A numerical study of time-dependent schr?dinger equation for multiphoton vibrational interaction of NO molecule, modelled as Morse oscillator, with intense far-infrared femtosecond lasers

For the NO molecule, modelled as a Morse oscillator, time-dependent (TD) nuclear Schr?dinger equation has been numerically solved for the multiphoton vibrational dynamics of the molecule under a far-infrared laser of wavelength 10503 nm, and four different intensities,I = 1 × 10⁸, 1 × 10¹³, 5 × 10¹⁶, and 5 × 10¹⁸ W cm⁻² respectively. Starting from the vibrational ground state at zero time, various TD quantities such as the norm, dissociation probability, potential energy curve and dipole moment are examined. Rich high-harmonics generation (HHG) spectra and above-threshold dissociation (ATD) spectra, due to the multiphoton interaction of vibrational motions with the laser field, and consequent elevation to the vibrational continuum, have been obtained and analysed. Dedicated to Professor C N R Rao on his 70th birthday An erratum to this article is available at .     

Robust Dynamics and Control of a Partially Observed Markov Chain

In a seminal paper, Martin Clark (Communications Systems and Random Process Theory, Darlington, 1977, pp. 721–734, 1978) showed how the filtered dynamics giving the optimal estimate of a Markov chain observed in Gaussian noise can be expressed using an ordinary differential equation. These results offer substantial benefits in filtering and in control, often simplifying the analysis and an in some settings providing numerical benefits, see, for example Malcolm et al. (J. Appl. Math. Stoch. Anal., 2007, to appear). Clark’s method uses a gauge transformation and, in effect, solves the Wonham-Zakai equation using variation of constants. In this article, we consider the optimal control of a partially observed Markov chain. This problem is discussed in Elliott et al. (Hidden Markov Models Estimation and Control, Applications of Mathematics Series, vol. 29, 1995). The innovation in our results is that the robust dynamics of Clark are used to compute forward in time dynamics for a simplified adjoint process. A stochastic minimum principle is established.     

On the Use of the Restitution Condition in Flexible Body Dynamics

The difference between the classical treatment offlexible body impact and the treatment of impact in flexiblemultibody dynamics is due to several fundamental reasons. Inthe classical impact theory, simple structures such as beamsand plates are used. Infinite dimensional models can bedeveloped for these simple structural elements to study theimpact dynamics and the wave propagation problem. Flexiblemultibody impact problems, on the other hand, involve bodieswith complex geometry that cannot be modeled using infinitenumber of degrees of freedom. Furthermore, the classicalimpact theory has been mainly concerned with the impactbetween a rigid mass that moves without constraints beforeit impacts a simple flexible structure. This is not amultibody simulation scenario in which the impact occursbetween kinematically constrained bodies that are subjectedto impulsive constraint forces in addition to the impactforces. These constraint forces can influence the motion ofthe two bodies immediately after impact, and as aconsequence, the simple classical theory scenario of impactdoes not apply. It is the objective of this paper to discussthe use of the restitution condition in flexible multibodyimpact problems and demonstrate that the use of thisapproach does not exclude the classical formulation.Nonetheless, the impulse momentum balance approach can serveas an effective and efficient procedure for solving theimpact problem in finite dimensional models that do not obeythe classical wave theory. Energy results of simplestructural elements are presented in order to demonstratethe consistency of using the impulse momentum balanceapproach in solving impact problems in finite dimensionalflexible body applications.     

The effect of nanoparticle shape on polymer‐nanocomposite rheology and tensile strength

Nanoparticles can influence the properties of polymer materials by a variety of mechanisms. With fullerene, carbon nanotube, and clay or graphene sheet nanocomposites in mind, we investigate how particle shape influences the melt shear viscosity η and the tensile strength τ, which we determine via molecular dynamics simulations. Our simulations of compact (icosahedral), tube or rod‐like, and sheet‐like model nanoparticles, all at a volume fraction ? ≈ 0.05, indicate an order of magnitude increase in the viscosity η relative to the pure melt. This finding evidently can not be explained by continuum hydrodynamics and we provide evidence that the η increase in our model nanocomposites has its origin in chain bridging between the nanoparticles. We find that this increase is the largest for the rod‐like nanoparticles and least for the sheet‐like nanoparticles. Curiously, the enhancements of η and τ exhibit opposite trends with increasing chain length N and with particle shape anisotropy. Evidently, the concept of bridging chains alone cannot account for the increase in τ and we suggest that the deformability or flexibility of the sheet nanoparticles contributes to nanocomposite strength and toughness by reducing the relative value of the Poisson ratio of the composite. The molecular dynamics simulations in the present work focus on the reference case where the modification of the melt structure associated with glass‐formation and entanglement interactions should not be an issue. Since many applications require good particle dispersion, we also focus on the case where the polymer‐particle interactions favor nanoparticle dispersion. Our simulations point to a substantial contribution of nanoparticle shape to both mechanical and processing properties of polymer nanocomposites. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1882–1897, 2007     

Capacity augmentation of a supply chain for a short lifecycle product: A system dynamics framework

For an innovative product characterized by short product lifecycle and high demand uncertainty, investment in capacity buildup has to be done cautiously. Otherwise either the product’s market diffusion is impeded or the manufacturer is left with unutilized capacity. Using the right information for making capacity augmentation decisions is critical in facing this challenge. In this paper, we propose a method for identifying critical information flows using the system dynamics model of a two-echelon supply chain. The fundamental premise of system dynamics methodology is that (system) structure determines (its) behavior. Using loop dominance analysis method we study the feedback loop structure of the supply chain system. The outcome is a set of dominant loops that determine the dynamics of capacity growth. It is revealed that the delivery delay information has little effect while the loop that connects retail sales with production order affects the dynamics significantly. Modifying this loop yields appropriate capacity augmentation decisions resulting in higher performance. What-if analyses bring out effects of modifying other structural elements. In conclusion, we claim that the information feedback based methodology is general enough to be useful in designing decision support systems for capacity augmentation. The limitations of the model are also discussed and possible extensions identified.     

现代热力学的完整分类系统--非平衡非耗散热力学新领域

在同一体系中同时有多个不可逆过程时，不可逆过程之间会有相互影响，原来的非自发过程有可能在其他自发过程的影响下得以进行，这种现象就称为热力学耦合或反应耦合，长期以来，经典热力学把热力学第二定律的等式作为平衡体系的充分必要条件，其中隐含了一个前提性的假定，即经典热力学的对象只限于非耦合的体系，摈弃这一隐含的前提性假定以后，热力学自身就发展成为一个现代热力学的完整学术体系，适用于任何宏观体系（包括极其复杂的生命体系），现代热力学的完整学术体系中包含了一个崭新的非平衡非耗散热力学新领域，由于该领域属于热力学第二定律的等式部分，因此可以定量计算，并得到一系列理论计算的非平衡相图，与文献上报道的激尖低压金刚石合成等的大量实验数据相符。     

Density functional theory study on antiferromagnetic interactions in a silver (I) complex of nitronyl nitroxide

A one-dimensional (1D) silver (I) complex of nitronyl nitroxide with fairly strong antiferromagnetic interaction, in which the metal ions are diamagnetic, is investigated by means of the ab initio crystal orbital method based on the density functional theory. The calculated values of the magnetic coupling constant (J) are close to the experimental measured J value in the periodic system. The magneto-structural correlation reveals that the existence of an antiferromagnetic coupling pathway along nitronyl nitroxide units via silver (I) ion in this system. The spin population distribution also shows the existence of spin delocalization along the ONCNO–Ag–ONCNO, which affords a rational interpretation for the antiferromagnetic interaction mechanism.     

General synchronization dynamics of coupled Van der Pol–Duffing oscillators

This paper considers the general synchronization dynamics of coupled Van der Pol–Duffing oscillators. The linear and nonlinear stability analysis on the synchronization process is derived through the Whittaker method and the Floquet theory in addition to the multiple time scales method. A stability map displaying different dynamical states of the system is performed. Numerical simulation is carried out to support and to complement the accuracy of the analytical treatment.