One-dimensional Cylindrical Geometry Research Articles

Numerical Study and Ann-Based Prediction for Stefan-Type Outward Ablation in One-Dimensional Cylindrical Geometry

Numerical Study and Ann-Based Prediction for Stefan-Type Outward Ablation in One-Dimensional Cylindrical Geometry

Surface modification with highly-homogeneous porous silica layer for enzyme immobilization in capillary enzyme microreactors

Immobilized enzyme micro-reactors (IMERs) are of vital importance in developing miniaturized bioanalytical systems and have promising applications in various biomanufacturing. An inherent limitation in designing IMERs is the one-dimensional cylindrical geometry of micro-channels that offers limited exposed surface area for molecular reorganization and enzyme immobilization. In this study, we report a robust capillary-IMER based on a three dimensional porous layer open tubular (3D-PLOT) column which is prepared by an easy-to-control surface modification strategy via single-step in situ biphasic reaction. The 3D-PLOT column with highly uniform porous geometry and narrow distribution of porosity can greatly enhance the surface-area-to-volume ratio of the micro-channels, showing the beneficial effects for enzyme immobilization to enhance reaction efficiency and shorten analysis time. Taking trypsin as a model enzyme, enzymatic activities of immobilized enzyme are analyzed. We compare enzyme assays using the proposed 3D-PLOT-IMER with those using normal capillary-IEMR without surface modification as well as free trypsin. The 3D-PLOT-IMER exhibits excellent stability and inter/intra-day reproducibility, and these characteristics imply the reliability of the proposed IMERs for accurate enzyme assay. The feasibility of the proposed method for potential application in biological analysis is demonstrated by coupling the 3D-PLOT-IMER with a nano-LC-MS/MS system for online digestion of standard proteins, cell extraction and living Hela cells. Our study show that the surface modification with the proposed 3D-porous layer is a simple and efficient approach for enzyme immobilization, and could be widely suitable for different kinds of IMERs.

On the necessity and the role of descriptors of neutron activated structural and shielding materials of nuclear installations for future decommissioning

Existing situation in nuclear industry is characterized with simultaneous development of the following two processes: design and construction of new generation of nuclear installations and decommissioning of installations of older generations. Significant amounts of radioactive wastes generated during the decommissioning phase are determined both for the first and the second types of installations by the induced activity of neutron irradiated structural and shielding materials. Concentration of the so-called radioactivity-hazardous nuclides in primary building and construction materials is the most important characteristics determining the resulting levels of induced activity. Values of these concentrations for the same type of material extracted from different geological deposits may differ by one or two orders of magnitude. Information about concentrations of radiation-hazardous elements in radiation shielding materials is fragmented and, as a rule, unsuitable for practical application. The purpose of the present study was to substantiate the necessity of compiling and recording the data on the concentrations of radioactivity-hazardous nuclides for building and structural materials for nuclear installations during the phases of design, operation and decommissioning. Three types of shielding concrete compositions were selected for the investigation. Concentrations of radioactivity-hazardous nuclides were mainly obtained by neutron activation technique. Neutron transport calculations were performed in one-dimensional cylindrical geometry at the core mid-plane according to usual core-vessel-shielding model of modern VVER reactor unit including 2-m thick concrete shield. Both transport and activation calculations were undertaken using modules of SCALE system. The obtained results allow estimating neutron-induced activation levels in the material as the function of irradiation time, amounts and categories of radioactive waste and their evolution during the decay time from 1 to 100 years. It was established that neutron-induced activity of shielding concrete strongly depends on the actual concentrations of radioactivity-hazardous nuclides in the concrete including ‘trace’ concentrations (other factors being the same). It was also shown that failure to take such concentrations into account may lead to the underestimation of neutron-induced activation levels and amounts of radioactive wastes and their category. The obtained results confirmed the necessity of compiling and maintaining data records on the concentrations of radioactivity-hazardous nuclides for materials used in structural and shielding materials of nuclear installations. Proposals were formulated on the potential accumulation of information, composition and formatting of descriptors of chemical composition of shielding and structural materials of nuclear installations.

Development of a fast reactor multigroup cross section generation code EXUS-F capable of direct processing of evaluated nuclear data files

Abstract The methods and performance of a fast reactor multigroup cross section (XS) generation code EXUS-F are described that is capable of directly processing Evaluated Nuclear Data File format nuclear data files. RECONR of NJOY is used to generate pointwise XS data, and Doppler broadening is incorporated by the Gauss–Hermite quadrature method. The self-shielding effect is incorporated in the ultrafine group XSs in the resolved and unresolved resonance ranges. Functions to generate scattering transfer matrices and fission spectrum matrices are realized. The extended transport approximation is used in zero-dimensional calculations, whereas the collision probability method and the method of characteristics are used for one-dimensional cylindrical geometry and two-dimensional hexagonal geometry problems, respectively. Verification calculations are performed first for various homogeneous mixtures and cylindrical problems. It is confirmed that the spectrum calculations and the corresponding multigroup XS generations are performed adequately in that the reactivity errors are less than 50 pcm with the McCARD Monte Carlo solutions. The nTRACER core calculations are performed with the EXUS-F–generated 47 group XSs for the two-dimensional Advanced Burner Reactor 1000 benchmark problem. The reactivity error of 160 pcm and the root mean square error of the pin powers of 0.7% indicate that EXUF-F generates properly the broad-group XSs.

Kinetic Diffusion Equation in a One-Dimensional Cylindrical Geometry

The neutron transport equation can be expressed in the form of the elementary diffusion equation. The kinetic equation in this form is defined as the kinetic diffusion equation. A derivation of the kinetic diffusion equation in a one-dimensional cylindrical geometry with arbitrary scattering anisotropy and an external source is presented. The principle for obtaining a numerical solution of the equation defined as the kinetic diffusion method is expounded. The physical meaning of the parameters in the equation is illustrated for the example of the numerical determination of the effective boundary condition on the surface of a black cylinder.

Capillary-based immunoassays, immunosensors and DNA sensors – steps towards integration and multi-analysis

This review deals with immunoassays, immunosensors and DNA sensors based on capillaries. The one-dimensional cylindrical geometry of capillaries offers several advantages over other types of solid supports. Capillary assays are fast, sensitive and easy to automate. The small capillary dimensions permit low consumption of reagents and samples, while capillary walls can act as light waveguides and fluid cells. We review detection schemes developed for capillary-based single-analyte and multi-analyte binding assays and sensors.

A Neutron Transport Benchmark in One-Dimensional Cylindrical Geometry: Revisited

A new benchmark for monoenergetic neutron transport in one-dimensional cylindrical geometry is presented. In the past, several accurate benchmarks (i.e., numerical solutions) in cylindrical geometry, based on the singular eigenfunction expansion of the solution to the corresponding pseudoproblem, have appeared in the literature. In the new formulation, called the direct FN method in cylindrical geometry, we base the FN solution directly on the integro-differential equation satisfied by the pseudoproblem. Through appropriate projections, a straightforward FN formulation results in singular integral equations for both the flux and current. Enhanced by convergence acceleration, the FN approximation accurately reproduces published benchmark solutions for both fixed sources and criticality. Thus, we have developed an entirely pedagogical self-contained and highly accurate benchmark based on an alternative application of FN theory.

Cryosurgery of Dunning AT-1 Rat Prostate Tumor: Thermal, Biophysical, and Viability Response at the Cellular and Tissue Level

This study investigates cryodestruction of the Dunning AT-1 rat prostate tumor at the single cell, tissue slice, andin vivolevels. The thermal history around a 3-mm-diameter cylindrical cryosurgical probe was predicted by solving the bioheat equation in a one-dimensional cylindrical geometry. At various radial positions in the iceball this thermal history was approximated by a constant cooling rate and a final, steady-state temperature (or end-temperature). The predicted cooling rates and end temperatures ranged from ≥1000°C/min to 5°C/min and −196°C to −20°C, respectively. These cooling rates and end-temperatures were then imposed on single AT-1 cells, AT-1 tissue slicesin vitroand AT-1 tumorsin vivo.The single cells and tissue slices were frozen by LN2immersion, copper block slam-freezing, or controlled cooling on a cryomicroscope or a directional solidification stage. LN2immersion is lethal to AT-1 cells (presumably due to intracellular ice formation), while cooling at 5–100°C/min leaves some viable cells (at end-temperatures ranging between −20 and −40°C). AT-1 tumor slices show extensive intracellular ice formation due to slam cooling, extensive dehydration at 100°C/min, and total dehydration at rates ≤10°C/min to end temperatures below −10°C. Postfreeze culture and histology of the AT-1 tissue show that extensive intracellular ice formation is lethal, while cellular dehydration and vascular engorgement leave viable cells (at end-temperatures between −20 and −40°C). Based solely on the single cell andin vitrotissue damage achieved by cooling rates and end-temperatures, a sizable portion of a cryosurgically frozen tumor would be expected to survive. However,in vivocryosurgery performed on AT-1 tumors demonstrated that the tissue was damaged throughout the cryolesion, even at the periphery where the thermal history would be expected to allow single cells and tissue slices to survivein vitro.Taken together, these results suggest that damage mechanisms other than those due to cooling rate and end-temperature may be responsible for the increased cellular destruction at the periphery of the iceballin vivoand that cooling rate is less important than end-temperature in determining cryosurgical damage in AT-1 tumors. Experiments are ongoing to determine if the time held at an end temperature, thawing rate, vascular response, or other mechanisms are primarily responsible for the enhanced destructive capabilityin vivo.

Solution of the transport equation in integral form in a one-dimensional cylindrical geometry with linearly anisotropic scattering

Solution of the transport equation in integral form in a one-dimensional cylindrical geometry with linearly anisotropic scattering

An Ne-like Fe laser resonantly photo-pumped by Ne X Ly-α radiation

We propose using the Ne X Ly-α emission line generated by a neon Z-pinch to photo-pump neon-like iron ( Z=26) resonantly and produce lasing on several 3 p→3 s transitions ranging from 200 to 400 Å. By modeling the Ne Z-pinch output obtained on SATURN experiments as an X-ray source, the time-dependent properties of the Fe lasant are studied. The effect on the gain of varying parameters such as the ion density of the Fe lasant and the output of the Z-pinch is investigated. Our model yields a maximum gain of 4 and 13 cm -1 on the dominant laser lines at 254 and 387 Å, respectively. However when the impact of radiation transfer on the gain of the various laser lines is considered in a one-dimensional cylindrical geometry, more realistic gains of 2–4 cm -1 are calculated on these lines.

A new 3He gas loop blanket for fusion reactor systems

A new concept of tritium breeding blankets is introduced for fusion reactor systems using a 3He gas loop combined with neutron multipliers and moderators. To verify the tritium breeding capability of this 3He based blanket, several neutronic calculations have been made in one-dimensional cylindrical geometry and compared with those for the current Li based blankets. The results show that the tritium breeding ratio of the 3He gas loop blanket can exceed unity with a reasonable blanket thickness. In particular, the possibility of a “thin” tritium breeding blanket is suggested in a homogenized system of Be and 3He. With these neutronic survey calculations, the T-3He fuel cycle has been modelled to estimate the required amounts of tritium and 3He supplies. The feasibility of the 3He gas loop blanket system is discussed through considerations on the merits of this T-3He fuel cycle.

The characteristic equation in radiation transport problems in elongated cylindrical regions

To investigate asymptotic phenomena in radiation transport problems in elongated, convex, vertically homogeneous, cylindrical regions, an equation is constructed which is similar to the transport equation in one-dimensional cylindrical geometry. It plays the role of the characteristic equation. Using the theory of completely continuous operators, the spectrum of the equation is studied, and the properties of the first eigenvalue are establishing as a function of the asymptotic parameter k≡ (−1, +1). Analysis of these properties implies that the characteristic equation is solvable at least in problems with isotropic scattering, provided the cross-sectional diameter of the region is sufficiently large.

Analysis and elimination of the discrete-ordinates flux dip

Abstract A new theoretical analysis is presented for the discrete-ordinates flux dip in one-dimensional spherical geometry. It is found that the flux dip is due to an inconsistency between the discrete-ordinates equations (in the diffusion limit) and the diffusion equation. It is theoretically shown that this inconsistency (and hence the flux dip) can be completely eliminated through the use of a simple angular weighted-diamond difference scheme. Computational results are given which confirm the theoretical analysis. The technique has been extended to one-dimensional cylindrical geometry and has been found to be equally effective. Extensions to multi-dimensional geometries appear to be straightforward, but they have not been investigated.

Benchmark Values for Monoenergetic Neutron Transport in One-Dimensional Cylindrical Geometry with Linearly Anisotropic Scattering

The integral transform method (ITN) has been extended to the treatment of one-dimensional homogeneous media with linearly anisotropic scattering. A previously obtained formula linking the isotropic and the anisotropic one-dimensional kernels allows for calculation of the anisotropic matrix elements in the form of linear combinations of a few isotropic matrix elements. In practice, to solve the anisotropic problem of order N one needs only to calculate the isotropic collision matrix of order (N + 2) in plane and spherical geometries and of order (N + 1) in cylindrical geometry. The method is applied to the calculation of critical parameters for bare cylinders. Highly accurate values, to be used as benchmarks, are obtained and illustrate the precision and fast convergence rate of the method.

Evaluation of the Radiative Heat Flux in Absorbing, Emitting and Linear-Anisotropically Scattering Cylindrical Media

The contribution of thermal radiation to heat transfer in an emitting, absorbing and linear-anisotropically scattering medium of one-dimensional cylindrical geometry is investigated. It is assumed that the radial temperature distribution in the medium is known or is found in conjunction with overall conservation of energy. The exact solution results in a first-order integral equation in the radial coordinate which is a substantial improvement over previous formulations developed for nonscattering media. Also, two approximate methods are established and tested for their accuracy. The first method is the differential approximation modified to accommodate linear-anisotropic scattering. The second method consists of an exponential kernel approximation in which the geometric integrand functions are replaced by simple exponential functions. The results presented indicate that in engineering applications either approximate method may be used to accurately model the radiative contribution to overall heat transfer rates, reducing the nonlinear integrodifferential energy conservation equation to a nonlinear differential equation.

Investigations of the suitability of the reflector drums as control mechanism for thermionic reactors in space craft with 233U as fuel and ZrH1,7 as moderator

The suitability of borated reflector drums has been investigated and shown as a control mechanism for thermomionic space craft reactors with 233U as fuel and ZrH1,7 as moderator due mainly to their extreme compactness. By optimal total cost of the reactor a reactivity change of 12% has been achieved. This allows the use of reflector drums which keep the cone diameter and the mass of the radiation shield to a minimum. In addition, reflector drums do not cause any kinematical disturbance.All important neutron physics calculations have been carried out with the multigroup SN methods. 123 energy groups, S4-P3 approximation by one-dimensional cylindrical geometry and four energy groups, S4-P1 approximation by r-θ geometry have been used.Further, the behaviour of the neutron generation density function during different phases of the reactor control operation has been investigated.

Calculating Space-Dependent Reactor Transfer Functions Using Statics Techniques

A method has been developed by which statics techniques can be used to calculate source transfer functions in the multigroup, multidimensional approximation. With the flux resolved into steady and fluctuating components, the time-dependent neutron balance equations are satisfied by the fluctuating part alone. Assuming that the external source and the flux response are sinusoidal, the original time-dependent equations transform into a set of complex equations dependent on space and frequency but independent of time. Separating the equations into real and imaginary parts yields coupled, inhomogeneous differential equations (two for each group). These can be solved by well-known statics techniques for the real and imaginary components φR and φI of the complex amplitudes of the fluxes, in turn yielding the gain and phase shift for each frequency of interest.This method was applied to the NORA reactor for which the space-dependent transfer function had been determined experimentally. The two-group telegrapher's equations were programmed for one-dimensional cylindrical geometry and the difference equations solved by direct matrix inversion and also by interative techniques. Results of the calculations closely reproduce the reported experimental results for gain and phase shift.

Effective Diffusion Coefficient in Void Regions

"Effective Diffusion Coefficient in Void Regions." Nuclear Science and Engineering, 13(2), p. 200