Relative Rms Deviations Research Articles

Effective thermal conductivity of high porosity open-cell metal foams

In this paper, a model for effective thermal conductivity of high porosity open-cell metal foams is developed by assuming the foam morphology as 3D tetradecahedron structure. The effective thermal conductivity of metal foams is first studied using the numerical simulation method, which the geometrical model (the ratio of the edge length of node to the radius of ligament) is calibrated with the experimental data. The geometrical model is divided into four distinctive layers along the heat transfer direction. The effective thermal conductivity of four layers is then determined by fitting the numerical results. Consequently, the model for effective thermal conductivity of metal foams is proposed based on the Fourier law. Several other analytical models and the experimental data are used to verify the effectiveness of the present model. The results show that the present model can be satisfactorily accurate to calculate the effective thermal conductivity of metal foam by considering the ratio of the edge length of node to the radius of ligament as a second order polynomial function of the porosity. The effective thermal conductivity of each layer is related to the porosity of each layer and overall porosity of metal foam. Compared with the experimental data, the present model has high accuracy with relative RMS deviation of less than 10%. The finding of this study can help guide the thermal design of porous media.

Brightness-dependent Tarpley model for global solar radiation estimation using GOES satellite images: Application to Uruguay

A statistical model based on Tarpley’s original solar irradiation model is proposed and evaluated using data from seven new ground stations in Uruguay. The model estimates hourly global solar irradiation on a horizontal surface using GOES-East satellite images. We show that the introduction of a simple brightness dependence in the model parameters drastically improves the accuracy of the estimates. The implementations of the original and the improved models are explained in detail. For each case, the parameters are adjusted using controlled quality solar irradiation data and a comprehensive performance analysis, on an hourly and daily basis, is carried out using data from independent measurement sites. The relative RMS deviations for the estimates of the brightness-dependent model are 7.1% for the daily estimates and 14.0% for the hourly estimates, relative to the mean of the measurements. This represents a reduction of approximately 45% (daily) and 25% (hourly) in the relative RMS deviations of the original model. The improved model provides a good balance between simplicity and accuracy.

SU‐E‐T‐334: Clinical Implementation of Gating and Dose Verification with Scanned Ion Beams at HIT

Purpose: Medical physics aspects of gated irradiation to moving tumors using scanned ion beams. Methods: At our institute, more than 700 patients have been treated with proton and carbon ion beams since its start. The first patient has now been treated with the application of gating. For this purpose, the Anzai respiratory motion detection and gating system was interfaced with the treatment control system such as to control spill pausing. The patient presented with a liver tumor moving with peak‐to‐peak amplitude of ∼1cm due to breathing. Treatment planning was performed using the Siemens Syngo RT‐Planning system on a 3DCT dataset. The gating window was determined from 4DCT. Plan verification was performed in a motion phantom, consisting of a PMMA block equipped with a 3D set of 24 pinpoint chambers mounted on the Quasar moving platform. The breathing motion perpendicular to the beam was simulated based on the trajectory obtained from the Anzai system during 4DCT acquisition. Dose was measured at three conditions: static phantom, moving phantom with continuous beam delivery, and moving phantom with gated irradiation. The statically delivered dose distribution was used as a reference. Further, a 4D dose calculation was performed on the 4DCT dataset using a research treatment planning system. Results: The relative rms deviations in the homogenous dose region were ∼18% without gating, and ∼6% with gating. The 4D dose calculation showed a decrease in target coverage by ∼20% and ∼6%, respectively, for the 95% isodose line. Conclusions: Gating of a scanned carbon ion beam was applied for treatment of a moving liver tumor and a workflow was developed to verify the dose to be actually delivered. With respect to continuous dose delivery, the target dose improvement achieved due to gating is considered to be significant for this patient.

Multisectional KrF laser with a pulse repetition rate of 4 kHz and inductive-capacitive discharge stabilisation

An electric-discharge KrF laser with an inductive-capacitive discharge stabilisation and a pulse repetition rate up to 4 kHz is developed. The multisectional discharge gap with a total length of 25 cm is formed by 25 pairs of anode-cathode plates. A discharge width of no more than 1 mm is realised. Ne and He are used as the buffer gases, and F2 serves as the fluorine donor. The maximum output pulse energy is ∼6 mJ for the Ne—Kr—F2 mixture at a total pressure of 1.6—3.2 atm. The maximum efficiency of the laser is ∼1.4%. An original optical technique is worked out for measuring the gas velocity in the working gap. The maximum gas velocity in the gap between the electrodes is found to be 19 ms-1 in the experiments. The average output power of the laser for a pulse repetition rate of 3—4 kHz is ∼12 W, while the relative rms deviation of the laser pulse energy lies in the range 2%—3.8%. It is shown that the refractive index gradient of the active medium, which is related to the free electron concentration in the discharge plasma, plays a significant role in the formation of laser radiation field in the resonator. The characteristic value of the refractive index gradient is found to be no less than 10-5 cm-1 for the KrF laser wavelength.

TU‐D‐T‐617‐07: Treatment Plan Validation of the Xoft AXXENT™ X‐Ray Source

Purpose: Accuracy of delivered dose compared to BrachyVision™ generated treatment plans was tested using both a calibrated miniature air ionization chamber to measure dose at the prescription point, and radiochromic film to map isodose contour lines. Quantitative and qualitative comparisons of the total dose and contour shapes were made. Method and Materials: Xoft applicator balloons were held in a water phantom with a Solid Water™ fixture. A PTW model 34013 ionization chamber connected to a PTW UniDos electrometer, and read into a computer, were used to measure the dose at the prescription point. Films were held in the fixture in the plane of the source, offset by 5 mm. The Xoft Axxent controller performed sample treatments including stepping of the source for four combinations of balloon size and operating voltage. Film samples were digitized and converted to dose values through a specially developed calibration curve. Comparison of isodose contours with the film‐measured dose was accomplished with specially written image analysis algorithms, which compared the measured values with predicted along the isodose contours. Results: Dosimeter based dose measurements agreed with prescription to within 11% worst case, with an RMS error of 8%. Film analyses quantified deviation from isodose contours as a function of polar angle, with relative RMS deviations well under 10%. However limitations in the accuracy of film calibration limited absolute accuracy to just over 20%, with systematic behavior attributable to limitations of the fitting function. Conclusion: Validation of treatment plans were performed using direct dosimetry and film based measurements. Novel image analysis tools were developed to allow numerical evaluation of film dose to isodose contours. Conflict of Interest: Research was supported by Xoft, Inc.

Precision Spectrometric Determination of Th and Pu in Solutions with Arsenazo III Using Internal Standardization

A spectrophotometric procedure with internal standardization was suggested for precision determination of the concentrations of Th and Pu in the form of colored complexes with arsenazo III in nitric acid solutions. The sensitivity of the method was significantly improved owing to the use of colored complexes. The optical density optimum (0.3-0.5) of the solutions for spectrophotometric measurements can be achieved at concentrations in solution of the element analyzed as low as (2-3) ×10-6 M, at the arsenazo and HNO3 concentrations of 1 ×10-4 and 6 M, respectively. With this composition of the solution, the relative rms deviation of the results for a single run is no greater than 0.15 and 0.3% for thorium and plutonium, respectively.

Alcator C-Mod predictive modeling

Predictive simulations for the Alcator C-mod tokamak [I. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] are carried out using the BALDUR integrated modeling code [C. E. Singer et al., Comput. Phys. Commun. 49, 275 (1988)]. The results are obtained for temperature and density profiles using the Multi-Mode transport model [G. Bateman et al., Phys. Plasmas 5, 1793 (1998)] as well as the mixed-Bohm/gyro-Bohm transport model [M. Erba et al., Plasma Phys. Controlled Fusion 39, 261 (1997)]. The simulated discharges are characterized by very high plasma density in both low and high modes of confinement. The predicted profiles for each of the transport models match the experimental data about equally well in spite of the fact that the two models have different dimensionless scalings. Average relative rms deviations are less than 8% for the electron density profiles and 16% for the electron and ion temperature profiles.

Eigenstates for an Anderson model of an ordered-lattice-disordered-lattice junction.

We analyze the eigenstates in one dimension of a semi-infinite ordered lattice in contact with a semi-infinite disordered lattice described by an Anderson model. Specifically, we study the site wave functions in the disordered region at distances N from the interface which are small compared to the localization length ${\ensuremath{\xi}}_{0}$. The wave functions at these length scales are relevant for conduction in the metallic regime of a disordered lattice of finite size. From a perturbation expansion for weak disorder we obtain qualitatively different results for the random (N-dependent) rates of exponential growth of wave functions in different domains corresponding to the energy band of an infinite nondisordered chain. Their mean values are anomalous near the band center and near the band edges, while corresponding to a fixed central limit (${\ensuremath{\xi}}_{0}^{\mathrm{\ensuremath{-}}1}$) between these limits, up to oscillatory terms. The study of the relative rms deviations of the above rates shows that they are self-averaging in a range of finite N\ensuremath{\gg}1, at any energy. At the intermediate energies the weak disorder expansion is valid for any length scale, while near the band center and near the band edges it ceases to converge beyond a characteristic length ${\ensuremath{\xi}}_{1}$. The length ${\ensuremath{\xi}}_{1}$ defines the border between scales N\ensuremath{\ll}${\ensuremath{\xi}}_{1}$, where the wave functions are weakly perturbed Bloch amplitudes, and scales N\ensuremath{\gg}${\ensuremath{\xi}}_{1}$, where the weak disorder acts as a strong perturbation, leading to localized states with stationary positive Lyapunov exponents (${\ensuremath{\xi}}_{0}^{\mathrm{\ensuremath{-}}1}$). We find that ${\ensuremath{\xi}}_{1}$ scales with the disorder in the same way as does ${\ensuremath{\xi}}_{0}$, while being less than an order of magnitude smaller than ${\ensuremath{\xi}}_{0}$. Finally, we relate our results for wave-function growth rates at finite length scales to the resistance of a quasimetallic sample, using a simple Ansatz for the transmission coefficient. The resistance is found to be Ohmic, but anomalous, near the band center and strongly non-Ohmic near the band edges.

Effective hard-sphere diameters and equations of state

A simple way to derive and express accurate effective diameters for simple fluids is given. Effective hard-sphere diameters are essential to write explicit equations of state. The procedure relies on a density expansion of the effective diameters and is illustrated for systems with purely repulsive forces. Equations for the free energy and pressure of a system with an inverse-12 potential are obtained. The pressure equation has a relative RMS deviation of 0·15% with respect to Monte Carlo data over the entire fluid range.

Method of measuring the fluctuations of bremsstrahlung beam parameters

Measurement of Dose-rate Fluctuations. In the first approximation we can assume that at the output of the radiometric channel we record J = ~I, where ~ and I are independent random variables with ~ = i; ~ characterizes the dose-rate fluctuations from pulse to pulse and I characterizes the interaction of photons with the material of the object under study and the process of photon detection by a detector. The relative rms deviation of J is estimated from

Alanyl dipeptide potential‐derived net atomic charges and bond dipoles, and their variation with molecular conformation

AbstractThe elctric potential around the alanyl dipeptide in various conformations was calculated from ab initio 6–31G wave functions. Seven conformations were selected to correspond to calculated local energy minima of the isolated molecule. Five additional conformations were selected corresponding to the alanylalanine crystal structure and the polypeptide conformations in a right‐handed α‐helix, left‐handed α‐helix, parallel β‐sheet, and anti‐parallel β‐sheet. The electric potential surrounding each conformer was fitted with either net charges at atomic sites or dipolles at bond sites by least squares. Either choice reproduced the electric potential with relative rms deviations of 1.9–4.8%. Values for net atomic charges or bond dipoles were usually in line with expectations based on electronegativity. The imino and carbonyl groups showed their expected polarities, although there were considerable deviations from zero group charge. Net atomic charges on and near the α‐carbon changed substantially with the conformation angles; bond dipoles around the α‐carbon showed analogous behavior.

MRD-CI potential surfaces using balanced basis sets. IV. The H2 molecule and the H3 surface

The utility of midbond functions in molecular calculations was tested in two cases where the correct results are known: the H2 potential curve and the collinear H3 potential surface. For H2, a variety of basis sets both with and without bond functions was compared to the exact nonrelativistic potential curve of Kolos and Wolniewicz [J. Chem. Phys. 43, 2429 (1965)]. It was found that optimally balanced basis sets at two levels of quality were the double zeta single polarization plus sp bond function basis (BF1) and the triple zeta double polarization plus two sets of sp bond function basis (BF2). These gave bond dissociation energies De =4.7341 and 4.7368 eV, respectively (expt. 4.7477 eV). Four basis sets were tested for basis set superposition errors, which were found to be small relative to basis set incompleteness and therefore did not affect any conclusions regarding basis set balance. Basis sets BF1 and BF2 were used to construct potential surfaces for collinear H3, along with the corresponding basis sets DZ*P and TZ*PP which contain no bond functions. Barrier heights of 12.52, 10.37, 10.06, and 9.96 kcal/mol were obtained for basis sets DZ*P, TZ*PP, BF1, and BF2, respectively, compared to an estimated limiting value of 9.60 kcal/mol. Difference maps, force constants, and relative rms deviations show that the bond functions improve the surface shape as well as the barrier height.

The Erosion Rates of Arc Cathode Spots by Crater Formation

AbstractThe erosion of arc cathodes is caused by evaporation and by forced fluid motion of the molten metal layer at the spot surface. The gross erosion rates (X1 X2) of both components are derived from the equations of stationary and non‐stationary cathode spot models in a first approximation. These rates depend mainly on thermal properties of the metal, the atomic mass and the ionization state of the cathodic plasma. The calculated total gross rates Xt are between 67 μg/As (Be) and 3300 μg/As (Bi); the measured net rates (X̃) amount to about 10% ⃛30% of these gross rates. The range of the ratio X2/X1 = v is 0,56 (Cd) ≦ v ≦ 2,64 (Mo). The various gross rates X1.2t are strongly correlated with the net rates X̃ the relative rms deviations σrel from a power law fit are between about 15% and 30%. Resistive heating results in a worse correlation of the rates than ion impact heating. Probable causes of the deviations from exact functional dependencies are discussed.

Experimental Study of Effect of Crystallite Size Statistics on X-Ray Diffractometer Intensities

The relative rms deviation σ of the intensity of a rapidly rotating polycrystallite specimen is σ=[6.5R sinθ]/[h(mNeff)½], where R=goniometer radius, θ=Bragg angle, h=(hf+hs)/2, hf=length of focal spot, hs=length of receiving slit, m=multiplicity factor, and Neff the effective number of irradiated crystallites. Experimental data on silicon powder specimens are presented to show the dependence of σ on crystallite sizes, choice of x-ray wavelengths and various other experimental parameters. Comparisons of data for rapidly rotating and stationary specimens having crystallite sizes in the 30–50 μ range show that rotation improves σ by a factor of 7 or 8 for peak intensities and 4 or 5 for integrated intensities, using a standard diffractometer.