535 research outputs found
Giant Leaps and Minimal Branes in Multi-Dimensional Flux Landscapes
There is a standard story about decay in multi-dimensional flux landscapes:
that from any state, the fastest decay is to take a small step, discharging one
flux unit at a time; that fluxes with the same coupling constant are
interchangeable; and that states with N units of a given flux have the same
decay rate as those with -N. We show that this standard story is false. The
fastest decay is a giant leap that discharges many different fluxes in unison;
this decay is mediated by a 'minimal' brane that wraps the internal manifold
and exhibits behavior not visible in the effective theory. We discuss the
implications for the cosmological constant.Comment: Minor updates to agree with published version. 9 pages, 4 figure
Can one see the fundamental frequency of a drum?
We establish two-sided estimates for the fundamental frequency (the lowest
eigenvalue) of the Laplacian in an open subset G of R^n with the Dirichlet
boundary condition. This is done in terms of the interior capacitary radius of
G which is defined as the maximal possible radius of a ball B which has a
negligible intersection with the complement of G. Here negligibility of a
subset F in B means that the Wiener capacity of F does not exceed gamma times
the capacity of B, where gamma is an arbitrarily fixed constant between 0 and
1. We provide explicit values of constants in the two-sided estimates.Comment: 18 pages, some misprints correcte
Dynamical Belyi maps
We study the dynamical properties of a large class of rational maps with
exactly three ramification points. By constructing families of such maps, we
obtain infinitely many conservative maps of degree ; this answers a question
of Silverman. Rather precise results on the reduction of these maps yield
strong information on the rational dynamics.Comment: 21 page
Electrostatic colloid-membrane complexation
We investigate numerically and on the scaling level the adsorption of a
charged colloid on an oppositely charged flexible membrane. We show that the
long ranged character of the electrostatic interaction leads to a wrapping
reentrance of the complex as the salt concentration is varied. The membrane
wrapping depends on the size of the colloid and on the salt concentration and
only for intermediate salt concentration and colloid sizes we find full
wrapping. From the scaling model we derive simple relations for the phase
boundaries between the different states of the complex, which agree well with
the numerical minimization of the free energy.Comment: 7 page, 11 figure
Solving the brachistochrone and other variational problems with soap films
We show a method to solve the problem of the brachistochrone as well as other
variational problems with the help of the soap films that are formed between
two suitable surfaces. We also show the interesting connection between some
variational problems of dynamics, statics, optics, and elasticity.Comment: 16 pages, 11 figures. This article, except for a small correction,
has been submitted to the American Journal of Physic
The shape of jamming arches in two-dimensional deposits of granular materials
We present experimental results on the shape of arches that block the outlet
of a two dimensional silo. For a range of outlet sizes, we measure some
properties of the arches such as the number of particles involved, the span,
the aspect ratio, and the angles between mutually stabilizing particles. These
measurements shed light on the role of frictional tangential forces in arching.
In addition, we find that arches tend to adopt an aspect ratio (the quotient
between height and half the span) close to one, suggesting an isotropic load.
The comparison of the experimental results with data from numerical models of
the arches formed in the bulk of a granular column reveals the similarities of
both, as well as some limitations in the few existing models.Comment: 8 pages; submitted to Physical Review
Band structures of P-, D-, and G-surfaces
We present a theoretical study on the band structures of the electron
constrained to move along triply-periodic minimal surfaces. Three well known
surfaces connected via Bonnet transformations, namely P-, D-, and G-surfaces,
are considered. The six-dimensional algebra of the Bonnet transformations [C.
Oguey and J.-F. Sadoc, J. Phys. I France 3, 839 (1993)] is used to prove that
the eigenstates for these surfaces are interrelated at a set of special points
in the Brillouin zones. The global connectivity of the band structures is,
however, different due to the topological differences of the surfaces. A
numerical investigation of the band structures as well as a detailed analysis
on their symmetry properties is presented. It is shown that the presence of
nodal lines are closely related to the symmetry properties. The present study
will provide a basis for understanding further the connection between the
topology and the band structures.Comment: 21 pages, 8 figures, 3 tables, submitted to Phys. Rev.
Optimal time travel in the Godel universe
Using the theory of optimal rocket trajectories in general relativity,
recently developed in arXiv:1105.5235, we present a candidate for the minimum
total integrated acceleration closed timelike curve in the Godel universe, and
give evidence for its minimality. The total integrated acceleration of this
curve is lower than Malament's conjectured value (Malament, 1984), as was
already implicit in the work of Manchak (Manchak, 2011); however, Malament's
conjecture does seem to hold for periodic closed timelike curves.Comment: 16 pages, 2 figures; v2: lower bound in the velocity and reference
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