SURFACE FLUXES AND CURRENTS FOR VARIOUS SHIELDED RADIATION SOURCES

A series of critical experiments was completed with mixed plutonium-uranium solutions having Pu/(Pu + U) ratios of approximately 0.4. These experiments were a part of the Criticality Data Development Program between the United States Department of Energy (USDOE), and the Power Reactor and Nuclear Fuel Development Corporation (PNC) of Japan. A complete description of, and data from, the experiments are included in this report. The experiments were performed with mixed plutonium-uranium solutions in cylinqrical and slab geometries and included measurements with a water reflector, a concrete reflector, and without an added reflector. The concentration was varied from 105 to 436 g (Pu + U)/liter. The ratio of plutonium to total heavy metal (plutonium plus uranium) was 0.4 for all experiments.

A general quasi-linear transport parameter for particle drift in arbitrary turbulence geometry is presented. The new drift coefficient is solely characterized by a nonresonant term and is evaluated for slab and two-dimensional turbulence geometry. The calculations presented here demonstrate that fluctuating electric fields are a key quantity for understanding quasi-linear particle drift in slab geometry. It is shown that particle drift does not exist in unpolarized and purely magnetic slab fluctuations. This is in stark contrast to previous models, which are restricted to slab geometry and the field line random walk limit. The evaluation of the general transport parameter for two-dimensional turbulence geometry, presented here for the first time for dynamical magnetic turbulence, results in a drift coefficient valid for a magnetic power spectrum and turbulence decay rate varying arbitrarily in wavenumber. For a two-component, slab/two-dimensional turbulence model, numerical calculations are presented. The new quasi-linear drift, induced by the magnetic perturbations, is compared with a standard drift expression related to the curvature and gradient of an unperturbed heliospheric background magnetic field. The considerations presented here offer a solid ground and natural explanation for the hitherto puzzling observation that drift models often describe observations much better when drift effects are reduced.

This paper reports on a seminumerical technique developed for solving the transport equation in slab geometry that is adopted for a point isotropic source of gamma rays in spherical geometry. Only Compton scattering is dealt with currently. Two quantities, namely surface flux and surface source, are introduced to circumvent singularities at the origin. A collision-by-collision iterative approach is followed to solve the coupled form of integral transport equations separating the spatial and energy transmission kernels. The spatial transmission kernel for obtaining surface flux from surface source is derived. The energy angle transmission kernels are evaluated by taking recourse to Legendre polynomial expansions. The uncollided and first collision surface fluxes are obtained analytically. An appropriate functional form is chosen for the spatial interpolation of flux and source facilitating large spatial mesh widths. The computer program ASFIT-Sphere is written on the basis of these formulations. Energy flux spectra and angular distributions obtained by the current method of scattered photons 2 and 3 mean-free-paths away from a {sup 137}Cs source in water are compared with the data of ANS-6 shielding benchmark experiments. Comparison with calculations by other methods is also included.

While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer, Phys. Fluids B, vol. 3, 1991, pp. 2805–2821; 2822–2834; Plunk & Helander, J. Plasma Phys., vol. 84, 2018, 905840205), we have obtained the first such solutions using a vacuum surface expansion formalism. We obtain a single nonlinear parabolic partial differential equation for a function $\eta$ such the field strength satisfies $B = B(\eta )$ . Closed-form solutions are obtained in cylindrical, slab and isodynamic geometries. Numerical solutions of the full nonlinear equations in general axisymmetric toroidal geometry are obtained, resulting in a class of quasihelical local vacuum equilibria near an axisymmetric surface. The analytic models provide additional insight into general features of the nonlinear solutions, such as localization of the surface perturbations on the inboard side. The local solutions thus obtained can be continued globally only for special initial surfaces.

Understanding convective aggregation is very important for understanding tropical climate and climate sensitivity. However, we still lack a full understanding of how aggregation evolves in the real world or what phenomena and scales are analogous to the self-aggregation observed in idealized models. In this study, we apply the moist static energy (MSE) variance budget framework to ERA5 reanalysis data to study the evolution of large-scale aggregation over tropical oceans at basinwide scales. Our novel phase space diagnostics focus on the variability of observed aggregation compared to most previous self-aggregation studies, which focus more on the aggregated mean state. We visualize observed aggregation to evolve anomalously around a mean state in a cyclical fashion forming aggregation–disaggregation cycles. We find horizontal advection of MSE to play the primary role in determining when the domain aggregates or disaggregates. In contrast, all advective, radiative, and surface flux feedbacks are found important for determining the magnitude of the aggregation anomalies. Surface fluxes and horizontal advection tend to dampen aggregation anomalies, while radiative fluxes and vertical advection tend to amplify aggregation anomalies. Looking deeper into the advection terms, we find that changes in vertical advection are dominated by enhanced low-level subsidence over the dry regions during the more aggregated states. This creates an anomalous drying tendency over the dry regions, which maintains aggregation anomalies. In contrast, horizontal advection changes are found to be dominated by increased moisture advection out of the moist columns with stronger aggregation. Significance Statement The purpose of this study is to characterize and understand the evolution of large-scale convective aggregation in the real world through reanalysis data. While most previous observational studies have focused on the evolution of clouds and cloud populations with aggregation, we focus on the energetics and the impact of aggregation on redistributing moisture throughout the domain. Our framework highlights that aggregation can be visualized as a continuously occurring cyclic feature at large scales in the tropics. Further, our work provides a deeper insight into the changes in large-scale circulation that accompany aggregation and characterizes the similarities and differences between the different regions in the tropics.

BackgroundNon-invasive planar fluorescence reflectance imaging (FRI) is used for accessing physiological and molecular processes in biological tissue. This method is efficiently used to detect superficial fluorescent inclusions. FRI is based on recording the spatial radiance distribution (SRD) at the surface of a sample. SRD provides information for measuring structural parameters of a fluorescent source (such as radius and depth). The aim of this article is to estimate the depth and radius of the source distribution from SRD, measured at the sample surface. For this reason, a theoretical expression for the SRD at the surface of a turbid sample arising from a spherical light source embedded in the sample, was derived using a steady-state solution of the diffusion equation with an appropriate boundary condition.MethodsThe SRD was approximated by solving the diffusion equation in an infinite homogeneous medium with solid spherical sources in cylindrical geometry. Theoretical predications were verified by experiments with fluorescent sources of radius 2-6 mm embedded at depths of 2-4 mm in a tissue-like phantom.ResultsThe experimental data were compared with the theoretical values which shows that the root mean square (RMS) error in depth measurement for nominal depth values d = 2, 2.5, 3, 3.5, 4 mm amounted to 17%, 5%, 2%, 1% and 5% respectively. Therefore, the average error in depth estimation was ≤ 4% for depths larger than the photon mean free path.ConclusionsAn algorithm is proposed that allows estimation of the location and radius of a spherical source in a homogeneous tissue-like phantom by accounting for anisotropic light scattering effect using FRI modality. Surface SRD measurement enabled accurate estimates of fluorescent depth and radius in FRI modality, and can be used as an element of a more general tomography reconstruction algorithm.

Abstract. We use observations of surface and top-of-the-atmosphere (TOA) broadband radiation fluxes determined from the Atmospheric Radiation Measurement programme mobile facility, the Geostationary Earth Radiation Budget (GERB) and Spinning Enhanced Visible and Infrared Imager (SEVIRI) instruments and a range of meteorological variables at a site in the Sahel to test the ability of the ECMWF Integrated Forecasting System cycle 43r1 to describe energy budget variability. The model has daily average biases of −12 and 18 W m−2 for outgoing longwave and reflected shortwave TOA radiation fluxes, respectively. At the surface, the daily average bias is 12(13) W m−2 for the longwave downwelling (upwelling) radiation flux and −21(−13) W m−2 for the shortwave downwelling (upwelling) radiation flux. Using multivariate linear models of observation–model differences, we attribute radiation flux discrepancies to physical processes, and link surface and TOA fluxes. We find that model biases in surface radiation fluxes are mainly due to a low bias in ice water path (IWP), poor description of surface albedo and model–observation differences in surface temperature. We also attribute observed discrepancies in the radiation fluxes, particularly during the dry season, to the misrepresentation of aerosol fields in the model from use of a climatology instead of a dynamic approach. At the TOA, the low IWP impacts the amount of reflected shortwave radiation while biases in outgoing longwave radiation are additionally coupled to discrepancies in the surface upwelling longwave flux and atmospheric humidity.

: The development of design principles for constructing atomic warfare shelters for naval shore establishments is descrived. part of this problem is evaluating various systems for protection against nuclear radiation. this report presents the results of an investigation to determine which part of the earth covering a buried shelter is the most important as a radiation shield. the following equations: (1-f) e1(uix) equals e1(uix sec theta) when solved for the critical angle, theta will define the volume of earth which provides the fraction, f, of the total shielding to the shelter system. e1 is the expontial integral; ui is the effective linear absorption coefficient for the shield material; x is the effective shield thickness. computations have been completed for slab and hemisphere geometry for fractions, f, of 0.99 and 0.999. for slab geometry x is equivalent to tm, the thickness of the slab shield. for hemispherical geometry x is equivalent to rm which is the sum of the radius of the hemisphere plus the minimum cover over the arch. in order to preserve the shielding integrity of the shelter system, the shielding volume defined by theta should not be violated by openings of any sort such as vents, ducts, and entranceways.

Heat transfer in double-sided cooking of meat patties considering two-dimensional geometry and radial shrinkage

Design and optimization of HPLWR high pressure Turbine gamma ray shield

The transport equation in slab geometry is solved by means of the DPN “surface flux” method, based on a Pn polynomial expansion in both angle and space and a double Pn approximation of the angular distribution at interval surfaces. The method, which has been incorporated into the multigroup transport code SURCU, is compared to a number of different codes such as ANISN, DIT, etc. For a given accuracy in the flux SURCU turns out to be faster than other codes since it needs fewer spatial flux moments than other programs need regions or space points. In addition, the required DPN surface flux approximation is much lower than the corresponding Sn approximation. A number of similarities between the present method and both Sn theory and collision probabilities are discussed.

The meteorology at the Cabauw tower site in the Netherlands has been modelled for 2005 using a local scale prognostic meteorological and air pollution model called TAPM. A number of performance measures have been used to assess model accuracy, including comparison statistics such as root-mean-square error (RMSE) and index of agreement (IOA). Results show that the model performs very well for prediction of wind and temperature at the six tower levels that range from 10 to 200 m above the ground, as well as performing well for radiation and surface fluxes. The model simulation shows almost no bias in mean and standard deviations of wind and temperature at each tower height level, with small RMSE (e.g. RMSE of 1.2 m s−1 for 10-m wind speed, and 1.6°C for 10-m temperature) and high correlation and IOA (e.g. IOA of 0.92 for 10-m wind speed and 0.98 for 10-m temperature). Results for radiation and surface fluxes also show good performance, although some biases were seen for these variables, and possibilities for future model development were identified. An examination of model sensitivity also explored several aspects of the model configuration and input.

In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on semi-infinite slab approximations of the heat equation. The main result is the approximation of χ under the influence of V and τ based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate χ well in cylindrical geometry, the relationships between heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate χ, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which χ, V, and τ can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and τ in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and τ based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated.

Results of a 24-day, two-dimensional integration of tropical cloud systems forced by large-scale ascent, surface fluxes and radiation in a typical sheared tropical environment are presented. A non-hydrostatic, cloud-resolving numerical model containing sophisticated microphysical parametrizations as well as turbulence, surface flux and short/long-wave radiative representations was used. A predominant cloud-system hierarchy was identified: fast westward-moving mesoscale convective systems, producing extensive cirrus anvils and a strong radiative effect; and slow-moving regions of enhanced precipitation, causing a significant modification of the fast-moving cloudsystem behaviour on the time-scale of about one day. The experimental set-up was similar to that used by Sui et al. The demonstrated episodic convective activity and the fundamental role of organized deep convection by and large agrees with their analysis. However, despite many similarities, the results for the mean thermodynamic statistical equilibrium are dramatically different: a warm and humid regime, as opposed to the cold and dry regime of Sui et al. High relative humidities and very high upper-tropospheric cirrus cloud amount led to a strong greenhouse effect with low outgoing long-wave radiation at the top of the atmosphere (120–150 W m−2). At the same time, these clouds screened the ocean surface from the solar radiation and caused very low solar radiation absorption at the surface (only about 30 W m−2 when averaged over a diurnal cycle). The surface net cloud forcing was very large, about −200 W m−2 which is in accord with earlier findings of Ramanathan and Collins. The above numbers should be considered as an upper limit of effects of deep convection on radiative fluxes in the tropics because of the warm and moist regime demonstrated in the experiment.

The problem of radially directed fluid flow through a deformable porous shell is considered. General nonlinear diffusion equations are developed for spherical, cylindrical and planar geometries. Solutions for steady flow are found in terms of an exact integral and perturbation solutions are also developed. For unsteady flow, perturbation methods are used to find approximate small-time solutions and a solution valid for slow compression rates. These solutions are used to investigate the deformation of the porous material with comparisons made between the planar and the cylindrical geometries.