270 research outputs found
Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field
The complexity of the neutron transport phenomenon throws its shadows on
every physical system wherever neutron is produced or used. In the current
study, an ab initio derivation of the neutron self-shielding factor to solve
the problem of the decrease of the neutron flux as it penetrates into a
material placed in an isotropic neutron field. We have employed the theory of
steady-state neutron transport, starting from Stuart's formula. Simple formulae
were derived based on the integral cross-section parameters that could be
adopted by the user according to various variables, such as the neutron flux
distribution and geometry of the simulation at hand. The concluded formulae of
the self-shielding factors comprise an inverted sigmoid function normalized
with a weight representing the ratio between the macroscopic total and
scattering cross-sections of the medium. The general convex volume geometries
are reduced to a set of chord lengths, while the neutron interactions
probabilities within the volume are parameterized to the epithermal and thermal
neutron energies. The arguments of the inverted-sigmoid function were derived
from a simplified version of neutron transport formulation. Accordingly, the
obtained general formulae were successful in giving the values of the
experimental neutron self-shielding factor for different elements and different
geometries.Comment: 14 pages, 5 figures, 1 graphical abstract, 73 references, and 2
tables, include improvement of illustration and story-telling writing styl
Stimulated perturbation on the neutron flux distribution in the mutually-dependent source-to-absorber geometry
The complexity of the neutron transport phenomenon throws its shadows on
every physical system wherever neutron is produced or absorbed. The Monte Carlo
N-Particle Transport Code (MCNP) was used to investigate the flux perturbations
in the neutron field caused by an absorber. The geometry of the present
experiment was designed to reach a simulation of an isotopic neutron field. The
neutron source was a AmBe with the production physics of neutrons is
dependent only on alpha-beryllium interaction and is independent of what
happened to the neutron after it was generated. The geometries have been
designed to get a volume of uniform neutron densities within a spherical volume
of radius 15 cm in every neutron energy group up to 10 MeV. Absorbers of
different dimensions were placed within the volume to investigate the field
perturbation. Different neutron absorbers were used to correlate the phenomenon
to the integral cross-section of the absorber. Flux density inside and outside
the absorber samples was determined, while the spatial neutron flux
distribution produced by the AmBe source without an absorber was taken as a
reference. This study displayed that absorbers of various dimensions perturb
the neutron field in a way that is dependent on the absorption and scattering
cross-sections, particularly in the neutron resonance region. Unlike the simple
picture of reducing the number density of neutrons, the perturbation was found
to influence the moderation of neutrons in the medium, significantly above 1
MeV.Comment: 10 pages, 13 figures, 26 reference
The Top-Dog Index: A New Measurement for the Demand Consistency of the Size Distribution in Pre-Pack Orders for a Fashion Discounter with Many Small Branches
We propose the new Top-Dog-Index, a measure for the branch-dependent historic
deviation of the supply data of apparel sizes from the sales data of a fashion
discounter. A common approach is to estimate demand for sizes directly from the
sales data. This approach may yield information for the demand for sizes if
aggregated over all branches and products. However, as we will show in a
real-world business case, this direct approach is in general not capable to
provide information about each branch's individual demand for sizes: the supply
per branch is so small that either the number of sales is statistically too
small for a good estimate (early measurement) or there will be too much
unsatisfied demand neglected in the sales data (late measurement). Moreover, in
our real-world data we could not verify any of the demand distribution
assumptions suggested in the literature. Our approach cannot estimate the
demand for sizes directly. It can, however, individually measure for each
branch the scarcest and the amplest sizes, aggregated over all products. This
measurement can iteratively be used to adapt the size distributions in the
pre-pack orders for the future. A real-world blind study shows the potential of
this distribution free heuristic optimization approach: The gross yield
measured in percent of gross value was almost one percentage point higher in
the test-group branches than in the control-group branches.Comment: 22 pages, 15 figure
Integrating production scheduling and transportation procurement through combinatorial auctions
This study uses the winner determination problem (WDP) to integrate auction transportation procurement with decisions related to production scheduling. The basic problem arises when a manufacturer has to clear a combinatorial auction to decide whether to cover transportation needs by using the in-house fleet or to procure transportation through auction. Thus, the manufacturer should include an additional decision level by integrating the WDP with production scheduling to gain efficiency and achieve savings in the logistics system. To the best of our knowledge, this is the first time production and transportation procurement problems are being solved simultaneously in an integrated manner. The study proposes a mathematical formulation and develops two heuristic approaches for solving the integrated problem. Extensive computational experiments and sensitivity analyses are reported to validate the model, assess the performance of the heuristics, and show the effect of integration on total cost. © 2020 The Authors. Networks published by Wiley Periodicals LLC
Criticality Analysis of Activity Networks under Interval Uncertainty
Dedicated to the memory of Professor Stefan Chanas - The extended abstract version of this paper has appeared in Proceedings of 11th International Conference on Principles and Practice of Constraint Programming (CP2005) ("Interval Analysis in Scheduling", Fortin et al. 2005)International audienceThis paper reconsiders the Project Evaluation and Review Technique (PERT) scheduling problem when information about task duration is incomplete. We model uncertainty on task durations by intervals. With this problem formulation, our goal is to assert possible and necessary criticality of the different tasks and to compute their possible earliest starting dates, latest starting dates, and floats. This paper combines various results and provides a complete solution to the problem. We present the complexity results of all considered subproblems and efficient algorithms to solve them
- …