9,914 research outputs found
On the behavior of clamped plates under large compression
We determine the asymptotic behavior of eigenvalues of clamped plates under large compression by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then carry out a numerical study of the extremal domains for the first eigenvalue, from which we see that these depend on the value of the compression, and start developing a boundary structure as this parameter is increased. The corresponding number of nodal domains of the first eigenfunction of the extremal domain also increases with the compression.This work was partially supported by the Funda ̧c Ìao para a CiËencia e a Tecnologia(Portugal) through the program âInvestigador FCTâ with reference IF/00177/2013 and the projectExtremal spectral quantities and related problems(PTDC/MAT-CAL/4334/2014).info:eu-repo/semantics/publishedVersio
Spontaneous formation of domain wall lattices in two spatial dimensions
We show that the process of spontaneous symmetry breaking can trap a field
theoretic system in a highly non-trivial state containing a lattice of domain
walls. In one large compact space dimension, a lattice is inevitably formed. In
two dimensions, the probability of lattice formation depends on the ratio of
sizes L_x, L_y of the spatial dimensions. We find that a lattice can form even
if R=L_y/L_x is of order unity. We numerically determine the number of walls in
the lattice as a function of L_x and L_y.Comment: 6 pages, 6 figures. Background material added and minor corrections
included. Final version to be published in Phys. Rev.
The Thermodynamics of Cosmic String densities in U(1) Scalar Field Theory
We present a full characterization of the phase transition in U(1) scalar
field theory and of the associated vortex string thermodynamics in 3D. We show
that phase transitions in the string densities exist and measure their critical
exponents, both for the long string and the short loops. Evidence for a natural
separation between these two string populations is presented. In particular our
results strongly indicate that an infinite string population will only exist
above the critical temperature. Canonical initial conditions for cosmic string
evolution are show to correspond to the infinite temperature limit of the
theory.Comment: 4 pages, 4 figures, RevTe
Kinky Brane Worlds
We present a toy model for five-dimensional heterotic M-theory where bulk
three-branes, originating in 11 dimensions from M five-branes, are modelled as
kink solutions of a bulk scalar field theory. It is shown that the vacua of
this defect model correspond to a class of topologically distinct M-theory
compactifications. Topology change can then be analysed by studying the time
evolution of the defect model. In the context of a four-dimensional effective
theory, we study in detail the simplest such process, that is the time
evolution of a kink and its collision with a boundary. We find that the kink is
generically absorbed by the boundary thereby changing the boundary charge. This
opens up the possibility of exploring the relation between more complicated
defect configurations and the topology of brane-world models.Comment: 31 pages, Latex, 6 eps-figure
The role of dissipation in biasing the vacuum selection in quantum field theory at finite temperature
We study the symmetry breaking pattern of an O(4) symmetric model of scalar
fields, with both charged and neutral fields, interacting with a photon bath.
Nagasawa and Brandenberger argued that in favourable circumstances the vacuum
manifold would be reduced from S^3 to S^1. Here it is shown that a selective
condensation of the neutral fields, that are not directly coupled to photons,
can be achieved in the presence of a minimal ``external'' dissipation, i.e. not
related to interactions with a bath. This should be relevant in the early
universe or in heavy-ion collisions where dissipation occurs due to expansion.Comment: Final version to appear in Phys. Rev. D, 2 figures added, 2 new
sub-section
Predicting the critical density of topological defects in O(N) scalar field theories
O(N) symmetric field theories describe many critical
phenomena in the laboratory and in the early Universe. Given N and ,
the dimension of space, these models exhibit topological defect classical
solutions that in some cases fully determine their critical behavior. For N=2,
D=3 it has been observed that the defect density is seemingly a universal
quantity at T_c. We prove this conjecture and show how to predict its value
based on the universal critical exponents of the field theory. Analogously, for
general N and D we predict the universal critical densities of domain walls and
monopoles, for which no detailed thermodynamic study exists. This procedure can
also be inverted, producing an algorithm for generating typical defect networks
at criticality, in contrast to the canonical procedure, which applies only in
the unphysical limit of infinite temperature.Comment: 4 pages, 3 figures, uses RevTex, typos in Eq.(11) and (14) correcte
Repair in traumatic ascending aortic rupture and valve insufficiency
An 18-year-old patient who had chronic traumatic ascending aortic lesion and valve insufficiency, with severe LV dysfunction, was treated by repair of the aortic wall without prosthesis and of the aortic valve by a gluteraldehyde-treated autologous pericardial patch. The patient had an uneventful recovery and minimal residual aortic regurgitation at one-month echocardiographic follow-up. Conservative surgery of these lesions is feasible, with good results, in some cases
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