The mathematical formulation of numerous physical problems a results in differential
equations actually partial or ordinary differential equations.In our study we are
interested in solutions of partial differential equations.The aim of this work is
to calculate the concentrations of the pollution, by solving the atmospheric diffusion
equation(ADE) using different mathematical methods of solution. It is difficult to
solve the general form of ADE analytically, so we use some assumptions to get its
solution.The solutions of it depend on the eddy diffusivity profiles(k) and the wind
speed u. We use some physical assumptions to simplify its formula and solve it. In
the present work, we solve the ADE analytically in three dimensions using Green's
function method, Laplace transform method, normal mode method and these separation
of variables method. Also, we use ADM as a numerical method. Finally, comparisons
are made with the results predicted by the previous methods and the observed data.$$$$
The paper looks at problems concerning the recovery of operators from noisy information
in non-Euclidean metrics. A number of general theorems are proved and applied
to recovery problems for functions and their derivatives from the noisy Fourier transform.
In some cases, a family of optimal methods is found, from which the methods requiring
the least amount of original information are singled out. Bibliography: 25 titles$$$$
Reports are on: - Measurement of Cross-Sections for Neutron Induced Reactions at 14
MeV. - Level Schemes and Gamma Ray Angular Distribution Measurements in ^{28}Si,
^{46}Ti, and ^{53}Mn. - A Study of Neutron-Induced Reaction ''1''2C
(n.n')3α at E_{n} =17.4 MeV. - A Study on Nuclear Evaporation in Nuclear Emulsion
Exposed to 3.0 GeV/c Mesons. - Spectroscopy of ^{64}Cu using the (^{3}He,p)
Reaction at 18 MeV.$$$$
We present an evolutionary computational approach for the solution of nonlinear ordinary
differential equations (NLODEs). The mathematical modeling is performed by a feed-forward
artificial neural network that defines an unsupervised error. The training of these
networks is achieved by a hybrid intelligent algorithm, a combination of global search
with genetic algorithm and local search by pattern search technique. The applicability
of this approach ranges from single order NLODEs, to systems of coupled differential
equations. We illustrate the method by solving a variety of model problems and present
comparisons with solutions obtained by exact methods and classical numerical methods.
The solution is provided on a continuous finite time interval unlike the other numerical
techniques with comparable accuracy. With the advent of neuroprocessors and digital
signal processors the method becomes particularly interesting due to the expected
essential gains in the execution speed. (authors)$$$$
The paper is concerned with the topological analysis of the Chaplygin integrable case
in the dynamics of a rigid body in a fluid. A full list of the topological
types of Chaplygin systems in their dependence on the energy level is compiled on
the basis of the Fomenko-Zieschang theory. An effective description of the topology
of the Liouville foliation in terms of natural coordinate variables is also presented,
which opens a direct way to calculating topological invariants. It turns out
that on all nonsingular energy levels Chaplygin systems are Liouville equivalent to
the well-known Euler case in the dynamics of a rigid body with fixed point. Bibliography:
23 titles$$$$
Methods used to address protection issues in graphite-gas reactors 11 MB - http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/46/034/46034786.pdf - Text Version by Brisbois, Jacques; Commissariat a l'Energie Atomique - CEA, Centre d'Etudes Nucleaires de Fontenay-aux-Roses,
Direction des Piles Atomiques, Departement des Etudes de Piles, Service d'Etudes de
Protections de Piles (France) Read MoreCollapse
[en]
Protection issues are problems related to the presence of neutron and gamma radiations:
biological dose, material heating, Wigner effect, gas ionization. The objective is
then to determine the biological doses which are predictable in some reactor areas,
and to assess the effects of irradiation on materials during the reactor lifetime.
For these purposes, problems of particle propagation are addressed, and the effects
of radiations related to one phenomenon or another are studied with respect to radiation
energy. The author first describes methods used to compute general propagation. These
are mainly codes using Monte Carlo or multi-group scattering methods. These methods
are experimentally controlled on a sub-critical graphite-natural uranium set. In a
second part, the author presents the different radiation sources which are to be taken
into account in calculations. Then he indicates the nuclear constants to be used in
the different codes, as well as the response functions to be used to calculate a specific
phenomenon (steel, graphite Wigner effect, so on) from the particle spectrum. In the
fourth part, the author describes the different methods which can be used to solve
problems which are specific to graphite reactors. In the last part, obtained calculated
results are compared with experimental measurements performed on power reactors$$$$
A practical implementation of the higher-order transverse-integrated nodal diffusion
method http://dx.doi.org/10.1016/j.anucene.2014.01.010 by Prinsloo, Rian H. (Necsa, Building 1900, Elias Motsoaledi Street Extension, R104 Pelindaba,
Brits Magisterial District, Madibeng Municipality, North West Province 0240 (South
Africa)); Tomašević, Djordje I. (Necsa, Building 1900, Elias Motsoaledi Street Extension,
R104 Pelindaba, Brits Magisterial District, Madibeng Municipality, North West Province
0240 (South Africa)); Moraal, Harm (North West University, Physics Department, Hoffman
Street, Potchefstroom Campus, Potchefstroom, North West Province (South Africa)),
E-mail: rian.prinsloo@necsa.co.za, E-mail: djordje.tomasevic@necsa.co.za, E-mail:
Harm.Moraal@nwu.ac.za Read MoreCollapse
[en]
Highlights: • A practical higher-order nodal method is developed for diffusion calculations.
• The method resolves the issue of the transverse leakage approximation. • The method
achieves much superior accuracy as compared to standard nodal methods. • The calculational
cost is only about 50% greater than standard nodal methods. • The method is packaged
in a module for connection to existing nodal codes. - Abstract: Transverse-integrated
nodal diffusion methods currently represent the standard in full core neutronic simulation.
The primary shortcoming of this approach is the utilization of the quadratic transverse
leakage approximation. This approach, although proven to work well for typical LWR
problems, is not consistent with the formulation of nodal methods and can cause accuracy
and convergence problems. In this work, an improved, consistent quadratic leakage
approximation is formulated, which derives from the class of higher-order nodal methods
developed some years ago. Further, a number of iteration schemes are developed around
this consistent quadratic leakage approximation which yields accurate node average
results in much improved calculational times. The most promising of these iteration
schemes results from utilizing the consistent leakage approximation as a correction
method to the standard quadratic leakage approximation. Numerical results are demonstrated
on a set of benchmark problems and further applied to a realistic reactor problem,
particularly the SAFARI-1 reactor, operating at Necsa, South Africa. The final optimal
solution strategy is packaged into a standalone module which may simply be coupled
to existing nodal diffusion codes$$$$
Fullerenes and disk-fullerenes http://dx.doi.org/10.1070/RM2013v068n04ABEH004850 by Deza, M (Ecole Normale Superieure, Paris (France)); Dutour Sikirić, M (Rudjer
Boškovic Institute, Zagreb (Croatia)); Shtogrin, M I (P.G.Demidov Yaroslavl State
University (Russian Federation)) Read MoreCollapse
[en]
A geometric fullerene, or simply a fullerene, is the surface of a simple closed convex
3-dimensional polyhedron with only 5- and 6-gonal faces. Fullerenes are
geometric models for chemical fullerenes, which form an important class of organic
molecules. These molecules have been studied intensively in chemistry, physics, crystallography,
and so on, and their study has led to the appearance of a vast literature on fullerenes
in mathematical chemistry and combinatorial and applied geometry. In particular, several
generalizations of the notion of a fullerene have been given, aiming at various
applications. Here a new generalization of this notion is proposed: an n-disk-fullerene.
It is obtained from the surface of a closed convex 3-dimensional polyhedron which
has one n-gonal face and all other faces 5- and 6-gonal, by removing the n-gonal face.
Only 5- and 6-disk-fullerenes correspond to geometric fullerenes. The notion
of a geometric fullerene is therefore generalized from spheres to compact simply
connected two-dimensional manifolds with boundary. A two-dimensional surface is said
to be unshrinkable if it does not contain belts, that is, simple cycles consisting
of 6-gons each of which has two neighbours adjacent at a pair of opposite edges.
Shrinkability of fullerenes and n-disk-fullerenes is investigated. Bibliography: 87
titles$$$$
Heavy steel reflector evaluation using diffusion theory 242 KB - http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/45/091/45091439.pdf - Text Version by Piovezan, Pamela; Carluccio, Thiago (Centro Tecnologico da Marinha (CTMSP), Sao Paulo,
SP (Brazil). Dept. de Neutronica e Blindagem); Abe, Alfredo; Santos, Adimir dos (Instituto
de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)), E-mail:
pamela.piovezan@ctmsp.mar.mil.br, E-mail: thiago.carluccio@ctmsp.mar.mil, E-mail:
alfredo@ctmsp.mar.mil.br, E-mail: asantos@ipen.br; Associacao Brasileira de Energia Nuclear (ABEN), Rio de Janeiro, RJ (Brazil) Read MoreCollapse
[en]
A new component named heavy reflector that did not exist in actual nuclear power plants
was introduced recently by the EPR reactor. The component was designed to partially
reflect neutrons inside the core to increase fuel efficiency and protect the vessel
during its 60-year operational life. Recently, an experiment was designed and performed
to address the real neutron reflector contribution due to the stainless steel in the
IPEN/MB-01 research reactor. The experiment consisted of several plates of stainless
steel which were conveniently positioned at water reflector region of the reactor
core. The main experimental results were the critical control bank positions and reactivity
as a function of the number of stainless steel plates. The main outcome of the experimental
results showed a quite clear effect on neutron absorption and neutron reflection due
to the stainless steel plates. The objective of this preliminary work is to address
theoretically this experiment using the diffusion theory code CITATION, besides existing
evaluation using Monte Carlo (MCNP and Tripoli) and transport (TORT) codes, in order
to verify the performance of diffusion theory for the reflector region. (author)$$$$