Use Of Diffusion Theory Research Articles

USE OF THE SIMPLIFIED PN EQUATIONS AND TRANSPORT CORRECTIONS IN THE WIMS/PANTHER EMBEDDED SUPERCELL METHOD

The WIMS/PANTHER Embedded Supercell Method (ESM) provides a significant improvement in prediction accuracy in radial power distributions for pressurised water reactors compared to the standard “two-step” approach, without the need for a significant increase in computational resource.A companion paper presents validation of the ESM as previously presented, using PANTHER pin-by-pin diffusion to correct interface errors arising from the standard two-step approach. However, in principle any reference method can be used to solve the embedded supercells and correct the basic solution – this is a significant advantage of the ESM.A paper presented at PHYSOR 2016 demonstrated that use of diffusion theory introduces significant error relative to transport theory only in the high energy range, due to the discontinuous fission source when modelling the interface between two types of pincell.This paper investigates further improvement of the PANTHER solution through use of simplified PN in the fast energy groups. This solution method can be implemented without the need for any significant change to the calculation route and further improves agreement with a transport reference for a small computational cost.The remaining error in the solution is examined by derivation of an effective diffusion coefficient from a heterogeneous transport reference. This suggests a simple characterisation of the discrepancy, which can be easily corrected.Results are presented in comparison to WIMS for supercells and the KAIST benchmark. For the KAIST small core benchmark assembly power errors relative to a WIMS fine group transport reference are shown to be less than 0.5 %. Results are also presented in comparison to Monte Carlo for the Watts Bar benchmark.

Impurity Diffusion as a Possible Metal Chronometer for Pre-Detonation Nuclear Forensics

Abstract The ability to determine the age of seized nuclear material—that is, the time that has passed since it was formed— would provide crucial data to be used in its investigation. This paper reviews the methods and mathematical reasoning behind the use of diffusion theory, as previously applied to analysis of metals in ancient artifacts and other objects, to modern investigations in nuclear science. We here examine the time-dependent processes of diffusion, including grain boundary diffusion and discontinuous precipitation, and we assess the utility of examining the profiles of impurity and alloying element concentrations for use as a tool in pre-detonation nuclear forensics. I. Introduction Interdiction of metallic nuclear material raises many questions of provenance, only some of which can be satisfactorily addressed today [ 1 – 3 ] . For example, we can analyze for the date of last chemical purification by examining progeny isotopes. This analysis technique develops the approach to answer another key question: when was the specimen cast or formed? We address this question by examining impurity diffusion in the microstructure of the metal. An enhanced capability in nuclear forensics—one that determines the material’s critical parameters, such as its timeline of processing—would support investigations of seized illicit materials. Earlier casework has demonstrated that information important to the investigation can be garnered not just from the nuclear materials themselves, but also from the containers, shields, and assorted other components associated with a seized illicit article

Applying diffusion theory to destination stakeholder understanding of sustainable tourism development: a case from Thailand

The concept of sustainable tourism development is widely considered to be necessary for successful tourism development, but there is uncertainty over destination stakeholders’ understanding and thus ability to implement the concept. Utilising diffusion theory, this paper explores the diffusion of the sustainable tourism development concept among stakeholders in the tourism destination of Kret Island, Thailand. The primary data collection involved semi-structured, in-depth interviews undertaken with 10 local government authorities and 45 local residents, and data were analysed using content analysis. Interpersonal communication was the key channel for the concept's diffusion, and the involvement of opinion leaders, change agents and social networks in this diffusion was explored. Many local residents were laggards in the diffusion of sustainable tourism development thinking in comparison with local government and local opinion leaders. It is argued that both interpersonal and media communication and the identification of key actors in the community are needed to effectively diffuse sustainable tourism ideas among destination stakeholders. The results validate the use of diffusion theory as a means to understand the transfer of the sustainable tourism development concept among stakeholders, and they also provide information useful for the design of information dissemination programmes.

The use of diffusion theory for the assessment of mixing in a rotary coating pan.

Abstract The effectiveness of a coating pan in treating all the contained tablets identically depends upon its being a good mixing device; the mechanics of particle motion within such a pan are therefore of interest. One measure of the mixing rate in rotary drum mixers is the coefficient of self diffusion, a parameter difficult to measure in a coating pan. Three methods of measuring such a coefficient are reported and compared: linear sampling, total compartmenting of the bed, and high speed cinéphotography. The third method is the best, and a technique is described for treating the pictorial data to obtain quantitative results.

Sensitivity Analysis based on Transport Theory

To estimate the uncertainty of the neutronic parameters it is required to calculate sensitivity coefficients to cross section changes. The sensitivity coefficients are usually calculated based on the diffusion theory. However, the accuracy of the sensitivity coefficients becomes doubtful because of the use of diffusion theory. The purpose of this paper is to derive the generalized perturbation theory using the transport theory, and to evaluate transport effect on the sensitivity coefficients. Sensitivity calculations were performed in 70 energy groups. The calculated sensitivity coefficients were compared with those obtained from direct transport calculations to check the accuracy of the present method, and those obtained from the generalized perturbation calculation based on the diffusion theory to investigate the transport effect on sensitivity coefficients. From the comparison, the difference was remarkably large for the neutronic parameters such as reaction rate distribution, reaction rate ratio, and reactivity worth. For example, the sensitivity coefficient of the 238U capture to 239Pu fission rate ratio in the lower core region of the under-moderated LWR core was large in the energy range 17.6–22.6 eV, and the sensitivity to 238U capture cross section calculated by the transport theory was 20% larger than that by the diffusion theory.

Sci‐PM Fri ‐ 03: Potential use of diffusion theory for quantitative in vivo fluorescence and bioluminescence imaging

In recent years, there has been increasing interest in the potential of optical methods to detect and monitor in vivo minimal residual disease and metastasis in animal cancer models. The overall objective of the present work is to develop analytical methods and instrumentation to construct quantitative bioluminescence and fluorescence images of bone metastases. The diffusion approximation was investigated as a mathematical model of light propagation in tissue. Testing of the model against Monte Carlo simulation data showed that the optical properties could be retrieved from a reflectance curve with an accuracy of better than 2%. The evaluation of the model was also performed on liquid tissue‐simulating phantoms by using the tip of an optical fiber to simulate a point source. A charge‐coupled device (CCD) camera was used to acquire images of the surface of the phantom with the point source inserted at different depths. In addition, a non‐invasive measurement of the optical properties of the phantom was performed. Results showed that, for the depth ranges where diffusion theory was expected to be valid, the depth could be reconstructed with 15% accuracy and the fitted relative intensities of the source were consistent to expected values within 30%.

Practical and adequate approach to modeling light propagation in an adult head with low-scattering regions by use of diffusion theory

A practical and adequate approach to modeling light propagation in an adult head with a low-scattering cerebrospinal fluid (CSF) region by use of diffusion theory was investigated. The diffusion approximation does not hold in a nonscattering or low-scattering regions. The hybrid radiosity-diffusion method was adopted to model the light propagation in the head with a nonscattering region. In the hybrid method the geometry of the nonscattering region is acquired as a priori information. In reality, low-level scattering occurs in the CSF region and may reduce the error caused by the diffusion approximation. The partial optical path length and the spatial sensitivity profile calculated by the finite-element method agree well with those calculated by the Monte Carlo method in the case in which the transport scattering coefficient of the CSF layer is greater than 0.3 mm(-1). Because it is feasible to assume that the transport scattering coefficient of a CSF layer is 0.3 mm(-1), it is practical to adopt diffusion theory to the modeling of light propagation in an adult head as an alternative to the hybrid method.

Neutron noise theory in the P 1 approximation

The validity of the use of the diffusion approximation in neutron noise theory is investigated through a comparison with P 1 theory. The motivation comes from the fact that both static and dynamic perturbations act as non-isotropic sources in the P 1 expansion of the static angular flux and the angular noise, respectively, and the neglection of these terms, which would allow the use of diffusion theory, is not obvious. In addition, the effect of noise sources that affect primarily the scattering cross section (diffusion coefficient) has not been the subject of a thorough investigation before. The P 1 theory of static and dynamic perturbations is developed in this paper and the results show the corrections introduced by P 1 theory. It is found that for cases when the fluctuation of the absorption cross section dominates, the quantitative difference between the diffusion and P 1 theory results is negligible in general. For cases when the perturbation leads to the fluctuation of the scattering cross section only, such as in cases of density fluctuations in a heavy water moderator or even a small light water reactor, P 1 theory needs to be used and the results differ markedly from the noise induced by an equivalent absorption cross section fluctuation in diffusion theory. Some concrete cases are investigated both qualitatively and quantitatively.

Assessment of the size, position, and optical properties of breast tumors in vivo by noninvasive optical methods

We present a method for the noninvasive determination of the size, position, and optical properties (absorption and reduced scattering coefficients) of tumors in the human breast. The tumor is first detected by frequency-domain optical mammography. It is then sized, located, and optically characterized by use of diffusion theory as amodel for the propagation of near-infrared light in breast tissue. Our method assumes that the tumor is a spherical inhomogeneity embedded in an otherwise homogeneous tissue. We report the results obtained on a 55-year-old patient with a papillary cancer in the right breast. We found that the tumor absorbs and scatters near-infrared light more strongly than the surrounding healthytissue. Our method has yielded a tumor diameter of 2.1 ? 0.2cm, which is comparable with the actual size of 1.6 cm, determined after surgery. From the tumor absorption coefficients at two wavelengths (690 and 825 nm), we calculated the total hemoglobin concentration (40 ? 10 muM) and saturation (71 ? 9%) of the tumor. These results can provide the clinical examiner with more detailed information about breast lesions detected by frequency-domain optical mammography, thereby enhancing its potential for specificity.

A critique of diffusion theory as a managerial framework for understanding adoption of software engineering innovations

Promoters of new software engineering innovations (e.g., U.S. Government) and managers responsible for facilitating the use of these innovations express the need for a model of technology adoption that enables prediction of outcomes of planned technology-transition efforts. In this paper, the authors provide a brief overview of classical diffusion theory and suggest the potential applicability of this theory to problems related to predicting the adoption of technological innovations, including those related to software engineering. Unlike previous papers advocating the use of diffusion theory, the current paper critically evaluates the theory by presenting elements of the theory which must be extended and modified before it can be applied to technology transition, in general, and software engineering, specifically. Incorporated in this discussion are specific suggestions on ways these limitations might be overcome.

Three-dimensional nodal diffusion and transport methods for the analysis of fast-reactor critical experiments

An interface-current nodal formulation is developed for the solution of the multigroup neutron diffusion and transport equations in three-dimensional Cartesian geometry. The nodal diffusion method uses polynomial approximations equivalent to those used in the nodal expansion method (NEM), while the nodal transport method is based on the approximation of exact one-dimensional integral equations. The transport scheme employs a double P-1 expansion of the surface angular fluxes in conjunction with either isotropic or angle-dependent approximations to the angular dependence of the transverse-leakage terms. The transport formulation does not involve an iteration on the scattering source, and identical iterative strategies are used to solve the interface-current equations obtained in both methods. Numerical results for a ZPPR fast-reactor critical experiment show that the nodal diffusion method produces spatially-converged solutions with significant reductions in computational cost relative to the finite-difference method. Use of the nodal transport scheme eliminates over 80% of the error due to the use of diffusion theory, with computational costs within a factor of two of nodal diffusion theory.

On the stability of gas bubbles in liquid-gas solutions

It was shown some time ago by use of diffusion theory that a gas bubble in a liquid-gas solution was unstable. This problem has been reconsidered recently in two papers both of which propose to develop a stability analysis solely from thermodynamic considerations. The first of these studies purports to find stability for a gas bubble in a liquid-gas solution. Some possible sources of error in this analysis are mentioned here. The second study considers a particular system of a bubble in a liquid drop immersed in a second liquid in which the gas is insoluble. A condition of stability is then found. This system is reconsidered here simply in terms of the ideas of diffusion theory. The stability conditions may then be stated in simple physical terms.

Improved model for parallel-plate drift-tube experiments

The validity of analysis of parallel-plate drift-tube experiments by use of diffusion theory is examined. Monte Carlo simulations demonstrate the inadequacy of such analyses for electron motion near an absorbing cathode. However, diffusion theory results are verified for situations in which cathodic absorption is negligible, provided that a parameter $\ensuremath{\beta}$, the ratio of energy relaxation distance to drift-tube length, is much smaller than unity. For experimental circumstances in which cathode effects may be distinguished from those of anodic absorption, circuit time constant, and ionization, the Monte Carlo results can be used to augment diffusion theory for interpretation of the observed transients in terms of transport coefficients.

A comparative study of two-dimensional transport methods for BWR lattice geometries

Current BWR fuel assembly designs contain a number of features which present problems to an accurate neutronics analysis. This paper describes a series of idealised model problems which have been analysed with the aid of the lattice code LWR-WIMS. This code contains modules which provide flux solutions by the methods of diffusion theory, S n transport theory and collision probability theory with and without pin cell homogenisation. The results of the study indicate that homogenisation errors can be significant, particularly for pins containing burnable poison and that, due to cancelling error effects, the subsequent use of diffusion theory with a comparatively coarse mesh is often preferable to an accurate solution of the homogenised transport equation.

The structure of supernova shock waves

The structure of strong shock waves is calculated over the range of shock energies (1 to 100 MeV nucleon/sup -1/) and initial number densities (10/sup 15/--10/sup 22/ cm/sup -3/) believed likely to occur in the red-giant-like envelopes of stars undergoing Type II supernova explosions. The general equations governing the structure of such shocks are developed on the basis of a plasma composed of ions, electrons, positrons, and photons, making use of diffusion theory to evaluate the dissipative and transfer terms. The present treatment differs from previous calculations in that the effects of radiation transport on the energy and momentum balance in the shock are taken into account, as well as the relativistic contributions to radiative emission rates due to nondipole electron-ion bremsstrahlung, electron-electron bremsstrahlung, and radiative Compton scattering. An implicit treatment of inverse Compton scattering is also developed in terms of the creation and diffusion of effective photons.Severalmodels of strong shock structure are formulated and solved on the basis of these equations and physical processes. (AIP)

Comments on Michael's Criticism of the Use of Diffusion Theory for the Study of Thermal Neutrons in Beryllium

"Comments on Michael's Criticism of the Use of Diffusion Theory for the Study of Thermal Neutrons in Beryllium." Nuclear Science and Engineering, 24(1), pp. 94–95

A Criticism of the Use of Diffusion Theory for the Study of Thermal Neutrons in Beryllium

"A Criticism of the Use of Diffusion Theory for the Study of Thermal Neutrons in Beryllium." Nuclear Science and Engineering, 24(1), pp. 93–94