共查询到20条相似文献,搜索用时 281 毫秒
1.
Tian Li-xin 《应用数学和力学(英文版)》1994,15(10):973-980
In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operator in natural boundary space.make preparation for the further study longtime chaotic behaxior of infinite dimensiondynamics system in nonlinear Schrodinger equation. 相似文献
2.
沈惠川 《应用数学和力学(英文版)》1986,7(12):1125-1142
This work is the continuation and the distillation of the discussion of Refs. [1-4].(A)From complementarity principle we build up dissipation mechanics in this paper.It is a dissipative theory of correspondence with the quantum mechanics.From this theorywe can unitedly handle problems of macroscopic non-equilibrium thermodynamics andviscous hydrodynamics. and handle each dissipative and irreversible problems in quantummechanics.We prove the basic equations of dissipation mechanics to eigenvalues equationsof correspondence with the Schr(?)dinger equation or Dirac equation in this paper.(B)We unitedly merge the basic nonlinear equations of dissipative type, especially theNavier-Stokes equation as a basic equation for macroscopic non-equilibrium ther-modynamics and viscous hydrodynamics into integrability condition of basic equation ofdissipation mechanics. And we can obtain their exact solutions by the inverse scatteringmethod in this paper. 相似文献
3.
Within continuum dislocation theory the plane constrained uniaxial extension of a single crystal strip deforming in single or double slip is analyzed. For the single and symmetric double slip, the closed-form analytical solutions are found which exhibits the energetic and dissipative thresholds for dislocation nucleation, the Bauschinger translational work hardening, and the size effect. Numerical solutions for the non-symmetric double slip are obtained by finite element procedures. 相似文献
4.
Within continuum dislocation theory the plastic deformation of bicrystals under a mixed deformation of plane constrained uniaxial extension and shear is investigated with regard to the nucleation of dislocations and the dislocation pile-up near the phase boundaries of a model bicrystal with one active slip system within each single crystal. For plane uniaxial extension, we present a closed-form analytical solution for the evolution of the plastic distortion and of the dislocation network in the case of symmetric slip planes (i.e. for twins), which exhibits an energetic as well as a dissipative threshold for the dislocation nucleation. The general solution for non-symmetric slip systems is obtained numerically. For a combined deformation of extension and shear, we analyze the possibility of linearly superposing results obtained for both loading cases independently. All solutions presented in this paper also display the Bauschinger effect of translational work hardening and a size effect typical to problems of crystal plasticity. 相似文献
5.
A coupled nonlinear Schrodinger equations is considered in 2-D space. Based upon the conservation of mass and energy, local identities is established by the study of the limit behavior of the solutions, and L^2-concentration for the blow-up solutions with radially symmetry is obtained. 相似文献
6.
ATTACTORSOFDISSIPATIVESOLITONEQUATIONTianLi-xin(田立新)(DepartmentofMathematicsandPhysics,JiangsuUniversityofScienceandTechnolog... 相似文献
7.
Energy conservation of nonlinear Schrodinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory. 相似文献
8.
Energy conservation of nonlinear Schrodinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory. 相似文献
9.
We propose a new notion of weak solutions (dissipative solutions) for non-isotropic, degenerate, second-order, quasi-linear parabolic equations. This class of solutions is an extension of the notion of dissipative solutions for scalar conservation laws introduced by L. C. Evans. We analyze the relationship between the notions of dissipative and entropy weak solutions for non-isotropic, degenerate, second-order, quasi-linear parabolic equations. As an application we prove the strong convergence of a general relaxation-type approximation for such equations. 相似文献
10.
This paper revisits an extension of the Lagrangian-Hamiltonian mechanics that incorporates dissipative and non-potential fields, and non-integrable constraints in a compact form, such that one may obtain invariants of motion or possible invariant trajectories through an extension of Noether's theorem. A new concept of umbra-time has been introduced for this extension. This leads to a new form of equation, which is termed as the umbra-Lagrange's equation. The underlying variational principle, which is based on a recursive minimization of functionals, is presented. The introduction of the concept of umbra-time extends the classical manifold over which the system evolves. An extension of the Lagrangian-Hamiltonian mechanics over vector fields in this extended space has been presented. The idea of umbra time is then carried forward to propose the basic concept of umbra-Hamiltonian, which is used along with the extended Noether's theorem to provide an insight into the dynamics of systems with symmetries. Gauge functions for umbra-Lagrangian are also introduced. Extension of the Poincare-Cartan integral for the umbra-Lagrangian theory is also proposed, and its implications have been discussed. Several examples are presented to illustrate all these concepts. 相似文献
11.
DISSIPATIVEEFFECTSOFANISOLATEDBUBBLEINWATERONTHESOUNDWAVEHunagJing-quan(黄景泉)LiFu-xin(李福新)(NorthwesternPolytechnicUniversity,X... 相似文献
12.
This paper, as an extension of Maquin and Pierron (Mech Mater 41(8):928–942, 2009), presents an experimental procedure developed to macroscopically estimate the energy balance during the very first cycles
of a uniaxially loaded metallic specimen at low stress levels. This energy balance is performed by simultaneously measuring
the plastic input energy using a load cell and a strain gauge, and the dissipative energy using the temperature field provided
by an infrared camera. Some experimental limitations led to restrain the present procedure to positive stress ratios, and
to complement this energy balance by a second measurement while the material plastic work per cycle is negligible compared
to the dissipative energy. Some results obtained on a cold rolled low carbon steel specimen are presented. First, a sensitivity
study is undertaken to precisely determine the detection threshold on both thermal and plastic energies. Then, after having
verified the homogeneity of the dissipative source fields, energy balances have been performed at different stress levels.
It was thus confirmed that the slow variations of the dissipative sources occurring during the first cycles are due to micro-plastic
adaptation, and that the dissipative sources remaining after some hundreds of cycles are due to viscoelastic (internal friction)
phenomena. This procedure provides a better understanding of dissipation based approaches to fatigue found in the literature
and an advanced tool to study viscoelastic phenomena in uniaxial loading. 相似文献
13.
Hyperbolic–parabolic systems have spatially homogenous stationary states. When the dissipation is weak, one can derive weakly
nonlinear-dissipative approximations that govern perturbations of these constant states. These approximations are quadratically
nonlinear. When the original system has an entropy, the approximation is formally dissipative in a natural Hilbert space.
We show that when the approximation is strictly dissipative it has global weak solutions for all initial data in that Hilbert
space. We also prove a weak-strong uniqueness theorem for it. In addition, we give a Kawashima type criterion for this approximation
to be strictly dissipative. We apply the theory to the compressible Navier–Stokes system. 相似文献
14.
The dissipative quantum Zakharov equations are mainly studied. The existence and uniqueness of the solutions for the dissipative quantum Zakharov equations are proved by the standard Galerkin approximation method on the basis of a priori estimate. Meanwhile, the asymptotic behavior of solutions and the global attractor which is constructed in the energy space equipped with the weak topology are also investigated. 相似文献
15.
M. Torrilhon 《Continuum Mechanics and Thermodynamics》2000,12(5):289-301
Extended thermodynamics derives dissipative, hyperbolic field equations for monatomic gases. One example is the system of
the 13-field-case, which is a dissipative extension of the Euler equations. In this paper the system is investigated by solving
a Riemann problem. Additionally some model equations are introduced so as to discuss the main properties in a transparent
manner. There arises an interesting interplay of the characteristic waves and the dissipation in the system. For the 13-field-case
it turns out that not every Riemann problem has a solution, because of the loss of hyperbolicity of the system.
Received April 13, 2000 相似文献
16.
Q. M. Li 《Archive of Applied Mechanics (Ingenieur Archiv)》1999,69(6):379-392
Summary A dissipative flow model is presented to describe dissipative deformation processes in a macroscopic solid continuum. Dissipative
process may consist of material plasticity, material damage and other intrinsic mechanical phenomena represented by internal
variables. The concept of a dissipative surface is introduced in the paper to distinguish between conservative and dissipative
processes. Conventional plastic yielding and damage initiation are expressed by a unique condition which may else include
other possible intrinsic mechanical dissipations. The proposed model is based on the principles of irreversible thermodynamics
and the minimum free energy theorem. A modified material stability postulate, modified Drucker's postulate, in thermodynamic
stress space is also used to obtain the same results.
Received 1 July 1998; accepted for publication 13 January 1999 相似文献
17.
We employ a new bilinear estimate to show that solutions to the subcritical dissipative quasi-geostrophic equations with initial
data in the scaling-invariant Lebesgue space are analytic in space variables. Some decay in time estimates for space–time
derivatives are also obtained. 相似文献
18.
Summary The stability properties of zonal circulations induced by external forcing in a rotating atmosphere are investigated making
use of a truncated model of the barotropic vorticity equation for forced, dissipative non-divergent flow in spherical geometry.
Sufficient conditions for global and local asymptotic stability are found as a function of the dissipation time-scale, the
coefficients of non-linear interaction between zonal flow and wave components, and the absolute rotation speed of the atmosphere.
For weak, axisymmetric forcing fields the corresponding forced zonal circulation is a global attractor for states belonging
to the configuration space of the model, while for larger forcing intensities it is only locally attracting, the extension
of the basin of attraction being an increasing function of the absolute angular velocity of the atmosphere.
This research was partly supported by C.N.R. through G.N.F.M. 相似文献
Sommario Si analizzano le proprietà di stabilità di circolazioni zonali forzate in una atmosfera rotante facendo uso di un modello troncato a pochi modi dell'equazione di vorticità barotropica per flussi dissipativi in geometria sferica. Si determinano condizioni sufficienti per la stabilità asintotica sia locale che globale in funzione delle scale di tempo dissipative e di interazione nonlineare.
This research was partly supported by C.N.R. through G.N.F.M. 相似文献
19.
Lie-Hori canonical perturbation theory provides asymptotic solutions for conservative Hamiltonian systems. This restriction prevents the canonical method from being applied directly to dissipative mechanical systems. There are, however, two main alternatives to overcome this difficulty, enabling the application of canonical perturbation methods. The first one consists in constructing a time-dependent Hamiltonian, through a generating function, related to the energy dissipation pattern of the system. The second embeds the original phase space into a double dimensional one where the dynamics of the system can be formulated in a Hamiltonian way. In this paper, a modified Lie-Hori method that avoid the disadvantages of the former approaches is proposed. Namely, it is not necessary to find out a time-dependent generating function, nor doubling the number of the canonical variables of the original problem. The new algorithm provides first order analytical solutions for a certain set of dissipative non-linear dynamical systems. It is based on a suitable modification of the Hori kernel in the double-dimensional embedding phase space, allowing the inclusion of the dissipative (or generalized) forces. By means of this redefined auxiliary system, the path-integrals of the method can be performed in a domain of the phase space with the same dimensionality as the original problem. 相似文献
20.
A type of quasilinear Schrodinger equations in two space dimensions which describe attractive Bose-Einstein condensates in physics is discussed. By establishing the property of the equation and applying the energy method, the blowup of solutions to the equation are proved under certain conditions. At the same time, by the variational method, a sutficient condition of global existence which is related to the ground state of a classical elliptic equation is obtained. 相似文献