Non-mean-field theory of anomalously large double-layer capacitance

Mean-field theories claim that the capacitance of the double-layer formed at a metal/ionic conductor interface cannot be larger than that of the Helmholtz capacitor, whose width is equal to the radius of an ion. However, in some experiments the apparent width of the double-layer capacitor is substantially smaller. We propose an alternate, non-mean-field theory of the ionic double-layer to explain such large capacitance values. Our theory allows for the binding of discrete ions to their image charges in the metal, which results in the formation of interface dipoles. We focus primarily on the case where only small cations are mobile and other ions form an oppositely-charged background. In this case, at small temperature and zero applied voltage dipoles form a correlated liquid on both contacts. We show that at small voltages the capacitance of the double-layer is determined by the transfer of dipoles from one electrode to the other and is therefore limited only by the weak dipole-dipole repulsion between bound ions, so that the capacitance is very large. At large voltages the depletion of bound ions from one of the capacitor electrodes triggers a collapse of the capacitance to the much smaller mean-field value, as seen in experimental data. We test our analytical predictions with a Monte Carlo simulation and find good agreement. We further argue that our ``one-component plasma" model should work well for strongly asymmetric ion liquids. We believe that this work also suggests an improved theory of pseudo-capacitance.Comment: 19 pages, 14 figures; some Monte Carlo results and a section about aqueous solutions adde

Nonlinear Dynamics of the Perceived Pitch of Complex Sounds

We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility

The Inverse Variational Problem for Autoparallels

We study the problem of the existence of a local quantum scalar field theory in a general affine metric space that in the semiclassical approximation would lead to the autoparallel motion of wave packets, thus providing a deviation of the spinless particle trajectory from the geodesics in the presence of torsion. The problem is shown to be equivalent to the inverse problem of the calculus of variations for the autoparallel motion with additional conditions that the action (if it exists) has to be invariant under time reparametrizations and general coordinate transformations, while depending analytically on the torsion tensor. The problem is proved to have no solution for a generic torsion in four-dimensional spacetime. A solution exists only if the contracted torsion tensor is a gradient of a scalar field. The corresponding field theory describes coupling of matter to the dilaton field.Comment: 13 pages, plain Latex, no figure

Essential nonlinearities in hearing

Our hearing organ, the cochlea, evidently poises itself at a Hopf bifurcation to maximize tuning and amplification. We show that in this condition several effects are expected to be generic: compression of the dynamic range, infinitely shrap tuning at zero input, and generation of combination tones. These effects are "essentially" nonlinear in that they become more marked the smaller the forcing: there is no audible sound soft enough not to evoke them. All the well-documented nonlinear aspects of hearing therefore appear to be consequences of the same underlying mechanism.Comment: 4 pages, 3 figure

Diffuse-Charge Dynamics in Electrochemical Systems

The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The ``weakly nonlinear'' limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter $\epsilon = \lambda_D/L$, where $\lambda_D$ is the screening length and $L$ the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of $\lambda_D L / D$ (not $\lambda_D^2/D$), where $D$ is the ionic diffusivity, but nonlinearity violates this common picture and introduce multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, $L^2/D$. In the ``strongly nonlinear'' regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference

Mechanisms, functions and ecology of colour vision in the honeybee.

notes: PMCID: PMC4035557types: Journal Article© The Author(s) 2014.This is an open access article that is freely available in ORE or from Springerlink.com. Please cite the published version available at: http://link.springer.com/article/10.1007%2Fs00359-014-0915-1Research in the honeybee has laid the foundations for our understanding of insect colour vision. The trichromatic colour vision of honeybees shares fundamental properties with primate and human colour perception, such as colour constancy, colour opponency, segregation of colour and brightness coding. Laborious efforts to reconstruct the colour vision pathway in the honeybee have provided detailed descriptions of neural connectivity and the properties of photoreceptors and interneurons in the optic lobes of the bee brain. The modelling of colour perception advanced with the establishment of colour discrimination models that were based on experimental data, the Colour-Opponent Coding and Receptor Noise-Limited models, which are important tools for the quantitative assessment of bee colour vision and colour-guided behaviours. Major insights into the visual ecology of bees have been gained combining behavioural experiments and quantitative modelling, and asking how bee vision has influenced the evolution of flower colours and patterns. Recently research has focussed on the discrimination and categorisation of coloured patterns, colourful scenes and various other groupings of coloured stimuli, highlighting the bees' behavioural flexibility. The identification of perceptual mechanisms remains of fundamental importance for the interpretation of their learning strategies and performance in diverse experimental tasks.Biotechnology and Biological Sciences Research Council (BBSRC

The reference frame for encoding and retention of motion depends on stimulus set size

YesThe goal of this study was to investigate the reference frames used in perceptual encoding and storage of visual motion information. In our experiments, observers viewed multiple moving objects and reported the direction of motion of a randomly selected item. Using a vector-decomposition technique, we computed performance during smooth pursuit with respect to a spatiotopic (nonretinotopic) and to a retinotopic component and compared them with performance during fixation, which served as the baseline. For the stimulus encoding stage, which precedes memory, we found that the reference frame depends on the stimulus set size. For a single moving target, the spatiotopic reference frame had the most significant contribution with some additional contribution from the retinotopic reference frame. When the number of items increased (Set Sizes 3 to 7), the spatiotopic reference frame was able to account for the performance. Finally, when the number of items became larger than 7, the distinction between reference frames vanished. We interpret this finding as a switch to a more abstract nonmetric encoding of motion direction. We found that the retinotopic reference frame was not used in memory. Taken together with other studies, our results suggest that, whereas a retinotopic reference frame may be employed for controlling eye movements, perception and memory use primarily nonretinotopic reference frames. Furthermore, the use of nonretinotopic reference frames appears to be capacity limited. In the case of complex stimuli, the visual system may use perceptual grouping in order to simplify the complexity of stimuli or resort to a nonmetric abstract coding of motion information