共查询到20条相似文献,搜索用时 806 毫秒
1.
François Monard Plamen Stefanov Gunther Uhlmann 《Communications in Mathematical Physics》2015,337(3):1491-1513
We study the geodesic X-ray transform X on compact Riemannian surfaces with conjugate points. Regardless of the type of the conjugate points, we show that we cannot recover the singularities and, therefore, this transform is always unstable (ill-posed). We describe the microlocal kernel of X and relate it to the conjugate locus. We present numerical examples illustrating the cancellation of singularities. We also show that the attenuated X-ray transform is well posed if the attenuation is positive and there are no more than two conjugate points along each geodesic; but it is still ill-posed if there are three or more conjugate points. Those results follow from our analysis of the weighted X-ray transform. 相似文献
2.
A theoretical model for interaction of a submerged moving body with the conjugate flow in a three-layer fluid is proposed to depict the internal flat solitary wave, which is observed in experiments conducted by the present authors. A set of coupled nonlinear algebraic equations is derived for the interracial displacements. The numerical results indicate that (a) the conjugate flow due to a two-dimensional body moving at the bottom possesses an apparent behaviour with two convex interfaces, (b) the solution satisfying the existence criterion is always unique near the relatively stable state of system. Theoretical analysis is qualitatively consistent with the experimental results obtained. 相似文献
3.
In quantum optics, some models are considered to
describe many aspects of the dynamics of atoms coupled to an
electromagnetic field (laser). The simplest atomic model is of
course the two-level-atom which is governed by the Bloch optical
equations. In general this system is solved in the steady state or
by using some approximations. An extended analytic approach is
considered for this coupled equations. The separation approach of
coupled differential equations is always possible with a sequence
of special transformation into nonlinear differential equations.
The conditions that permit an exact solution of three coupled
systems are extracted in a natural manner. The case of sodium atom
moving along the axis of a standing-wave is investigated in some
details. 相似文献
4.
M. B. Mensky 《Journal of Russian Laser Research》2006,27(4):332-340
The well-known Heisenberg’s uncertainty relation is an inequality between uncertainties of canonically conjugate observables
in a given state. In this interpretation, the Heisenberg’s uncertainty relation is a rigorous mathematical theorem and is,
therefore, always valid. However, the same inequality is often applied in the situation of measurement, where it is illustrated
in a quite different way. The uncertainty relation is then an inequality connecting the precision (resolution) of the measurement
of one observable and the uncertainty of the conjugate observable in the state arising after the measurement. It turns out
that in such an interpretation the Heisenberg’s inequality may be violated for some measurement readouts that emerge with
small but finite probabilities. Making use of the uncertainties averaged in a special way over all possible measurement readouts,
one may formulate an inequality of the type of Heisenberg’s inequality but valid for any measurement.
Paper submitted by the author in English on 28 April 2006. 相似文献
5.
6.
IGCC系统中新一代先进燃气轮机透平通流部分处于高温高湿的工作环境,因此其内部流动存在固有的复杂的流热耦合问题。为指导燃气轮机透平叶片冷却系统设计必须开展对流热耦合问题的试验与数值研究。本文在一平板气膜冷却流热耦合实验台上开展了模拟新一代燃气轮机透平通流部分高温高湿工作条件的流热耦合机理研究,并进行了数值模拟。研究工作... 相似文献
7.
8.
研究变质量Chetaev型非完整系统Appell方程的Mei对称性和Mei守恒量.建立变质量Chetaev型非完整系统的Appell方程和系统的运动微分方程; 给出函数沿系统运动轨道曲线对时间t全导数的表示式,并在群的无限小变换下,给出变质量Chetaev型非完整系统Appell方程Mei对称性的定义和判据;得到用Appell函数表示的Mei对称性的结构方程和Mei守恒量的表达式,并举例说明结果的应用.
关键词:
变质量
非完整系统
Appell方程
Mei守恒量 相似文献
9.
Martin C Gutzwiller 《Annals of Physics》1981,133(2):304-331
The periodic Toda lattice consists of N particles which move along a closed line and are coupled with an exponential spring to their immediate neighbors. This system, in contrast to the open Toda lattice, has only bound states. In the method of Kac and Van Moerbeke, the classical periodic Toda chain is transformed to a new of set of canonically conjugate variables, μ and ν, which are closely related to the natural coordinates of an open Toda chain with one particle less. The quantum mechanical eigenfunctions for this reduced system are constructed explicitly, and this allows the quantum mechanical analogs of μ and ν to be defined. The bounds states for the periodic Toda chain are then written as linear combinations of functions resembling the wave functions of the reduced open chain. These functions satisfy a set of remarkably simple recursion formulas, and the coefficients in the expansion can be written essentially as a product of as many factors as pairs of conjugate variables μ and ν. Each factor is given as a solution of a second order difference equation which can be recognized as a quantum analog for the equations of motion of one pair μ and ν. The quantization conditions result from cancelling out the exponential growth in the overall wave function, and are phrased in terms of certain phase angles being submultiples of π according as the representation of the group of cyclic permutations. The calculations are simple for N = 3, and moderately tricky for N = 4 although the results are always fairly obvious. 相似文献
10.
J. L. Torres 《Il Nuovo Cimento D》1991,13(2):177-185
Summary It is assumed that Darwin's principle translates into optimal regimes of operation along metabolical pathways in a biological
system. Fitness is then defined in terms of the distance of a given individual's thermodynamic parameters from their optimal
values. The method is illustrated testing maximum power as a criterion of merit satisfied in ATP synthesis.
The author of this paper has agreed to not receive the proofs for correction.
Support from Secretaría de Educación Pública and CONACYT-México is gratefully acknowledged.
Permanent address. 相似文献
11.
Jean Fisch Marc Henneaux James Stasheff Claudio Teitelboim 《Communications in Mathematical Physics》1989,120(3):379-407
A complete canonical formulation of the BRST theory of systems with redundant gauge symmetries is presented. These systems includep-form gauge fields, the superparticle, and the superstring. We first define the Koszul-Tate differential and explicitly show how the introduction of the momenta conjugate to the ghosts of ghosts makes it acyclic. The global existence of the BRST generator is then demonstrated, and the BRST charge is proved to be unique up to canonical transformations in the extended phase space, which includes the ghosts. Finally, the BRST cohomology in classical mechanics is investigated and shown to be equal to the cohomology of the exterior derivative along the gauge orbits, as in the irreducible case. This is done by re-expressing the exterior algebra along the gauge orbits as a free differential algebra containing generators of higher degree, which are identified with the ghosts of ghosts. The quantum cohomology is not dealt with.Aspirant du Fonds National de la Recherche Scientifique (Belgium)Chercheur qualifié au Fonds National de la Recherche Scientifique (Belgium) 相似文献
12.
We have developed a way to represent Mohr–Coulomb failure within a mantle-convection fluid dynamics code. We use a viscous model of deformation with an orthotropic viscoplasticity (a different viscosity is used for pure shear to that used for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation, neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane, which is formally equivalent in any symmetric formulation. We also allow for strain-weakening of the material. The material can remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-integration-point finite element code and show a number of examples of extension and compression of a crustal block with a Mohr–Coulomb failure criterion. The formulation itself is general and applies to 2- and 3-dimensional problems. 相似文献
13.
The spin-orbit problem in celestial mechanics describes the motion of an oblate satellite moving on a Keplerian orbit around a primary body. We apply the conjugate points criterion for the nonexistence of rotational invariant tori. We treat both the conservative case and a case including a dissipative effect modeling a tidal torque generated by internal nonrigidity. As a by-product of the conjugate points criterion we obtain a global view of the dynamics, thanks to the introduction of a tangent orbit indicator, which allows us to discern the dynamical character of the motion. 相似文献
14.
光折变介质的相位共轭波强度的近似表达式 总被引:1,自引:0,他引:1
以光折变介质中非线性耦合波微分方程的一种精确解为基础,对在推导这种精确解过程中起重要作用的一个守恒量进行讨论,通过初等变换,在不同的特殊条件下得到相位共轭波强度的几处近似表达式。与报道的其它近似方法相比,本近似方法不需要建立及求解简化的微分方程因而具有普适,简单的特点。 相似文献
15.
Jie Sha Lixiang Zhang & Chuijie Wu 《advances in applied mathematics and mechanics.》2015,7(6):754-779
This paper is concerned with a low-dimensional dynamical system model
for analytically solving partial differential equations (PDEs). The model proposed is
based on a posterior optimal truncated weighted residue (POT-WR) method, by which
an infinite dimensional PDE is optimally truncated and analytically solved in required
condition of accuracy. To end that, a POT-WR condition for PDE under consideration
is used as a dynamically optimal control criterion with the solving process. A set of
bases needs to be constructed without any reference database in order to establish a
space to describe low-dimensional dynamical system that is required. The Lagrangian
multiplier is introduced to release the constraints due to the Galerkin projection, and
a penalty function is also employed to remove the orthogonal constraints. According
to the extreme principle, a set of ordinary differential equations is thus obtained
by taking the variational operation of the generalized optimal function. A conjugate
gradient algorithm by FORTRAN code is developed to solve the ordinary differential
equations. The two examples of one-dimensional heat transfer equation and nonlinear
Burgers’ equation show that the analytical results on the method proposed are good
agreement with the numerical simulations and analytical solutions in references, and
the dominant characteristics of the dynamics are well captured in case of few bases
used only. 相似文献
16.
The fundamental group and rational cohomology of the configuration spaces of the Skyrme and Faddeev-Hopf models are computed.
Physical space is taken to be a compact oriented 3-manifold, either with or without a marked point representing an end at
infinity. For the Skyrme model, the codomain is any Lie group, while for the Faddeev-Hopf model it is S2. It is determined when the topology of configuration space permits fermionic and isospinorial quantization of the solitons
of the model within generalizations of the frameworks of Finkelstein-Rubinstein and Sorkin. Fermionic quantization of Skyrmions
is possible only if the target group contains a symplectic or special unitary factor, while fermionic quantization of Hopfions
is always possible. Geometric interpretations of the results are given.
The first author was partially supported by NSF grant DMS-0204651
The second author was partially supported by EPSRC grant GR/R66982/01 相似文献
17.
A universal criterion for effectiveness of linear transformation of waves with locally close characteristic exponents in smoothly inhomogeneous media is obtained. The same criterion is applicable for estimating the effectiveness of nonadiabatic transitions in slow atomic collisions. The formalism developed for an analysis of the linear interaction of waves is based of the WKB asymptotic form of the solution of a scalar nth order ordinary differential equation. The obtained criterion can be applied in any practical problem for drawing a conclusion about the effectiveness of the linear interaction of modes if only the characteristic equation of waves in a homogeneous medium and the coefficients of the initial differential equation are known. In this case, the solution of the problem is reduced to elementary arithmetic calculations. 相似文献
18.
A derivation of the conjugation criterion for a rotating disc is reported. Characteristics of conjugate heat transfer on a
single disc and in a cavity formed by two discs, one rotating and the other stationary, are analysed. 相似文献
19.
The criterion, known from optics, of wave phase conjugation quality is accommodated for acoustical experiment. An incident focused sound beam at 5 MHz is propagated towards a supercritical magnetoelastic conjugator through an introduced random phase layer, and the conjugate beam propagates backwards through the layer to the source. 1D and 2D distributions of wave field are measured for the conjugate beam of finite amplitude using a membrane hydrophone. The maximum sound intensity of 640 W/cm2 and acoustic power of 4 W are registered in the focal maximum of the conjugate wave. The quality of WPC is calculated from the ratio between the power in the central maximum and the total power of the conjugate beam. The method is applied to compare two operation modes of a supercritical parametric conjugator. It is shown that in the linear mode the conjugator provides higher quality than in the nonlinear (0.54 compared to 0.24). 相似文献
20.
We propose a criterion for the separability of quantum pure states using the concept of a partial Hermitian conjugate. It is equivalent to the usual positive partial transposition criteria, with a simple physical interpretation. 相似文献