Theory of linear sweep voltammetry with diffuse charge: Unsupported electrolytes, thin films, and leaky membranes

Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. In this paper, we provide a comprehensive mathematical theory of voltammetry in electrochemical cells with unsupported electrolytes and for other situations where diffuse charge effects play a role, and present analytical and simulated solutions of the time-dependent Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions for a 1:1 electrolyte and a simple reaction. Using these solutions, we construct theoretical and simulated current-voltage curves for liquid and solid thin films, membranes with fixed background charge, and cells with blocking electrodes. The full range of dimensionless parameters is considered, including the dimensionless Debye screening length (scaled to the electrode separation), Damkohler number (ratio of characteristic diffusion and reaction times), and dimensionless sweep rate (scaled to the thermal voltage per diffusion time). The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, although capacitive charging of the electrical double layers is also studied, for early time transients at reactive electrodes and for nonreactive blocking electrodes. Our work highlights cases where diffuse charge effects are important in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.

A finite volume method and experimental study of a stator of a piezoelectric traveling wave rotary ultrasonic motor

Piezoelectric traveling wave rotary ultrasonic motors are motors that generate torque by using the friction force between a piezoelectric composite ring (or disk-shaped stator) and a metallic ring (or disk-shaped rotor) when a traveling wave is excited in the stator. The motor speed is proportional to the amplitude of the traveling wave and, in order to obtain large amplitudes, the stator is excited at frequencies close to its resonance frequency. This paper presents a non-empirical partial differential equations model for the stator, which is discretized using the finite volume method. The fundamental frequency of the discretized model is computed and compared to the experimentally-measured operating frequency of the stator of Shinsei USR60 piezoelectric motor.

Modeling of composite piezoelectric structures with the finite volume method

Piezoelectric devices, such as piezoelectric traveling- wave rotary ultrasonic motors, have composite piezoelectric structures. A composite piezoelectric structure consists of a combination of two or more bonded materials, at least one of which is a piezoelectric transducer. Piezoelectric structures have mainly been numerically modeled using the finite element method. An alternative approach based on the finite volume method offers the following advantages: 1) the ordinary differential equations resulting from the discretization process can be interpreted directly as corresponding circuits; and 2) phenomena occurring at boundaries can be treated exactly. This paper presents a method for implementing the boundary conditions between the bonded materials in composite piezoelectric structures modeled with the finite volume method. The paper concludes with a modeling example of a unimorph structure.

A finite locus effect diffusion model for the evolution of a quantitative trait

A diffusion model is constructed for the joint distribution of absolute locus effect sizes and allele frequencies for loci contributing to an additive quantitative trait under selection in a haploid, panmictic population. The model is designed to approximate a discrete model exactly in the limit as both population size and the number of loci affecting the trait tend to infinity. For the case when all loci have the same absolute effect size, formal multiple-timescale asymptotics are used to predict the long-time response of the population trait mean to selection. For the case where loci can take on either of two distinct effect sizes, not necessarily with equal probability, numerical solutions of the system indicate that response to selection of a quantitative trait is insensitive to the variability of the distribution of effect sizes when mutation is negligible.

Advances in random matrix theory, zeta functions, and sphere packing

Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues ("the energy levels") follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks.

Computational modeling of orientation tuning dynamics in monkey primary visual cortex

In the primate visual pathway, orientation tuning of neurons is first observed in the primary visual cortex. The LGN cells that comprise the thalamic input to V1 are not orientation tuned, but some V1 neurons are quite selective. Two main classes of theoretical models have been offered to explain orientation selectivity: feedforward models, in which inputs from spatially aligned LGN cells are summed together by one cortical neuron; and feedback models, in which an initial weak orientation bias due to convergent LGN input is sharpened and amplified by intracortical feedback. Recent data on the dynamics of orientation tuning, obtained by a cross-correlation technique, may help to distinguish between these classes of models. To test this possibility, we simulated the measurement of orientation tuning dynamics on various receptive field models, including a simple Hubel-Wiesel type feedforward model: a linear spatiotemporal filter followed by an integrate-and-fire spike generator. The computational study reveals that simple feedforward models may account for some aspects of the experimental data but fail to explain many salient features of orientation tuning dynamics in V1 cells. A simple feedback model of interacting cells is also considered. This model is successful in explaining the appearance of Mexican-hat orientation profiles, but other features of the data continue to be unexplained.

Current concepts in clinical therapeutics: disease-modifying drugs for rheumatoid arthritis

The epidemiology, pathophysiology, clinical features, diagnosis, and clinical course of rheumatoid arthritis (RA) and the role of disease-modifying antirheumatic drugs (DMARDs) in its treatment are reviewed. RA, a widespread disease affecting people of all races and sexes around the world, has an unknown and perhaps multifactorial etiology. Conflicting evidence supports an immune-complex, infectious, metabolic, or genetic basis for RA. The disease affects diarthrodial joints and begins as an immune response to unknown antigenic stimuli. A proliferative process ensues, leading to formation of a vascular lesion called a pannus, which then infiltrates into cartilage, subchrondral bone, and tendon. This destructive phase leads to classic RA symptoms of pain, limitation of motion, swelling, heat, and redness of the affected joint. Symptoms and laboratory tests form the basis for diagnosis. For most RA patients, conservative therapy provides substantial benefit. In those patients who suffer from unrelenting and progressively destructive disease, more aggressive intervention is necessary to prevent permanent disability. The DMARDs are reserved for treatment of this group of patients. DMARDs include such diverse agents as the gold compounds aurothioglucose, auranofin, and gold sodium thiomalate; the antimalarials hydroxychloroquine sulfate and chloroquine phosphate; penicillamine; and the cytotoxic agents azathioprine, methotrexate, and cyclophosphamide. DMARDs are effective but toxic therapeutic agents. Because of the toxicities of these agents, careful monitoring at regular intervals is necessary throughout the duration of therapy. For patients in whom these drugs demonstrate efficacy and are tolerated, the DMARDs may attenuate the disabling effects of long-term erosive disease.

Effect of sucralfate on ibuprofen absorption in normal volunteers

The effect of the concurrent administration of sucralfate on the absorption of a single dose of ibuprofen was studied in nine normal volunteers using a random crossover design. Each participant received a single 600-mg dose of ibuprofen for the control phase, and a 600-mg dose of ibuprofen following 5 g of sucralfate given in 1-g divided doses for the treatment phase. Blood samples were obtained at regular intervals for 12 hours following the administration of ibuprofen, and pharmacokinetic and statistical analyses were performed. Analysis of time to peak serum concentration, maximum serum concentration, elimination rate constant, and half-life showed no significant difference between the control and treatment phases. Mean total area under the curve for ibuprofen decreased by 11.8% in the treatment phase, but this decrease was not statistically significant. The concurrent administration of sucralfate did not significantly alter the absorption of a single 600-mg dose of ibuprofen in healthy subjects.