Differential–algebraic equations in multibody system modeling

Numerical methods for the efficient integration of both stiff and nonstiff equations of motion of multibody systems having the form of differential-algebraic equations (DAE) of index 3 are discussed. Linear multi-step ABM and BDF methods are considered for the non-iterational integration of nonstiff DAE. The Park method is proposed for integration of stiff equations. This revised version was published online in June 2006 with corrections to the Cover Date.     

Tunnelling in periodically driven systems

Tunnelling in periodically driven bistable symmetric potential wells is investigated in an analytical approximation in a domain where the driving frequency is large compared to the tunnelling frequency and only the four lowest lying levels contribute significantly. The influence of finite level widths is taken into account, and a smooth variation of the amplitude of the driving field is allowed for.     

Influence of concentration on the activation energy for diffusion in polymer-solvent systems

The self-diffusion of benzene, toluene, and ethylbenzene in polystyrene have been analyzed using the Vrentas/Duda free-volume diffusion model. Diffusion coefficient predictions suggest an exponential concentration dependence of the activation energy required to overcome attractive forces, E. Without the use of any diffusion data approximating E as zero over the entire concentration range yields self-diffusion coefficient predictions which are in good agreement with experimental data. © 1992 John Wiley & Sons, Inc.     

On interrelation between the internal pressure and the cohesion energy density

The question about the definition of the “internal pressure” concept is being discussed. It is shown that the previously found differential relation between the cohesion energy density and the internal pressure is one of the examples of an absolutely general interrelation between definitely connected differential functions. It is ascertained that the ratio (the internal pressure divided by the cohesion energy density) is a structuresensitive parameter inherent to the calorific (thermal) equation of a liquid state.     

Assembly and Photophysics of Ternary Luminescent Lanthanide Molecular Complex Systems

In this paper, according to the molecular fragment principle, a series of eight ternary luminescent lanthanide complex systems were assembled, and whose compositions were determined with elemental analysis and infrared spectrum: Ln(MA)₃(L)·H₂O, where Ln = Sm, Eu, Tb, Dy; HMA = α‐methylacrylic acid; L = 1,10‐phenanthroline (phen), 2,2′‐bipyridine (bipy). The photophysical properties of these functional molecular systems were studied with ultraviolet‐visible absorption spectrum, and fluorescence excitation and emission spectrum. It was found that the heterocylic compounds (phen and bipy) act as the main energy donor and luminescence sensitizer for their suitable energy match and effective energy transfer to the emission energy level of Ln³⁺ ions. MMA ligand was only used as the terminal structural ligand to influence the luminescence. Especially terbium complex systems show the strongest luminescence for the optimum energy match and transfer between phen (bipy) and Tb³⁺ ion.     

Earnshaw (1805–1888) and Passive Magnetic Levitation

S. Earnshaw, a mathematical physicist born in England two centuries ago, was the author of studies on the transmission of sound and light. His theory on the transmission of light by “detached particles” has also influenced some studies on the stability of bodies in potential fields, particularly studies on the levitation of permanent magnets, i.e. on passive magnetic levitation. This theorem was so well known that even Maxwell mentioned it, and is today cited almost as an axiom in the ambit of passive magnetization. However, what is less well known is that the theory actually only relates to magnetostatics. In this paper, the mathematic model of the theory that refers to stability is outlined, along with some works that refer to it, in particular those on passive magnetic levitation. It is then pointed out that spaces of low instability exist in magnetostatics, and that stability may exist in the magneto-stationary and in magneto-dynamic ambit.     

A note on an SOR-like method for augmented systems

Golub et al. (2001, BIT, 41, 71–85) gave a generalizedsuccessive over-relaxation method for the augmented systems.In this paper, the connection between the SOR-like method andthe preconditioned conjugate gradient (PCG) method for the augmentedsystems is investigated. It is shown that the PCG method isat least as accurate (fast) as the SOR-like method. Numericalexamples demonstrate that the PCG method is much faster thanthe SOR-like method.     

Asymptotic analysis of the effect of arrival model uncertainties in some optimal routing problems

We study the effect of arrival model uncertainties on the optimal routing in a system of parallel queues. For exponential service time distributions and Bernoulli routing, the optimal mean system delay generally depends on the interarrival time distribution. Any error in modeling the arriving process will cause a model-based optimal routing algorithm to produce a mean system delay higher than the true optimum. In this paper, we present an asymptotic analysis of the behavior of this error under heavy traffic conditions for a general renewal arrival process. An asymptotic analysis of the error in optimal mean delay due to uncertainties in the service time distribution for Poisson arrivals was reported in Ref. 6, where it was shown that, when the first moment of the service time distribution is known, this error in performance vanishes asymptotically as the traffic load approaches the system capacity. In contrast, this paper establishes the somewhat surprising result that, when only the first moment of the arrival distribution is known, the error in optimal mean delay due to uncertainties in the arrival model is unbounded as the traffic approaches the system capacity. However, when both first and second moments are known, the error vanishes asymptotically. Numerical examples corroborating the theoretical results are also presented.This work was supported by the National Science Foundation under Grants ECS-88-01912 and EID-92-12122 and by NASA under Contract NAG 2-595.The authors wish to thank an anonymous referee for pointing out Ref. 20, thus avoiding the need for an explicit proof of convexity of the cost function considered in the paper.     

Self-organization in aggregating colloids

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.     

Exact solutions and geometric phase factor of time-dependent three-generator quantum systems

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