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  • 1
    Electronic Resource
    Electronic Resource
    Asymptotic scattering operators and drift velocity in charged particle transport problems (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 4668-4691 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this article the long-time behavior of the evolution of one species of charged particles in a neutral gas under the influence of an acceleration field is studied. After a short review of the literature on runaway phenomenon, the mathematical definitions of drift velocity and runaway phenomenon based on the distribution function are given. The linear Boltzmann equation in a three-dimensional spatially homogeneous system is considered. Under suitable conditions on the acceleration field and on the collision frequency, the existence of asymptotic operators is proven in a three-dimensional setting. Then wave operators are introduced and are used to characterize the long-time behavior of the solutions. Finally, using such operators the long-time behavior of the drift velocity is estimated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530364
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Streaming operators and semigroups (1979)
    Springer
    Meccanica 14 (1979), S. 119-128 
    Details
    ISSN: 1572-9648
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Summary We consider some types of boundary conditions for the streaming operator T in the radiation theory. First, we study the streaming operator in a finite convex body with diffuse reflection boundary conditions and with mixed type boundary conditions. In both cases, we prove that T is the generator of a strongly continuous semigroup, by assuming a suitable smoothness of a surface of the boundary. We also investigate the specular reflection boundary conditions. In this case, physical considerations suggest the form of the semigroup leading the evolution of the system. Finally, a complete description of the corresponding generator is given.
    Notes: Sommario Si considerano alcuni tipi di condizioni al contorno per l'operatore di streaming T in teoria della radiazione. Innanzitutto, si studia l'operatore di streaming T in un mezzo finito convesso con condizioni al contorno di riflessione diffusa e con condizioni di tipo misto. In entrambi i casi si prova che T è il generatore di un semigruppo fortemente continuo, sotto l'ipotesi che la superficie del contorno sia sufficientemente regolare. Si indaga poi il caso della riflessione speculare. Costruito il relativo semigruppo di evoluzione con considerazioni fisiche, si dà infine un'esatta descrizione del corrispondente generatore.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02128504
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  • 3
    Electronic Resource
    Electronic Resource
    Energy and radiation transfer in a finite convex body with general boundary conditions (1984)
    Springer
    Meccanica 19 (1984), S. 282-290 
    Details
    ISSN: 1572-9648
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Summary We consider a nonlinear system of equations describing the interaction of radiation with matter through a balance of the specific intensity of radiation and the specific internal energy in a convex bounded body. The boundary conditions are not homogeneous. However, suitable additive decompositions of the unknown functions lead to systems with homogeneous boundary conditions and known source terms. We give two such decompositions: one of these, suggested by physical considerations, arises from the study of a nonhomogeneous linear integral equation in a convenient Banach space. The system is studied by using the theory of semigroups of linear operators and nonlinear perturbations in an L 1 setting. We prove the existence and uniqueness of a positive differentiable solution, which is global in time.
    Notes: Sommario Si considera un sistema non lineare di equazioni che descrivono l'interazione della radiazione con la materia e rappresentano il bilancio dell'intensità specifica di radiazione e dell'energia specifica internu in un mezzo finito convesso. Le condizioni al contorno sono di tipo generale e non omogenee; l'introduzione di opportune scomposizioni della funzione incognita permette di ricondurci a sistemi con condizioni al contorno omogenee; ciò comporta l'introduzione di termini di sorgente noti. Si presentano due esempi di scomposizione, uno dei quali, suggerito da considerazioni fisiche, scaturisce dallo studio di un'equazione integrale lineare non omogenea in un opportuno spazio di Banach. Si riduce quindi il problema ad un'equazione di evoluzione non lineare in uno spazio di Banach di norma L 1. Si prova l'esistenza di un'unica soluzione forte non negativa, utilizzando la teoria dei semigruppi e delle perturbazioni non lineari; tale soluzione risulta inoltre globale nel tempo.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01556324
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  • 4
    Electronic Resource
    Electronic Resource
    Functional methods in three-dimensional neutron transport theory (1976)
    Springer
    Meccanica 11 (1976), S. 127-132 
    Details
    ISSN: 1572-9648
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Summary In this work, we are concerned with the stationary neutron transport Boltzmann equation (in its integral form) in a parallelepiped. Functional methods allow us to prove that the integral transport operator, which is defined in L2 space, has eigenvalues depending continuously and monotonically on geometrical and physical parameters. We show that the eigenfunctions are continuous with respect to set of the spatial variables and the optical parameters. Finally, we remark that the same results are valid if the study is carried out in the Banach space C.
    Notes: Sommario In questo lavoro consideriamo l'equazione stazionaria di Boltzmann (nella forma integrale) per neutroni monoenergetici nel caso di un sistema tridimensionale a forma di parallelepipedo. L'uso di alcuni metodi dell'analisi funzionale ci permette di provare che l'operatore integrale del trasporto, definito nello spazio L2, ha autovalori che dipendono continuamente dai parametri geometrici e fisici. Si prova che le autofunzioni sono continue rispetto all'insieme delle variabili spaziali e dei parametri ottici. Infine, si osserva che gli stessi risultati sono validi se l'operatore del trasporto agisce nello spazio di Banach C.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02133863
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  • 5
    Electronic Resource
    Electronic Resource
    Book reviews (1993)
    Springer
    Meccanica 28 (1993), S. 69-72 
    Details
    ISSN: 1572-9648
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00990291
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  • 6
    Electronic Resource
    Electronic Resource
    Some remarks on neutron transport in homogeneous slabs and spheres (1973)
    Springer
    Meccanica 8 (1973), S. 211-215 
    Details
    ISSN: 1572-9648
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Summary In this work we are concerned with the stationary neutron transport Boltzmann equation (in its integral form) in plane and spherical symmetry; both the study of the properties of the exact and approximate solution are based on functional analysis. We have taken advantage of the fact that the kernel of the integral equation is even, to semplify the general discussion; among the results, we quote that relating to the continuity of the solution with respect to the optical thickness. Moreover we emphasized that the Ritz method seems the most convenient one for the approximate evaluation of the solution; in this connexion, some observations have been made about the convergence of the approximate solutions to the exact one.
    Notes: Sommario In questo lavoro consideriamo l'equazione stazionaria di Boltzmann (nella forma integrale) in simmetria piana e sferica; l'uso di alcuni metodi dell'analisi funzionale ci consente di studiare sia le proprietà della soluzione esatta che di quella approssimata. La semplice osservazione che il nucleo dell'equazione integrale è pari, ci ha permesso di semplificare la discussione generale; tra i risultati segnaliamo quello riguardante la continuità della soluzione rispetto allo spessore ottico. Inoltre abbiamo sottolineato che il metodo di Ritz ci sembra il più opportuno punto di partenza per il calcolo approssimato della soluzione; in relazione a ciò, vengono fatte alcune osservazioni a proposito della convergenza delle soluzioni approssimate verso quella esatta.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02342406
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  • 7
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    Strict solution of a nonlinear evolution problem in a time dependent domain (1980)
    Elsevier
    Details
    Publication Date: 1980-11-01
    Print ISSN: 0362-546X
    Electronic ISSN: 1873-5215
    Topics: Mathematics
    Published by Elsevier
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  • 8
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    A nonlinear problem of evolution arising from radiation transfer theory (1979)
    Elsevier
    Details
    Publication Date: 1979-11-01
    Print ISSN: 0362-546X
    Electronic ISSN: 1873-5215
    Topics: Mathematics
    Published by Elsevier
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  • 9
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    Asymptotic scattering operators and drift velocity in charged particle transport problems (1993)
    American Institute of Physics
    Details
    Publication Date: 1993-10-01
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
    Published by American Institute of Physics
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  • 10
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    Comparing 2HDM + scalar and pseudoscalar simplified models at LHC (2020)
    Springer
    Details
    Publication Date: 2020-06-01
    Print ISSN: 1126-6708
    Electronic ISSN: 1029-8479
    Topics: Physics
    Published by Springer
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