Ratzel, A. C., III; Howell, J. R.
Radiative energy transfer in a gray absorbing, emitting and isotropically scattering medium is considered in a two-dimensional (2-D) rectangular enclosure using the P-N differential approximation. The 2-D moment of intensity partial differential equations (PDE's) are combined to yield a single second-order PDE for the P-1 approximation and four coupled second-order PDE's for the P-3 approximation. P-1 approximation results are obtained from separation of variables solutions, and P-3 results are obtained numerically using successive-over-relaxation methods. The P-N approximation results are compared with numerical Hottel zone results and with results from an approximation method developed by Modest. The studies show that the P-3 approximation can be used to predict emissive power distributions and heat transfer rates in 2-D media with opacities of unity or greater. The P-1 approximation is identical to the diffusion solution and is thus applicable only if the medium is optically dense.
Ratzel, A. C., III; Howell, J. R.
The combined steady state conduction and radiation heat transfer problem for a gray medium within a rectangular enclosure is considered using the differential approximation. The P-1 and P-3 spherical harmonics approximations for the intensity distribution are incorporated in the equation of transfer, and modified Marshak-type boundary conditions are used in the formulation. The enclosure walls are assumed to be isothermal black surfaces. Two and five coupled second-order nonlinear partial differential equations are developed for the P-1 and P-3 approximations, respectively, using the energy conservation and moment of intensity expressions. The P-1 equations have been numerically solved using finite element techniques, while the P-3 relations have been solved using a finite difference successive-over-relaxation (SOR) algorithm. Two-dimensional temperature profiles and hot wall heat transfer results are presented for square enclosures and different optical width rectangular enclosures for a range of conduction-radiation parameters.
Ratzel, A. C., III; Howell, J. R.
The combined steady state conduction and radiation heat transfer problem for a gray medium within a rectangular enclosure is considered using the differential approximation. The P-1 and P-3 spherical harmonics approximations for the intensity distribution are incorporated in the equation of transfer, and modified Marshak-type boundary conditions are used in the formulation. The enclosure walls are assumed to be isothermal black surfaces. Two and five coupled second order nonlinear partial differential equations are developed for the P-1 and P-3 approximations, respectively, using the energy conservation and moment-of-intensity expressions. The P-1 equations have been numerically solved using finite element techniques, while the P-3 relations have been solved using a finite difference successive-over-relaxation (SOR) algorithm. Two dimensional temperature profiles and hot wall heat transfer results are presented for square enclosures and different optical width rectangular enclosures for a range of Stark numbers.
Brantley, Patrick Shawn
geometry PN approximation. The SPN approximation was proposed in the early 1960's but has not gained wide acceptance because of its weak theoretical basis. Our goal is to establish a sound theoretical basis for the Simplified PN approximation, in the hopes that it will find broader application with increased confidence. In particular, we examine the Simplified P3 approximation and show that it more accurately computes higher-order spatial and angular moments than the P1 (diffusion) approximation. Then, we derive the multigroup Simplified P3 approximation using a variational analysis that yields the SP3 equations along with interface and Marshak-like boundary conditions. We also develop an efficient explicit iterative algorithm for solving the multigroup SP3 equations. Finally, we present numerical solutions of transport problems that verify the accuracy of the multigroup SP3 approximation.
Ivanov, Boyan D.
The progress in the Nuclear Engineering field leads to developing new generations of Nuclear Power Plants (NPP) with complex rector core designs, such as cores loaded partially with mixed-oxide (MOX) fuel, high burn-up loadings, and cores with advanced designs of fuel assemblies and control rods. Such heterogeneous cores introduce challenges for the diffusion theory that has been used for several decades for calculations of the current Pressurized Water Rector (PWR) cores. To address the difficulties the diffusion approximation encounters new core calculation methodologies need to be developed by improving accuracy, while preserving efficiency of the current reactor core calculations. In this thesis, an advanced core calculation methodology is introduced, based on embedded transport calculations. Two different approaches are investigated. The first approach is based on embedded finite element (FEM), simplified P3 approximation (SP3), fuel assembly (FA) homogenization calculation within the framework of the diffusion core calculation with NEM code (Nodal Expansion Method). The second approach involves embedded FA lattice physics eigenvalue calculation based on collision probability method (CPM) again within the framework of the NEM diffusion core calculation. The second approach is superior to the first because most of the uncertainties introduced by the off-line cross-section generation are eliminated.
Finlay, Jarod C.; Zhu, Timothy C.; Dimofte, Andreea; Friedberg, Joseph S.; Cengel, Keith A.; Hahn, Stephen M.
We present the results of a series of spectroscopic measurements made in vivo in patients undergoing photodynamic therapy (PDT). The patients studied here were enrolled in Phase II clinical trials of Photofrin-mediated PDT for the treatment of non-small cell lung cancer and cancers with pleural effusion. Patients were given Photofrin at dose of 2 mg per kg body weight 24 hours prior to treatment. Each patient received surgical debulking of the tumor followed by intracavity PDT at 630nm to a dose of 60 J/cm2. Dose was monitored continuously using implanted isotropic fiber-based light detectors. We measured the diffuse reflectance spectra before and after PDT in various positions within the cavity, including tumor, diaphragm, pericardium, skin, and chest wall muscle in 10 patients. The measurements were acquired using a specially designed fiber optic-based probe consisting of one fluorescence excitation fiber, one white light delivery fiber, and 9 detection fibers spaced at distances from 0.36 to 7.8 mm from the source, all of which are imaged via a spectrograph onto a CCD, allowing measurement of radially-resolved diffuse reflectance and fluorescence spectra. The absorption spectra were analyzed using an analytical model of light propagation in diffuse media based on the P3 approximation to radiative transport, assuming a known basis set of absorbers including hemoglobin in its oxygenated and deoxygenated forms and Photofrin. We find significant variation in hemodynamics and sensitizer concentration among patients and within tissues in a single patient.
Pérez-González, Adriana; Galano, Annia
The electron-donating capability (EDC) and the ease of deprotonation (ED) of 26 edaravone derivatives have been evaluated. Their first ionization energies have been used to assess their EDC. Four different approaches to obtain vertical ionization energies were tested, using a set of structurally related compounds. Those based on the electron propagator theory (EPT) were identified as the best ones. In particular, the partial third order (P3) approximation led to the lowest mean unsigned error (MUE = 0.10 eV). Two descriptors were used to evaluate ED: the proton affinity (PA) and the pK(a). It was found that pK(a) values are better descriptors than PA values. Ideal candidates to perform as efficiently as, or even better than, edaravone itself are proposed. The recommendations were based on the simultaneous analyses of EDC and ED, and they should be particularly valid when the electron transfer mechanism plays an important role in the antioxidant activity of the studied compounds. © 2011 American Chemical Society
Übeyli, Mustafa; Yapıcı, Hüseyin
ARIES-RS is one of the major magnetic fusion energy reactor designs that uses a blanket having vanadium alloy structure cooled by lithium [1, 2]. It is a deuterium-tritium (DT) fusion driven reactor, having a fusion power of 2170 MW [1, 2]. This study presents the neutronic analysis of the ARIES-RS fusion reactor using heavy metal molten salts in which Li2BeF4 as the main constituent was mixed with increased mole fractions of heavy metal salt (ThF4 or UF4) starting by 2 mol.% up to 12 mol.%. Neutron transport calculations were carried out with the help of the SCALE 4.3 system by solving the Boltzmann transport equation with the XSDRNPM code in 238 neutron groups and a S 8- P 3 approximation. According to the numerical results, tritium self-sufficiency was attained for the coolants, Flibe with 2% UF4 or ThF4 and 4% UF4. In addition, higher energy multiplication values were found for the salt with UF4 compared to that with ThF4. Furthermore, significant amount of high quality nuclear fuel was produced to be used in external reactors.
Xu, Kexin; Han, Yonghui; Ni, Yong; Hu, Youzhou
Accurate measurement of tissue optical properties is a key problem in study on optical distribution in tissue. Especially in near infrared range, it is still a hard problem because of affection of strong absorption of water. In this paper, P3 approximation for high absorption was applied theoretically, then device with high precision was designed experimentally for non-scattering transmission measurement and fluence rate measurement. SNR and measuring accuracy were improved by using dual-beam. With added absorber technique at both 632.8nm and 1064nm, optical parameters of 2% intralipid at 1064nm and 1% intralipid at 632.8nm wavelength were obtained. The radial distribution of light through application of Monte Carlo simulation agreed well with the experimental result, which indicated that the experiment system were accurate with root mean square (RMS) less than 8%, and that CuSO4 as added absorber at 1064nm and NIR was feasible. Optical parameters of turbid media can be measured in NIR.
Joint derivation method for determining optical properties based on steady-state spatially resolved diffuse reflectance measurement at small source-detector separations and large reduced albedo range: theory and simulation.
Shi, Zhenzhi; Fan, Ying; Zhao, Huijuan; Xu, Kexin
Accurate determination of the optical properties (the absorption coefficient μ(a) and the reduced scattering coefficient μ(s) (')) of tissues is very important in a variety of diagnostic and therapeutic procedures. Optical diffusion theory is frequently used as the forward model for describing the photon transfer in media with large reduced albedos (a(')) and in large source-detector separations (SDS). Several other methods (PN approximation, hybrid diffusion-P3 approximation) have also been published that describe photon transfer in media with low a(') or small SDSs. We studied the theoretical models for the steady-state spatially resolved diffuse reflectance measurement to accurately determine μ(a) and μ(s) (') at large a(') range but small SDSs. Instead of using a single model, a joint derivation method is proposed. The developed method uses one of the best aforementioned theoretical methods separately in five ranges of a(') determined from several forward models. In the region of small SDSs (the range between 0.4 and 8 mm) and large a(') range (between 0.5 and 0.99), the best theoretical derivation model was determined. The results indicate that the joint derivation method can improve the derivation accuracy and that a(') range can be determined by the steady-state spatially resolved diffuse reflectance measurement.
Two methods for determining the diffusion parameters of thermal neutrons for non-moderator and non-multiplicator media have been developed. The first one, which is a pulsed method, is based on thermal neutrons relaxation coefficients measurement in a moderator, with and without the medium of interest that plays the role of reflector. For the experimental results interpretation using the diffusion theory, a corrective factor which takes into account the neutron cooling by diffusion has been introduced. Its dependence on the empirically obtained relaxation coefficients is in a good agreement with the calculations made in P3L2 approximation. The difference between linear extrapolation lengths of the moderator and the reflector has been taken into account, by developing the scalar fluxes in Bessel function series which automatically satisfy the boundary conditions at the extrapolated surfaces of the two media. The obtained results for iron are in a good agreement with those in the literature. The second method is time independent, based on the 'flux albedo' measurements interpretation (concept introduced by Amaldi and Fermi) by P3 approximation in the one group transport theory. The independent sources are introduced in the Marshak boundary conditions. An angular albedo matrix has been used to deal with multiple reflections and to take into account the distortion of the current vector when entering a medium, after being reflected by this latter. The results obtained by this method are slightly different from those given in the literature. The analysis of the possible sources causing this discrepancy, particulary the radial distribution of flux in cylindrical geometry and the flux depression at medium-black body interface, has shown that the origin of this discrepancy is the neutron heating by diffusion.
Corzo, H H; Galano, Annia; Dolgounitcheva, O; Zakrzewski, V G; Ortiz, J V
Two accurate and computationally efficient electron-propagator (EP) methods for calculating the valence, vertical ionization energies (VIEs) of closed-shell molecules have been identified through comparisons with related approximations. VIEs of a representative set of closed-shell molecules were calculated with EP methods using 10 basis sets. The most easily executed method, the diagonal, second-order (D2) EP approximation, produces results that steadily rise as basis sets are improved toward values based on extrapolated coupled-cluster singles and doubles plus perturbative triples calculations, but its mean errors remain unacceptably large. The outer valence Green function, partial third-order and renormalized partial third-order methods (P3+), which employ the diagonal self-energy approximation, produce markedly better results but have a greater tendency to overestimate VIEs with larger basis sets. The best combination of accuracy and efficiency with a diagonal self-energy matrix is the P3+ approximation, which exhibits the best trends with respect to basis-set saturation. Several renormalized methods with more flexible nondiagonal self-energies also have been examined: the two-particle, one-hole Tamm-Dancoff approximation (2ph-TDA), the third-order algebraic diagrammatic construction or ADC(3), the renormalized third-order (3+) method, and the nondiagonal second-order renormalized (NR2) approximation. Like D2, 2ph-TDA produces steady improvements with basis set augmentation, but its average errors are too large. Errors obtained with 3+ and ADC(3) are smaller on average than those of 2ph-TDA. These methods also have a greater tendency to overestimate VIEs with larger basis sets. The smallest average errors occur for the NR2 approximation; these errors decrease steadily with basis augmentations. As basis sets approach saturation, NR2 becomes the most accurate and efficient method with a nondiagonal self-energy.
Marin, Nena Maribel
Fluorescence and diffuse reflectance spectroscopy are two new optical technologies, which have shown promise to aid in the real time, non-invasive identification of cancers and precancers. Spectral patterns carry a fingerprint of scattering, absorption and fluorescence properties in tissue. Scattering, absorption and fluorescence in tissue are directly affected by biological features that are diagnostically significant, such as nuclear size, micro-vessel density, volume fraction of collagen fibers, tissue oxygenation and cell metabolism. Thus, analysis of spectral patterns can unlock a wealth of information directly related with the onset and progression of disease. Data from a Phase II clinical trial to assess the technical efficacy of fluorescence and diffuse reflectance spectroscopy acquired from 850 women at three clinical locations with two research grade optical devices is calibrated and analyzed. Tools to process and standardize spectra so that data from multiple spectrometers can be combined and analyzed are presented. Methodologies for calibration and quality assurance of optical systems are established to simplify design issues and ensure validity of data for future clinical trials. Empirically based algorithms, using multivariate statistical approaches are applied to spectra and evaluated as a clinical diagnostic tool. Physically based algorithms, using mathematical models of light propagation in tissue are presented. The presented mathematical model combines a diffusion theory in P3 approximation reflectance model and a 2-layer fluorescence model using exponential attenuation and diffusion theory. The resulting adjoint fluorescence and reflectance model extracts twelve optical properties characterizing fluorescence efficiency of cervical epithelium and stroma fluorophores, stromal hemoglobin and collagen absorption, oxygen saturation, and stromal scattering strength and shape. Validations with Monte Carlo simulations show that adjoint model extracted