model). DCc(z) turns out to peak mainly at z close to 1. The analysis of new data on muon pair production in neutrino reactions points to such a behaviour of the DCc(z) function. The obtained fragmentation function, contrary to those, used earlier, leads to a charmed particle (average) multiplicity in e+e?-annihilation independent of energy. 相似文献
10.
A. Dermoune 《Journal of statistical physics》1997,88(3-4):873-883
We study the discontinuities (shocks) of the solution to the Burgers equation in the limit of vanishing viscosity (the inviscid limit) when the initial value is the opposite of the standard Poisson process p. We show that this solution is only defined for t ε (0, 1). Let T 0 = 0 and T n , n≧1, be the successive jumps of p. We prove that for all M > 0 the inviscid limit is characterized on the region x ε (-∞, M], t ε (0, 1) by the increasing process $N(t) = \sup \{ n \in \mathbb{N} {\text{| }}M + nt > T_n \} $ and the random set I(x) = {n ε {0,..., N(t)}‖T n -nt≦x<T n+1 - nt}. The positions of shocks are given in a precise manner. We give the distribution of N(t) and also the distribution of its first jump. We also prove similar results when the initial value is u μ(y, 0) = -μp(y/μ2) + μ-1 max(y, 0), μ ε (0, 1). 相似文献
11.
From the nuclear spin-lattice relaxation of the out-of-layer 19F nuclei in magnetic fields perpendicular to the c-axis the low-frequency component of the autocorrelation function 〈Sz(t)Sz(O)〉 of Ni in ordered K2Mn0.975Ni0.025F4 is found to be substantially reduced relative to the Mn host. The experimental rates vs temperature are in accord with those for relaxation involving two spin excitations calculated with local Green's functions. 相似文献
12.
A.J. Buras 《Nuclear Physics B》1973,56(1):275-286
Multiplicity distributions Ψn(k) in the generalized Feynman gas model of order k (defined by saying that all integrated correlation functions fn except f1,…,fk are zero) are derived and expressed in terms of Poisson distributions with different ”average multiplicities”, which are related to the integrated correlation functions. The relations between Ψn(k) and Ψn(j) for arbitrary positive integers k,j are found. An intuitive picture to gain a better feeling for these relations is developed.On the basis of our formulae we show that the experimentally observed multiplicity distributions (between 50 GeV/c and 303 GeV/c incoming momentum) can be well reproduced by those of a Feynman gas model of order two. Other applications of our formulae are suggested. 相似文献
13.
The cross sections for the reactions N14(n, α)B11 and N14(n, t)C12 have been measured in the neutron energy range 4.0 to 6.4 MeV and at 2.5 MeV. Mono-energetic neutrons were produced in the D(d, n) He3 reaction using a gas target. The (n, α) and (n, t) disintegrations were detected in a gridded ionization chamber filled with an argonnitrogen mixture. The response of the chamber under different operation conditions is described. The excitation functions, measured with a neutron energy resolution of 40 to 50 keV, are given for theα 0 group from the N14(n,α)B11 reaction over the entire neutron energy range and for theα 1 group and the t0 group from N14(n, t) C12 for neutron energies above 4.3 and 5.6 MeV, respectively. 相似文献
14.
We consider one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in current experiments with ultracold Bose-Fermi mixtures. We apply the Bethe ansatz technique to find the exact ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We use it to prove the absence of the demixing, contrary to prediction of a mean-field approximation. Combining exact solution with local density approximation in a harmonic trap, we calculate the density profiles and frequencies of collective modes in various limits. In the strongly interacting regime, we predict the appearance of low-lying collective oscillations which correspond to the counterflow of the two species. In the strongly interacting regime, we use exact wavefunction to calculate the single particle correlation functions for bosons and fermions at low temperatures under periodic boundary conditions. Fourier transform of the correlation function is a momentum distribution, which can be measured in time-of-flight experiments or using Bragg scattering. We derive an analytical formula, which allows to calculate correlation functions at all distances numerically for a polynomial time in the system size. We investigate numerically two strong singularities of the momentum distribution for fermions at kf and kf + 2kb. We show, that in strongly interacting regime correlation functions change dramatically as temperature changes from 0 to a small temperature ∼Ef/γ ? Ef, where Ef = (π?n)2/(2m), n is the total density and γ = mg/(?2n) ? 1 is the Lieb-Liniger parameter. A strong change of the momentum distribution in a small range of temperatures can be used to perform a thermometry at very small temperatures. 相似文献
15.
In this paper, we consider a class of five-dimensional Ricci-flat vacuum solutions, which contain two arbitrary functions μ(t) and ν(t). It is shown that μ(t) can be rewritten as a new arbitrary function f(z) in terms of redshift z and the f(z) can be determined by choosing particular deceleration parameters q(z) which gives early deceleration and late time acceleration. In this way, the 5D cosmological model can be reconstructed and the evolution of the universe can be determined.
PACS: 04.50.+h, 98.80.-k 相似文献
16.
D.G. Hummer 《Journal of Quantitative Spectroscopy & Radiative Transfer》1983,30(3):281-287
The generalized exponential-integral function V(x, y) defined here includes as special cases the function E(2)1(x) = V(x, 0) introduced by van de Hulst and functions M0(x) = V(x, 1) and N0(x) = V(x, -1) introduced by Kourganoff in connection with integrals of the form ∫ En)t)Em(t±x), which play an important role in the theory of monochromatic radiative transfer. Series and asymptotic expressions are derived and, for the most important special cases, y = 0 and y = 1, Chebyshev expansions and rational approximations are obtained that permit the function to be evaluated to at least 10 sf on 0<x<∞ using 16 sf arithmetic. 相似文献
17.
We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h α ? J. Such a perturbation treated in the lowest nonvanishing order over h α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s z (t, r)s z (0, 0)》 ∝ h z 2 f(t, r), where f(t, r) ∝ [max(t, Jr)]–4. We have studied the effects of the next order of perturbation in h z and found an additional term of the order h z 4 in the correlation function 《s z (t, r)s z (0, 0)》 which scales as h z 4 cosγ/r 3 at Jt? r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by the weak imaginary vector potential A x ∝ i h z 2 . 相似文献
18.
The general solution of the equation of motion for the quantum mechanical distribu tion functionf 2(r 1 P 1,r 2 p 2;t)in the two particle space is given by means of the Schrödinger scattering functions. A special initial condition leads to the usual Boltzmann equation plus density correction terms, which depend on the scattering matrixt(p′,p). In the long wavelength limit and in lowest order oft(p′,p) the Landau corrections to the simple Boltzmann streaming part are obtained. 相似文献
19.
For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this paper.Under the gap-condition that|Ek(s)-En(s)|λ0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,respectively.As an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough. 相似文献
20.
Leif Arkeryd 《Journal of statistical physics》1983,31(2):347-361
This paper studies the boundedness of solutionsf of the initial-value problem for the space-homogeneous Boltzmann equation for inverse kth power forces, whenk>5, and under angular cutoff. The main result is that if the initial value isf 0 ? 0 with (1 + ¦υ¦2)φ0 εL 1 and (1 + ¦υ¦)s f 0ε L∞ for somes > 2, then (1 + ¦υ¦s'f tεL ∞ fort>0 and essυ,t sup(1 + ¦υ¦)s'f(υ, t,) < ∞ for anys′ ? s whens ? 5, and anys′ ? s ifs > 5. 相似文献