288 research outputs found
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 , where is the
screening length and the electrode separation. At leading order, the system
initially behaves like an RC circuit with a response time of
(not ), where 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, . 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
Das Problem in ein Postulat verwandeln: Cassirer und Einsteins Unterscheidung von konstruktiven und Prinzipien-Theorien
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
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