586 research outputs found
The spike train statistics for consonant and dissonant musical accords
The simple system composed of three neural-like noisy elements is considered.
Two of them (sensory neurons or sensors) are stimulated by noise and periodic
signals with different ratio of frequencies, and the third one (interneuron)
receives the output of these two sensors and noise. We propose the analytical
approach to analysis of Interspike Intervals (ISI) statistics of the spike
train generated by the interneuron. The ISI distributions of the sensory
neurons are considered to be known. The frequencies of the input sinusoidal
signals are in ratios, which are usual for music. We show that in the case of
small integer ratios (musical consonance) the input pair of sinusoids results
in the ISI distribution appropriate for more regular output spike train than in
a case of large integer ratios (musical dissonance) of input frequencies. These
effects are explained from the viewpoint of the proposed theory.Comment: 22 pages, 6 figure
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
Point vortices on the sphere: a case with opposite vorticities
We study systems formed of 2N point vortices on a sphere with N vortices of
strength +1 and N vortices of strength -1. In this case, the Hamiltonian is
conserved by the symmetry which exchanges the positive vortices with the
negative vortices. We prove the existence of some fixed and relative
equilibria, and then study their stability with the ``Energy Momentum Method''.
Most of the results obtained are nonlinear stability results. To end, some
bifurcations are described.Comment: 35 pages, 9 figure
Object knowledge modulates colour appearance
We investigated the memory colour effect for colour diagnostic artificial objects. Since knowledge about these objects and their colours has been learned in everyday life, these stimuli allow the investigation of the influence of acquired object knowledge on colour appearance. These investigations are relevant for questions about how object and colour information in high-level vision interact as well as for research about the influence of learning and experience on perception in general. In order to identify suitable artificial objects, we developed a reaction time paradigm that measures (subjective) colour diagnosticity. In the main experiment, participants adjusted sixteen such objects to their typical colour as well as to grey. If the achromatic object appears in its typical colour, then participants should adjust it to the opponent colour in order to subjectively perceive it as grey. We found that knowledge about the typical colour influences the colour appearance of artificial objects. This effect was particularly strong along the daylight axis
On the Discovery of Monocular Rivalry by Tscherning in 1898:Translation and Review
Monocular rivalry was named by Breese in 1899. He made prolonged observation of superimposed orthogonal gratings; they fluctuated in clarity with either one or the other grating occasionally being visible alone. A year earlier, Tscherning observed similar fluctuations with a grid of vertical and horizontal lines and with other stimuli; we draw attention to his prior account. Monocular rivalry has since been shown to occur with a wide variety of superimposed patterns with several independent rediscoveries of it. We also argue that Helmholtz described some phenomenon other than monocular rivalry in 1867
Historical roots of gauge invariance
Gauge invariance is the basis of the modern theory of electroweak and strong
interactions (the so called Standard Model). The roots of gauge invariance go
back to the year 1820 when electromagnetism was discovered and the first
electrodynamic theory was proposed. Subsequent developments led to the
discovery that different forms of the vector potential result in the same
observable forces. The partial arbitrariness of the vector potential A brought
forth various restrictions on it. div A = 0 was proposed by J. C. Maxwell;
4-div A = 0 was proposed L. V. Lorenz in the middle of 1860's . In most of the
modern texts the latter condition is attributed to H. A. Lorentz, who half a
century later was one of the key figures in the final formulation of classical
electrodynamics. In 1926 a relativistic quantum-mechanical equation for charged
spinless particles was formulated by E. Schrodinger, O. Klein, and V. Fock. The
latter discovered that this equation is invariant with respect to
multiplication of the wave function by a phase factor exp(ieX/hc) with the
accompanying additions to the scalar potential of -dX/cdt and to the vector
potential of grad X. In 1929 H. Weyl proclaimed this invariance as a general
principle and called it Eichinvarianz in German and gauge invariance in
English. The present era of non-abelian gauge theories started in 1954 with the
paper by C. N. Yang and R. L. Mills.Comment: final-final, 34 pages, 1 figure, 106 references (one added with
footnote since v.2); to appear in July 2001 Rev. Mod. Phy
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 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
From Lagrangian to Quantum Mechanics with Symmetries
We present an old and regretfully forgotten method by Jacobi which allows one
to find many Lagrangians of simple classical models and also of nonconservative
systems. We underline that the knowledge of Lie symmetries generates Jacobi
last multipliers and each of the latter yields a Lagrangian. Then it is shown
that Noether's theorem can identify among those Lagrangians the physical
Lagrangian(s) that will successfully lead to quantization. The preservation of
the Noether symmetries as Lie symmetries of the corresponding Schr\"odinger
equation is the key that takes classical mechanics into quantum mechanics.
Some examples are presented.Comment: To appear in: Proceedings of Symmetries in Science XV, Journal of
Physics: Conference Series, (2012
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