61,123 research outputs found
Ancient multiple-layer solutions to the Allen-Cahn equation
We consider the parabolic one-dimensional Allen-Cahn equation The steady state , connects, as a "transition layer" the stable phases
and . We construct a solution with any given number of transition
layers between and . At main order they consist of time-traveling
copies of with interfaces diverging one to each other as .
More precisely, we find where the functions
satisfy a first order Toda-type system. They are given by
for certain explicit constants $\gamma_{jk}.
Ancient shrinking spherical interfaces in the Allen-Cahn flow
We consider the parabolic Allen-Cahn equation in , ,
We construct an ancient radially symmetric solution with any
given number of transition layers between and . At main order they
consist of time-traveling copies of with spherical interfaces distant
one to each other as . These interfaces are
resemble at main order copies of the {\em shrinking sphere} ancient solution to
mean the flow by mean curvature of surfaces: . More
precisely, if denotes the heteroclinic 1-dimensional solution of given by we have where
\rho_j(t)=\sqrt{-2(n-1)t}+\frac{1}{\sqrt{2}}\left(j-\frac{k+1}{2}\right)\log\left(\frac
{|t|}{\log |t| }\right)+ O(1),\quad j=1,\ldots ,k.$
Quantum gauge fixing and vortex dominance
We introduce quantum gauge fixing (QGF) as a new class of gauge fixings.
While the maximal center gauge might not show vortex dominance, the confining
properties of the vortices observed in past lattice calculations are argued to
have been obtained in a gauge more akin to QGF than to the strict maximal
center gauge.Comment: talk presented at LATTICE99(confinement), Pisa, Italy, 3 pages, 2
figures, LaTeX using espcrc2.st
The SU(2) Confining Vacuum as a Dual Superconductor
We investigate the dual superconductivity hypothesis in pure SU(2) lattice
gauge theory. We find evidence of the dual Meissner effect both in the
maximally Abelian gauge and without gauge fixing. We also obtain a rather good
extimation of the string tension using the value of the London penetration
length.Comment: 4 pages, uuencoded compressed (using GNU's gzip) tar file containing
1 LaTeX2e file, 5 encapsulated Postscript figures, and espcrc2.sty.
Contribution to Lattice 9
Vortes solutions in nonabelian Higgs theories
A new class of vortex solutions is found in SU(2) gauge theories with two
adjoint representation Higgs bosons. Implications of these new solutions and
their possible connection with Center Gauge fixed pure gauge theories are
discussed.Comment: 8 pages, added references, other changes, including title and
abstrac
The abelian projection revisited
Abelian projection is reanalysed in the frame of the SU(N) Higgs model. The
extension to QCD is discussed. It is shown that dual superconductivity of the
vacuum is an intrinsic property independent of the choice of the abelian
projection.Comment: 3 pages, 1 figure, Lattice2003(topology
Can the Services Sector Be an Engine of Economic Growth for the Philippines?
With the services sector outpacing the Philippines' manufacturing sector in terms of growth and contribution to the country's gross domestic product (GDP) for decades now, is it prudent, as some quarters propose, for the government to "abandon" the manufacturing sector and shift its policy in support of the services sector as the engine of economic growth for the Philippines? This Policy Notes emphatically says "no" and highlights the arguments against such policy shift.services sector, manufacturing sector, deindustrialization
Some Cautionary Remarks on Abelian Projection and Abelian Dominance
Some critical remarks are presented, concerning the abelian projection theory
of quark confinement.Comment: Talk presented at LATTICE96(topology) plenary session, uses psfig and
espcrc2 package
The modular structure of an ontology: Atomic decomposition
Extracting a subset of a given ontology that captures all the ontology’s knowledge about a specified set of terms is a well-understood task. This task can be based, for instance, on locality-based modules. However, a single module does not allow us to understand neither topicality, connectedness, structure, or superfluous parts of an ontology, nor agreement between actual and intended modeling. The strong logical properties of locality-based modules suggest that the family of all such modules of an ontology can support comprehension of the ontology as a whole. However, extracting that family is not feasible, since the number of localitybased modules of an ontology can be exponential w.r.t. its size. In this paper we report on a new approach that enables us to efficiently extract a polynomial representation of the family of all locality-based modules of an ontology. We also describe the fundamental algorithm to pursue this task, and report on experiments carried out and results obtained.
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