On a convergent DSA preconditioned source iteration for a DGFEM method for radiative transfer

We consider the numerical approximation of the radiative transfer equation using discontinuous angular and continuous spatial approximations for the even parts of the solution. The even-parity equations are solved using a diffusion synthetic accelerated source iteration. We provide a convergence analysis for the infinite-dimensional iteration as well as for its discretized counterpart. The diffusion correction is computed by a subspace correction, which leads to a convergence behavior that is robust with respect to the discretization. The proven theoretical contraction rate deteriorates for scattering dominated problems. We show numerically that the preconditioned iteration is in practice robust in the diffusion limit. Moreover, computations for the lattice problem indicate that the presented discretization does not suffer from the ray effect. The theoretical methodology is presented for plane-parallel geometries with isotropic scattering, but the approach and proofs generalize to multi-dimensional problems and more general scattering operators verbatim

Toksikološka procjena hrane za životinje kontaminirane mikotoksinima uporabom luminiscentnih mikroorganizama Photobacterium phosphoreum

The possibility of using luminescent microorganisms Photobacterium phosphoreum (strain IMB B-7071; Sq3) for rapid toxicological evaluation of feed contaminated with mycotoxins was examined based on the reduction of the luminescence intensity. Under the conditions of this study, feed with Ochratoxin A mycotoxin content at the level of maximum residue limits (MRL 0.05 mg/ kg) is characterized as non-toxic, while for T2-mycotoxin, deoxynivalenol, fumonisins and aflatoxin B1 (MRL 0.1, 1.0, 5.0, and 0.01 mg/kg, respectively) is characterized as toxic, and for zearalenone (MRL 1.0 mg/kg) as highly toxic. This indicates the need for further research to study the toxicological characteristics of mycotoxins in the body of laboratory and productive animals, possibly with further revision of the maximum allowable levels of relevant contaminants in feed in Ukraine.Na bazi redukcije intenziteta luminiscencije uspostavljena je mogućnost uporabe luminiscentnih mikroorganizama Photobacterium phosphoreum (soj IMB B-7071; Sq3) za izražavanje (do 30 minuta) toksikološke procjene hrane za životinje kontaminirane mikotoksinima. Međutim, ako je za okratoksin A u uvjetima ispitivanja hrane za životinje s udjelom mikotoksina pri razini najvećih dopuštenih količina rezidua (MRL) (0,05 mg/kg) hrana za životinje okarakterizirana kao netoksična, tada je za T2- mikotoksin, deoksinivalenol, fumonizin i aflatoksin B1 pri MRL (0,1; 1,0; 5,0, odnosno 0,01 mg/kg) hrana za životinje okarakterizirana kao toksična, a za zearalenon (MRL 1,0 mg/kg) – kao visoko toksična, što ukazuje na potrebu dodatnog istraživanja da se ispitaju toksikološke karakteristike mikotoksina u tijelu laboratorijskih i produktivnih životinja, moguće s dodatnom revizijom (naniže) najvećih dopuštenih količina relevantnih kontaminanata u hrani za životinje u Ukrajini

STATYSTYCZNE METODY OCENY DANYCH EKSPERYMENTALNYCH DOTYCZĄCYCH WYKORZYSTANIA KOMPETENCJI MATEMATYCZNYCH W BADANIACH NA RZECZ ODPORNEJ GOSPODARKI

The description of the problems, solved within the statistics evaluation of the results of educational (pedagogical) experiment in resilient economy is given. Comparison of the two average samplings and hypothesis verification relative to dispersions of the two samplings are considered. It is shown the hypothesis that teaching and methodical training system of subjects of higher mathematics in technical universities, suggested on the base of the modern interactive technologies, significantly improves the quality of the base level of professional competence of future engineers. The methods for statistical processing of the obtained results, which very thoroughly research all the indexes which compose the suggested learning and methodical system for teaching higher mathematics in technical universities are used.Podano opis problemów rozwiązywanych w ramach statystycznej oceny wyników eksperymentu edukacyjnego (pedagogicznego) w gospodarce odpornej. Rozważa się porównanie dwóch średnich prób i weryfikację hipotezy w odniesieniu do dyspersji dwóch prób. Wykazano hipotezę, że system nauczania i szkolenia metodycznego przedmiotów matematyki wyższej na uczelniach technicznych, zaproponowany w oparciu o nowoczesne technologie interaktywne, znacząco poprawia jakość podstawowego poziomu kompetencji zawodowych przyszłych inżynierów. Zastosowano metody statystycznego przetwarzania uzyskanych wyników, które bardzo dokładnie badają wszystkie wskaźniki składające się na proponowany system nauczania i metodycznego nauczania matematyki wyższej w uczelniach technicznych

A phase-space discontinuous Galerkin approximation for the radiative transfer equation in slab geometry

We derive and analyze a symmetric interior penalty discontinuous Galerkin scheme for the approximation of the second-order form of the radiative transfer equation in slab geometry. Using appropriate trace lemmas, the analysis can be carried out as for more standard elliptic problems. Supporting examples show the accuracy and stability of the method also numerically. For discretization, we employ quadtree-like grids, which allow for local refinement in phase-space, and we show exemplary that adaptive methods can efficiently approximate discontinuous solutions

On a convergent DSA preconditioned source iteration for a DGFEM method for radiative transfer

We consider the numerical approximation of the radiative transfer equation using discontinuous angular and continuous spatial approximations for the even parts of the solution. The even-parity equations are solved using a diffusion synthetic accelerated source iteration. We provide a convergence analysis for the infinite-dimensional iteration as well as for its discretized counterpart. The diffusion correction is computed by a subspace correction, which leads to a convergence behavior that is robust with respect to the discretization. The proven theoretical contraction rate deteriorates for scattering dominated problems. We show numerically that the preconditioned iteration is in practice robust in the diffusion limit. Moreover, computations for the lattice problem indicate that the presented discretization does not suffer from the ray effect. The theoretical methodology is presented for plane-parallel geometries with isotropic scattering, but the approach and proofs generalize to multi-dimensional problems and more general scattering operators verbatim

On robustly convergent and efficient iterative methods for anisotropic radiative transfer

This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the discretization parameters and the physical parameters we develop preconditioned Richardson iterations in Hilbert spaces. The preconditioner is constructed in two steps where the first step ensures mesh independence while the second step aims at reducing the influence of the optical parameters. We show convergence of the resulting scheme when applied to the second-order formulation of the radiative transfer equation, viz. the even-parity equations. We discuss in detail the efficient implementation and application of the discrete operators. In particular, for the considered discontinuous spherical elements, the scattering operator becomes dense and we show that $\mathcal{H}$- or $\mathcal{H}^2$-matrix compression can be applied in a black-box fashion to obtain almost linear or linear complexity when applying the corresponding approximations. The effectiveness of the proposed method is shown in numerical examples

Influence of probiotic microorganisms on microbial biofilms in feeds

At different stages of feed production and storage, it is possible to contaminate both feed and their components with various pathogenic and opportunistic microorganisms that can cause infectious diseases not only among animals but also have epidemiological significance. The aim of the study was to isolate biofilm-forming strains of microorganisms from feed, as well as to study the inhibitory activity of the probiotic complex of bacteria of the genus Bacillus against microbial biofilms. Identification and species affiliation of isolated bacterial field isolates were performed by cultural-morphological and biochemical properties. The formation of biofilms was studied by determining the ability of isolates of microbial associations and individual species of microorganisms to adhere to the surface of a 96-well polystyrene tablet according to the method of O'Toole & Kolter, 1998. Determination of microbial contamination of 50 industrial batches of feed from 4 pig farms in two regions of Ukraine (barley, compound feed SK-31 for rearing, SK-51 for fattening pigs, EXCELL starter for pigs 15%, shop prestarter, compound feed for lactating sows). In 11 experimental batches of barley (68.8%) and 13 batches of 3 types of feed (SK-31, SK-51, feed for lactating sows) identified associations with different microorganisms Pasteurella multocida, Corynebacterium striatum, Bacillus subtilis, Leptothrix ochracea, Haemophilus parasuis and yeast Candida albicans. The association of Actinobacillus pleuropneumonia bacteria with B. subtilis was identified in 2 batches (50%) of the shop prestarter. Moderate, by optical density, biofilm formation for associations of microorganisms P. multocida + C. striatum + C. albicans (D620=3.59) and P. multocida + L. ochracea + C. albicans (D620=3.62). Planktonic forms of C. striatum and P. multocida showed low film-forming activity at the level (D620<1.51). Inhibitory activity of the probiotic complex of bacteria of the genus Bacillus (B. subtilis, B. licheniformis, B. amyloliquefaciens) was determined by isolated variations of microbial biofilms in 5 feed species, which displaced all biofilm-forming microorganisms except H. parasui

Script underlying the paper "On Robustly Convergent and Efficient Iterative Methods for Anisotropic Radiative Transfer"

*** Solver for anisotropic radiative transfer in an XY-geometry *** authors: J. Dölz, O. Palii, M. Schlottbom  corresponding author: Matthias Schlottbom, University of Twente, [email protected] *** Scientific reference *** Jürgen Dölz, Olena Palii, Matthias Schlottbom On robustly convergent and efficient iterative methods for anisotropic radiative transfer.  Journal of Scientific Computing 90 (94), 2022.  https://doi.org/10.1007/s10915-021-01757-9 When using this code, cite that paper. *** Description *** For using the code, unzip the repository and run solve.m.  In lines 4-12, there are parameters regarding the solver and meshes used. In line 51, a function is called that specifies the optical parameters.</p