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

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

The occlusion illusion: partial modal completion or apparent distance?

In the occlusion illusion, the visible portion of a partly occluded object (eg a semicircle partly hidden behind a rectangle) appears to be significantly larger than a physically identical region that is fully visible. This illusion may occur either because the visual system 'fills in' a thin strip along the occluded border (the partial-modal-completion hypothesis) or because the partly occluded object is perceived as farther away (the apparent-distance hypothesis). We measured the magnitude of the occlusion illusion psychophysically in several experiments to investigate its causes. The results of experiments 1-3 are consistent with the general proposal that the magnitude of the illusion varies with the strength of the evidence for occlusion, supporting the inference that it is due to occlusion. Experiment 4 provides a critical test between apparent-distance and partial-modal-completion explanations by determining whether the increase in apparent size of the occluded region results from a change in its perceived shape (due to the modal extension of the occluded shape along the occluding edge, as predicted by the partial-modal-completion hypothesis) or from a change in its perceived overall size (as predicted by the apparent-distance hypothesis). The results more strongly support the partial-modal-completion hypothesis

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

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

Physically Similar Systems - A History of the Concept

PreprintThe concept of similar systems arose in physics, and appears to have originated with Newton in the seventeenth century. This chapter provides a critical history of the concept of physically similar systems, the twentieth century concept into which it developed. The concept was used in the nineteenth century in various fields of engineering (Froude, Bertrand, Reech), theoretical physics (van der Waals, Onnes, Lorentz, Maxwell, Boltzmann) and theoretical and experimental hydrodynamics (Stokes, Helmholtz, Reynolds, Prandtl, Rayleigh). In 1914, it was articulated in terms of ideas developed in the eighteenth century and used in nineteenth century mathematics and mechanics: equations, functions and dimensional analysis. The terminology physically similar systems was proposed for this new characterization of similar systems by the physicist Edgar Buckingham. Related work by Vaschy, Bertrand, and Riabouchinsky had appeared by then. The concept is very powerful in studying physical phenomena both theoretically and experimentally. As it is not currently part of the core curricula of STEM disciplines or philosophy of science, it is not as well known as it ought to be

Bayesian Modeling of Perceived Surface Slant from Actively-Generated and Passively-Observed Optic Flow

We measured perceived depth from the optic flow (a) when showing a stationary physical or virtual object to observers who moved their head at a normal or slower speed, and (b) when simulating the same optic flow on a computer and presenting it to stationary observers. Our results show that perceived surface slant is systematically distorted, for both the active and the passive viewing of physical or virtual surfaces. These distortions are modulated by head translation speed, with perceived slant increasing directly with the local velocity gradient of the optic flow. This empirical result allows us to determine the relative merits of two alternative approaches aimed at explaining perceived surface slant in active vision: an “inverse optics” model that takes head motion information into account, and a probabilistic model that ignores extra-retinal signals. We compare these two approaches within the framework of the Bayesian theory. The “inverse optics” Bayesian model produces veridical slant estimates if the optic flow and the head translation velocity are measured with no error; because of the influence of a “prior” for flatness, the slant estimates become systematically biased as the measurement errors increase. The Bayesian model, which ignores the observer's motion, always produces distorted estimates of surface slant. Interestingly, the predictions of this second model, not those of the first one, are consistent with our empirical findings. The present results suggest that (a) in active vision perceived surface slant may be the product of probabilistic processes which do not guarantee the correct solution, and (b) extra-retinal signals may be mainly used for a better measurement of retinal information

A theory of moving form perception: Synergy between masking, perceptual grouping, and motion computation in retinotopic and non-retinotopic representations

Because object and self-motion are ubiquitous in natural viewing conditions, understanding how the human visual system achieves a relatively clear perception for moving objects is a fundamental problem in visual perception. Several studies have shown that the visible persistence of a briefly presented stationary stimulus is approximately 120 ms under normal viewing conditions. Based on this duration of visible persistence, we would expect moving objects to appear highly blurred. However, in human vision, objects in motion typically appear relatively sharp and clear. We suggest that clarity of form in dynamic viewing is achieved by a synergy between masking, perceptual grouping, and motion computation across retinotopic and non-retinotopic representations. We also argue that dissociations observed in masking are essential to create and maintain this synergy