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Results for “GAUSS FUNCTION”

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At least 19 records

Studies of the Magnetocaloric and Electrical Properties of La{sub 0.7}Er{sub 0.05}Sr{sub 0.15}Ca{sub 0.1}Mn{sub 1−x}In{sub x}O{sub 3} (0 ≤ x ≤ 0.30)

We report on the study of In substitution for Mn on the magnetic and transport properties of layered manganese oxides La{sub 0.7}Er{sub 0.05}Sr{sub 0.15}Ca{sub 0.1}Mn{sub 1−x}In{sub x}O{sub 3} (0 ≤ x ≤ 0.30) synthesized via sol-gel method. For all the samples, all peaks are satisfactorily indexed in the rhombohedra structure with R 3-bar c space group. Magnetic data, under a magnetic field of 0.05 T, revealed that our compounds exhibit a continuous (second-order) transition from a ferromagnetic (FM) to a paramagnetic (PM) state upon decreasing the temperature. Also, magnetic entropy change and relative cooling power for magnetic field variation were predicted. Then, we have fitted the experimental data of resistivity using non-linear curve fitting, a typical mathematical function (Gauss function). This function can describe the carrier transport behavior of manganites as a function of temperature around the electrical phase transition. The obtained results were discussed. These predicted parameters agree with the experimental data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A method for the characterization of intra-pixel response of infrared sensor

Due to the response variations within a pixel, response of sensor varies with the positions of the point target. The accurate measurement of intra-pixel response of the sensor is the key to high-precision centroid estimation and radiometric calibration. In this paper, we establish an intra-pixel response model based on the pixel structure and use Gauss function to describe the beam spot profile. We further calculate the full width at half maximum (FWHM) of the Gauss function and the fill factor of the infrared sensor using the grid search algorithm. Experimental results show that the Gauss function FWHM differences among different pixels using the same radius could be less than 6%. The fill factors are not constant in different pixels because of errors in the process of manufacture and assembly, and the error between model and measured values is less than 3.6%. This work could be useful for stellar calibration and centroid estimation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Localization of Carriers in Quantum Dots with Uniaxial Anisotropy of Shape and Composition

The electronic and hole states in quantum dots (QD) of cubic II–VI semiconductors with a spheroidal shape and uniaxial anisotropy have been studied theoretically. The smooth potential energy profiles simulated by the Gauss function in all three spatial directions are considered. The energy level lowering and the energy splitting of the hole state from the valence band top Γ{sub 8} by momentum 3/2 into the states with projections ±3/2, ±1/2 on the anisotropy axis are analyzed. The QD anisotropies of three types are considered: the QD size anisotropy, the QD potential barrier anisotropy, and the combined anisotropy. In the first case, flattened quantum dots, in which the characteristic size in the structure plane is larger than the size along the anisotropy axis, are considered. In the second case, QDs, in which the potential barrier height in the plane is lower than that along the anisotropy axis, are considered. In the third case, flattened quantum dots with the anisotropy of the size and the potential barrier are considered. The conditions of the charge carrier localization inside QD have been found, and the influence of the form and composition anisotropies on the energies of exciton transitions in the structures with Cd{sub x}Zn{sub 1 –} {sub x}Se quantum dots are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quantitative comparison of self-healing ability between Bessel–Gaussian beam and Airy beam

The self-healing ability during propagation process is one of the most important properties of non-diffracting beams. This ability has crucial advantages to light sheet-based microscopy to reduce scattering artefacts, increase the quality of the image and enhance the resolution of microscopy. Based on similarity between two infinite-dimensional complex vectors in Hilbert space, the ability to a Bessel–Gaussian beam and an Airy beam have been studied and compared. Comparing the evolution of the similarity of Bessel–Gaussian beam with Airy beam under the same conditions, we find that Bessel–Gaussian beam has stronger self-healing ability and is more stable than that of Airy beam. To confirm this result, the intensity profiles of Bessel–Gaussian beam and Airy beam with different similarities are numerically calculated and compared.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions

Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes' rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multifractal analysis of time series generated by discrete Ito equations

In this study, we show that discrete Ito equations with short-tail Gaussian marginal distribution function generate multifractal time series. The multifractality is due to the nonlinear correlations, which are hidden in Markov processes and are generated by the interrelation between the drift and the multiplicative stochastic forces in the Ito equation. A link between the range of the generalized Hurst exponents and the mean of the squares of all averaged net forces is suggested.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Photoacoustic effect generated by moving optical sources: Motion in one dimension

Although the photoacoustic effect is typically generated by pulsed or amplitude modulated optical beams, it is clear from examination of the wave equation for pressure that motion of an optical source in space will result in the production of sound as well. Here, the properties of the photoacoustic effect generated by moving sources in one dimension are investigated. The cases of a moving Gaussian beam, an oscillating delta function source, and an accelerating Gaussian optical sources are reported. The salient feature of one-dimensional sources in the linear acoustic limit is that the amplitude of the beam increases in time without bound.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SU-F-BRD-06: Robust Dose Calculation in Intensity Modulated Proton Therapy

Purpose: Commissioning data for intensity modulated proton therapy (IMPT) must be post-processed by fits to ad-hoc functions to derive the dose calculation kernel parameters in a treatment planning system (TPS). Whether from experimental measurement or Monte Carlo simulation, the limited and noisy nature of such data makes this task very challenging. We present a method to improve the modeling of the lateral dose distribution of clinical energy proton beams in water to commission an in-house IMPT dose calculation engine. Methods: A linear sum of three Gaussian distribution functions was fitted to the lateral dose data in logarithmic scale. Starting values of fitting solutions were determined from the Generalized Highland Approximation. We exhaustively optimized the combinations of data weights with upper bounds of the fitting solutions to minimize confidence intervals of the fitting solutions while maintaining the coefficient of determination (R{sup 2}). Results: Across all energies, average confidence bounds improved 72.88% [Max: 88.28%, Min: 55.05%] for small angle coulomb scattering, 114.25% [409.13%, 66.72%,] for nuclear scattering, and 68.66% [141.09%, 33.27%] for large angle coulomb scattering, while the coefficients of determination of the fits (R{sup 2}) remained comparable. On average R {sup 2} only changed 0.18% and were very close to 1 (approx. 0.999). Wilcoxon signed rank tests comparing unweighted/unbounded fits with weighted/bounded fits averaged 0.0146 (Max: 0.177, Min: 7.05×10−{sup 7}) for small angle Coulomb, 0.0903 (0.945, 7.05×10−{sup 7}) for nuclear, and 0.254 (0.871, 1.86×10−{sup 6}) for large angle Coulomb scattering. This allows rejection of the null hypothesis for small angle Coulomb scattering at the 0.015 level and nuclear interaction at the 0.1 level. Conclusion: Optimal weights assigned to IMPT lateral dose data minimized fitting to stochastic noise in the tail region. Optimizing the upper bounds of fitting parameters improved the robustness of fitting solutions. Both led to a more physically meaningful dose calculation kernel for the TPS. NIH/NCI K25CA168984, Eagles Cancer Research Career Development, The Lawrence W. and Marilyn W. Matteson Fund for Cancer Research, Mayo ASU Seed Grant, and The Kemper Marley Foundation.

60 APPLIED LIFE SCIENCES↗

Statistical properties of Charney-Hasegawa-Mima zonal flows

A theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent plasma transport events in unforced zonal flows is provided within the Charney-Hasegawa-Mima (CHM) model. The governing equation is solved numerically with various prescribed density gradients that are designed to produce different configurations of parallel and anti-parallel streams. Long-lasting vortices form whose flow is governed by the zonal streams. It is found that the numerically generated PDFs can be matched with analytical predictions of PDFs based on the instanton method by removing the autocorrelations from the time series. In many instances, the statistics generated by the CHM dynamics relaxes to Gaussian distributions for both the electrostatic and vorticity perturbations, whereas in areas with strong nonlinear interactions it is found that the PDFs are exponentially distributed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An optical tweezer in asymmetrical vortex Bessel-Gaussian beams

We study an optical micromanipulation that comprises trapping, rotating, and transporting 5-μm polystyrene microbeads in asymmetric Bessel-Gaussian (BG) laser beams. The beams that carry orbital angular momentum are generated by means of a liquid crystal microdisplay and focused by a microobjective with a numerical aperture of NA = 0.85. We experimentally show that given a constant topological charge, the rate of microparticle motion increases near linearly with increasing asymmetry of the BG beam. Asymmetric BG beams can be used instead of conventional Gaussian beam for trapping and transferring live cells without thermal damage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

STAR FORMATION IN TURBULENT MOLECULAR CLOUDS WITH COLLIDING FLOW

Using self-gravitational hydrodynamical numerical simulations, we investigated the evolution of high-density turbulent molecular clouds swept by a colliding flow. The interaction of shock waves due to turbulence produces networks of thin filamentary clouds with a sub-parsec width. The colliding flow accumulates the filamentary clouds into a sheet cloud and promotes active star formation for initially high-density clouds. Clouds with a colliding flow exhibit a finer filamentary network than clouds without a colliding flow. The probability distribution functions (PDFs) for the density and column density can be fitted by lognormal functions for clouds without colliding flow. When the initial turbulence is weak, the column density PDF has a power-law wing at high column densities. The colliding flow considerably deforms the PDF, such that the PDF exhibits a double peak. The stellar mass distributions reproduced here are consistent with the classical initial mass function with a power-law index of –1.35 when the initial clouds have a high density. The distribution of stellar velocities agrees with the gas velocity distribution, which can be fitted by Gaussian functions for clouds without colliding flow. For clouds with colliding flow, the velocity dispersion of gas tends to be larger than the stellar velocity dispersion. The signatures of colliding flows and turbulence appear in channel maps reconstructed from the simulation data. Clouds without colliding flow exhibit a cloud-scale velocity shear due to the turbulence. In contrast, clouds with colliding flow show a prominent anti-correlated distribution of thin filaments between the different velocity channels, suggesting collisions between the filamentary clouds.

79 ASTRONOMY AND ASTROPHYSICS↗

THE BIMODAL STRUCTURE OF THE SOLAR CYCLE

Some properties of the 11 yr solar cycle can be explained by the current solar dynamo models. However, some other features remain not well understood such as the asymmetry of the cycle, the double-peaked structure, and the “Waldmeier effect” that a stronger cycle tends to have less rise time and a shorter cycle length. We speculate that the solar cycle is governed by a bi-dynamo model forming two stochastic processes depicted by a bimodal Gaussian function with a time gap of about 2 yr, from which the above features can be reasonably explained. The first one describes the main properties of the cycle dominated by the current solar dynamo models, and the second one occurs either in the rising phase as a short weak explosive perturbation or in the declining phase as a long stochastic perturbation. The above function is the best one selected from several in terms of the Akaike information criterion. Through analyzing different distributions, one might speculate about the dominant physical process inside the convection zone. The secondary (main) process is found to be closely associated with complicated (simple) active ranges. In effect, the bi-dynamo model is a reduced form of a multi-dynamo model, which could occur from the base of the convection zone through its envelope and from low to high heliographic latitude, reflecting the active belts in the convection zone. These results are insensitive to the hemispheric asymmetry, smoothing filters, and distribution functions selected and are expected to be helpful in understanding the formation of solar and stellar cycles.

79 ASTRONOMY AND ASTROPHYSICS↗

Three independent one-dimensional margins for single-fraction frameless stereotactic radiosurgery brain cases using CBCT

Purpose: Setting a proper margin is crucial for not only delivering the required radiation dose to a target volume, but also reducing the unnecessary radiation to the adjacent organs at risk. This study investigated the independent one-dimensional symmetric and asymmetric margins between the clinical target volume (CTV) and the planning target volume (PTV) for linac-based single-fraction frameless stereotactic radiosurgery (SRS).Methods: The authors assumed a Dirac delta function for the systematic error of a specific machine and a Gaussian function for the residual setup errors. Margin formulas were then derived in details to arrive at a suitable CTV-to-PTV margin for single-fraction frameless SRS. Such a margin ensured that the CTV would receive the prescribed dose in 95% of the patients. To validate our margin formalism, the authors retrospectively analyzed nine patients who were previously treated with noncoplanar conformal beams. Cone-beam computed tomography (CBCT) was used in the patient setup. The isocenter shifts between the CBCT and linac were measured for a Varian Trilogy linear accelerator for three months. For each plan, the authors shifted the isocenter of the plan in each direction by ±3 mm simultaneously to simulate the worst setup scenario. Subsequently, the asymptotic behavior of the CTV V{sub 80%} for each patient was studied as the setup error approached the CTV-PTV margin.Results: The authors found that the proper margin for single-fraction frameless SRS cases with brain cancer was about 3 mm for the machine investigated in this study. The isocenter shifts between the CBCT and the linac remained almost constant over a period of three months for this specific machine. This confirmed our assumption that the machine systematic error distribution could be approximated as a delta function. This definition is especially relevant to a single-fraction treatment. The prescribed dose coverage for all the patients investigated was 96.1%± 5.5% with an extreme 3-mm setup error in all three directions simultaneously. It was found that the effect of the setup error on dose coverage was tumor location dependent. It mostly affected the tumors located in the posterior part of the brain, resulting in a minimum coverage of approximately 72%. This was entirely due to the unique geometry of the posterior head.Conclusions: Margin expansion formulas were derived for single-fraction frameless SRS such that the CTV would receive the prescribed dose in 95% of the patients treated for brain cancer. The margins defined in this study are machine-specific and account for nonzero mean systematic error. The margin for single-fraction SRS for a group of machines was also derived in this paper.

61 RADIATION PROTECTION AND DOSIMETRY↗

Structural features and the microscopic dynamics of the three-component Zr{sub 47}Cu{sub 46}Al{sub 7} system: Equilibrium melt, supercooled melt, and amorphous alloy

The structural and dynamic properties of the three-component Zr{sub 47}Cu{sub 46}Al{sub 7} system are subjected to a molecular dynamics simulation in the temperature range T = 250–3000 K at a pressure p = 1.0 bar. The temperature dependences of the Wendt–Abraham parameter and the translation order parameter are used to determine the glass transition temperature in the Zr{sub 47}Cu{sub 46}Al{sub 7} system, which is found to be T{sub c} ≈ 750 K. It is found that the bulk amorphous Zr{sub 47}Cu{sub 46}Al{sub 7} alloy contains localized regions with an ordered atomic structures. Cluster analysis of configuration simulation data reveals the existence of quasi-icosahedral clusters in amorphous metallic Zr–Cu–Al alloys. The spectral densities of time radial distribution functions of the longitudinal (C̃{sub L}(k, ω)) and transverse (C̃{sub T}(k, ω)) fluxes are calculated in a wide wavenumber range in order to study the mechanisms of formation of atomic collective excitations in the Zr{sub 47}Cu{sub 46}Al{sub 7} system. It was found that a linear combination of three Gaussian functions is sufficient to reproduce the (C̃{sub L}(k, ω)) spectra, whereas at least four Gaussian contributions are necessary to exactly describe the (C̃{sub T}(k, ω)) spectra of the supercooled melt and the amorphous metallic alloy. It is shown that the collective atomic excitations in the equilibrium melt at T = 3000 K and in the amorphous metallic alloy at T = 250 K are characterized by two dispersion acoustic-like branches related with longitudinal and transverse polarizations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Influence of Intermittency on the Quasi-perpendicular Scaling in Three-dimensional Magnetohydrodynamic Turbulence

Solar wind fluctuations reveal the ubiquity of intermittency, which is believed to affect the spectral signatures of turbulence. In this work, based on simulation of driven compressible MHD turbulence, we apply the wavelet technique to the magnetic field and velocity to identify intermittency, and we analyze the influence of the intermittency on the quasi-perpendicular scaling in the inertial range. The numerical results show that the original magnetic and velocity fluctuations are anisotropic, and have a power anisotropy with a spectral index approaching the Iroshnikov–Kraichnan −3/2 scaling in the direction quasi-perpendicular to the local mean magnetic field. As in observations of the solar wind fluctuations, as the scale decreases in the simulation, the calculated probability distribution functions (pdfs) of the wavelet coefficients become extended on both tails of the non-Gaussian distribution, with a rapid increase in flatness. After intermittency has been removed from the driven turbulence, at each scale, the pdfs approach a Gaussian distribution, with the flatness being ∼3. Meanwhile, the quasi-perpendicular scaling for both fluctuations becomes steeper and close to a Kolmogorov −5/3 scaling, which may be a result of the stronger intermittency in the quasi-perpendicular direction and at the smaller scales. These results suggest that there is intermittency superposed on the “background” turbulence that seems to have the Kolmogorov scaling, whereby the overall slope is getting flatter with the involvement of intermittency.

79 ASTRONOMY AND ASTROPHYSICS↗