Sobol' indices for problems defined in non-rectangular domains

A novel theoretical and numerical framework for the estimation of Sobol sensitivity indices for models in which inputs are confined to a non-rectangular domain (e.g., in presence of inequality constraints) is developed. Two numerical methods, namely the quadrature integration method which may be very efficient for problems of low and medium dimensionality and the MC/QMC estimators based on the acceptance-rejection sampling method are proposed for the numerical estimation of Sobol sensitivity indices. Several model test functions with constraints are considered for which analytical solutions for Sobol sensitivity indices were found. These solutions were used as benchmarks for verifying numerical estimates. The method is shown to be general and efficient

Optimisation of ex vivo memory B cell expansion/differentiation for interrogation of rare peripheral memory B cell subset responses

Background: Human memory B cells play a vital role in the long-term protection of the host from pathogenic re-challenge. In recent years the importance of a number of different memory B cell subsets that can be formed in response to vaccination or infection has started to become clear. To study memory B cell responses, cells can be cultured ex vivo, allowing for an increase in cell number and activation of these quiescent cells, providing sufficient quantities of each memory subset to enable full investigation of functionality. However, despite numerous papers being published demonstrating bulk memory B cell culture, we could find no literature on optimised conditions for the study of memory B cell subsets, such as IgM + memory B cells. Methods: Following a literature review, we carried out a large screen of memory B cell expansion conditions to identify the combination that induced the highest levels of memory B cell expansion. We subsequently used a novel Design of Experiments approach to finely tune the optimal memory B cell expansion and differentiation conditions for human memory B cell subsets. Finally, we characterised the resultant memory B cell subpopulations by IgH sequencing and flow cytometry. Results: The application of specific optimised conditions induce multiple rounds of memory B cell proliferation equally across Ig isotypes, differentiation of memory B cells to antibody secreting cells, and importantly do not alter the Ig genotype of the stimulated cells.  Conclusions: Overall, our data identify a memory B cell culture system that offers a robust platform for investigating the functionality of rare memory B cell subsets to infection and/or vaccination

Mass transport corrected Tafel analysis for electrochemically reversible systems of complex stoichiometry

An expression which allowed Tafel analysis of electrochemically reversible systems at hydrodynamic electrodes such as the rotating disk was investigated. It was found that under hydrodynamic conditions the mass transport of species occured within a diffusion layer of thickness δD adjacent to the surface of the electrode. Newton’s method was used for solution of generally non-linear algebric equations arising from discretization. The results show that Tafel analysis of the simulated waveshapes reveals the deviation from the prediced values

Mass transport corrected Tafel analysis for electrochemically reversible systems of complex stoichiometry

An expression which allowed Tafel analysis of electrochemically reversible systems at hydrodynamic electrodes such as the rotating disk was investigated. It was found that under hydrodynamic conditions the mass transport of species occured within a diffusion layer of thickness δD adjacent to the surface of the electrode. Newton's method was used for solution of generally non-linear algebric equations arising from discretization. The results show that Tafel analysis of the simulated waveshapes reveals the deviation from the prediced values

Mass transport limited currents at the tubular electrode

The convective-diffusion equation describing mass transport in a hydrodynamic tubular electrode is given and is solved using the alternating direction implicit method. Models which simplify the full mass transport equation are described and are compared with the approximate Levich theory for flow in a tubular electrode. Limiting currents are compared and the conditions for which the radial and axial diffusion terms are important are determined. © 2004 Elsevier B.V. All rights reserved

The theory of electrodeposition in the presence of forced convection: transport controlled nucleation of hemispheres

A new equation to describe the diffusion controlled nucleation of hemispherical centres under conditions of forced convection is derived, in a manner similar to that of the Scharifker and Mostany equation (J. Electroanal. Chem. 177 (1984) 13). It has been shown that the transients measured under these conditions should show a monotonically rising transient, followed by convergence to a limiting current. The accuracy and validity of the model is tested by comparison with experimental data obtained using a 5 mM Co/Co2+ system, sonicated at 66 W cm-2. Excellent fits are obtained, and the parameters derived are in agreement with those derived from independent experiments. © 2002 Elsevier Science B.V. All rights reserved

Importance of correct prediction of initial concentrations in voltammetric scans: contrasting roles of thermodynamics, kinetics, and natural convection.

In order to successfully model an electrochemical reaction mechanism one must ensure that all the equations, including initial conditions, satisfy the pertinent thermodynamic and kinetic relationships. Failure to do so may lead to invalid results even if they are mathematically correct. This fact has been previously emphasized (Luo, W.; Feldberg, S. W.; Rudolph, M. J. Electroanal. Chem. 1994, 368, 109 - 113; Rudolph, M. Digital Simulation in Electrochemistry. In Physical Electrochemistry; Rubenstein, I., Ed.; Marcel Dekker: New York, 1995; Chapter 3) and existing computer software for electrochemical simulations, such as DigiSim (Rudolph, M.; Reddy, D. P.; Feldberg, S. W. Anal. Chem. 1994, 66, 589A; http://www.basinc.com/products/ec/digisim/), offer the option of enforcing the so-called "pre-equilibration" which evaluates thermodynamic concentrations of all species prior to beginning a voltammetric scan. Although this approach allows setting consistent thermodynamic values it may result in a nonrealistic initial concentrations set because it corresponds to the whole solution status at infinite time for infinite kinetic constants. However, the perturbation created by the working electrode poised at its rest potential is necessarily limited by the size of the electrode, reaction kinetics, and duration of the rest period. Furthermore, natural convection limits even more the importance of the perturbation. This is analyzed theoretically through comparison of simulation results by DigiSim and KISSA-1D software for certain common electrochemical mechanisms in order to illustrate the importance of correct prediction of initial concentrations

In situ and online monitoring of hydrodynamic flow profiles in microfluidic channels based upon microelectrochemistry: optimization of electrode locations.

Herein, we extend our previous approach concerning the reconstruction of profiles of pressure-driven hydrodynamic flow in microfluidic channels based on current measurements at band electrode(s) [see the preceding paper ChemPhysChem 2005, 6, 1581]. We address the central issue of optimization of geometrical parameters describing the electrode(s) assembly (a single band and two bands working in generator-collector mode) within the channel flow cell to enhance the speed and precision of the flow profile reconstruction method

The theory of electrodeposition in the presence of forced convection: Transport controlled nucleation of hemispheres

A new equation to describe the diffusion controlled nucleation of hemispherical centres under conditions of forced convection is derived, in a manner similar to that of the Scharifker and Mostany equation (J. Electroanal. Chem. 177 (1984) 13). It has been shown that the transients measured under these conditions should show a monotonically rising transient, followed by convergence to a limiting current. The accuracy and validity of the model is tested by comparison with experimental data obtained using a 5 mM Co/Co2+ system, sonicated at 66 W cm-2. Excellent fits are obtained, and the parameters derived are in agreement with those derived from independent experiments. © 2002 Elsevier Science B.V. All rights reserved