21,859 research outputs found
Metastable states of a ferromagnet on random thin graphs
We calculate the mean number of metastable states of an Ising ferromagnet on
random thin graphs of fixed connectivity c. We find, as for mean field spin
glasses that this mean increases exponentially with the number of sites, and is
the same as that calculated for the +/- J spin glass on the same graphs. An
annealed calculation of the number of metastable states of energy E
is carried out. For small c, an analytic result is obtained. The result is
compared with the one obtained for spin glasses in order to discuss the role
played by loops on thin graphs and hence the effect of real frustration on the
distribution of metastable states.Comment: 15 pages, 3 figure
Multiple scattering of ultrasound in weakly inhomogeneous media: application to human soft tissues
Waves scattered by a weakly inhomogeneous random medium contain a predominant
single scattering contribution as well as a multiple scattering contribution
which is usually neglected, especially for imaging purposes. A method based on
random matrix theory is proposed to separate the single and multiple scattering
contributions. The experimental set up uses an array of sources/receivers
placed in front of the medium. The impulse responses between every couple of
transducers are measured and form a matrix. Single-scattering contributions are
shown to exhibit a deterministic coherence along the antidiagonals of the array
response matrix, whatever the distribution of inhomogeneities. This property is
taken advantage of to discriminate single from multiple-scattered waves. This
allows one to evaluate the absorption losses and the scattering losses
separately, by comparing the multiple scattering intensity with a radiative
transfer model. Moreover, the relative contribution of multiple scattering in
the backscattered wave can be estimated, which serves as a validity test for
the Born approximation. Experimental results are presented with ultrasonic
waves in the MHz range, on a synthetic sample (agar-gelatine gel) as well as on
breast tissues. Interestingly, the multiple scattering contribution is found to
be far from negligible in the breast around 4.3 MHz.Comment: 35 pages, 11 figures, final version, contains the appendix of the
original articl
The Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential
As a continuation of our series works on the Boltzmann equation without
angular cutoff assumption, in this part, the global existence of solution to
the Cauchy problem in the whole space is proved in some suitable weighted
Sobolev spaces for hard potential when the solution is a small perturbation of
a global equilibrium
Dense heteroclinic tangencies near a Bykov cycle
This article presents a mechanism for the coexistence of hyperbolic and
non-hyperbolic dynamics arising in a neighbourhood of a Bykov cycle where
trajectories turn in opposite directions near the two nodes --- we say that the
nodes have different chirality. We show that in the set of vector fields
defined on a three-dimensional manifold, there is a class where tangencies of
the invariant manifolds of two hyperbolic saddle-foci occur densely. The class
is defined by the presence of the Bykov cycle, and by a condition on the
parameters that determine the linear part of the vector field at the
equilibria. This has important consequences: the global dynamics is
persistently dominated by heteroclinic tangencies and by Newhouse phenomena,
coexisting with hyperbolic dynamics arising from transversality. The
coexistence gives rise to linked suspensions of Cantor sets, with hyperbolic
and non-hyperbolic dynamics, in contrast with the case where the nodes have the
same chirality.
We illustrate our theory with an explicit example where tangencies arise in
the unfolding of a symmetric vector field on the three-dimensional sphere
Control of quantum fluctuations for a Yukawa interaction in the Kaluza Klein picture
We study a system of fermions interacting with a scalar field, in 4+1
dimensions where the 5th dimension is compactified, using an exact functional
method, where quantum fluctuations are controlled by the amplitude of the bare
fermion mass. The integration of our equationsleads to the properties of the
dressed Yukawa coupling, that we study at one-loop so as to show the
consistency of the approach. Beyond one loop, the non-perturbative aspect of
the method gives us the possibility to derive the dynamical fermion mass. The
result obtained is cut off independent and this derivation proposes an
alternative to the Schwinger-Dyson approach.Comment: extended discussion on the scalar effective potentia
The Dark Z' Portal: Direct, Indirect and Collider Searches
We perform a detailed study of the dark Z' portal using a generic
parametrization of the Z'-quarks couplings, both for light (8-15)GeV and heavy
(130-1000)GeV dark matter scenarios. We present a comprehensive study of the
collider phenomenology including jet clustering, hadronization, and detector
artifacts, which allows us to derive accurate bounds from the search for new
resonances in dijet events and from mono-jet events in the LHC 7TeV, LHC 8TeV,
and Tevatron 1.96 TeV data. We also compute the dark matter relic abundance,
the relevant scattering cross sections and pair-annihilation spectrum, and
compare our results with the current PLANCK, Fermi-LAT and XENON100/LUX bounds.
Lastly, we highlight the importance of complementary searches for dark matter,
and outline the excluded versus still viable parameter space regions of the
dark Z' portal.Comment: 29 pages, 21 figure
On Takens' Last Problem: tangencies and time averages near heteroclinic networks
We obtain a structurally stable family of smooth ordinary differential
equations exhibiting heteroclinic tangencies for a dense subset of parameters.
We use this to find vector fields -close to an element of the family
exhibiting a tangency, for which the set of solutions with historic behaviour
contains an open set. This provides an affirmative answer to Taken's Last
Problem (F. Takens (2008) Nonlinearity, 21(3) T33--T36). A limited solution
with historic behaviour is one for which the time averages do not converge as
time goes to infinity. Takens' problem asks for dynamical systems where
historic behaviour occurs persistently for initial conditions in a set with
positive Lebesgue measure.
The family appears in the unfolding of a degenerate differential equation
whose flow has an asymptotically stable heteroclinic cycle involving
two-dimensional connections of non-trivial periodic solutions. We show that the
degenerate problem also has historic behaviour, since for an open set of
initial conditions starting near the cycle, the time averages approach the
boundary of a polygon whose vertices depend on the centres of gravity of the
periodic solutions and their Floquet multipliers.
We illustrate our results with an explicit example where historic behaviour
arises -close of a -equivariant vector field
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