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At least 91 records · Page 5

Evaluation of Genetic Algorithm Concepts using Model Problems: Single-Objective Optimization - Part 1

A genetic-algorithm-based optimization approach is described and evaluated using a simple hill-climbing model problem. The model problem utilized herein allows for the broad specification of a large number of search spaces including spaces with an arbitrary number of genes or decision variables and an arbitrary number hills or modes. In the present study, only single objective problems are considered. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all problems attempted. The most difficult problems - those with large hyper-volumes and multi-mode search spaces containing a large number of genes - require a large number of function evaluations for GA convergence, but they always converge.

Holst, Terry L.

Hybrid diversity method utilizing adaptive diversity function for recovering unknown aberrations in an optical system

A method of recovering unknown aberrations in an optical system includes collecting intensity data produced by the optical system, generating an initial estimate of a phase of the optical system, iteratively performing a phase retrieval on the intensity data to generate a phase estimate using an initial diversity function corresponding to the intensity data, generating a phase map from the phase retrieval phase estimate, decomposing the phase map to generate a decomposition vector, generating an updated diversity function by combining the initial diversity function with the decomposition vector, generating an updated estimate of the phase of the optical system by removing the initial diversity function from the phase map. The method may further include repeating the process beginning with iteratively performing a phase retrieval on the intensity data using the updated estimate of the phase of the optical system in place of the initial estimate of the phase of the optical system, and using the updated diversity function in place of the initial diversity function, until a predetermined convergence is achieved.

Dean, Bruce H.

Background Oriented Schlieren Applied to Study Shock Spacing in a Screeching Circular Jet

Background oriented schlieren (BOS) is a recent development of the schlieren and shadowgraph methods. The BOS technique has the ability to provide visualizations of the density gradient in both the axial and radial directions. The resultant magnitude of the density gradients allows for comparison with shadowgraph images. This paper first compares data obtained by the BOS and shadowgraph techniques at identical conditions in a free jet. The patterns and spacing of the shock trains obtained by the two techniques are found to be consistent with one another. This provides confidence in the shock spacing measurement by the BOS technique. Due to its simpler setup, BOS is then applied to investigate the shock spacing associated with the screech phenomenon, especially during stage jumps. Screech frequencies from a 37.6 mm convergent nozzle, as a function of jet Mach number (M(sub j)), are shown to exhibit various stages. As many as eight stages are identified with the present nozzle over the range 1.0 < M(sub j) <1.7. BOS images are acquired at various screech conditions and the shock spacing is examined as a function of M(sub j).

Clem, Michelle M.

Recursive Branching Simulated Annealing Algorithm

This innovation is a variation of a simulated-annealing optimization algorithm that uses a recursive-branching structure to parallelize the search of a parameter space for the globally optimal solution to an objective. The algorithm has been demonstrated to be more effective at searching a parameter space than traditional simulated-annealing methods for a particular problem of interest, and it can readily be applied to a wide variety of optimization problems, including those with a parameter space having both discrete-value parameters (combinatorial) and continuous-variable parameters. It can take the place of a conventional simulated- annealing, Monte-Carlo, or random- walk algorithm. In a conventional simulated-annealing (SA) algorithm, a starting configuration is randomly selected within the parameter space. The algorithm randomly selects another configuration from the parameter space and evaluates the objective function for that configuration. If the objective function value is better than the previous value, the new configuration is adopted as the new point of interest in the parameter space. If the objective function value is worse than the previous value, the new configuration may be adopted, with a probability determined by a temperature parameter, used in analogy to annealing in metals. As the optimization continues, the region of the parameter space from which new configurations can be selected shrinks, and in conjunction with lowering the annealing temperature (and thus lowering the probability for adopting configurations in parameter space with worse objective functions), the algorithm can converge on the globally optimal configuration. The Recursive Branching Simulated Annealing (RBSA) algorithm shares some features with the SA algorithm, notably including the basic principles that a starting configuration is randomly selected from within the parameter space, the algorithm tests other configurations with the goal of finding the globally optimal solution, and the region from which new configurations can be selected shrinks as the search continues. The key difference between these algorithms is that in the SA algorithm, a single path, or trajectory, is taken in parameter space, from the starting point to the globally optimal solution, while in the RBSA algorithm, many trajectories are taken; by exploring multiple regions of the parameter space simultaneously, the algorithm has been shown to converge on the globally optimal solution about an order of magnitude faster than when using conventional algorithms. Novel features of the RBSA algorithm include: 1. More efficient searching of the parameter space due to the branching structure, in which multiple random configurations are generated and multiple promising regions of the parameter space are explored; 2. The implementation of a trust region for each parameter in the parameter space, which provides a natural way of enforcing upper- and lower-bound constraints on the parameters; and 3. The optional use of a constrained gradient- search optimization, performed on the continuous variables around each branch s configuration in parameter space to improve search efficiency by allowing for fast fine-tuning of the continuous variables within the trust region at that configuration point.

Bolcar, Matthew

Cosmological constraints using Minkowski functionals from the first year data of the Hyper Suprime-Cam

We use Minkowski functionals to analyse weak lensing convergence maps from the first-year data release of the Subaru Hyper Suprime-Cam (HSC-Y1) survey. Minkowski functionals provide a description of the morphological properties of a field, capturing the non-Gaussian features of the Universe matter-density distribution. Using simulated catalogues that reproduce survey conditions and encode cosmological information, we emulate Minkowski functionals predictions across a range of cosmological parameters to derive the best-fit from the data. By applying multiple scales cuts, we rigorously mitigate systematic effects, including baryonic feedback and intrinsic alignments. From the analysis, combining constraints of the angular power spectrum and Minkowski functionals, we obtain S8≡σ8Ωm/0.3=0.808−0.046+0.033 and Ωm=0.293−0.043+0.157⁠. These results represent a 40 per cent improvement on the S8 constraints compared to using power spectrum only. Minkowski functionals results are consistent with other two-point, and higher order statistics constraints using the same data, being in agreement with CMB results from the Planck S8 measurements. Our study demonstrates the power of Minkowski functionals beyond two-point statistics to constrain and break the degeneracy between Ωm and σ8⁠.

79 ASTRONOMY AND ASTROPHYSICS

Oscillatory supersonic kernel function method for interfering surfaces

In the method presented in this paper, a collocation technique is used with the nonplanar supersonic kernel function to solve multiple lifting surface problems with interference in steady or oscillatory flow. The pressure functions used are based on conical flow theory solutions and provide faster solution convergence than is possible with conventional functions. In the application of the nonplanar supersonic kernel function, an improper integral of a 3/2 power singularity along the Mach hyperbola is described and treated. The method is compared with other theories and experiment for two wing-tail configurations in steady and oscillatory flow.

Cunningham, A. M., Jr.

A variable phase function approach for the inversion of lidar return signals

A variable phase function is developed. This function may be used for the inversion of lidar data in an iterative process. Numerical simulations of this method were performed successfully, demonstrating fast convergence of the particulate phase function. The method will be used in the future to evaluate extinction and backscattering corrections for an Ultra-Violet Differential Absorption Lidar (UV-DIAL) system measuring tropospheric ozone concentrations.

Kovalev, V. A.

Degenerate coupled-cluster theory

A size-extensive, converging, black-box, ab initio coupled-cluster (ΔCC) ansatz is introduced that computes the energies and wave functions of states from any degenerate or nondegenerate Slater-determinant references with any numbers of α- and β-spin electrons, any patterns of orbital occupancy, any spin multiplicities, and any spatial symmetries. For a nondegenerate reference, it reduces to the single-reference coupled-cluster ansatz. For a degenerate multireference, it is a natural coupled-cluster extension of degenerate Møller–Plesset perturbation (ΔMP) theory. For ionized and electron-attached references, it is a coupled-cluster Green’s function, although the present theory is convergent toward the full-configuration-interaction limits, while the Feynman–Dyson many-body Green’s function (MBGF) theory generally is not. Its single-excitation instance is a projection Hartree–Fock theory as per the Thouless theorem, which may be useful for core ionizations, high-spin states, and possibly electron affinities. Additionally, a new multireference coupled-cluster theory for a general model space is developed. This quasidegenerate coupled-cluster (QCC) theory is exactly converging, but not black-box, and intended for strong correlation. Determinant-based, general-order algorithms of ΔCC and QCC theories are implemented and compared with configuration-interaction (CI) and equation-of-motion coupled-cluster (EOM-CC) theories through octuple excitations and with ΔMP and MBGF theories up to the nineteenth order. An algebraic, optimal-scaling algorithm of the ΔCC theory is computer-synthesized at the levels of single excitations (ΔCCS) and of single and double excitations (ΔCCSD). As a result, the order of performance is QCC ≈ ΔCC > EOM-CC > CI at the same order or QCC ≈ ΔCC > ΔMP > MBGF at the same cost scaling.

Hirata, So [University of Illinois at Urbana-Champ

NASA information systems commonality and convergence

Efforts to identify high payback functions performed by the Office of Space Science Applications (OSSA) data systems package existing operationally proven implementations as system building blocks and foster their use in the OSSA environment. An overview is given of the current state of OSSA data systems and the major challenges facing system developers over the next five years. Current trends in system commonality are discussed, and development is examined in the context of system design. Central system engineering approaches to solving the commonality and interoperability challenges are described. Efforts to package three diverse building blocks and to foster their reuse are documented.

Handley, Thomas H., Jr.

Impact buckling of thin bars in the elastic range for any end condition

Following a qualitative discussion of the complicated process involved in a short-period, longitudinal force applied to an originally not quite straight bar, the actual process is substituted by an idealized process for the purpose of analytical treatment. The simplifications are: the assumption of an infinitely high rate of propagation of the elastic longitudinal waves in the bar, limitation to slender bars, disregard of material damping and of rotatory inertia, the assumption of consistently small elastic deformations, the assumption of cross-sectional dimensions constant along the bar axis, the assumption of a shock-load constant in time, and the assumption of eccentricities on one plane. Then follow the mathematical principles for resolving the differential equation of the simplified problem, particularly the developability of arbitrary functions with steady first and second and intermittently steady third and fourth derivatives into one convergent series, according to the natural functions of the homogeneous differential equation.

Taub, Josef

Improvements to the kernel function method of steady, subsonic lifting surface theory

The application of a kernel function lifting surface method to three dimensional, thin wing theory is discussed. A technique for determining the influence functions is presented. The technique is shown to require fewer quadrature points, while still calculating the influence functions accurately enough to guarantee convergence with an increasing number of spanwise quadrature points. The method also treats control points on the wing leading and trailing edges. The report introduces and employs an aspect of the kernel function method which apparently has never been used before and which significantly enhances the efficiency of the kernel function approach.

Medan, R. T.

Reporting Recommended Patch Density from Vehicle Panel Vibration Convergence Studies using both DAF and TBL Fits of the Spatial Correlation Function

Using the patch method to represent the continuous spatial correlation function of a phased pressure field over a structural surface is an approximation. The approximation approaches the continuous function as patches become smaller. Plotting comparisons of the approximation vs the continuous function may provide insight revealing: (1) For what patch size/density should the approximation be very good? (2) What the approximation looks like when it begins to break down? (3) What the approximation looks like when the patch size is grossly too large. Following these observations with a convergence study using one FEM may allow us to see the importance of patch density. We may develop insights that help us to predict sufficient patch density to provide adequate convergence for the intended purpose frequency range of interest

Smith, Andrew M.

Flavor Dependence of Charged Pion Fragmentation Functions

We have measured the flavor dependence of multiplicities for π + and π - production in semi-inclusive deep-inelastic scattering (SIDIS) on proton and deuteron to explore a possible charge symmetry violation in fragmentation functions. The experiment used an electron beam with energies of 10.2 and 10.6 GeV at Jefferson Lab and the Hall-C spectrometers. The electron kinematics spanned the range 0.3 < x < 0.6, 2 < Q 2 < 5.5 GeV2, and 2.2 < W < 3.2 GeV. The pion fractional momentum range was 0.3 < z < 0.7, and the transverse momentum range was 0 < p T < 0.25 GeV/c. Assuming factorization and allowing for isospin breaking, the results can be described by two “favored” and two “unfavored” effective low p T fragmentation functions that are flavor-dependent. We find each pair converges to a common flavor-independent fragmentation function at the highest W, where factorization is most applicable.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

The phase-integral method for radiative transfer problems with highly-peaked phase functions

Complete solutions to the radiative transfer equation, including both azimuth and depth dependence, are provided by the discrete-ordinate method of Chandrasekhar, but these solutions are often limited because of large computer requirements. This paper presents a 'phase-integral' method which greatly reduces the number of discrete ordinates needed in the solution for highly peaked phase functions. A composite quadrature method is shown to be effective in further reducing the number of discrete ordinates required for highly anisotropic phase functions. Examples are given to indicate convergence requirements and expected accuracy in the complete solution for Henyey-Greenstein and cloud-type phase functions.

Fricke, C. L.

The Dissociation Energies of He2, HeH, and ArH; A Bond Function Study

The bond energies and bond lengths are determined for He2, HeH, and ArH at the CCSD(T) level using both atom-centered basis sets and those that include bond functions. The addition of bond functions dramatically improves the rate of convergence of the results with respect to the size of the atom-centered basis set; with bond functions, triple zeta atom-centered basis set, outperform quintuple zeta basis sets without bond functions. The addition of bond functions also reduces the number of diffuse functions that must be added to the atom-centered sets. Employing bond functions appear to offer a very cost effective method of computing the interaction between weakly bound systems, especially for He.

Bauschlicher, Charles W., Jr.

Multiresolution Quantum Chemistry: Nonlinear Response Properties at the Basis Set Limit

We benchmark the accuracy of Dunning correlation-consistent Gaussian basis sets for computing frequencydependent second-order hyperpolarizabilities relevant to second-harmonic generation (SHG), using multiresolution analysis (MRA) as a reference. Basis set errors are analyzed using a unit-sphere representation of the effective hyperpolarizability vector, enabling direct assessment of directional error structure. We introduce a relative RMS total error metric that integrates directional deviations over the unit sphere and complement it with signed projection errors that distinguish over- and underestimation. Unsupervised clustering based on these signed directional metrics reveals four distinct convergence behaviors across a set of 68 molecules. Unitsphere visualizations of representative systems show that basis set errors are often highly anisotropic and localized along specific bond directions, even when global error measures appear small. Doubly augmented basis sets consistently outperform singly augmented ones, and core-polarization functions are required for uniform convergence in second-row systems. Overall, this work demonstrates that directional analysis combined with clustering provides a robust framework for understanding basis set convergence in nonlinear optical response properties.

Basis sets

Quick-and-Easy Validation of Protein–Ligand Binding Models Using Fragment-Based Semiempirical Quantum Chemistry

Electronic structure calculations in enzymes converge very slowly with respect to the size of the model region that is described using quantum mechanics (QM), requiring hundreds of atoms to obtain converged results and exhibiting substantial sensitivity (at least in smaller models) to which amino acids are included in the QM region. As such, there is considerable interest in developing automated procedures to construct a QM model region based on well-defined criteria. However, testing such procedures is burdensome due to the cost of large-scale electronic structure calculations. Here, we show that semiempirical methods can be used as alternatives to density functional theory (DFT) to assess convergence in sequences of models generated by various automated protocols. The cost of these convergence tests is reduced even further by means of a many-body expansion. We use this approach to examine convergence (with respect to model size) of protein–ligand binding energies. Fragment-based semiempirical calculations afford well-converged interaction energies in a tiny fraction of the cost required for DFT calculations. Two-body interactions between the ligand and single-residue amino acid fragments afford a low-cost way to construct a “QM-informed” enzyme model of reduced size, furnishing an automatable active-site model-building procedure. This provides a streamlined, user-friendly approach for constructing ligand binding-site models that needs neither a priori information nor manual adjustments. Extension to model-building for thermochemical calculations should be straightforward.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH