284 research outputs found
Symbolic integration of a product of two spherical bessel functions with an additional exponential and polynomial factor
We present a mathematica package that performs the symbolic calculation of
integrals of the form \int^{\infty}_0 e^{-x/u} x^n j_{\nu} (x) j_{\mu} (x) dx
where and denote spherical Bessel functions of
integer orders, with and . With the real parameter
and the integer , convergence of the integral requires that . The package provides analytical result for the integral in its most
simplified form. The novel symbolic method employed enables the calculation of
a large number of integrals of the above form in a fraction of the time
required for conventional numerical and Mathematica based brute-force methods.
We test the accuracy of such analytical expressions by comparing the results
with their numerical counterparts.Comment: 17 pages; updated references for the introductio
Review Work on Body Weight and Egg Production Performance of Chickens in Ethiopia
Different breeds of exotic chickens were imported to Ethiopia with the aim of improving chicken productivity. Moreover, one way of improving low genetic potential of local chickens is crossbreeding programs of local chickens with exotic chicken breeds. For further improvement in production traits, understanding performance of economic traits in chicken is important for the formulation of breeding plans. Therefore, the objective of this review paper is to review egg and body weight performance of chickens in Ethiopia. Breed of chicken used, environmental conditions, and management practices are the main factor that affects chicken productivity. The average egg production and body weight performance of chickens is higher in exotic breed followed by cross and local ones. However, poor performance of exotic chickens is observed in situations where the breeds are poorly managed. The performance of crossbreds reduces gradually as the percent of genes goes beyond 50 but the management gets down. With regard to local ones, better management and proper breeding technique do have a chance for upgrading. Therefore, better management, proper breeding activities and regulatory laws should be imposed to enhance chicken productivities. Keywords: Egg, Body weight, Local, Exotic, Crossbreed, Chicken DOI: 10.7176/JBAH/9-8-03 Publication date: April 30th 201
Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
In a recent series of papers, Gebremariam, Bogner, and Duguet derived a
microscopically based nuclear energy density functional by applying the Density
Matrix Expansion (DME) to the Hartree-Fock energy obtained from chiral
effective field theory (EFT) two- and three-nucleon interactions. Due to the
structure of the chiral interactions, each coupling in the DME functional is
given as the sum of a coupling constant arising from zero-range contact
interactions and a coupling function of the density arising from the
finite-range pion exchanges. Since the contact contributions have essentially
the same structure as those entering empirical Skyrme functionals, a
microscopically guided Skyrme phenomenology has been suggested in which the
contact terms in the DME functional are released for optimization to
finite-density observables to capture short-range correlation energy
contributions from beyond Hartree-Fock. The present paper is the first attempt
to assess the ability of the newly suggested DME functional, which has a much
richer set of density dependencies than traditional Skyrme functionals, to
generate sensible and stable results for nuclear applications. The results of
the first proof-of-principle calculations are given, and numerous practical
issues related to the implementation of the new functional in existing Skyrme
codes are discussed. Using a restricted singular value decomposition (SVD)
optimization procedure, it is found that the new DME functional gives
numerically stable results and exhibits a small but systematic reduction of our
test function compared to standard Skyrme functionals, thus justifying
its suitability for future global optimizations and large-scale calculations.Comment: 17 pages, 6 figure
Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions
The density matrix expansion (DME) of Negele and Vautherin is a convenient
tool to map finite-range physics associated with vacuum two- and three-nucleon
interactions into the form of a Skyme-like energy density functional (EDF) with
density-dependent couplings. In this work, we apply the improved formulation of
the DME proposed recently in arXiv:0910.4979 by Gebremariam {\it et al.} to the
non-local Fock energy obtained from chiral effective field theory (EFT)
two-nucleon (NN) interactions at next-to-next-to-leading-order (NLO). The
structure of the chiral interactions is such that each coupling in the DME Fock
functional can be decomposed into a cutoff-dependent coupling {\it constant}
arising from zero-range contact interactions and a cutoff-independent coupling
{\it function} of the density arising from the universal long-range pion
exchanges. This motivates a new microscopically-guided Skyrme phenomenology
where the density-dependent couplings associated with the underlying
pion-exchange interactions are added to standard empirical Skyrme functionals,
and the density-independent Skyrme parameters subsequently refit to data. A
Mathematica notebook containing the novel density-dependent couplings is
provided.Comment: 28 pages, 12 figures. Mathematica notebook provided with submission
Isovector part of nuclear energy density functional from chiral two- and three-nucleon forces
A recent calculation of the nuclear energy density functional from chiral
two- and three-nucleon forces is extended to the isovector terms pertaining to
different proton and neutron densities. An improved density-matrix expansion is
adapted to the situation of small isospin-asymmetries and used to calculate in
the Hartree-Fock approximation the density-dependent strength functions
associated with the isovector terms. The two-body interaction comprises of
long-range multi-pion exchange contributions and a set of contact terms
contributing up to fourth power in momenta. In addition, the leading order
chiral three-nucleon interaction is employed with its parameters fixed in
computations of nuclear few-body systems. With this input one finds for the
asymmetry energy of nuclear matter the value MeV,
compatible with existing semi-empirical determinations. The strength functions
of the isovector surface and spin-orbit coupling terms come out much smaller
than those of the analogous isoscalar coupling terms and in the relevant
density range one finds agreement with phenomenological Skyrme forces. The
specific isospin- and density-dependences arising from the chiral two- and
three-nucleon interactions can be explored and tested in neutron-rich systems.Comment: 14 pages, 7 figures, to be published in European Physical Journal
Low-Temperature Orientation Dependence of Step Stiffness on {111} Surfaces
For hexagonal nets, descriptive of {111} fcc surfaces, we derive from
combinatoric arguments a simple, low-temperature formula for the orientation
dependence of the surface step line tension and stiffness, as well as the
leading correction, based on the Ising model with nearest-neighbor (NN)
interactions. Our formula agrees well with experimental data for both Ag and
Cu{111} surfaces, indicating that NN-interactions alone can account for the
data in these cases (in contrast to results for Cu{001}). Experimentally
significant corollaries of the low-temperature derivation show that the step
line tension cannot be extracted from the stiffness and that with plausible
assumptions the low-temperature stiffness should have 6-fold symmetry, in
contrast to the 3-fold symmetry of the crystal shape. We examine Zia's exact
implicit solution in detail, using numerical methods for general orientations
and deriving many analytic results including explicit solutions in the two
high-symmetry directions. From these exact results we rederive our simple
result and explore subtle behavior near close-packed directions. To account for
the 3-fold symmetry in a lattice gas model, we invoke a novel
orientation-dependent trio interaction and examine its consequences.Comment: 11 pages, 8 figure
Nuclear energy density functional from chiral two- and three-nucleon interactions
An improved density-matrix expansion is used to calculate the nuclear energy
density functional from chiral two- and three-nucleon interactions. The
two-body interaction comprises long-range one- and two-pion exchange
contributions and a set of contact terms contributing up to fourth power in
momenta. In addition we employ the leading order chiral three-nucleon
interaction with its parameters and fixed in
calculations of nuclear few-body systems. With this input the nuclear energy
density functional is derived to first order in the two- and three-nucleon
interaction. We find that the strength functions and
of the surface and spin-orbit terms compare in the relevant
density range reasonably with results of phenomenological Skyrme forces.
However, an improved description requires (at least) the treatment of the
two-body interaction to second order. This observation is in line with the
deficiencies in the nuclear matter equation of state that remain
in the Hartree-Fock approximation with low-momentum two- and three-nucleon
interactions.Comment: 16 pages, 12 figures, submitted to Eur. Phys. J.
Instabilities in the Nuclear Energy Density Functional
In the field of Energy Density Functionals (EDF) used in nuclear structure
and dynamics, one of the unsolved issues is the stability of the functional.
Numerical issues aside, some EDFs are unstable with respect to particular
perturbations of the nuclear ground-state density. The aim of this contribution
is to raise questions about the origin and nature of these instabilities, the
techniques used to diagnose and prevent them, and the domain of density
functions in which one should expect a nuclear EDF to be stable.Comment: Special issue "Open Problems in Nuclear Structure Theory" of
Jour.Phys.G - accepted. 7 pages, 2 figure
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