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At least 109 records · Page 6

Molecular structure calculations: A unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation

We elaborate on the theory for the variational solution of the Schroedinger equation of small atomic and molecular systems without relying on the Born-Oppenheimer paradigm. The all-particle Schroedinger equation is solved in a numerical procedure using the variational principle, Cartesian coordinates, parameterized explicitly correlated Gaussian functions with polynomial prefactors, and the global vector representation. As a result, non-relativistic energy levels and wave functions of few-particle systems can be obtained for various angular momentum, parity, and spin quantum numbers. A stochastic variational optimization of the basis function parameters facilitates the calculation of accurate energies and wave functions for the ground and some excited rotational-(vibrational-)electronic states of H{sub 2}{sup +} and H{sub 2}, three bound states of the positronium molecule, Ps{sub 2}, and the ground and two excited states of the {sup 7}Li atom.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effect of asymmetric concentration profile on thermal conductivity in Ge/SiGe superlattices

The effect of the chemical composition in Si/Ge-based superlattices on their thermal conductivity has been investigated using molecular dynamics simulations. Simulation cells of Ge/SiGe superlattices have been generated with different concentration profiles such that the Si concentration follows a step-like, a tooth-saw, a Gaussian, and a gamma-type function in direction of the heat flux. The step-like and tooth-saw profiles mimic ideally sharp interfaces, whereas Gaussian and gamma-type profiles are smooth functions imitating atomic diffusion at the interface as obtained experimentally. Symmetry effects have been investigated comparing the symmetric profiles of the step-like and the Gaussian function to the asymmetric profiles of the tooth-saw and the gamma-type function. At longer sample length and similar degree of interdiffusion, the thermal conductivity is found to be lower in asymmetric profiles. Furthermore, it is found that with smooth concentration profiles where atomic diffusion at the interface takes place the thermal conductivity is higher compared to systems with atomically sharp concentration profiles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Study on statistical breakdown delay time in argon gas using a W-band millimeter-wave gyrotron

In this study, we investigated plasma initiation delay times for argon volume breakdown at the W-band frequency regime. The threshold electric field is defined as the minimum electric field amplitude needed for plasma breakdown at various pressures. The measured statistical delay time showed an excellent agreement with the theoretical Gaussian distribution and the theoretically estimated formative delay time. Also, we demonstrated that the normalized effective electric field as a function of the product of pressure and formative time shows an outstanding agreement to that of 1D particle-in-cell simulation coupled with a Monte Carlo collision model [H. C. Kim and J. P. Verboncoeur, Phys. Plasmas 13, 123506 (2006)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dose-shaping using targeted sparse optimization

Purpose: Dose volume histograms (DVHs) are common tools in radiation therapy treatment planning to characterize plan quality. As statistical metrics, DVHs provide a compact summary of the underlying plan at the cost of losing spatial information: the same or similar dose-volume histograms can arise from substantially different spatial dose maps. This is exactly the reason why physicians and physicists scrutinize dose maps even after they satisfy all DVH endpoints numerically. However, up to this point, little has been done to control spatial phenomena, such as the spatial distribution of hot spots, which has significant clinical implications. To this end, the authors propose a novel objective function that enables a more direct tradeoff between target coverage, organ-sparing, and planning target volume (PTV) homogeneity, and presents our findings from four prostate cases, a pancreas case, and a head-and-neck case to illustrate the advantages and general applicability of our method.Methods: In designing the energy minimization objective (E{sub tot}{sup sparse}), the authors utilized the following robust cost functions: (1) an asymmetric linear well function to allow differential penalties for underdose, relaxation of prescription dose, and overdose in the PTV; (2) a two-piece linear function to heavily penalize high dose and mildly penalize low and intermediate dose in organs-at risk (OARs); and (3) a total variation energy, i.e., the L{sub 1} norm applied to the first-order approximation of the dose gradient in the PTV. By minimizing a weighted sum of these robust costs, general conformity to dose prescription and dose-gradient prescription is achieved while encouraging prescription violations to follow a Laplace distribution. In contrast, conventional quadratic objectives are associated with a Gaussian distribution of violations, which is less forgiving to large violations of prescription than the Laplace distribution. As a result, the proposed objective E{sub tot}{sup sparse} improves tradeoff between planning goals by 'sacrificing' voxels that have already been violated to improve PTV coverage, PTV homogeneity, and/or OAR-sparing. In doing so, overall plan quality is increased since these large violations only arise if a net reduction in E{sub tot}{sup sparse} occurs as a result. For example, large violations to dose prescription in the PTV in E{sub tot}{sup sparse}-optimized plans will naturally localize to voxels in and around PTV-OAR overlaps where OAR-sparing may be increased without compromising target coverage. The authors compared the results of our method and the corresponding clinical plans using analyses of DVH plots, dose maps, and two quantitative metrics that quantify PTV homogeneity and overdose. These metrics do not penalize underdose since E{sub tot}{sup sparse}-optimized plans were planned such that their target coverage was similar or better than that of the clinical plans. Finally, plan deliverability was assessed with the 2D modulation index.Results: The proposed method was implemented using IBM's CPLEX optimization package (ILOG CPLEX, Sunnyvale, CA) and required 1-4 min to solve with a 12-core Intel i7 processor. In the testing procedure, the authors optimized for several points on the Pareto surface of four 7-field 6MV prostate cases that were optimized for different levels of PTV homogeneity and OAR-sparing. The generated results were compared against each other and the clinical plan by analyzing their DVH plots and dose maps. After developing intuition by planning the four prostate cases, which had relatively few tradeoffs, the authors applied our method to a 7-field 6 MV pancreas case and a 9-field 6MV head-and-neck case to test the potential impact of our method on more challenging cases. The authors found that our formulation: (1) provided excellent flexibility for balancing OAR-sparing with PTV homogeneity; and (2) permitted the dose planner more control over the evolution of the PTV's spatial dose distribution than conventional objective functions. In particular, E{sub tot}{sup sparse}-optimized plans for the pancreas case and head-and-neck case exhibited substantially improved sparing of the spinal cord and parotid glands, respectively, while maintaining or improving sparing for other OARs and markedly improving PTV homogeneity. Plan deliverability for E{sub tot}{sup sparse}-optimized plans was shown to be better than their associated clinical plans, according to the two-dimensional modulation index.Conclusions: These results suggest that our formulation may be used to improve dose-shaping and OAR-sparing for complicated disease sites, such as the pancreas or head and neck. Furthermore, our objective function and constraints are linear and constitute a linear program, which converges to the global minimum quickly, and can be easily implemented in treatment planning software. Thus, the authors expect fast translation of our method to the clinic where it may have a positive impact on plan quality for challenging disease sites.

61 RADIATION PROTECTION AND DOSIMETRY↗

Nature of the effective interaction between dendrimers

We have performed fully atomistic classical molecular dynamics simulations to calculate the effective interaction between two polyamidoamine dendrimers. Using the umbrella sampling technique, we have obtained the potential of mean force (PMF) between the dendrimers and investigated the effects of protonation level and dendrimer size on the PMF. Our results show that the interaction between the dendrimers can be tuned from purely repulsive to partly attractive by changing the protonation level. The PMF profiles are well-fitted by the sum of an exponential and a Gaussian function with the weight of the exponential function dominating over that of the Gaussian function. This observation is in disagreement with the results obtained in previous analytic [C. Likos, M. Schmidt, H. Löwen, M. Ballauff, D. Pötschke, and P. Lindner, Macromolecules 34, 2914 (2001)] and coarse-grained simulation [I. Götze, H. Harreis, and C. Likos, J. Chem. Phys. 120, 7761 (2004)] studies which predicted the effective interaction to be Gaussian.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Efficiency-enhanced photon sieve using Gaussian/overlapping distribution of pinholes

A class of photon sieve is introduced whose structure is based on the overlapping pinholes in the innermost zones. This kind of distribution is produced by, for example, a particular form of Gaussian function. The focusing property of the proposed model was examined theoretically and experimentally. It is shown that under He-Ne laser and white light illumination, the focal spot size of this novel structure has considerably smaller FWHM than a photon sieve with randomly distributed pinholes and a Fresnel zone plate. In addition, secondary maxima have been suppressed effectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Charge asymmetry in rovibrationally excited HD{sup +} determined using explicitly correlated all-particle Gaussian functions

Very accurate non-Born-Oppenheimer quantum-mechanical calculations are performed to determine the average values of the interparticle distances and the proton-deuteron density function for the rovibrationally excited HD{sup +} ion. The states corresponding to excitations to all bound vibrational states (v = 0, …, 22) and simultaneously excited to the first excited rotational state (N = 1) are considered. To describe each state up to 8000 explicitly correlated all-particle Gaussian functions are used. The nonlinear parameters of the Gaussians are variationally optimized using a procedure that employs the analytical energy gradient determined with respect to these parameters. The results show an increasing asymmetry in the electron distribution with the vibrational excitation as the electron density shifts towards deuteron and away from the proton.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Algorithms for calculating mass-velocity and Darwin relativistic corrections with n-electron explicitly correlated Gaussians with shifted centers

Algorithms for calculating the leading mass-velocity (MV) and Darwin (D) relativistic corrections are derived for electronic wave functions expanded in terms of n-electron explicitly correlated Gaussian functions with shifted centers and without pre-exponential angular factors. The algorithms are implemented and tested in calculations of MV and D corrections for several points on the ground-state potential energy curves of the H{sub 2} and LiH molecules. The algorithms are general and can be applied in calculations of systems with an arbitrary number of electrons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Constraining scale-dependent non-Gaussianity with future large-scale structure and the CMB

We forecast combined future constraints from the cosmic microwave background and large-scale structure on the models of primordial non-Gaussianity. We study the generalized local model of non-Gaussianity, where the parameter f{sub NL} is promoted to a function of scale, and present the principal component analysis applicable to an arbitrary form of f{sub NL}(k). We emphasize the complementarity between the CMB and LSS by using Planck, DES and BigBOSS surveys as examples, forecast constraints on the power-law f{sub NL}(k) model, and introduce the figure of merit for measurements of scale-dependent non-Gaussianity.

79 ASTRONOMY AND ASTROPHYSICS↗

Characteristics of the 2 m long scintillation counters measured by detecting 90 MeV protons

The characteristics of scintillation counters measured in a 90-MeV proton beam have been presented. Two-meter long scintillators BC-404 and BC-408, which were viewed from both ends with photoelectron multipliers R1828-01 (PMT) have been used. Both the amplitude and time distributions of the PMT signals are well described by the Gaussian function. It turned out that the amplitude resolution σ(А)/А weakly depends on the type of scintillator and the proton position along the counter, and lies in the interval between 4 and 5%. The best time resolution σ(T) is about 50 ps near the counter ends and 63 ps at the center.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Identification of subsurface structures using electromagnetic data and shape priors

We consider the inverse problem of identifying large-scale subsurface structures using the controlled source electromagnetic method. To identify structures in the subsurface where the contrast in electric conductivity can be small, regularization is needed to bias the solution towards preserving structural information. We propose to combine two approaches for regularization of the inverse problem. In the first approach we utilize a model-based, reduced, composite representation of the electric conductivity that is highly flexible, even for a moderate number of degrees of freedom. With a low number of parameters, the inverse problem is efficiently solved using a standard, second-order gradient-based optimization algorithm. Further regularization is obtained using structural prior information, available, e.g., from interpreted seismic data. The reduced conductivity representation is suitable for incorporation of structural prior information. Such prior information cannot, however, be accurately modeled with a gaussian distribution. To alleviate this, we incorporate the structural information using shape priors. The shape prior technique requires the choice of kernel function, which is application dependent. We argue for using the conditionally positive definite kernel which is shown to have computational advantages over the commonly applied gaussian kernel for our problem. Numerical experiments on various test cases show that the methodology is able to identify fairly complex subsurface electric conductivity distributions while preserving structural prior information during the inversion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Efficient simulation of the impact of interface grading on the transport and optical properties of semiconductor heterostructures

An efficient model is proposed to evaluate the impact of interface grading on the properties of semiconductor heterostructures. In the plane-wave approximation, the interface grading is taken into account by simply multiplying the Fourier components of the potential by a Gaussian function, which results only in a very small increase of the computation time. We show that the interface grading may affect the transition energies, the field strength for resonant coupling of subbands, and even the miniband formation in complex systems such as quantum-cascade lasers. This model provides a convenient tool for the incorporation of interface grading into the design of heterostructures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Prediction of {sup 1}P Rydberg energy levels of beryllium based on calculations with explicitly correlated Gaussians

Benchmark variational calculations are performed for the seven lowest 1s{sup 2}2s np ({sup 1}P), n = 2…8, states of the beryllium atom. The calculations explicitly include the effect of finite mass of {sup 9}Be nucleus and account perturbatively for the mass-velocity, Darwin, and spin-spin relativistic corrections. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. Basis sets of up to 12 500 optimized Gaussians are used. The maximum discrepancy between the calculated nonrelativistic and experimental energies of 1s{sup 2}2s np ({sup 1}P) →1s{sup 2}2s{sup 2} ({sup 1}S) transition is about 12 cm{sup −1}. The inclusion of the relativistic corrections reduces the discrepancy to bellow 0.8 cm{sup −1}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Basis functions for electronic structure calculations on spheres

We introduce a new basis function (the spherical Gaussian) for electronic structure calculations on spheres of any dimension D. We find general expressions for the one- and two-electron integrals and propose an efficient computational algorithm incorporating the Cauchy-Schwarz bound. Using numerical calculations for the D = 2 case, we show that spherical Gaussians are more efficient than spherical harmonics when the electrons are strongly localized.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

{sup 1}D states of the beryllium atom: Quantum mechanical nonrelativistic calculations employing explicitly correlated Gaussian functions

Very accurate finite-nuclear-mass variational nonrelativistic calculations are performed for the lowest five {sup 1}D states (1s{sup 2} 2p{sup 2}, 1s{sup 2} 2s{sup 1} 3d{sup 1}, 1s{sup 2} 2s{sup 1} 4d{sup 1}, 1s{sup 2} 2s{sup 1} 5d{sup 1}, and 1s{sup 2} 2s{sup 1} 6d{sup 1}) of the beryllium atom ({sup 9}Be). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The calculations exemplify the level of accuracy that is now possible with Gaussians in describing bound states of a four-electron system where some of the electrons are excited into higher angular states.

74 ATOMIC AND MOLECULAR PHYSICS↗

Effect of quantum dot size and size distribution on the intersublevel transitions and absorption coefficients of III-V semiconductor quantum dot

The intersublevel absorption peak energy and absorption coefficient of non-uniform quantum dot (QD) ensembles are calculated analytically. The effect of size variations and size distribution of QDs on their energy states is analyzed. The dots are considered as a quantum box with finite potential at the barriers and the size distribution described by a Gaussian function. The influence of the aspect ratio (base to height ratio) of the QDs on the optical transitions is studied. Our model predicts the dot size (height and base) accurately to determine the absorption peaks and corresponding absorption coefficient. We also compute the absorption coefficient of the QD with different size distributions to verify the results calculated using this model with the reported experimental and other theoretical results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Transconvolution and the virtual positron emission tomograph-A new method for cross calibration in quantitative PET/CT imaging

Purpose: Positron emission tomography (PET)/computed tomography (CT) measurements on small lesions are impaired by the partial volume effect, which is intrinsically tied to the point spread function of the actual imaging system, including the reconstruction algorithms. The variability resulting from different point spread functions hinders the assessment of quantitative measurements in clinical routine and especially degrades comparability within multicenter trials. To improve quantitative comparability there is a need for methods to match different PET/CT systems through elimination of this systemic variability. Consequently, a new method was developed and tested that transforms the image of an object as produced by one tomograph to another image of the same object as it would have been seen by a different tomograph. The proposed new method, termed Transconvolution, compensates for differing imaging properties of different tomographs and particularly aims at quantitative comparability of PET/CT in the context of multicenter trials. Methods: To solve the problem of image normalization, the theory of Transconvolution was mathematically established together with new methods to handle point spread functions of different PET/CT systems. Knowing the point spread functions of two different imaging systems allows determining a Transconvolution function to convert one image into the other. This function is calculated by convolving one point spread function with the inverse of the other point spread function which, when adhering to certain boundary conditions such as the use of linear acquisition and image reconstruction methods, is a numerically accessible operation. For reliable measurement of such point spread functions characterizing different PET/CT systems, a dedicated solid-state phantom incorporating {sup 68}Ge/{sup 68}Ga filled spheres was developed. To iteratively determine and represent such point spread functions, exponential density functions in combination with a Gaussian distribution were introduced. Furthermore, simulation of a virtual PET system provided a standard imaging system with clearly defined properties to which the real PET systems were to be matched. A Hann window served as the modulation transfer function for the virtual PET. The Hann's apodization properties suppressed high spatial frequencies above a certain critical frequency, thereby fulfilling the above-mentioned boundary conditions. The determined point spread functions were subsequently used by the novel Transconvolution algorithm to match different PET/CT systems onto the virtual PET system. Finally, the theoretically elaborated Transconvolution method was validated transforming phantom images acquired on two different PET systems to nearly identical data sets, as they would be imaged by the virtual PET system. Results: The proposed Transconvolution method matched different PET/CT-systems for an improved and reproducible determination of a normalized activity concentration. The highest difference in measured activity concentration between the two different PET systems of 18.2% was found in spheres of 2 ml volume. Transconvolution reduced this difference down to 1.6%. In addition to reestablishing comparability the new method with its parameterization of point spread functions allowed a full characterization of imaging properties of the examined tomographs. Conclusions: By matching different tomographs to a virtual standardized imaging system, Transconvolution opens a new comprehensive method for cross calibration in quantitative PET imaging. The use of a virtual PET system restores comparability between data sets from different PET systems by exerting a common, reproducible, and defined partial volume effect.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Hot-electron generation by “cavitating” Langmuir turbulence in the nonlinear stage of the two-plasmon–decay instability

The kinetic reduced-description particle-in-cell simulation technique has been applied to study the nonlinear stage of two-plasmon–decay (TPD) instability in an inhomogeneous plasma driven by crossed laser beams. The TPD instability is found to be a prolific generator of “cavitating” Langmuir turbulence. Langmuir “cavitons”—localized longitudinal electric fields, oscillating near the local electron plasma frequency, trapped in ponderomotive density depressions—collapse to dimensions of a few electron Debye lengths, where the electric field energy is collisionlessly transferred to electron kinetic energy. The resulting hot electrons can attain instantaneous temperatures up to 100 keV with net suprathermal heat flux out of the system of up to a few percent of the input laser energy. Scaling laws for this hot-electron generation by TPD, in regimes motivated by recent experiments on the Omega laser, were presented recently by Vu et al. (H. X. Vu, D. F. DuBois, D. A. Russell, and J. F. Myatt, Phys. Plasmas 19, 102703 (2012)). This paper concentrates on the microscopic mechanisms for hot-electron generation. The spatial distribution of the maxima of the electric field envelope modulus is found to be very spiky, with the distribution of electric field envelope maxima obeying Gaussian statistics. The cavitons are produced in density-depletion trenches produced by the combined ponderomotive interference of the crossed laser beams and the ponderomotive beats of the primary backward-going TPD Langmuir waves (LWs) resulting from the crossed beams. The Langmuir turbulence is strongest in the electron-density region near 0.241× the laser's critical density, where the forward LWs from the crossed-beam TPD are degenerate. Nucleation of cavitons is assisted by the modulation of the electron density in the trenches, which in turn is caused by the beating of the common forward-going LW and the pair of backward-going LWs. The autocorrelation function of the LW envelope field provides a near-universal shape for intense cavitons—in the neighborhood of the local field maxima. The hot-electron temperature is found to be approximately a linear function of the “caviton temperature” determined from the Gaussian distribution of caviton maxima. These diagnostics provide strong evidence for the importance of Langmuir caviton collapse in the generation of hot electrons by TPD. Extended Zakharov model predictions for TPD exhibit the same qualitative phenomena.

Vu, H. X.↗