Matthew Braunstein

Optimum beam configurations in tomographic intensity modulated radiation therapy

We review and extend the theory of tomographic dose reconstruction for intensity modulated radiotherapy (IMRT). We derive the basis for a saturation with beam number of dose conformation, and provide an analysis which ranks particular beam orientations in terms of the contribution to the delivered dose. Preferred beam directions are found which effectively reduce the number of beams necessary to achieve a given level of dose conformation. The analysis is a new application of the tomographic projection-slice theorem to the problem of beam orientation determination. The effects of the beam front filter and the positivity constraint arising from the tomographic approach are analysed, and modifications of the beam front filter for small beam numbers are suggested. The theory is applied to simple geometric shapes in two dimensions. A Gaussian ellipse, where analytical results are obtained, and simple hard-edged convex prescribed dose shapes are examined to illustrate beam selection based on the beam overlap metric. More complex concave prescribed dose shapes which contain a sensitive organ are also analysed and for low beam numbers are found to have preferred beam directions.

Theoretical study of the N(2D)+O2(X 3Σg−)→O+NO reaction

Potential energy surfaces are computed for all electronic states relevant for the reaction N(2D)+O2(X 3Σg−)→O+NO at the complete-active-space-self-consistent-field plus second-order perturbation theory (CASSCF-MP2) level using a 6311G(d) basis set. For those states with barriers low enough to contribute significantly at low to moderate temperatures, adiabatic global potential energy surfaces are fit with a functional form using at least 1000 computed ab initio points. Quasi-classical trajectory (QCT) calculations, excluding nonadiabatic effects, are performed and rates and final state vibrational distributions are compared with available experimental data. The peaked vibrational distribution observed in the experimental data is reproduced in these calculations, slightly shifted to higher vibration. These calculations show that from low to moderate temperatures the dynamics are dominated by the 2 2A′ and 1 2A″ states of NO2, which have similar bent, early entrance channel barriers. Although production of O...

Global potential energy surfaces for O(P3)+H2O(A11) collisions

Global analytic potential energy surfaces for O((3)P) + H(2)O((1)A(1)) collisions, including the OH + OH hydrogen abstraction and H + OOH hydrogen elimination channels, are presented. Ab initio electronic structure calculations were performed at the CASSCF + MP2 level with an O(4s3p2d1f)/H(3s2p) one electron basis set. Approximately 10(5) geometries were used to fit the three lowest triplet adiabatic states corresponding to the triply degenerate O((3)P) + H(2)O((1)A(1)) reactants. Transition state theory rate constant and total cross section calculations using classical trajectories to collision energies up to 120 kcal  mol(-1) (∼11 km  s(-1) collision velocity) were performed and show good agreement with experimental data. Flux-velocity contour maps are presented at selected energies for H(2)O collisional excitation, OH + OH, and H + OOH channels to further investigate the dynamics, especially the competition and distinct dynamics of the two reactive channels. There are large differences in the contributions of each of the triplet surfaces to the reactive channels, especially at higher energies. The present surfaces should support quantitative modeling of O((3)P) + H(2)O((1)A(1)) collision processes up to ∼150 kcal  mol(-1).

The convergence of complete active space self-consistent-field energies to the complete basis set limit

Examination of the convergence of full valence complete active space self-consistent-field energies with expansion of the one-electron basis set reveals a pattern very similar to the convergence of single determinant Hartree-Fock energies. Calculations on 26 molecular examples with the sequence of ntuple-zeta augmented polarized (nZaP) basis sets (n=2, 3, 4, 5, and 6) are used to evaluate complete basis set extrapolation schemes. The most effective extrapolation reduces the rms one-electron basis set truncation errors from 3.03, 0.58, and 0.12 mhartree to 0.23, 0.05, and 0.014 mhartree for the 3ZaP, 4ZaP, and 5ZaP basis sets, respectively.

Potential surfaces and dynamics of the O(P3)+H2O(XA111)→OH(XΠ2)+OH(XΠ2) reaction

We present global potential energy surfaces for the three lowest triplet states in O(P3)+H2O(XA11) collisions and present results of classical dynamics calculations on the O(P3)+H2O(XA11)→OH(XΠ2)+OH(XΠ2) reaction using these surfaces. The surfaces are spline-based fits of ∼20000 fixed geometry ab initio calculations at the complete-active-space self-consistent field+second-order perturbation theory (CASSCF+MP2) level with a O(4s3p2d1f)/H(3s2p) one electron basis set. Computed rate constants compare well to measurements in the 1000–2500 K range using these surfaces. We also compute the total, rovibrationally resolved, and differential angular cross sections at fixed collision velocities from near threshold at ∼4kms−1 (16.9kcalmol−1 collision energy) to 11kms−1 (122.5kcalmol−1 collision energy), and we compare these computed cross sections to available space-based and laboratory data. A major finding of the present work is that above ∼40kcalmol−1 collision energy rovibrationally excited OH(XΠ2) products are...

Electronic structure and dynamics of O(3P)+CO(1Σ+) collisions

The potential energy surfaces of the three lowest electronic triplet states of CO2 which lead to O(3P)+CO(1Σ+), 3A′, 1 3A″, and 2 3A″, have been computed at the completeactive-space-self-consistent-field plus second-order perturbation theory (CASSCF-MP2) level with a modest 631+G(d) basis. Potential energy surfaces are fit with a global functional form. The 3A′ state has a well 0.9 eV deep and the 1 3A″ state has a 0.2 eV well with respect to the O(3P)+CO(1Σ+) dissociation threshold. The 3A′ and 1 3A″ states are both bent at their minima and have a barrier at 0.2 eV and 0.3 eV above threshold, respectively. The 2 3A″ state is mostly repulsive, and has a saddle at C2v geometries. We have run classical trajectory calculations for O(3P)+CO(1Σ+) collisions using these surfaces. Results agree well with available vibrational relaxation and oxygen atom exchange measurements except at low temperature. Comparisons are also made with measured vibrational excitation cross sections and infrared emission spectra of th...

Signal processing approaches to radio frequency interference (RFI) suppression

Ultra-wideband radar (UWB) has been shown to be among the most powerful techniques available for underground and obscured object detection. The value of such systems is that they combine the penetration enhancement associated with VHF/UHF (and lower) frequencies with the resolution of wide absolute bandwidth. Such systems necessarily make use of much of the frequency spectrum already in heavy use by other services, such as television and mobile communications. Although this spectral overlap provides occasion for adverse consequences in both directions, to date the principal consequence has been often-severe impact on UWB radar measurements. Even in remote locations, the average interference power often exceeds receiver noise by many dB, becoming the limiting factor on system sensitivity. Nor are UWB radar designers free to overcome this interference by increasing radar power, since regulatory sanction for UWB operation will depend on maintaining sufficiently low spectral power densities to assure that other, prior, services are not appreciably degraded. Given the importance of radio frequency interference (RFI) on practical ultrawide band ground penetrating radar systems, it is important to consider how and to what extent the effects of RFI noise may be reduced. The overall problem of RFI and its impacts will be described and several signal processing approaches to removal of RFI will be discussed. These include spectral estimation and coherent subtraction algorithms and various filter approaches, which have been developed and applied by the signal processing community in other contexts. These methods will be applied to several different real-world experimental data sets, and quantitative measures of the effectiveness of each of these algorithms in removing RFI noise will be presented. Although computationally-intensive, most of the techniques to be described achieve substantial increases in S/RFI without requiring concomitant increases in radar average power.

Classical dynamics of state-resolved hyperthermal O(3P) + H2O(1A1) collisions

Classical dynamics calculations are performed for O((3)P) + H2O((1)A1) collisions from 2 to 10 km s(-1) (4.1-101.3 kcal mol(-1)), focusing on product internal energies. Several methods are used to produce ro-vibrationally state-resolved product cross sections and to enforce zero-point maintenance from analysis of the classical trajectories. Two potential energy surfaces are used: (1) a recently developed set of global reactive surfaces for the three lowest triplet states which model OH formation, H elimination to make H + OOH, O-atom exchange, and collisional excitation and (2) a non-reactive surface used in past classical and quantum collision studies. Comparisons to these previous studies suggest that for H2O vibrational excitation, classical dynamics which include gaussian binning procedures and/or selected zero-point maintenance algorithms can produce results which approximate quantum scattering cross sections fairly well. Without these procedures, the classical cross sections can be many orders of magnitude greater than the quantum cross sections for exciting the bending vibration of H2O, especially near threshold. The classical cross section over-estimate is due to energy borrowing from stretching modes which dip below zero-point values. For results on the reactive surfaces, the present calculations show that at higher velocities there is an unusually large amount of product internal excitation. For OOH, where 40% of available collision energy goes into internal motion, the excited product vibrational and rotational energy distributions are relatively flat and values of the OOH rotational angular momentum exceed J = 100. Other product channel distributions show an exponential fall-off with energy consistent with an energy gap law. The present detailed distributions and cross sections can serve as a guide for future hyperthermal measurements of this system.

Direct simulation Monte Carlo modeling of high energy chemistry in molecular beams: Chemistry models and flowfield effects

Benchmark state-to-state vibrational energy excitation cross sections have been calculated for O+CO. The rate constants derived from these cross sections agree with available equilibrium measurements, but the cross sections extend to much higher energies. These benchmark cross sections provide an opportunity to test a widely used DSMC chemistry model at a detailed level and provide insight on one of its adjustable parameters. It is shown that extrapolations to the higher energy regime can be in error by an order of magnitude or more. The benchmark cross sections are used in direct simulation Monte Carlo (DSMC) modeling of molecular beam experiments. The simulations are intended to remove a major source of experimental uncertainty in the rates derived from molecular beam measurements by computing local concentrations of reactants in the molecular beam chamber. Furthermore, by keeping track of multi-collision events in the reaction chamber, the present simulations will allow experiments to be designed which...

Three-dimensional tomographic reconstruction of an absorptive perturbation with diffuse photon density waves.

A three-dimensional tomographic reconstruction algorithm for an absorptive perturbation in tissue is derived. The input consists of multiple two-dimensional projected views of tissue that is backilluminated with diffuse photon density waves. The algorithm is based on a generalization of the projection-slice theorem and consists of depth estimation, image deconvolution, filtering, and backprojection. The formalism provides estimates of the number of views necessary to achieve a given spatial resolution in the reconstruction. The algorithm is demonstrated with data simulated to mimic the absorption of a contrast agent in human tissue. The effects of noise and uncertainties in the depth estimate are explored.