The transient response of a CSTR containing porous catalyst pellets. Asymptotic solutions

Transient response of a CSTR containing porous catalyst pellets is analyzed theoretically using a matched asymptotic expansion technique. This singular perturbation technique leads directly to the conditions under which the minima of reservoir concentration occur. The existence of the minima may be used to estimate some inherent parameters of the catalyst pellet.

Approximate analytical solutions for porous catalysts with nonuniform activity

Using a novel finite integral transform technique, the problem of diffusion and chemical reaction in a porous catalyst with general activity profile is investigated theoretically. Analytical expressions for the effectiveness factor are obtained for pth order and Michaelis-Menten kinetics. Perturbation methods are employed to provide useful asymptotic solutions for large or small values of Thiele modulus and Biot number.

Transient response of diffusion cell containing a porous solid

Transient response of an adsorbing or non-adsorbing tracer injected as step or square pulse input in a diffusion cell with two flowing streams across the pellet is theoretically investigated in this paper. Exact solutions and the asymptotic solutions in the time domain and in three different limits are obtained by using an integral transform technique and a singular perturbation technique, respectively. Parametric dependence of the concentrations in the top and bottom chambers can be revealed by investigating the asymptotic solutions, which are far simpler than their exact counterpart. In the time domain investigation, it is found that the bottom-chamber concentration is very sensitive to the value of the macropore effective diffusivity. Therefore this concentration could be used to extract diffusivity by fitting in the time domain. The bottom-chamber concentration is also sensitive to flow rate, pellet length chamber volume and the type of input (step and square input).

Contraction of the human diaphragm during rapid postural adjustments

1. The response of the diaphragm to the postural perturbation produced by rapid flexion of the shoulder to a visual stimulus was evaluated in standing subjects. Gastric, oesophageal and transdiaphragmatic pressures were measured together with intramuscular and oesophageal recordings of electromyographic activity (EMG) in the diaphragm. To assess the mechanics of contraction of the diaphragm, dynamic changes in the length of the diaphragm were measured with ultrasonography. 2. With rapid flexion of the shoulder in response to a visual stimulus, EMG-activity in the costal and crural diaphragm occurred about 20 ms prior to the onset of deltoid EMG. This anticipatory contraction occurred irrespective of the phase of respiration in which arm movement began. The onset of diaphragm EMG-coincided with that of transversus abdominis. 3. Gastric and transdiaphragmatic pressures increased in association with the rapid arm flexion by 13.8 +/- 1.9 (mean +/- S.E.M.) and 13.5 +/- 1.8 cmH(2)O, respectively. The increases occurred 49 +/- 4 ms after the onset of diaphragm EMG, but preceded the onset of movement of the limb by 63 +/- 7 ms. 4. Ultrasonographic measurements revealed that the costal diaphragm shortened and then lengthened progressively during the increase in transdiaphragmatic pressure. 5. This study provides definitive evidence that the human diaphragm is involved in the control of postural stability during sudden voluntary movement of the limbs.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Sensitive detection of sodium in a flame using parametric four-wave mixing and seeded parametric four-wave mixing

Two-photon resonant parametric four-wave mixing and a newly developed variant called seeded parametric four-wave mixing are used to detect trace quantities of sodium in a flame. Both techniques are simple, requiring only a single laser to generate a signal beam at a different wavelength which propagates collinearly with the pump beam, allowing efficient signal recovery. A comparison of the two techniques reveals that seeded parametric four-wave mixing is more than two orders of magnitude more sensitive than parametric four-wave mixing, with an estimated detection sensitivity of 5 x 10(9) atoms/cm(3). Seeded parametric four-wave mixing is achieved by cascading two parametric four-wave mixing media such that one of the parametric fields generated in the first high-density medium is then used to seed the same four-wave mixing process in a second medium in order to increase the four-wave mixing gain. The behavior of this seeded parametric four-wave mixing is described using semiclassical perturbation theory. A simplified small-signal theory is found to model most of the data satisfactorily. However, an anomalous saturationlike behavior is observed in the large signal regime. The full perturbation treatment, which includes the competition between two different four-wave mixing processes coupled via the signal field, accounts for this apparently anomalous behavior.

Reactivity of chars and carbons: New insights through molecular modeling

A new model proposed for the gasification of chars and carbons incorporates features of the turbostratic nanoscale structure that exists in such materials. The model also considers the effect of initial surface chemistry and different reactivities perpendicular to the edges and to the faces of the underlying crystallite planes comprising the turbostratic structure. It may be more realistic than earlier models based on pore or grain structure idealizations when the carbon contains large amounts of crystallite matter. Shrinkage of the carbon particles in the chemically controlled regime is also possible due to the random complete gasification of crystallitic planes. This mechanism can explain observations in the literature of particle size reduction. Based on the model predictions, both initial surface chemistry and the number of stacked planes in the crystallites strongly influence the reactivity and particle shrinkage. Its test results agree well with literature data on the air-oxidation of Spherocarb and show that it accurately predicts the variation of particle size with conversion. Model parameters are determined entirely from rate measurements.

Simulation and optimization of heated, inviscid flows in scramjet ducts

A space-marching code for the simulation and optimization of inviscid supersonic flow in three dimensions is described. The now in a scramjet module with a relatively complex three-dimensional geometry is examined and wall-pressure estimates are compared with experimental data. Given that viscous effects are not presently included, the comparison is reasonable. The thermodynamic compromise of adding heat in a diverging combustor is also examined. The code is then used to optimize the shape of a thrust surface for a simpler (box-section) scramjet module in the presence of uniform and nonuniform heat distributions. The optimum two-dimensional profiles for the thrust surface are obtained via a perturbation procedure that requires about 30-50 now solutions. It is found that the final shapes are fairly insensitive to the details of the heat distribution.

Modeling the optical properties of AlSb, GaSb, and InSb

Optical constants of AlSb, GaSb, and InSb are modeled in the 1-6 eV spectral range. We employ an extension of Adachi's model of the optical constants of semiconductors. The model takes into account transitions at E-0, E-0 + Delta(0), E-1, and E-1 + Delta(1) critical points, as well as higher-lying transitions which are modeled with three damped harmonic oscillators. We do not consider indirect transitions contribution, since it represents a second-order perturbation and its strength should be low. Also, we do not take into account excitonic effects at E-1, E-1 + Delta(1) critical points, since we model the room temperature data. In spite of fewer contributions to the dielectric function compared to previous calculations involving Adachi's model, our calculations show significantly improved agreement with the experimental data. This is due to the two main distinguishing features of calculations presented here: use of adjustable line broadening instead of the conventional Lorentzian one, and employment of a global optimization routine for model parameter determination.

Beach water table fluctuations due to spring-neap tides: moving boundary effects

Tidal water table fluctuations in a coastal aquifer are driven by tides on a moving boundary that varies with the beach slope. One-dimensional models based on the Boussinesq equation are often used to analyse tidal signals in coastal aquifers. The moving boundary condition hinders analytical solutions to even the linearised Boussinesq equation. This paper presents a new perturbation approach to the problem that maintains the simplicity of the linearised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection-diffusion equation) with an oscillating velocity. The perturbation method is applied to the propagation of spring-neap tides (a bichromatic tidal system with the fundamental frequencies wt and wt) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the two primary tidal oscillations, generating a slowly damped water table fluctuation of frequency omega(1) - omega(2), i.e., the spring-neap tidal water table fluctuation. The analytical predictions are found to be consistent with recently published field observations. (C) 2000 Elsevier Science Ltd. All rights reserved.

Common chromosomal fragile site FRA16D sequence: identification of the FOR gene spanning FRA16D and homozygous deletions and translocation breakpoints in cancer cells

Fluorescence in situ hybridization of a tile path of DNA subclones has previously enabled the cytogenetic definition of the minimal DNA sequence which spans the FRA16D common chromosomal fragile site, located at 16q23.2. Homozygous deletion of the FRA16D locus has been reported in adenocarcinomas of stomach, colon, lung and ovary. We have sequenced the 270 kb containing the FRA16D fragile site and the minimal homozygously deleted region in tumour cells. This sequence enabled localization of some of the tumour cell breakpoints to regions which contain AT-rich secondary structures similar to those associated with the FRA10B and FRA16B rare fragile sites. The FRA16D DNA sequence also led to the identification of an alternatively spliced gene, named FOR (fragile site FRA16D oxidoreductase), exons of which span both the fragile site and the minimal region of homozygous deletion. In addition, the complete DNA sequence of the FRA16D-containing FOR intron reveals no evidence of additional authentic transcripts. Alternatively spliced FOR transcripts (FOR I, FOR II and FOR III) encode proteins which share N-terminal WW domains and differ at their C-terminus, with FOR III having a truncated oxidoreductase domain. FRA16D-associated deletions selectively affect the FOR gene transcripts. Three out of five previously mapped translocation breakpoints in multiple myeloma are also located within the FOR gene. FOR is therefore the principle genetic target for DNA instability at 16q23.2 and perturbation of FOR function is likely to contribute to the biological consequences of DNA instability at FRA16D in cancer cells.

Numerical modelling of single-layer folding: clarification of an issue regarding the possible effect of computer codes and the influence of initial irregularities

The influence of initial perturbation geometry and material propel-ties on final fold geometry has been investigated using finite-difference (FLAC) and finite-element (MARC) numerical models. Previous studies using these two different codes reported very different folding behaviour although the material properties, boundary conditions and initial perturbation geometries were similar. The current results establish that the discrepancy was not due to the different computer codes but due to the different strain rates employed in the two previous studies (i.e. 10(-6) s(-1) in the FLAC models and 10(-14) s(-1) in the MARC models). As a result, different parts of the elasto-viscous rheological field were bring investigated. For the same material properties, strain rate and boundary conditions, the present results using the two different codes are consistent. A transition in Folding behaviour, from a situation where the geometry of initial perturbation determines final fold shape to a situation where material properties control the final geometry, is produced using both models. This transition takes place with increasing strain rate, decreasing elastic moduli or increasing viscosity (reflecting in each case the increasing influence of the elastic component in the Maxwell elastoviscous rheology). The transition described here is mechanically feasible but is associated with very high stresses in the competent layer (on the order of GPa), which is improbable under natural conditions. (C) 2000 Elsevier Science Ltd. All rights reserved.

Finite element modelling of three-dimensional convection problems in fluid-saturated porous media heated from below

We use the finite element method to model three-dimensional convective pore-fluid flow in fluid-saturated porous media when they are heated from below. In particular, we employ the particle-tracking technique to mimic the trajectories of particles in three-dimensional fluid flow problems. The related numerical results demonstrated that: (1) The progressive asymptotic approach procedure, which was previously developed for the finite element modelling of two-dimensional convective pore-fluid flow problems, is equally applicable to the finite element modelling of three-dimensional convective pore-fluid flow in fluid-saturated porous media heated from below. (2) The perturbation of gravity at different planes has a significant effect on the pattern of three-dimensional convective pore-fluid flow and therefore, may influence the pattern of orebody formation and mineralization in three-dimensional hydrothermal systems. Copyright (C) 2001 John Wiley & Sons, Ltd.

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.

Perturbed upper limb movements cause short-latency postural responses in trunk muscles

Addition of a load to a moving upper limb produces a perturbation of the trunk due to transmission of mechanical forces. This experiment investigated the postural response of the trunk muscles in relation to unexpected limb loading. Subjects performed rapid, bilateral shoulder flexion in response to a stimulus. In one third of trials, an unexpected load was added bilaterally to the upper limbs in the first third of the movement. Trunk muscle electromyography, intra-abdominal pressure and upper limb and trunk motion were measured. A short-latency response of the erector spinae and transversus abdominis muscles occurred similar to 50 ms after the onset of the limb perturbation that resulted from addition of the load early in the movement and was coincident with the onset of the observed perturbation at the trunk. The results provide evidence of initiation of a complex postural response of the trunk muscles that is consistent with mediation by afferent input from a site distant to the lumbar spine, which may include afferents of the upper limb.