23,335 research outputs found
Microscopic study of induced fission dynamics of Th with covariant energy density functionals
Static and dynamic aspects of the fission process of Th are analyzed
in a self-consistent framework based on relativistic energy density
functionals. Constrained relativistic mean-field (RMF) calculations in the
collective space of axially symmetric quadrupole and octupole deformations,
based on the energy density functional PC-PK1 and a -force pairing, are
performed to determine the potential energy surface of the fissioning nucleus,
the scission line, the single-nucleon wave functions, energies and occupation
probabilities, as functions of deformation parameters. Induced fission dynamics
is described using the time-dependent generator coordinate method in the
Gaussian overlap approximation. A collective Schr\"odinger equation, determined
entirely by the microscopic single-nucleon degrees of freedom, propagates
adiabatically in time the initial wave packet built by boosting the
ground-state solution of the collective Hamiltonian for Th. The
position of the scission line and the microscopic input for the collective
Hamiltonian are analyzed as functions of the strength of the pairing
interaction. The effect of static pairing correlations on the pre-neutron
emission charge yields and total kinetic energy of fission fragments is
examined in comparison with available data, and the distribution of fission
fragments is analyzed for different values of the initial excitation energy.Comment: 25 pages, 14 figures, accepted for publication in Phys. Rev.
Equivariant wave maps exterior to a ball
We consider the exterior Cauchy-Dirichlet problem for equivariant wave maps
from 3+1 dimensional Minkowski spacetime into the three-sphere. Using mixed
analytical and numerical methods we show that, for a given topological degree
of the map, all solutions starting from smooth finite energy initial data
converge to the unique static solution (harmonic map). The asymptotics of this
relaxation process is described in detail. We hope that our model will provide
an attractive mathematical setting for gaining insight into
dissipation-by-dispersion phenomena, in particular the soliton resolution
conjecture.Comment: 16 pages, 9 figure
Small ball probability, Inverse theorems, and applications
Let be a real random variable with mean zero and variance one and
be a multi-set in . The random sum
where are iid copies of
is of fundamental importance in probability and its applications.
We discuss the small ball problem, the aim of which is to estimate the
maximum probability that belongs to a ball with given small radius,
following the discovery made by Littlewood-Offord and Erdos almost 70 years
ago. We will mainly focus on recent developments that characterize the
structure of those sets where the small ball probability is relatively
large. Applications of these results include full solutions or significant
progresses of many open problems in different areas.Comment: 47 page
Spectroscopy of reflection-asymmetric nuclei with relativistic energy density functionals
Quadrupole and octupole deformation energy surfaces, low-energy excitation
spectra and transition rates in fourteen isotopic chains: Xe, Ba, Ce, Nd, Sm,
Gd, Rn, Ra, Th, U, Pu, Cm, Cf, and Fm, are systematically analyzed using a
theoretical framework based on a quadrupole-octupole collective Hamiltonian
(QOCH), with parameters determined by constrained reflection-asymmetric and
axially-symmetric relativistic mean-field calculations. The microscopic QOCH
model based on the PC-PK1 energy density functional and -interaction
pairing is shown to accurately describe the empirical trend of low-energy
quadrupole and octupole collective states, and predicted spectroscopic
properties are consistent with recent microscopic calculations based on both
relativistic and non-relativistic energy density functionals. Low-energy
negative-parity bands, average octupole deformations, and transition rates show
evidence for octupole collectivity in both mass regions, for which a
microscopic mechanism is discussed in terms of evolution of single-nucleon
orbitals with deformation.Comment: 36 pages, 21 figures, Accepted for Publication in Physical Review
On the determination of the deceleration parameter from Supernovae data
Supernovae searches have shown that a simple matter-dominated and
decelerating universe should be ruled out. However a determination of the
present deceleration parameter through a simple kinematical description
is not exempt of possible drawbacks. We show that, with a time dependent
equation of state for the dark energy, a bias is present for : models
which are very far from the so-called Concordance Model can be accommodated by
the data and a simple kinematical analysis can lead to wrong conclusions. We
present a quantitative treatment of this bias and we present our conclusions
when a possible dynamical dark energy is taken into account.Comment: 4 pages, 3 figures, submitte
Smooth analysis of the condition number and the least singular value
Let \a be a complex random variable with mean zero and bounded variance.
Let be the random matrix of size whose entries are iid copies of
\a and be a fixed matrix of the same size. The goal of this paper is to
give a general estimate for the condition number and least singular value of
the matrix , generalizing an earlier result of Spielman and Teng for
the case when \a is gaussian.
Our investigation reveals an interesting fact that the "core" matrix does
play a role on tail bounds for the least singular value of . This
does not occur in Spielman-Teng studies when \a is gaussian.
Consequently, our general estimate involves the norm .
In the special case when is relatively small, this estimate is nearly
optimal and extends or refines existing results.Comment: 20 pages. An erratum to the published version has been adde
Fermion Resonances on a Thick Brane with a Piecewise Warp Factor
In this paper, we mainly investigate the problems of resonances of massive KK
fermions on a single scalar constructed thick brane with a piecewise warp
factor matching smoothly. The distance between two boundaries and the other
parameters are determined by one free parameter through three junction
conditions. For the generalized Yukawa coupling
with odd , the mass eigenvalue , width , lifetime
, and maximal probability of fermion resonances are obtained.
Our numerical calculations show that the brane without internal structure also
favors the appearance of resonant states for both left- and right-handed
fermions. The scalar-fermion coupling and the thickness of the brane influence
the resonant behaviors of the massive KK fermions.Comment: V3: 15 pages, 7 figures, published versio
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