278 research outputs found
An Index Theorem for Domain Walls in Supersymmetric Gauge Theories
The supersymmetric abelian Higgs model with N scalar fields admits multiple
domain wall solutions. We perform a Callias-type index calculation to determine
the number of zero modes of this soliton. We confirm that the most general
domain wall has 2(N-1) zero modes, which can be interpreted as the positions
and phases of (N-1) constituent domain walls. This implies the existence of
moduli for a D-string interpolating between N D5-branes in IIB string theory.Comment: 9 pages, REVTeX4; v2: reference adde
Nested recursions with ceiling function solutions
Consider a nested, non-homogeneous recursion R(n) defined by R(n) =
\sum_{i=1}^k R(n-s_i-\sum_{j=1}^{p_i} R(n-a_ij)) + nu, with c initial
conditions R(1) = xi_1 > 0,R(2)=xi_2 > 0, ..., R(c)=xi_c > 0, where the
parameters are integers satisfying k > 0, p_i > 0 and a_ij > 0. We develop an
algorithm to answer the following question: for an arbitrary rational number
r/q, is there any set of values for k, p_i, s_i, a_ij and nu such that the
ceiling function ceiling{rn/q} is the unique solution generated by R(n) with
appropriate initial conditions? We apply this algorithm to explore those
ceiling functions that appear as solutions to R(n). The pattern that emerges
from this empirical investigation leads us to the following general result:
every ceiling function of the form ceiling{n/q}$ is the solution of infinitely
many such recursions. Further, the empirical evidence suggests that the
converse conjecture is true: if ceiling{rn/q} is the solution generated by any
recursion R(n) of the form above, then r=1. We also use our ceiling function
methodology to derive the first known connection between the recursion R(n) and
a natural generalization of Conway's recursion.Comment: Published in Journal of Difference Equations and Applications, 2010.
11 pages, 1 tabl
The Hospitals/Residents Problem with Couples: complexity and integer programming models
The Hospitals / Residents problem with Couples (hrc) is a generalisation of the classical Hospitals / Residents problem (hr) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of (typically geographically close) hospitals. In this paper we give a new NP-completeness result for the problem of deciding whether a stable matching exists, in highly restricted instances of hrc, and also an inapproximability bound for finding a matching with the minimum number of blocking pairs in equally restricted instances of hrc. Further, we present a full description of the first Integer Programming model for finding a maximum cardinality stable matching in an instance of hrc and we describe empirical results when this model applied to randomly generated instances of hrc
Geometric acceleration of complex chemical equilibrium calculations —performance in two- to five-component systems
DATA AVAILABILITY : Data will be made available on request.Please read abstract in the article.Ex Mente Technologies and Glencore through their funding of the Chair in Pyrometallurgical Modelling at the University of Pretoria.http://www.elsevier.com/locate/calphadhj2023Materials Science and Metallurgical Engineerin
Scarred Patterns in Surface Waves
Surface wave patterns are investigated experimentally in a system geometry
that has become a paradigm of quantum chaos: the stadium billiard. Linear waves
in bounded geometries for which classical ray trajectories are chaotic are
known to give rise to scarred patterns. Here, we utilize parametrically forced
surface waves (Faraday waves), which become progressively nonlinear beyond the
wave instability threshold, to investigate the subtle interplay between
boundaries and nonlinearity. Only a subset (three main types) of the computed
linear modes of the stadium are observed in a systematic scan. These correspond
to modes in which the wave amplitudes are strongly enhanced along paths
corresponding to certain periodic ray orbits. Many other modes are found to be
suppressed, in general agreement with a prediction by Agam and Altshuler based
on boundary dissipation and the Lyapunov exponent of the associated orbit.
Spatially asymmetric or disordered (but time-independent) patterns are also
found even near onset. As the driving acceleration is increased, the
time-independent scarred patterns persist, but in some cases transitions
between modes are noted. The onset of spatiotemporal chaos at higher forcing
amplitude often involves a nonperiodic oscillation between spatially ordered
and disordered states. We characterize this phenomenon using the concept of
pattern entropy. The rate of change of the patterns is found to be reduced as
the state passes temporarily near the ordered configurations of lower entropy.
We also report complex but highly symmetric (time-independent) patterns far
above onset in the regime that is normally chaotic.Comment: 9 pages, 10 figures (low resolution gif files). Updated and added
references and text. For high resolution images:
http://physics.clarku.edu/~akudrolli/stadium.htm
Validity of numerical trajectories in the synchronization transition of complex systems
We investigate the relationship between the loss of synchronization and the
onset of shadowing breakdown {\it via} unstable dimension variability in
complex systems. In the neighborhood of the critical transition to strongly
non-hyperbolic behavior, the system undergoes on-off intermittency with respect
to the synchronization state. There are potentially severe consequences of
these facts on the validity of the computer-generated trajectories obtained
from dynamical systems whose synchronization manifolds share the same
non-hyperbolic properties.Comment: 4 pages, 4 figure
Cosmological model with interactions in the dark sector
A cosmological model is proposed for the current Universe consisted of
non-interacting baryonic matter and interacting dark components. The dark
energy and dark matter are coupled through their effective barotropic indexes,
which are considered as functions of the ratio between their energy densities.
It is investigated two cases where the ratio is asymptotically stable and their
parameters are adjusted by considering best fits to Hubble function data. It is
shown that the deceleration parameter, the densities parameters, and the
luminosity distance have the correct behavior which is expected for a viable
present scenario of the Universe.Comment: 6 pages, 8 figure
Three-body non-additive forces between spin-polarized alkali atoms
Three-body non-additive forces in systems of three spin-polarized alkali
atoms (Li, Na, K, Rb and Cs) are investigated using high-level ab initio
calculations. The non-additive forces are found to be large, especially near
the equilateral equilibrium geometries. For Li, they increase the three-atom
potential well depth by a factor of 4 and reduce the equilibrium interatomic
distance by 0.9 A. The non-additive forces originate principally from chemical
bonding arising from sp mixing effects.Comment: 4 pages, 3 figures (in 5 files
The -essence scalar field in the context of Supernova Ia Observations
A -essence scalar field model having (non canonical) Lagrangian of the
form where
with constant is shown to be consistent with luminosity
distance-redshift data observed for type Ia Supernova. For constant ,
satisfies a scaling relation which is used to set up a differential
equation involving the Hubble parameter , the scale factor and the
-essence field . and are extracted from SNe Ia data and using
the differential equation the time dependence of the field is found to
be: . The constants
have been determined. The time dependence is similar to that of the
quintessence scalar field (having canonical kinetic energy) responsible for
homogeneous inflation. Furthermore, the scaling relation and the obtained time
dependence of the field is used to determine the -dependence of the
function .Comment: 8 pages, 5 figures, Late
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Studies of Cosmic Ray Composition and Air Shower Structure with the Pierre Auger Observatory
These are presentations to be presented at the 31st International Cosmic Ray Conference, in Lodz, Poland during July 2009. It consists of the following presentations: (1) Measurement of the average depth of shower maximum and its fluctuations with the Pierre Auger Observatory; (2) Study of the nuclear mass composition of UHECR with the surface detectors of the Pierre Auger Observatory; (3) Comparison of data from the Pierre Auger Observatory with predictions from air shower simulations: testing models of hadronic interactions; (4) A Monte Carlo exploration of methods to determine the UHECR composition with the Pierre Auger Observatory; (5) The delay of the start-time measured with the Pierre Auger Observatory for inclined showers and a comparison of its variance with models; (6) UHE neutrino signatures in the surface detector of the Pierre Auger Observatory; and (7) The electromagnetic component of inclined air showers at the Pierre Auger Observatory
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