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Franceco Premuda 《Meccanica》1973,8(2):89-95
Summary In this paper many properties of the solutions of the monoenergetic neutron transport stationary integral equation are investigated for slabs and spheres in which the macroscopic cross sections depend on the position and the scattering is isotropic. Such an equation in spherical geometry is derived from the third form of the Boltzmann equation. It is proved that in the Hilbert space L2 the kernels, though asymmetric and discontinuous, are bounded and continuous in the mean and the associated integral operators are of finite double norm. This implies the boundedness and continuity of the total fluxes and the existence of a dominant positive eigenfunction, which represents the critical total flux. Finally the connection between the existence of the dominant eigenfunction and the convergence both in the mean and point-wise uniform and absolute of the Neumann series in all subcritical cases is shown.
Work performed under C.N.R. contract. 相似文献
Sommario In questo lavoro vengono esaminate molte proprietà delle soluzioni dell'equazione integrale del trasporto stazionaria per neutroni monoenergetici nel caso di lastre piane e sfere, in cui le sezioni d'urto macroscopiche dipendono dalla posizione e lo scattering è isotropo. Tale equazione in geometria sferica è ricavata dalla terza forma dell'equazione di Boltzmann. Si prova che nello spazio di Hilbert L2 i kernel, pur essendo asimmetrici e discontinui, sono limitati e continui in media e gli operatori integrali ad essi associati sono di doppia norma finita. Ciò implica la limitatezza e continuità dei flussi totali e l'esistenza di una auto funzione dominante positiva che rappresenta il flusso totale critico. Viene infine mostrata la connessione tra l'esistenza dell'auto funzione dominante e la convergenza sia in media che punto per punto uniforme ed assoluta della serie di Neumann in tutti i casi sottocritici.
Work performed under C.N.R. contract. 相似文献
2.
Francesco Premuda 《Meccanica》1971,6(4):204-211
Summary In this paper the behavior of the solution of the integral form of the neutron transport Boltzmann equation is investigated for slab and sphere geometry. The study of the properties of the integral transport operator K leads to interesting results concerning the following subjects: boundedness, continuity and positivity of the total flux; existence of a dominant critical eigenfunction; spectral properties of K; dependence of the critical eigenvalue on the dimensions of slab and sphere; uniform convergence of the Neumann series in subcritical conditions; approach to the criticality; summability of the solutions and neutron conservation.
Work performed under contract C.N.R. 相似文献
Sommario In questo lavoro viene esaminato il comportamento della soluzione della forma integrale dell'equazione di Boltzmann del trasporto dei neutroni nel caso di una lastra piana e di una sfera. Lo studio delle proprietà dell'operatore integrale del trasporto K porta ad interessanti risultati riguardanti i seguenti argomenti: limitatezza, continuità e positività del flusso totale; esistenza di una autofunzione dominante critica; proprietà spettrali di K; dipendenza dell'autovalore critico dalle dimensioni della lastra piana e della sfera; convergenza uniforme della serie di Neumann in condizioni sottocritiche; avvicinamento alla criticità; sommabilità delle soluzioni e conservazione dei neutroni.
Work performed under contract C.N.R. 相似文献
3.
D. Mostacci V. Molinari M. Premuda 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,70(1):127-132
The percolation of a liquid through a porous material is investigated with the help of equations of the Onsager type. An expression
is derived for the
molecular attraction, starting from Sutherland’s potential approximation to
the van der Waals interaction. Then appropriate Onsager equations
incorporating this molecular attraction are written from transport theory
considerations, in terms of dimensionless variables. As an application, the
system of self-similar equations so derived is applied to a simplified
situation. 相似文献
4.
V. Molinari D. Mostacci M. Premuda 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):89-93
In literature, surface tension has been investigated mainly from a
Thermodynamics standpoint, more rarely with kinetic methods. In the
present work, surface tension of drops is studied in the framework
of kinetic theory, starting from the Sutherland approximation to Van
Der Waals interaction between molecules. Surface tension is calculated
as a function of drop radius: it is found that it approaches swiftly
an asymptotic value, for radii of several times the distance of minimum
approach D of the Sutherland potential. This theoretical asymptotic
value is compared to experimental values of surface tension in plane
surfaces of a few liquids, and is found in reasonable agreement. 相似文献
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