Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Gas-surface interactions in the thermal and sub-thermal regime: A molecular dynamics study

Molecular dynamics simulations are used to study the interaction of low-energy Ar atoms with the Ni(001) surface, Angular scattering distributions, in and out of the plane of incidence, are investigated as a function of incident energy, angles of incidence, crystallographic orientation of the incident beam and surface temperature. The results show a clear transition to the structure scattering regime at around 2 eV. However, at lower energies, two sub-regimes are revealed by the simulations, Far energies up to 250 meV, scattering is mainly diffuse, and significant trapping on the surface is observed, At energies above this level, lobular patterns start to form and trapping decreases with the increase in energy, Generally, there is a weak temperature dependence, but variations in the angle of incidence and/or changes in the crystallographic direction, generate significant changes in the scattering patterns.

Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential

We consider the quantum dynamics of a neutral atom Bose-Einstein condensate in a double-well potential, including many-body hard-sphere interactions. Using a mean-field factorization we show that the coherent oscillations due to tunneling are suppressed when the number of atoms exceeds a critical value. An exact quantum solution, in a two-mode approximation, shows that the mean-field solution is modulated by a quantum collapse and revival sequence.

Conformational dynamics of thyroid hormones by variable temperature nuclear magnetic resonance: The role of side chain rotations and cisoid/transoid interconversions

H-1 NMR spectra of the thyroid hormone thyroxine recorded at low temperature and high field show splitting into two peaks of the resonance due to the H2,6 protons of the inner (tyrosyl) ring. A single resonance is observed in 600 MHz spectra at temperatures above 185 K. An analysis of the line shape as a function of temperature shows that the coalescence phenomenon is due to an exchange process with a barrier of 37 kJ mol(-1). This is identical to the barrier for coalescence of the H2',6' protons of the outer (phenolic) ring reported previously for the thyroid hormones and their analogues. It is proposed that the separate peaks at low temperature are due to resonances for H2,6 in cisoid and transoid conformers which are populated in approximately equal populations. These two peaks are averaged resonances for the individual H2 and H6 protons. Conversion of cisoid to transoid forms can occur via rotation of either the alanyl side chain or the outer ring, from one face of the inner ring to the other. It is proposed that the latter process is the one responsible for the observed coalescence phenomenon. The barrier to rotation of the alanyl side chain is greater than or equal to 37 kJ mol(-1), which is significantly larger than has previously been reported for Csp(2)-Csp(3) bonds in other Ph-CH2-X systems. The recent crystal structure of a hormone agonist bound to the ligand-binding domain of the rat thyroid hormone receptor (Wagner et al. Nature 1995, 378, 690-697) shows the transoid form to be the bound conformation. The significant energy barrier to cisoid/transoid interconversion determined in the current study combined with the tight fit of the hormone to its receptor suggests that interconversion between the forms cannot occur at the receptor site but that selection for the preferred bound form occurs from the 50% population of the transoid form in solution.

Antiphase dynamics of a chaotic multimode laser

Antiphase dynamics of an optically pumped NH3 bidirectional ring laser under the chaotic, phase-sensitive mode coupling is experimentally observed. Our experimental result suggests strongly that the dynamics is a generic behavior of the laser.

On the dynamics of mechanical milling in a vibratory mill

The dynamics of mechanical milling in a vibratory mill have been studied by means of mechanical vibration, shock measurements, computer simulation and microstructural evolution measurements. Two distinct modes of ball motion during milling, periodic and chaotic vibration, were observed. Mill operation in the regime of periodic vibration, in which each collision provides a constant energy input to milled powders, enabled a quantitative description of the effect of process parameters on system dynamics. An investigation of the effect of process parameters on microstructural development in an austenitic stainless steel showed that the impact force associated with collision events is an important process parameter for characterizing microstructural evolution. (C) 1997 Elsevier Science S.A.

Structure optimization combining soft-core interaction functions, the diffusion equation method, and molecular dynamics

Smoothing the potential energy surface for structure optimization is a general and commonly applied strategy. We propose a combination of soft-core potential energy functions and a variation of the diffusion equation method to smooth potential energy surfaces, which is applicable to complex systems such as protein structures; The performance of the method was demonstrated by comparison with simulated annealing using the refinement of the undecapeptide Cyclosporin A as a test case. Simulations were repeated many times using different initial conditions and structures since the methods are heuristic and results are only meaningful in a statistical sense.

Non-equilibrium energy and momentum accommodation coefficients of Ar atoms scattered from Ni(001) in the thermal regime: A molecular dynamics study

Molecular dynamics simulations are used to study energy and momentum transfer of low-energy Ar atoms scattered from the Ni(001) surface. The investigation concentrates on the dependence of these processes on incident energy, angles of incidence and surface temperature. Energy transfer exhibits a strong dependence on the surface temperature, at incident energies below 500 meV, and incident angles close to specular incidence. Above 500 meV, the surface temperature dependence vanishes, and a limiting value in the amount of energy transferred to the surface is attained. Momentum exchange is investigated in terms of tangential and normal components. Both components exhibit a weak surface temperature dependence, but they have opposite behaviours at all incidence angles. In each component, momentum can be lost or gained following the interaction with the surface. (C) 1997 Elsevier Science B.V.

Cell cycle model to describe animal cell size variation and lag between cell number and biomass dynamics

The use of cell numbers rather than mass to quantify the size of the biotic phase in animal cell cultures causes several problems. First, the cell size varies with growth conditions, thus yields expressed in terms of cell numbers cannot be used in the normal mass balance sense. Second, experience from microbial systems shows that cell number dynamics lag behind biomass dynamics. This work demonstrates that this lag phenomenon also occurs in animal cell culture. Both the lag phenomenon and the variation in cell size are explained using a simple model of the cell cycle. The basis for the model is that onset of DNA synthesis requires accumulation of G1 cyclins to a prescribed level. This requirement is translated into a requirement for a cell to reach a critical size before commencement of DNA synthesis. A slower gl-owing cell will spend more time in G1 before reaching the critical mass. In contrast, the period between onset of DNA synthesis and mitosis, tau(B), is fixed. The two parameters in the model, the critical size and tau(B), were determined from eight steady-state measurements of mean cell size in a continuous hybridoma culture. Using these parameters, it was possible to predict with reasonable accuracy the transient behavior in a separate shift-up culture, i.e., a culture where cells were transferred from a lean environment to a rich environment. The implications for analyzing experimental data for animal cell culture are discussed. (C) 1997 John Wiley & Sons, Inc.