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21.
We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx < 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations. 相似文献
22.
Extension of a combined analytical/numerical initial value problem solver for unsteady periodic flow
Here we describe analytical and numerical modifications that extend the Differential Reduced Ejector/ mixer Analysis (DREA), a combined analytical/numerical, multiple species ejector/mixing code developed for preliminary design applications, to apply to periodic unsteady flow. An unsteady periodic flow modelling capability opens a range of pertinent simulation problems including pulse detonation engines (PDE), internal combustion engine ICE applications, mixing enhancement and more fundamental fluid dynamic unsteadiness, e.g. fan instability/vortex shedding problems. Although mapping between steady and periodic forms for a scalar equation is a classical problem in applied mathematics, we will show that extension to systems of equations and, moreover, problems with complex initial conditions are more challenging. Additionally, the inherent large gradient initial condition singularities that are characteristic of mixing flows and that have greatly influenced the DREA code formulation, place considerable limitations on the use of numerical solution methods. Fortunately, using the combined analytical–numerical form of the DREA formulation, a successful formulation is developed and described. Comparison of this method with experimental measurements for jet flows with excitation shows reasonable agreement with the simulation. Other flow fields are presented to demonstrate the capabilities of the model. As such, we demonstrate that unsteady periodic effects can be included within the simple, efficient, coarse grid DREA implementation that has been the original intent of the DREA development effort, namely, to provide a viable tool where more complex and expensive models are inappropriate. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
23.
24.
This paper develops a mathematical model of the ring-spinning process that takes into account its non-stationary nature. A complex system of differential equations is obtained, which from a mathematical point of view constitutes a ‘free-boundary’ problem. Its solution involves definition of suitable boundary conditions related to the mechanical characteristics of the process and of the spinning machine itself. The boundary conditions which determine the solution are pointed out. A numerical solution of the system of differential equations can be obtained by the Finite-Segments method, as shown in an example. 相似文献
25.
The study of bed-load transport is of great significance both in theory and in practice. This paper discusses the saltation
of bed-load solid grains in flowing water. Experiments and theoretic analysis have been made by means of high-speed photographing
and advanced data processing technique with a combined method based on mechanical and statistical theories. It indicates that
the saltation is the main form of the bed-load transport under ordinary flowing conditions. In the meantime, taking successive
saltation as the model of bed-load transport, systematic analysis has been made with regard to the kinematic properties and
mechanism of saltation. The statistical analysis shows that the probability density functions of the relative height and length
of saltation are in conformity with Γ-type distribution, while the probability density functions of the relative velocities
of saltation are in conformity with the Gaussian distribution.
The project supported by National Natural Science Foundation of China 相似文献
26.
Summary The interceluster organization of a two-dimensional colloidal system undergoing diffusion-limited cluster-cluster aggregation
is considered. During this process the system evolves into a stationary, scaling state. In this state the organization arises
from effective intercluster repulsion due to the mutually exclusive depletion zones surrounding each cluster. It is shown
that in the scaling regime the relevant size of the depletion zones is determined by the separation between clusters, rather
than the cluster size.
Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994. 相似文献
27.
J.-Q. Shen H.-Y. Zhu P. Chen 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2003,23(2):305-313
There exist a number of typical and interesting systems and/or models, which possess three-generator Lie-algebraic structure,
in atomic physics, quantum optics, nuclear physics and laser physics. The well-known fact that all simple 3-generator algebras
are either isomorphic to the algebra sl (2, C) or to one of its real forms enables us to treat these time-dependent quantum systems in a unified way. By making use of
both the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper
obtains exact solutions of the time-dependent Schr?dinger equations governing various three-generator Lie-algebraic quantum
systems. For some quantum systems whose time-dependent Hamiltonians have no quasialgebraic structures, it is shown that the exact solutions can also be obtained by working in a
sub-Hilbert-space corresponding to a particular eigenvalue of the conserved generator (i.e., the time-independent invariant that commutes with the time-dependent Hamiltonian). The topological property of geometric phase factors and its adiabatic limit in time-dependent systems is briefly
discussed.
Received 6 July 2002 / Received in final form 21 October 2002 Published online 11 February 2003 相似文献
28.
用经典力学和双波量子力学计算了氢原子的固有电偶极矩。双波量子理论算得的结果在经典极限下与经典力学的结果一致。普通量子力学对氢原子Stark效应中表现出来的电偶极矩难以做出很好的解释,因为一个波函数描述的是系综而不是单个粒子。经典力学和双波量子力学可描述单个粒子的行为,对永久电偶极矩的计算和解释显得自然而合理。 相似文献
29.
Fabio Scardigli 《Foundations of Physics》2007,37(8):1278-1295
The Titius–Bode law for planetary distances is reviewed. A model describing the basic features of this rule in the “quantum-like”
language of a wave equation is proposed. Some considerations about the ’t Hooft idea on the quantum behavior of deterministic
systems with dissipation are discussed. 相似文献
30.
Nimrod Moiseyev Romanas Narevich 《International Journal of Theoretical Physics》2003,42(10):2131-2143
Resonances are defined as the poles of the scattering matrix. The poles are associated with the complex eigenvalues of the Hamiltonian which are embedded in the lower half of the complex plane. The asymptotes of the corresponding eigenfunctions are exponentially diverged. Therefore, the resonance eigenfunctions are not embedded in the Hermitian domain of the Hamiltonian. The time asymmetric problem is discussed for these types of non-Hermitian Hamiltonians and several solutions of this problem are proposed. 相似文献