Numerical algorithm for spectroscopic ellipsometry of thick transparent films

We present a numerical method for spectroscopic ellipsometry of thick transparent films. When an analytical expression for the dispersion of the refractive index (which contains several unknown coefficients) is assumed, the procedure is based on fitting the coefficients at a fixed thickness. Then the thickness is varied within a range (according to its approximate value). The final result given by our method is as follows: The sample thickness is considered to be the one that gives the best fitting. The refractive index is defined by the coefficients obtained for this thickness.

Using numerical classification of profiles based on Vis-NIR spectra to distinguish soils from the Piracicaba Region, Brazil

Considering that information from soil reflectance spectra is underutilized in soil classification, this paper aimed to evaluate the relationship of soil physical, chemical properties and their spectra, to identify spectral patterns for soil classes, evaluate the use of numerical classification of profiles combined with spectral data for soil classification. We studied 20 soil profiles from the municipality of Piracicaba, State of São Paulo, Brazil, which were morphologically described and classified up to the 3rd category level of the Brazilian Soil Classification System (SiBCS). Subsequently, soil samples were collected from pedogenetic horizons and subjected to soil particle size and chemical analyses. Their Vis-NIR spectra were measured, followed by principal component analysis. Pearson's linear correlation coefficients were determined among the four principal components and the following soil properties: pH, organic matter, P, K, Ca, Mg, Al, CEC, base saturation, and Al saturation. We also carried out interpretation of the first three principal components and their relationships with soil classes defined by SiBCS. In addition, numerical classification of the profiles based on the OSACA algorithm was performed using spectral data as a basis. We determined the Normalized Mutual Information (NMI) and Uncertainty Coefficient (U). These coefficients represent the similarity between the numerical classification and the soil classes from SiBCS. Pearson's correlation coefficients were significant for the principal components when compared to sand, clay, Al content and soil color. Visual analysis of the principal component scores showed differences in the spectral behavior of the soil classes, mainly among Argissolos and the others soils. The NMI and U similarity coefficients showed values of 0.74 and 0.64, respectively, suggesting good similarity between the numerical and SiBCS classes. For example, numerical classification correctly distinguished Argissolos from Latossolos and Nitossolos. However, this mathematical technique was not able to distinguish Latossolos from Nitossolos Vermelho férricos, but the Cambissolos were well differentiated from other soil classes. The numerical technique proved to be effective and applicable to the soil classification process.

Flow structures at an idealized bifurcation : a numerical experiment

River bifurcations are key nodes within braided river systems controlling the flow and sediment partitioning and therefore the dynamics of the river braiding process. Recent research has shown that certain geometrical configurations induce instabilities that lead to downstream mid-channel bar formation and the formation of bifurcations. However, we currently have a poor understanding of the flow division process within bifurcations and the flow dynamics in the downstream bifurcates, both of which are needed to understand bifurcation stability. This paper presents results of a numerical sensitivity experiment undertaken using computational fluid dynamics (CFD) with the purpose of understanding the flow dynamics of a series of idealized bifurcations. A geometric sensitivity analysis is undertaken for a range of channel slopes (0.005 to 0.03), bifurcation angles (22 degrees to 42 degrees) and a restricted set of inflow conditions based upon simulating flow through meander bends with different curvature on the flow field dynamics through the bifurcation. The results demonstrate that the overall slope of the bifurcation affects the velocity of flow through the bifurcation and when slope asymmetry is introduced, the flow structures in the bifurcation are modified. In terms of bifurcation evolution the most important observation appears to be that once slope asymmetry is greater than 0.2 the flow within the steep bifurcate shows potential instability and the potential for alternate channel bar formation. Bifurcation angle also defines the flow structures within the bifurcation with an increase in bifurcation angle increasing the flow velocity down both bifurcates. However, redistributive effects of secondary circulation caused by upstream curvature can very easily counter the effects of local bifurcation characteristics. Copyright (C) 2011 John Wiley & Sons, Ltd.

First-principles periodic calculation of four-body spin terms in high-Tc cuprate superconductors

A general mapping between the energy of pertinent magnetic solutions and the diagonal terms of the spin Hamiltonian in a local representation provides the first general framework to extract accurate values for the many body terms of extended spin Hamiltonians from periodic first-principle calculations. Estimates of these terms for La2CuO4, the paradigm of high-Tc superconductor parent compounds, and for the SrCu2O3 ladder compound are reported. For La2CuO4, present results support experimental evidence by Toader et al. [Phys. Rev. Lett. 94, 197202 (2005)]. For SrCu2O3 even larger four-body spin amplitudes are found together with Jl/Jr=1 and non-negligible ferromagnetic interladder exchange.

First-principles periodic calculation of four-body spin terms in high-Tc Cuprate superconductors

A general mapping between the energy of pertinent magnetic solutions and the diagonal terms of the spin Hamiltonian in a local representation provides the first general framework to extract accurate values for the many body terms of extended spin Hamiltonians from periodic first-principle calculations. Estimates of these terms for La2CuO4, the paradigm of high-Tc superconductor parent compounds, and for the SrCu2O3 ladder compound are reported. For La2CuO4, present results support experimental evidence by Toader et al. [Phys. Rev. Lett. 94, 197202 (2005)]. For SrCu2O3 even larger four-body spin amplitudes are found together with Jl/Jr=1 and non-negligible ferromagnetic interladder exchange.

State-to-state reaction probabilities within the quantum transition state framework

Rigorous quantum dynamics calculations of reaction rates and initial state-selected reaction probabilities of polyatomic reactions can be efficiently performed within the quantum transition state concept employing flux correlation functions and wave packet propagation utilizing the multi-configurational time-dependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of state-to-state reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H2(ν, j) → HD(ν′, j′) + H reaction for J = 0.

Prothèses totales de genoux. Analyse clinique et numérique des micromouvements de l'implant tibial [Total knee prosthesis. Clinical and numerical study of micromovements of the tibial implant].

INTRODUCTION: The importance of the micromovements in the mechanism of aseptic loosening is clinically difficult to evaluate. To complete the analysis of a series of total knee arthroplasties (TKA), we used a tridimensional numerical model to study the micromovements of the tibial implant. MATERIAL AND METHODS: Fifty one patients (with 57 cemented Porous Coated Anatomic TKAs) were reviewed (mean follow-up 4.5 year). Radiolucency at the tibial bone-cement interface was sought on the AP radiographs and divided in 7 areas. The distribution of the radiolucency was then correlated with the axis of the lower limb as measured on the orthoradiograms. The tridimensional numerical model is based on the finite element method. It allowed the measurement of the cemented prosthetic tibial implant's displacements and the micromovements generated at bone-ciment interface. A total load (2000 Newton) was applied at first vertically and asymetrically on the tibial plateau, thereby simulating an axial deviation of the lower limbs. The vector's posterior inclination then permitted the addition of a tangential component to the axial load. This type of effort is generated by complex biomechanical phenomena such as knee flexion. RESULTS: 81 per cent of the 57 knees had a radiolucent line of at least 1 mm, at one or more of the tibial cement-epiphysis jonctional areas. The distribution of these lucent lines showed that they came out more frequently at the periphery of the implant. The lucent lines appeared most often under the unloaded margin of the tibial plateau, when axial deviation of lower limbs was present. Numerical simulations showed that asymetrical loading on the tibial plateau induced a subsidence of the loaded margin (0-100 microns) and lifting off at the opposite border (0-70 microns). The postero-anterior tangential component induced an anterior displacement of the tibial implant (160-220 microns), and horizontal micromovements with non homogenous distribution at the bone-ciment interface (28-54 microns). DISCUSSION: Comparison of clinical and numerical results showed a relation between the development of radiolucent lines and the unloading of the tibial implant's margin. The deleterious effect of lower limbs' axial deviation is thereby proven. The irregular distribution of lucent lines under the tibial plateau was similar of the micromovements' repartition at the bone-cement interface when tangential forces were present. A causative relation between the two phenomenaes could not however be established. Numerical simulation is a truly useful method of study; it permits to calculate micromovements which are relative, non homogenous and of very low amplitude. However, comparative clinical studies remain as essential to ensure the credibility of results.

A Monte Carlo-based procedure for independent monitor unit calculation in IMRT treatment plans.

Intensity-modulated radiotherapy (IMRT) treatment plan verification by comparison with measured data requires having access to the linear accelerator and is time consuming. In this paper, we propose a method for monitor unit (MU) calculation and plan comparison for step and shoot IMRT based on the Monte Carlo code EGSnrc/BEAMnrc. The beamlets of an IMRT treatment plan are individually simulated using Monte Carlo and converted into absorbed dose to water per MU. The dose of the whole treatment can be expressed through a linear matrix equation of the MU and dose per MU of every beamlet. Due to the positivity of the absorbed dose and MU values, this equation is solved for the MU values using a non-negative least-squares fit optimization algorithm (NNLS). The Monte Carlo plan is formed by multiplying the Monte Carlo absorbed dose to water per MU with the Monte Carlo/NNLS MU. Several treatment plan localizations calculated with a commercial treatment planning system (TPS) are compared with the proposed method for validation. The Monte Carlo/NNLS MUs are close to the ones calculated by the TPS and lead to a treatment dose distribution which is clinically equivalent to the one calculated by the TPS. This procedure can be used as an IMRT QA and further development could allow this technique to be used for other radiotherapy techniques like tomotherapy or volumetric modulated arc therapy.

Stochastic models and numerical algorithms for a class of regulatory gene networks.

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

Calculation of wood volume and stem taper using terrestrial single-image close-range photogrammetry and contemporary software tools

Abstract

Accuracy of out-of-field dose calculation of tomotherapy and cyberknife treatment planning systems: A dosimetric study.

PURPOSE: Late toxicities such as second cancer induction become more important as treatment outcome improves. Often the dose distribution calculated with a commercial treatment planning system (TPS) is used to estimate radiation carcinogenesis for the radiotherapy patient. However, for locations beyond the treatment field borders, the accuracy is not well known. The aim of this study was to perform detailed out-of-field-measurements for a typical radiotherapy treatment plan administered with a Cyberknife and a Tomotherapy machine and to compare the measurements to the predictions of the TPS. MATERIALS AND METHODS: Individually calibrated thermoluminescent dosimeters were used to measure absorbed dose in an anthropomorphic phantom at 184 locations. The measured dose distributions from 6 MV intensity-modulated treatment beams for CyberKnife and TomoTherapy machines were compared to the dose calculations from the TPS. RESULTS: The TPS are underestimating the dose far away from the target volume. Quantitatively the Cyberknife underestimates the dose at 40cm from the PTV border by a factor of 60, the Tomotherapy TPS by a factor of two. If a 50% dose uncertainty is accepted, the Cyberknife TPS can predict doses down to approximately 10 mGy/treatment Gy, the Tomotherapy-TPS down to 0.75 mGy/treatment Gy. The Cyberknife TPS can then be used up to 10cm from the PTV border the Tomotherapy up to 35cm. CONCLUSIONS: We determined that the Cyberknife and Tomotherapy TPS underestimate substantially the doses far away from the treated volume. It is recommended not to use out-of-field doses from the Cyberknife TPS for applications like modeling of second cancer induction. The Tomotherapy TPS can be used up to 35cm from the PTV border (for a 390 cm(3) large PTV).

Evolution of Coordination in Social Networks: A Numerical Study

Coordination games are important to explain efficient and desirable social behavior. Here we study these games by extensive numerical simulation on networked social structures using an evolutionary approach. We show that local network effects may promote selection of efficient equilibria in both pure and general coordination games and may explain social polarization. These results are put into perspective with respect to known theoretical results. The main insight we obtain is that clustering, and especially community structure in social networks has a positive role in promoting socially efficient outcomes.