LTSN solution of the adjoint neutron transport equation with arbitrary source for high order of quadrature in a homogeneous slab

Gonçalves, Glênio Aguiar; Orengo, Gilberto; Vilhena, Marco T.; Graça, Cláudio O.

doi:10.1016/s0306-4549(01)00057-3

Cited by 9 publications

(4 citation statements)

References 10 publications

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“…Devido ao caráter idealizado deste problema, fizemos uma comparação com os resultados numéricos do método LTS N , com N variando de 300 a 1000, uma vez que sua convergência já foi demonstrada [24,25] e a equivalência entre as formulações A N e S 2N foi estabelecida [15]. Ademais, o método LTS N foi utilizado com sucesso em uma ampla classe de problemas de transporte [18,19,26]. Neste problema, as integrais de convolução provenientes das soluções LTA N , ELTA N e LTS N foram calculadas analiticamente.…”

Section: Resultados Numéricosunclassified

“…Baseados nos avanços obtidos pela formulação LTS N [18,19,26,27], nos quais foram superadas as limitações computacionais para trabalhar com problemas de transporte não-homogêneos que exigem altas ordens de quadratura, em trabalhos recentes, Cardona et al [4,9] propuseram uma formulação melhorada do método LTA N , extremamente robusta do ponto de vista computacional, pois permite trabalhar com problemas de transporte com uma fonte arbitrária e com altas ordens de quadratura (N variando até 650). Seguindo a idéia do método LTS N , este objetivo foi alcançado através da diagonização da matriz LTA N , a qualé uma matriz (2N) × (2N) resultante da aplicação da transformada de Laplace no conjunto das equações A N .…”

Section: Introductionunclassified

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Solução $ELTA_N$ para o Problema de Transporte com Fonte

Cardona¹,

Oliveira²

2009

TEMA - Tendências Em Matemática Aplicada E Computacional

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Resumo. Recentemente foi apresentada uma nova versão do método LTAN para resolver problemas de transporte lineares homogêneos em uma placa. Esta formulação foi denominada método ELTAN eé baseada na diagonalização de uma matriz N × N, em oposição a matriz (2N) × (2N) do método LTAN original. Neste trabalho estendemos essa formulação para resolver problemas de transporte não homogêneos. Simulações numéricas são apresentadas e os resultados são comparados aos resultados obtidos pelos métodos LTSN e LTAN. Introdução

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Section: Resultados Numéricosunclassified

Section: Introductionunclassified

Solução $ELTA_N$ para o Problema de Transporte com Fonte

Cardona¹,

Oliveira²

2009

TEMA - Tendências Em Matemática Aplicada E Computacional

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“…The techniques used in Ref. [8] might be particularly useful in the present context. In order to have a feeling of what can be expected for an explicit solution, in the following section a static EOS for QNM is obtained.…”

Section: Vlasov-uehling-ullenbeck Equations For Quark-nuclear Mattermentioning

confidence: 99%

Transport properties and equation of state of quark-nuclear matter

Graça

Krein

2003

Braz. J. Phys.

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Transport equations for composite nucleons and deconfined quarks in quark-nuclear matter (QNM) are derived. QNM is a many-body system containing hadrons and deconfined quarks. The starting point is a microscopic quark-meson coupling (QMC) Hamiltonian with a density-dependent quark-quark interaction. An effective quark-hadron Hamiltonian containing canonical hadron and quark field operators is constructed using a mapping procedure. For high densities, the effective Hamiltonian contains interactions that lead to quark decon-finement. Transport equations of the Ueling-Ullenbeck-Vlasov type for quarks and nucleons are obtained using standard many-body techniques with the effective quark-hadron Hamiltonian. I Introduction The study of the properties of high density hadronic matter is one of the most important problems in contemporary physics. The possibility of creating in laboratory a new state of matter through collisions of heavy nuclei has become feasible in recent years, with widespread opportunities for understanding several aspects of the strong interactions and matter in superdense stars and at the origin of the universe. One of the central questions in this field is the identification of the appropriate degrees of freedom to describe the different phases of hadronic matter. At densities much higher than the nuclear saturation density, a phase of deconfined matter composed of quarks and gluons is expected to occur. The study of the properties of such a state is possible with the methods of perturbative quantum chromodynamics (QCD). On the other hand, the study of matter at densities not much higher than the saturation density of nuclear matter-like the one existing in dense stars-is very complicated. The complication is due to the fact that this phase of matter is characterized by nonperturbative QCD phenomena and the use of tractable models and drastic approximations is presently the only practical way of tackling the problem. The quark-meson coupling (QMC) model [1] is a very useful model to study the different phases of hadronic matter. It is formulated in terms of quark-gluon degrees of freedom and is devised in such a way to incorporate in an explicit way hadron structure in the nuclear many-body problem. In this model, low-density hadronic matter is described as a system of independent baryons interacting through effective scalar-and vector-meson degrees of freedom which couple directly to the quarks. At very high density the quarks and gluons become deconfined and the entire system is confined by a bag, or potential. For a list of references and recent work, see Ref. [2]. In a recent paper [3] the QMC model was generalized to include quark deconfinement at high density. Starting from a relativistic quark potential model [4], a change of Fock-space representation is implemented through a unitary transformation. The unitary operator is constructed in an extended Fock space in such a way that single composite-hadrons of the model are redescribed in terms of elementary-particle field operators. The unitary...

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“…[3][4][5]. An alternative approach to the same problem uses the LTS N procedure (Laplace-Transform S N discrete ordinate equation procedure) [4][5][6][7][8] applying the Laplace-transform technique in the set of the A N ordinary differential equations with subsequent analytical solution of the resulting symbolic linear system with Laplace inversion of the transformed angular flux by Trzaska's method [9]. From a computational point of view, LTA N is known to be limited by virtue of terms with a singularity that appear the closer the polar angle cosine approaches zero and thus lead to overflows.…”

Section: Introductionmentioning

confidence: 99%

An improvement of the double discrete ordinate approximation solution by Laplace technique for radiative-transfer problems without azimuthal symmetry and high degree of anisotropy

et al. 2009

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One-dimensional radiative-transfer problems without azimuthal symmetry and with a high degree of anisotropy are solved using the double discrete ordinate approximation methods LTA N and ALTA N . The discussed methods start with projecting out azimuthal components of the original equation and results in an equation system. Then the collocation method is applied to the polar angle and the integral is approximated by a Gaussian quadrature scheme that yields the S N transport equation system. The subsequent application of the Laplace transform in the spatial variable opens pathways for application of the specific procedures that characterise the LTA N and the ALTA N methods. The results are solutions for the radiative-transport problem. We further report on numerical simulations and comparisons with the LTS N method.

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LTSN solution of the adjoint neutron transport equation with arbitrary source for high order of quadrature in a homogeneous slab

Cited by 9 publications

References 10 publications

Solução $ELTA_N$ para o Problema de Transporte com Fonte

Solução $ELTA_N$ para o Problema de Transporte com Fonte

Transport properties and equation of state of quark-nuclear matter

An improvement of the double discrete ordinate approximation solution by Laplace technique for radiative-transfer problems without azimuthal symmetry and high degree of anisotropy

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