30,875 research outputs found
Capillary Wave Theory of Adsorbed Liquid Films and the Structure of the Liquid-Vapor Interface
In this paper we try to work out in detail the implications of a microscopic
theory for capillary waves under the assumption that the density is given along
lines normal to the interface. Our study provides interface Hamiltonians for
adsorbed films in a variety of systems, and shows that the corrections to the
classical capillary wave spectrum are of the same order as the surface tension.
This implies that it is possible, at least in principle, to measure them in
x-ray surface scattering experiments. Interestingly, our study also sheds some
light on the nature of the liquid-vapor interface in the absence of external
fields and allows us to reconcile the Fisk-Widom scaling hypothesis with
capillary wave theory.Comment: Revised version, 51 pages, 4 figure
Clifford, William Kingdon
W.K. Clifford’s famous 1876 essay The Ethics of Belief contains one of the most memorable lines in the history of philosophy: "it is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence." The challenge to religious belief stemming from this moralized version of evidentialism is still widely discussed today
Toroidal and Klein bottle boundary slopes
Let M be a compact, connected, orientable, irreducible 3-manifold and T' an
incompressible torus boundary component of M such that the pair (M,T') is not
cabled. By a result of C. Gordon, if S and T are incompressible punctured tori
in M with boundary on T' and boundary slopes at distance d, then d is at most
8, and the cases where d=6,7,8 are very few and classified. We give a
simplified proof of this result (or rather, of its reduction process), based on
an improved estimate for the maximum possible number of mutually parallel
negative edges in the graphs of intersection of S and T. We also extend
Gordon's result by allowing either S or T to be an essential Klein bottle. to
the case where S or T is a punctured essential Klein bottle.Comment: Preliminary version, updated. We use a new approach that yields a
stronger conclusion. 28 pages, 18 figure
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Classification of Triadic Chord Inversions Using Kohonen Self-organizing Maps
In this paper we discuss the application of the Kohonen Selforganizing
Maps to the classification of triadic chords in inversions and root
positions. Our motivation started in the validation of Schönberg´s hypotheses of
the harmonic features of each chord inversion. We employed the Kohonen
network, which has been generally known as an optimum pattern classification
tool in several areas, including music, to verify that hypothesis. The outcomes
of our experiment refuse the Schönberg´s assumption in two aspects: structural
and perceptual/functional
Sceptical Theism and the Paradox of Evil
Given plausible assumptions about the nature of evidence and undercutting defeat, many believe that the force of the evidential problem of evil depends on sceptical theism’s being false: if evil is..
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