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1.
So far fluid mechanical Nambu brackets have mainly been given on an intuitive basis. Alternatively an algorithmic construction of such a bracket for the two-dimensional vorticity equation is presented here. Starting from the Lie-Poisson form and its algebraic properties it is shown how the Nambu representation can be explicitly constructed as the continuum limit from the structure preserving Zeitlin discretization. 相似文献
2.
Abstracting from Nambu’s work [1] on the generalization of Hamiltonian mechanics, we obtain the concept of a classical Nambu
algebra of type I (CNA-I). Consistency requirement of time evolution of the trilinear Nambu bracket leads to a new five point
identity (FPI). Incorporating the FPI into CNA-I, we obtain a classical Nambu algebra of type II (CNA-II). Nambu’s algorithm
for generalized classical mechanics turns out to be compatible with CNA-II. Tensor product composition of two CNA-I’s results
in another CNA-I whereas that of two CNA-II’s does not. This implies that interacting systems cannot be consistently treated
in Nambu’s framework. It is shown that the recent generalization of Nambu mechanics based on an arbitrary Lie group (instead
of the particular case of the rotation group as in the case of Nambu’s original algorithm) suggested by Biyalinicki-Birula
and Morrison [2], is compatible with CNA-I but not with CNA-II. Relaxation of the commutative and associative observable product
by making it nonassociative so as to arrive at the quantum counterpart meets with serious difficulties from the view point
of tensor product composition property. Thus neither CNA-I nor CNA-II have quantum counterparts. Implications of our results
are discussed with special reference to existing work on Nambu mechanics in the literature. 相似文献
3.
Salvatore De Gregorio 《Journal of statistical physics》1990,59(5-6):1251-1263
The one-dimensional model for the three-dimensional vorticity equation proposed by Constantin, Lax, and Majda is discussed. Some unsatisfactory points are examined, especially when the viscosity is introduced. A different model is suggested, which, while less solvable than the previous one, can be more strictly connected with the three-dimensional vorticity behavior. The study is of interest for the numerical treatment of the three-dimensional vorticity equation. 相似文献
4.
P. H. Chavanis A. Naso B. Dubrulle 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,77(2):167-186
Using a Maximum Entropy Production Principle (MEPP), we
derive a new type of relaxation equations for two-dimensional
turbulent flows in the case where a prior vorticity distribution is
prescribed instead of the Casimir constraints [R. Ellis, K. Haven,
B. Turkington, Nonlinearity 15, 239 (2002)]. The particular case of
a Gaussian prior is specifically treated in connection to minimum
enstrophy states and Fofonoff flows. These relaxation equations are
compared with other relaxation equations proposed by Robert and
Sommeria [Phys. Rev. Lett. 69, 2776 (1992)] and Chavanis
[Physica D 237, 1998 (2008)]. They can serve as numerical
algorithms to compute maximum entropy states and
minimum enstrophy states with appropriate constraints. We perform
numerical simulations of these relaxation equations in order to
illustrate geometry induced phase transitions in geophysical flows. 相似文献
5.
An algebraic analysis of the Hamiltonian formulation of the model two-dimensional gravity is performed. The crucial fact is
an exact coincidence of the Poisson brackets algebra of the secondary constraints of this Hamiltonian formulation with the
SO(2,1)-algebra. The eigenvectors of the canonical Hamiltonian H
c
are obtained and explicitly written in closed form. 相似文献
6.
G. G. Ékle 《Russian Physics Journal》1972,15(2):220-224
The first-order symmetry operators of the Dirac equation are classified according to their tensor properties under transformations of the homogeneous Lorentz group; a minimal system of generators for the ring of symmetry operators of the free Dirac equation is obtained, and the physical meaning of the spin operators is considered; fields are found which admit symmetry operators of first order.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 84–89, February, 1972.The author is grateful to V. N. Shapovalov for discussions and valuable suggestions. 相似文献
7.
This paper presents a direct algebraic method of searching for analytic solutions of the two-dimensional time-independent Schrödinger equation that is impossible to separate into two one-dimensional ones. As examples, two-dimensional polynomial and Morse-like potentials are discussed. Analytic formulas for the ground state wave functions and the corresponding energies are presented. These results cannot be obtained by another known method. 相似文献
8.
推导得到气压坐标中的动量叉乘形式的垂直涡度方程,这个动量叉乘形式的涡度方程包含了水平风的平流旋转效应,可称为平流涡度方程.由于水平风场的平流作用可由等压面天气图直观分析得到,因此平流涡度方程可方便用于实际天气分析.对2006年的Bilis台风移动过程中由经典涡度方程和平流涡度方程计算得到的垂直涡度倾向进行对比分析发现,二者计算得到的垂直涡度倾向变化的分布形式接近,但平流涡度方程计算得到的倾向的数值明显大于经典涡度方程的数值,正负涡度倾向区也更集中.对Bilis移动过程中的垂直涡度方程和平流涡度方程中各项的计算分析表明,水平风场的平流旋转作用是Bilis发展移动过程中垂直涡度变化的一个主要因素,是造成垂直涡度增强并发展的主要原因.因此,当水平风场平流旋转效应较强时,平流作用对垂直涡度倾向变化起主导作用,可直接用平流项来近似分析Bilis台风的涡度变化.而平流涡度方程中地转涡度和散度项的变化趋势与Bilis台风的移动路径有较好的一致性,这一项对台风的移动路径预报有更好的指示意义. 相似文献
9.
We study shock reflection for the two 2D Burgers equation. This model equation is an asymptotic limit of the Euler equations, and retains many of the features of the full equations. A von Neumann type analysis shows that the 2D Burgers equation has detachment, sonic, and Crocco points in complete analogy with gas dynamics. Numerical solutions support the detachment/sonic criterion for transition from regular to Mach reflection. There is also strong numerical evidence that the reflected shock in the 2D Burgers Mach reflection forms a smooth wave near the Mach stem, as proposed by Colella and Henderson in their study of the Euler equations. 相似文献
10.
M. I. Faingol'd 《Russian Physics Journal》1987,30(4):291-294
The coherent scattering of spin-S particles by a monatomic crystal film is considered, with rescattering taken into account. A relation between the amplitudes qj of different diffraction orders and the dielectric tensor
() of the two-dimensional crystal is found. The relation can be used to obtain
() for an arbitrary frequency (including resonant frequencies) in terms of elastic scattering data. The possibility of bound states of the particles in the monatomic film is demonstrated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 30–34, April, 1987.The author thanks V. L. Vinetskii for interest in the work and for useful discussions. 相似文献
11.
12.
Recently, a cryptosystem based on two-dimensional discretized chaotic maps was proposed [T. Xiang, et al., Phys. Lett. A 364 (2007) 252]. In this Letter, we cryptanalyze the proposal using algebraic methods. We give three different attacks that yield all the secret parameters of the cryptosystem. 相似文献
13.
Classical statistical theories of turbulence have shown their limitations, in that they cannot predict much more than the energy spectrum in an idealized setting of statistical homogeneity and stationarity. We explore the applicability of a conditional statistical modeling approach: can we sort out what part of the information should be kept, and what part should be modeled statistically, or, in other words, “dissipated”? Our mathematical framework is the initial value problem for the two-dimensional (2D) Euler equations, which we approximate numerically by solving the 2D Navier-Stokes equations in the vanishing viscosity limit. In order to obtain a good approximation of the inviscid dynamics, we use a spectral method and a resolution going up to 81922. We introduce a macroscopic concept of dissipation, relying on a split of the flow between coherent and incoherent contributions: the coherent flow is constructed from the large wavelet coefficients of the vorticity field, and the incoherent flow from the small ones. In previous work, a unique threshold was applied to all wavelet coefficients, while here we also consider the effect of a scale by scale thresholding algorithm, called scale-wise coherent vorticity extraction. We study the statistical properties of the coherent and incoherent vorticity fields, and the transfers of enstrophy between them, and then use these results to propose, within a maximum entropy framework, a simple model for the incoherent vorticity. In the framework of this model, we show that the flow velocity can be predicted accurately in the L2 norm for about 10 eddy turnover times. 相似文献
14.
We consider a system ofN hard disks in ?2 in the Boltzmann-Grad limit (i.e.N → ∞,d ↘ 0,N·d → λ?1>0, whered is the diameter of the disks). If λ is sufficiently small and if the joint distribution densities factorize at time zero, we prove that the time-evolved one-particle distribution converges for all times to the solution of the Boltzmann equation with the same initial datum. 相似文献
15.
Analytical solutions of a two-dimensional heat equation are obtained by the method of separation of variables. In the analysis
presented here, the partial differential equation is directly transformed into a set of ordinary differential equations. The
closed-form transient temperature distributions and heat transfer rates are generalized to a linear combination of the products
of Fourier-Bessel series of the exponential type. 相似文献
16.
17.
J. Zagrodziński 《Physics letters. A》1976,57(3):213-214
Three-parameter families of the solutions of sine-Gordon equation in two dimensions are presented. 相似文献
18.
A. Libin 《Journal of Experimental and Theoretical Physics》2012,115(6):1128-1139
A linear combination of a pair of dual anisotropic decaying Beltrami flows with spatially constant amplitudes (the Trkal solutions) with the same eigenvalue of the curl operator and of a constant velocity orthogonal vector to the Beltrami pair yields a triplet solution of the force-free Navier-Stokes equation. The amplitudes slightly variable in space (large scale perturbations) yield the emergence of a time-dependent phase between the dual Beltrami flows and of the upward velocity, which are unstable at large values of the Reynolds number. They also lead to the formation of large-scale curved prisms of streamlines with edges being the strings of singular vorticity. 相似文献
19.
The accurate and efficient computation of lattice sums for the three-dimensional Helmholtz equation is considered for the cases where the underlying lattice is one- or two-dimensional. We demonstrate, using careful numerical computations, that the reduction method, in which the sums for a two-dimensional lattice are expressed as a sum of one-dimensional lattice sums leads to an order-of-magnitude improvement in performance over the well-known Ewald method. In the process we clarify and improve on a number of results originally formulated by Twersky in the 1970s. 相似文献
20.
New numerical techniques are presented for the solution of a two-dimensional anomalous sub-diffusion equation with time fractional derivative. In these methods, standard central difference approximation is used for the spatial discretization, and, for the time stepping, two new alternating direction implicit (ADI) schemes based on the L1 approximation and backward Euler method are considered. The two ADI schemes are constructed by adding two different small terms, which are different from standard ADI methods. The solvability, unconditional stability and H1 norm convergence are proved. Numerical results are presented to support our theoretical analysis and indicate the efficiency of both methods. 相似文献