66 research outputs found
A 2D quantum antiferromagnet with a four-fold degenerate valence-bond-solid ground state
We study the competition between antiferromagnetic order and valence bond
solid formation in a two-dimensional frustrated spin-1/2 model. The J1-J2 model
on the square lattice is further frustrated by introducing products of
three-spin projectors which stabilize four dimer-product states as degenerate
ground states. These four states are reminiscent of the dimerized singlet
ground state of the Shastry-Sutherland model. Using exact diagonalizations, we
study the evolution of the ground state by varying theratio of interactions.
For a large range of parameters (J2 > 0.25J1), our model shows a direct
transition between the valence-bond-solid phase and the collinear
antiferromagnetic phase. For small values of J2, several intermediate phases
appear which are also analyzed
Inverse problem and Bertrand's theorem
The Bertrand's theorem can be formulated as the solution of an inverse
problem for a classical unidimensional motion. We show that the solutions of
these problems, if restricted to a given class, can be obtained by solving a
numerical equation. This permit a particulary compact and elegant proof of
Bertrand's theorem.Comment: 11 pages, 3 figure
Visser's Massive Gravity Bimetric Theory Revisited
A massive gravity theory was proposed by Visser in the late nineties. This
theory, based on a backgroung metric and on an usual
dynamical metric has the advantage of being free of ghosts
as well as discontinuities present in other massive theories proposed in the
past. In the present investigation, the equations of Visser's theory are
revisited with a particular care on the related conservation laws.\ It will be
shown that a multiplicative factor is missing in the graviton tensor originally
derived by Visser, which has no incidence on the weak field approach but
becomes important in the strong field regime when, for instance, cosmological
applications are considered. In this case, contrary to some previous claims
found in the literature, we conclude that a non-static background metric is
required in order to obtain a solution able to mimic the CDM
cosmology.Comment: 10 pages - Accepted for publication in Physical Review
Analytical calculation of the Peierls-Nabarro pinning barrier for one-dimensional parametric double-well models
Lattice effects on the kink families of two models for one-dimensional
nonlinear Klein-Gordon systems with double-well on-site potentials are
considered. The analytical expression of the generalized Peierls-Nabarro
pinning potential is obtained and confronted with numerical simulations.Comment: RevTex, 10 pages, 4 figure
Laws of crack motion and phase-field models of fracture
Recently proposed phase-field models offer self-consistent descriptions of
brittle fracture. Here, we analyze these theories in the quasistatic regime of
crack propagation. We show how to derive the laws of crack motion either by
using solvability conditions in a perturbative treatment for slight departure
from the Griffith threshold, or by generalizing the Eshelby tensor to
phase-field models. The analysis provides a simple physical interpretation of
the second component of the classic Eshelby integral in the limit of vanishing
crack propagation velocity: it gives the elastic torque on the crack tip that
is needed to balance the Herring torque arising from the anisotropic interface
energy. This force balance condition reduces in this limit to the principle of
local symmetry in isotropic media and to the principle of maximum energy
release rate for smooth curvilinear cracks in anisotropic media. It can also be
interpreted physically in this limit based on energetic considerations in the
traditional framework of continuum fracture mechanics, in support of its
general validity for real systems beyond the scope of phase-field models.
Analytical predictions of crack paths in anisotropic media are validated by
numerical simulations. Simulations also show that these predictions hold even
if the phase-field dynamics is modified to make the failure process
irreversible. In addition, the role of dissipative forces on the process zone
scale as well as the extension of the results to motion of planar cracks under
pure antiplane shear are discussed
A generalized theory for current-source density analysis in brain tissue
The current-source density (CSD) analysis is a widely used method in brain
electrophysiology, but this method rests on a series of assumptions, namely
that the surrounding extracellular medium is resistive and uniform, and in some
versions of the theory, that the current sources are exclusively made by
dipoles. Because of these assumptions, this standard model does not correctly
describe the contributions of monopolar sources or of non-resistive aspects of
the extracellular medium. We propose here a general framework to model electric
fields and potentials resulting from current source densities, without relying
on the above assumptions. We develop a mean-field formalism which is a
generalization of the standard model, and which can directly incorporate
non-resistive (non-ohmic) properties of the extracellular medium, such as ionic
diffusion effects. This formalism recovers the classic results of the standard
model such as the CSD analysis, but in addition, we provide expressions to
generalize the CSD approach to situations with non-resistive media and
arbitrarily complex multipolar configurations of current sources. We found that
the power spectrum of the signal contains the signature of the nature of
current sources and extracellular medium, which provides a direct way to
estimate those properties from experimental data, and in particular, estimate
the possible contribution of electric monopoles.Comment: Physical Review E, in press, 201
Algebraic damping in the one-dimensional Vlasov equation
We investigate the asymptotic behavior of a perturbation around a spatially
non homogeneous stable stationary state of a one-dimensional Vlasov equation.
Under general hypotheses, after transient exponential Landau damping, a
perturbation evolving according to the linearized Vlasov equation decays
algebraically with the exponent -2 and a well defined frequency. The
theoretical results are successfully tested against numerical -body
simulations, corresponding to the full Vlasov dynamics in the large limit,
in the case of the Hamiltonian mean-field model. For this purpose, we use a
weighted particles code, which allows us to reduce finite size fluctuations and
to observe the asymptotic decay in the -body simulations.Comment: 26 pages, 8 figures; text slightly modified, references added, typos
correcte
Numerical models of irrotational binary neutron stars in general relativity
We report on general relativistic calculations of quasiequilibrium
configurations of binary neutron stars in circular orbits with zero vorticity.
These configurations are expected to represent realistic situations as opposed
to corotating configurations. The Einstein equations are solved under the
assumption of a conformally flat spatial 3-metric (Wilson-Mathews
approximation). The velocity field inside the stars is computed by solving an
elliptical equation for the velocity scalar potential. Results are presented
for sequences of constant baryon number (evolutionary sequences). Although the
central density decreases much less with the binary separation than in the
corotating case, it still decreases. Thus, no tendency is found for the stars
to individually collapse to black hole prior to merger.Comment: Minor corrections, improved figure, 5 pages, REVTeX, Phys. Rev. Lett.
in pres
Defective Fas expression exacerbates neurotoxicity in a model of Parkinson's disease
Fas (CD95), a member of the tumor necrosis factor-receptor superfamily, has been studied extensively as a death-inducing receptor in the immune system. However, Fas is also widely expressed in a number of other tissues, including in neurons. Here, we report that defects in the Fas/Fas ligand system unexpectedly render mice highly susceptible to neural degeneration in a model of Parkinson's disease. We found that Fas-deficient lymphoproliferative mice develop a dramatic phenotype resembling clinical Parkinson's disease, characterized by extensive nigrostriatal degeneration accompanied by tremor, hypokinesia, and loss of motor coordination, when treated with the neurotoxin 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) at a dose that causes no neural degeneration or behavioral impairment in WT mice. Mice with generalized lymphoproliferative disease, which express a mutated Fas ligand, display an intermediate phenotype between that of lymphoproliferative and WT mice. Moreover, Fas engagement directly protects neuronal cells from MPTP/1-methyl-4-phenylpyridinium ion toxicity in vitro. Our data show that decreased Fas expression renders dopaminergic neurons highly susceptible to degeneration in response to a Parkinson-causing neurotoxin. These findings constitute the first evidence for a neuroprotective role for Fas in vivo
Constraints on the Variations of the Fundamental Couplings
We reconsider several current bounds on the variation of the fine-structure
constant in models where all gauge and Yukawa couplings vary in an
interdependent manner, as would be expected in unified theories. In particular,
we re-examine the bounds established by the Oklo reactor from the resonant
neutron capture cross-section of 149Sm. By imposing variations in \Lambda_{QCD}
and the quark masses, as dictated by unified theories, the corresponding bound
on the variation of the fine-structure constant can be improved by about 2
orders of magnitude in such theories. In addition, we consider possible bounds
on variations due to their effect on long lived \alpha- and \beta-decay
isotopes, particularly 147Sm and 187Re. We obtain a strong constraint on \Delta
\alpha / \alpha, comparable to that of Oklo but extending to a higher redshift
corresponding to the age of the solar system, from the radioactive life-time of
187Re derived from meteoritic studies. We also analyze the astrophysical
consequences of perturbing the decay Q values on bound state \beta-decays
operating in the s-process.Comment: 25 pages, latex, 5 eps figure
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