A study of the stability of subcycling algorithms in structural dynamics

Algorithms for explicit integration of structural dynamics problems with multiple time steps (subcycling) are investigated. Only one such algorithm, due to Smolinski and Sleith has proved to be stable in a classical sense. A simplified version of this algorithm that retains its stability is presented. However, as with the original version, it can be shown to sacrifice accuracy to achieve stability. Another algorithm in use is shown to be only statistically stable, in that a probability of stability can be assigned if appropriate time step limits are observed. This probability improves rapidly with the number of degrees of freedom in a finite element model. The stability problems are shown to be a property of the central difference method itself, which is modified to give the subcycling algorithm. A related problem is shown to arise when a constraint equation in time is introduced into a time-continuous space-time finite element model. (C) 1998 Elsevier Science S.A.

Comprehensive structural characterization of MCM-41: From mesopores to particles

In the present work the meso- and macro-structural characteristics of the mesoporous adsorbent MCM-41 have been estimated with the help of various techniques. The structure is found to comprise four different length scales: that of the mesopores, the crystallites, the grains and of the particles. It was found that the surface area estimated by the use of small angle scattering techniques is higher, while that estimated by mercury porosimetry is much lower, than that obtained from gas adsorption methods. Based on the macropore characterization by mercury porosimetry, and the considerable macropore area determined, it is seen that the actual mesopore area of MCM-41 may be significantly lower than the BET area. TEM studies indicated that MCM-41 does not have an ideal mesopore structure; however, it may still be treated as a model mesoporous material for gas adsorption studies because of the large radius of curvature of the channels.

Simultaneous steady state and dynamic design of process systems using structural indicators

The simultaneous design of the steady-state and dynamic performance of a process has the ability to satisfy much more demanding dynamic performance criteria than the design of dynamics only by the connection of a control system. A method for designing process dynamics based on the use of a linearised systems' eigenvalues has been developed. The eigenvalues are associated with system states using the unit perturbation spectral resolution (UPSR), characterising the dynamics of each state. The design method uses a homotopy approach to determine a final design which satisfies both steady-state and dynamic performance criteria. A highly interacting single stage forced circulation evaporator system, including control loops, was designed by this method with the goal of reducing the time taken for the liquid composition to reach steady-state. Initially the system was successfully redesigned to speed up the eigenvalue associated with the liquid composition state, but this did not result in an improved startup performance. Further analysis showed that the integral action of the composition controller was the source of the limiting eigenvalue. Design changes made to speed up this eigenvalue did result in an improved startup performance. The proposed approach provides a structured way to address the design-control interface, giving significant insight into the dynamic behaviour of the system such that a systematic design or redesign of an existing system can be undertaken with confidence.

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

Analysis of dynamic models for structural insight and model reduction .2. A multi-stage compressor shutdown case-study

In this second paper, the three structural measures which have been developed are used in the modelling of a three stage centrifugal synthesis gas compressor. The goal of this case study is to determine the essential mathematical structure which must be incorporated into the compressor model to accurately model the shutdown of this system. A simple, accurate and functional model of the system is created via three structural measures. It was found that the model can be correctly reduced into its basic modes and that the order of the differential system can be reduced from 51(st) to 20(th). Of the 31 differential equational 21 reduce to algebraic relations, 8 become constants and 2 can be deleted thereby increasing the algebraic set from 70 to 91 equations. An interpretation is also obtained as to which physical phenomena are dominating the dynamics of the compressor add whether the compressor will enter surge during the shutdown. Comparisons of the reduced model performance against the full model are given, showing the accuracy and applicability of the approach. Copyright (C) 1996 Elsevier Science Ltd

Structural ordering of coal char during heat treatment and its impact on reactivity

The effect of heat treatment on the structure of an Australian semi-anthracite char was studied in detail in the 850-1150degreesC temperature range using XRD, HRTEM, and electrical resistivity techniques. It was found that the carbon crystallite size in the char does not change significantly during heat treatment in the temperature range studied, for both the raw coal and its ash-free derivative obtained by acid treatment. However, the fraction of the organized carbon in the raw coal chars, determined by XRD, increased with increase of heat treatment time and temperature, while that for the ash-free coal chars remained almost unchanged. This suggests the occurrence of catalytic ordering during heat treatment, supported by the observation that the electrical resistivity of the raw coal chars decreased with heat treatment, while that of the ash-free coal chars did not vary significantly. Further confirmatory evidence was provided by high resolution transmission electron micrographs depicting well-organized carbon layers surrounding iron particles. It is also found that the fraction of organized carbon does not reach unity, but attains an apparent equilibrium value that increases with increase in temperature, providing an apparent heat of ordering of 71.7 kJ mol(-1) in the temperature range studied. Good temperature-independent correlation was found between the electrical resistivity and the organized carbon fraction, indicating that electrical resistivity is indeed structure sensitive. Good correlation was also found between the electrical resistivity and the reactivity of coal char. All these results strongly suggest that the thermal deactivation is the result of a crystallite-perfecting process, which is effectively catalyzed by the inorganic matter in the coal char. Based on kinetic interpretation of the data it is concluded that the process is diffusion controlled, most likely involving transport of iron in the inter-crystallite nanospaces in the temperature range studied. The activation energy of this transport process is found to be very low, at about 11.8 kJ mol(-1), which is corroborated by model-free correlation of the temporal variation of organized carbon fraction as well as electrical resistivity data using the superposition method, and is suggestive of surface transport of iron. (C) 2002 Elsevier Science Ltd. All rights reserved.

A partial velocity approach to subcycling structural dynamics

Subcycling, or the use of different timesteps at different nodes, can be an effective way of improving the computational efficiency of explicit transient dynamic structural solutions. The method that has been most widely adopted uses a nodal partition. extending the central difference method, in which small timestep updates are performed interpolating on the displacement at neighbouring large timestep nodes. This approach leads to narrow bands of unstable timesteps or statistical stability. It also can be in error due to lack of momentum conservation on the timestep interface. The author has previously proposed energy conserving algorithms that avoid the first problem of statistical stability. However, these sacrifice accuracy to achieve stability. An approach to conserve momentum on an element interface by adding partial velocities is considered here. Applied to extend the central difference method. this approach is simple. and has accuracy advantages. The method can be programmed by summing impulses of internal forces, evaluated using local element timesteps, in order to predict a velocity change at a node. However, it is still only statistically stable, so an adaptive timestep size is needed to monitor accuracy and to be adjusted if necessary. By replacing the central difference method with the explicit generalized alpha method. it is possible to gain stability by dissipating the high frequency response that leads to stability problems. However. coding the algorithm is less elegant, as the response depends on previous partial accelerations. Extension to implicit integration, is shown to be impractical due to the neglect of remote effects of internal forces acting across a timestep interface. (C) 2002 Elsevier Science B.V. All rights reserved.

Impacts of structural characteristics on activated sludge floc stability

Activated sludge samples from seven full-scale plants were investigated in order to determine the relationship between floc structure and floc stability. Floc stability was determined by shear sensitivity and floc strength. Floc structure was considered in terms of two size scales, the micro- and macrostructure. The microstructure refers to the organization of the floc components, such as the individual microorganisms. The macrostructure refers to the overall floc. The floc macrostructure was characterized by filament index, sludge volume index, size, and fractal dimension. It had a significant impact on floc stability. Large and open floes with low fractal dimensions containing large number of filaments were more shear sensitive and had lower floc strength compared to small and dense floes. Fluorescent in situ hybridization analysis indicated that the organization of the bacterial cells might also have an effect on the floc stability. (C) 2003 Elsevier Ltd. All rights reserved.

Structural and mechanical properties of nanostructured granular alumina catalysts

Granular gamma-Al2O3 support and 8 wt % CuO/gamma-Al2O3 catalyst were synthesized by a sol-gel granulation method. The pore structure, crush strength, hardness, and elasticity of these sol-gel-derived catalysts were studied and compared with similar commercial catalysts prepared by non-sol-gel methods. Alumina and CuO-coated alumina granular particles prepared by different methods have different macro- and microstructure. The sol-gel-derived granular gamma-alumina and CuO-coated gamma-alumina granular particles have a structure defined by compact packing of uniform, nanosized gamma-alumina crystallites. They are characterized by a more uniform pore size distribution and larger surface area as compared to similar commercial samples with a structure defined by packing of aggregates consisting of nonuniform gamma-alumina crystallites. Because of the differences in the macro- and microstructure, the sol-gel-derived granular samples offer higher crush strength and greater hardness than the commercial samples.

Reflection of structural waves at a solid/liquid interface

This paper investigates the reflection characteristics of structural or guided waves in rods at a solid/liquid interface. Structural waves, whose wavelengths are much larger than the diameter of the rod, are described in a first approximation by classical one-dimensional wave theory. The reflection characteristics of such waves at a solid/liquid (melting) interface has been reported by two different ultrasonic measurement techniques: first, measuring the fast regression rate of a melting interface during the burning of metal rod samples in an oxygen-enriched environment, and second, monitoring the propagation of the solid/liquid interface during the slow melting and solidification of a rod sample in a furnace. The second work clearly shows that the major reflection occurs from the solid/liquid interface and not the liquid/gas interface as predicted by plane longitudinal wave reflectivity theory. The present work confirms this observation by reporting on the results of some specially designed experiments to identify the main interface of reflection for structural waves in rods. Hence, it helps in explaining the fundamental discrepancy between the reflection characteristics at a solid/liquid interface between low frequency structural waves and high frequency bulk waves, and confirms that the detected echo within a burning metallic rod clearly represents a reflection from the solid/liquid interface. (C) 2003 Elsevier Science B.V. All rights reserved.

The structural characterization of carbon molecular sieve membrane (CMSM) via gas adsorption

The microstructure of a carbon molecular sieve membrane (CMSM) is characterized using adsorption equilibrium information. The pore size distributions of the CMSM derived from N-2 and CH4 adsorption isotherm are found to be consistent with each other and in agreement with the results of gas permeation experiments as well as the general characteristics of such molecular sieve materials. (C) 2003 Elsevier B.V. All rights reserved.

Structural, electrical, and optical analysis of ion implanted semi-insulating InP

Semi-insulating InP was implanted with MeV P, As, Ga, and In ions, and the resulting evolution of structural properties with increased annealing temperature was analyzed using double crystal x-ray diffractometry and cross sectional transmission electron microscopy. The types of damage identified are correlated with scanning spreading resistance and scanning capacitance measurements, as well as with previously measured Hall effect and time resolved photoluminescence results. We have identified multiple layers of conductivity in the samples which occur due to the nonuniform damage profile of a single implant. Our structural studies have shown that the amount and type of damage caused by implantation does not scale with implant ion atomic mass. (C) 2004 American Institute of Physics.

Engineering stable peptide toxins by means of backbone cyclization: Stabilization of the alpha-conotoxin MII

Conotoxins (CTXs), with their exquisite specificity and potency, have recently created much excitement as drug leads. However, like most peptides, their beneficial activities may potentially be undermined by susceptibility to proteolysis in vivo. By cyclizing the alpha-CTX MII by using a range of linkers, we have engineered peptides that preserve their full activity but have greatly improved resistance to proteolytic degradation. The cyclic MII analogue containing a seven-residue linker joining the N and C termini was as active and selective as the native peptide for native and recombinant neuronal nicotinic acetylcholine receptor subtypes present in bovine chromaffin cells and expressed in Xerl oocytes, respectively. Furthermore, its resistance to proteolysis against a specific protease and in human plasma was significantly improved. More generally, to our knowledge, this report is the first on the cyclization of disulfide-rich toxins. Cyclization strategies represent an approach for stabilizing bioactive peptides while keeping their full potencies and should boost applications of peptide-based drugs in human medicine.

Experimental and theoretical investigation of the structural, chemical, electronic, and high frequency dielectric properties of barium cadmium tantalate-based ceramics

Single-phase Ba(Cd1/3Ta2/3)O-3 powder was produced using conventional solid state reaction methods. Ba(Cd1/3Ta2/3)O-3 ceramics with 2 wt % ZnO as sintering additive sintered at 1550 degreesC exhibited a dielectric constant of similar to32 and loss tangent of 5x10(-5) at 2 GHz. X-ray diffraction and thermogravimetric measurements were used to characterize the structural and thermodynamic properties of the material. Ab initio electronic structure calculations were used to give insight into the unusual properties of Ba(Cd1/3Ta2/3)O-3, as well as a similar and more widely used material Ba(Zn1/3Ta2/3)O-3. While both compounds have a hexagonal Bravais lattice, the P321 space group of Ba(Cd1/3Ta2/3)O-3 is reduced from P (3) under bar m1 of Ba(Zn1/3Ta2/3)O-3 as a result of a distortion of oxygen away from the symmetric position between the Ta and Cd ions. Both of the compounds have a conduction band minimum and valence band maximum composed of mostly weakly itinerant Ta 5d and Zn 3d/Cd 4d levels, respectively. The covalent nature of the directional d-electron bonding in these high-Z oxides plays an important role in producing a more rigid lattice with higher melting points and enhanced phonon energies, and is suggested to play an important role in producing materials with a high dielectric constant and low microwave loss. (C) 2005 American Institute of Physics.