Variational method 3 - Steady state time dependent perturbation theory
Steady state time dependent perturbation theory and variational principles
Epstein, S. T.↗
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Nonlinear bending-torsional vibration and stability of rotating, pretwisted, preconed blades including Coriolis effects
The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by comparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.
Subrahmanyam, K. B.↗
Nonlinear vibration and stability of rotating, pretwisted, preconed blades including Coriolis effects
The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by conparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.
Subrahmanyam, K. B.↗
Reliable Spectroscopic Constants for CCH-, NH2- and Their Isotopomers from an Accurate Potential Energy Function
Accurate quartic force fields have been determined for the CCH- and NH2- molecular anions using the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, CCSD(T). Very large one-particle basis sets have been used including diffuse functions and up through g-type functions. Correlation of the nitrogen and carbon core electrons has been included, as well as other "small" effects, such as the diagonal Born-Oppenheimer correction, and basis set extrapolation, and corrections for higher-order correlation effects and scalar relativistic effects. Fundamental vibrational frequencies have been computed using standard second-order perturbation theory as well as variational methods. Comparison with the available experimental data is presented and discussed. The implications of our research for the astronomical observation of molecular anions will be discussed.
Lee, Timothy J.↗
Optical soliton perturbation with full nonlinearity by extended trial function method
The extended trial function scheme is applied to retrieve soliton solutions to the perturbed nonlinear Schrödinger’s equation with ten forms of fiber nonlinearity. Bright, dark and singular soliton solutions are retrieved that appear with their respective existence criteria. Some additional forms of nonlinear waves naturally emerge as a byproduct of the integration scheme.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Process-oriented stochastic perturbations applied to the parametrization of turbulence and shallow convection for ensemble prediction
Weather forecasting nowadays often requires some estimation of uncertainties associated with the output of meteorological models, in order to better inform decision making, especially in the context of intense weather events. Ensemble prediction systems provide such information through sets of possible scenarios which are designed to represent various uncertainty sources, including model uncertainties. A wide variety of methods have been proposed to estimate model uncertainties, among which perturbation methods targeting uncertain processes are a promising research field. Here, we focus on the representation of small-scale variability by process-oriented perturbation schemes applied to two key physical processes, namely turbulence and shallow convection. The perturbations are applied to a single-column version of the convection-permitting AROME model, in three idealized boundary-layer cases. Large-eddy simulations (LESs) of the same cases serve as a reference for the subgrid variability that has to be represented, and the results are also compared to those given by the Stochastically Perturbed Parametrization Tendencies (SPPT) method, which is a method commonly used by weather forecast centres to represent model uncertainty. The spread produced by our process-oriented perturbations of turbulence and shallow convection does not represent all the small-scale variability implied by the LESs for temperature and humidity. However, it is of a similar order of magnitude for the wind, thanks to perturbations generated by the stochastic turbulence scheme. The dispersion is structurally different from what is obtained with SPPT. It is non-negligible in the lower levels, where SPPT perturbations are usually suppressed because of numerical instabilities, indicating a possible complementarity between the schemes.
54 ENVIRONMENTAL SCIENCES↗
Multi-field inflation with random potentials: field dimension, feature scale and non-Gaussianity
We explore the super-horizon evolution of the two-point and three-point correlation functions of the primordial density perturbation in randomly-generated multi-field potentials. We use the Transport method to evolve perturbations and give full evolutionary histories for observables. Identifying the separate universe assumption as being analogous to a geometrical description of light rays, we give an expression for the width of the bundle, thereby allowing us to monitor evolution towards the adiabatic limit, as well as providing a useful means of understanding the behaviour in f{sub NL}. Finally, viewing our random potential as a toy model of inflation in the string landscape, we build distributions for observables by evolving trajectories for a large number of realisations of the potential and comment on the prospects for testing such models. We find the distributions for observables to be insensitive to the number of fields over the range 2 to 6, but that these distributions are highly sensitive to the scale of features in the potential. Most sensitive to the scale of features is the spectral index, with more than an order of magnitude increase in the dispersion of predictions over the range of feature scales investigated. Least sensitive was the non-Gaussianity parameter f{sub NL}, which was consistently small; we found no examples of realisations whose non-Gaussianity is capable of being observed by any planned experiment.
79 ASTRONOMY AND ASTROPHYSICS↗
A simulation study on chaotic behavior of light propagation in graded index fiber under random perturbation
Chaotic behavior of optical rays in a graded index fiber is studied with the help of nonlinear dynamical method under random perturbation of refractive index. The study indicates that behavior of the rays evolves from regular to chaotic due to the random perturbation. This causes irregularity of propagation of the rays in the graded index fiber, and then the performance of the fiber is reduced.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Electronic excitation spectra of molecules in solution calculated using the symmetry-adapted cluster-configuration interaction method in the polarizable continuum model with perturbative approach
A perturbative approximation of the state specific polarizable continuum model (PCM) symmetry-adapted cluster-configuration interaction (SAC-CI) method is proposed for efficient calculations of the electronic excitations and absorption spectra of molecules in solutions. This first-order PCM SAC-CI method considers the solvent effects on the energies of excited states up to the first-order with using the zeroth-order wavefunctions. This method can avoid the costly iterative procedure of the self-consistent reaction field calculations. The first-order PCM SAC-CI calculations well reproduce the results obtained by the iterative method for various types of excitations of molecules in polar and nonpolar solvents. The first-order contribution is significant for the excitation energies. The results obtained by the zeroth-order PCM SAC-CI, which considers the fixed ground-state reaction field for the excited-state calculations, are deviated from the results by the iterative method about 0.1 eV, and the zeroth-order PCM SAC-CI cannot predict even the direction of solvent shifts in n-hexane for many cases. The first-order PCM SAC-CI is applied to studying the solvatochromisms of (2,2{sup ′}-bipyridine)tetracarbonyltungsten [W(CO){sub 4}(bpy), bpy = 2,2{sup ′}-bipyridine] and bis(pentacarbonyltungsten)pyrazine [(OC){sub 5}W(pyz)W(CO){sub 5}, pyz = pyrazine]. The SAC-CI calculations reveal the detailed character of the excited states and the mechanisms of solvent shifts. The energies of metal to ligand charge transfer states are significantly sensitive to solvents. The first-order PCM SAC-CI well reproduces the observed absorption spectra of the tungsten carbonyl complexes in several solvents.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Interlaminar stresses in composite laminates: A perturbation analysis
A general method of solution for an elastic balanced symmetric composite laminate subject to a uniaxial extension was developed based upon a perturbation analysis of a limiting free body containing an interfacial plane. The solution satisfies more physical requirements and boundary conditions than previous investigations, and predicts smooth continuous interlaminar stresses with no instabilities. It determines the finite maximum intensity for the interlaminar normal stress in all laminates, provides mathematical evidences for the singular stresses in angle-ply laminates, suggests the need for the experimental determination of an important problem parameter, and introduces a viable means for solving related problems of practical interest.
Hsu, P. W.↗
Detecting and Testing for Structural Error in Computer Models with Application to the Community Atmospheric Model
Bayesian calibration/inversion methods for uncertain input parameters to simulation codes have generated an increasing amount of interest in the climate community in the recent years. This approach uses multiple disparate observational datasets related to the output of the simulator of interest to yield a probabilistic constraint on the uncertain inputs (i.e. probability distribution). A major challenge in applying Bayesian calibration methods to simulation codes is related to the possible presence of a large structural error in the output fields of interest; that is, the presence of discrepancy between the observed and the simulated output that is neither explained by the uncertainty in the inputs nor the observations. We present here methods to test for and visualize structural error in an ensemble of input-perturbed simulations. The methods are based on bootstrap (resmpling) test statistics and well-known metrics to quantify the difference between two probability distributions. The proposed methods are demonstrated using selected precipitation output fields of the Community Atmospheric Model (CAM), which are compared to observations provided by the Global Precipitation Climatology Project (GPCP). The methods are found to be useful in identifying regions and seasons with a large structural error. The proposed structural error detection methodology can be used to screen multiple observational datasets of interest for structural error, making it possible to retain only the datasets with a small structural error for use in Bayesian calibration. In addition, information about the amount of structural error can be valuable to model developers.
58 GEOSCIENCES↗
Fuel temperature reactivity coefficient calculation by Monte Carlo perturbation techniques
We present an efficient method to estimate the fuel temperature reactivity coefficient (FTC) by the Monte Carlo adjoint-weighted correlated sampling method. In this method, a fuel temperature change is regarded as variations of the microscopic cross sections and the temperature in the free gas model which is adopted to correct the asymptotic double differential scattering kernel. The effectiveness of the new method is examined through the continuous energy MC neutronics calculations for PWR pin cell problems. The isotope-wise and reaction-type-wise contributions to the FTCs are investigated for two free gas models - the constant scattering cross section model and the exact model. It is shown that the proposed method can efficiently predict the reactivity change due to the fuel temperature variation. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Quasielastic least-squares reverse time migration of PS reflections
Conventional analysis of amplitude variation with offset for elastic PS reflections is based on analytical reflection coefficients in a layered medium, and wave-equation-based PS migration is mainly used to produce a structural image. To overcome this problem, we have developed a least-squares reverse time migration (LSRTM) method for elastic PS reflections based on a quasielastic wave equation. Here, the quasielastic wave equation can accurately model PS reflections with elastic amplitudes under the first-order Born approximation. Our LSRTM method inverts for perturbations of the S-wave velocity and density by minimizing the L 2 norm of the difference between recorded and predicted PS reflections modeled using a quasielastic wave equation. We refer to our new method as quasielastic LSRTM of PS reflections. Numerical tests on synthetic and field data indicate that our method can properly handle the amplitudes of elastic PS reflections and provides an accurate estimate of the perturbations of S-wave velocity and density. Extending the method to the 3D case is not straightforward and might require incorporating certain PS data processing techniques into the inversion itself.
58 GEOSCIENCES↗
Enhancing the role of veterinary vaccines reducing zoonotic diseases of humans: Linking systems biology with vaccine development
The aim of research on infectious diseases is their prevention, and brucellosis and salmonellosis as such are classic examples of worldwide zoonoses for application of a systems biology approach for enhanced rational vaccine development. When used optimally, vaccines prevent disease manifestations, reduce transmission of disease, decrease the need for pharmaceutical intervention, and improve the health and welfare of animals, as well as indirectly protecting against zoonotic diseases of people. Advances in the last decade or so using comprehensive systems biology approaches linking genomics, proteomics, bioinformatics, and biotechnology with immunology, pathogenesis and vaccine formulation and delivery are expected to enable enhanced approaches to vaccine development. The goal of this paper is to evaluate the role of computational systems biology analysis of host:pathogen interactions (the interactome) as a tool for enhanced rational design of vaccines. Systems biology is bringing a new, more robust approach to veterinary vaccine design based upon a deeper understanding of the host pathogen interactions and its impact on the host's molecular network of the immune system. A computational systems biology method was utilized to create interactome models of the host responses to Brucella melitensis (BMEL), Mycobacterium avium paratuberculosis (MAP), Salmonella enterica Typhimurium (STM), and a Salmonella mutant (isogenic *sipA, sopABDE2) and linked to the basis for rational development of vaccines for brucellosis and salmonellosis as reviewed by Adams et al. and Ficht et al. [1,2]. A bovine ligated ileal loop biological model was established to capture the host gene expression response at multiple time points post infection. New methods based on Dynamic Bayesian Network (DBN) machine learning were employed to conduct a comparative pathogenicity analysis of 219 signaling and metabolic pathways and 1620 gene ontology (GO) categories that defined the host's biosignatures to each infectious condition. Through this DBN computational approach, the method identified significantly perturbed pathways and GO category groups of genes that define the pathogenicity signatures of the infectious agent. Our preliminary results provide deeper understanding of the overall complexity of host innate immune response as well as the identification of host gene perturbations that defines a unique host temporal biosignature response to each pathogen. The application of advanced computational methods for developing interactome models based on DBNs has proven to be instrumental in elucidating novel host responses and improved functional biological insight into the host defensive mechanisms. Evaluating the unique differences in pathway and GO perturbations across pathogen conditions allowed the identification of plausible host pathogen interaction mechanisms. Accordingly, a systems biology approach to study molecular pathway gene expression profiles of host cellular responses to microbial pathogens holds great promise as a methodology to identify, model and predict the overall dynamics of the host pathogen interactome. Thus, we propose that such an approach has immediate application to the rational design of brucellosis and salmonellosis vaccines.
59 BASIC BIOLOGICAL SCIENCES↗
Bridging the Transition from Mesoscale to Microscale Turbulence in Numerical Weather Prediction Models
With a focus towards developing multiscale capabilities in numerical weather prediction models, the specific problem of the transition from the mesoscale to the microscale is investigated. For that purpose, idealized one-way nested mesoscale to large-eddy simulation (LES) experiments were carried out using the Weather Research and Forecasting model framework. It is demonstrated that switching from one-dimensional turbulent diffusion in the mesoscale model to three-dimensional LES mixing does not necessarily result in an instantaneous development of turbulence in the LES domain. However, very large fetches are needed for the natural transition to turbulence to occur. The computational burden imposed by these long fetches necessitates the development of methods to accelerate the generation of turbulence on a nested LES domain forced by a smooth mesoscale inflow. To that end, four new methods based upon finite amplitude perturbations of the potential temperature field along the LES inflow boundaries are developed, and investigated under convective conditions. Each method accelerated the development of turbulence within the LES domain, with two of the methods resulting in a rapid generation of production and inertial range energy content associated to microscales that is consistent with non-nested simulations using periodic boundary conditions. The cell perturbation approach, the simplest and most efficient of the best performing methods, was investigated further under neutral and stable conditions. Successful results were obtained in all the regimes, where satisfactory agreement of mean velocity, variances and turbulent fluxes, as well as velocity and temperature spectra, was achieved with reference non-nested simulations. In contrast, the non-perturbed LES solution exhibited important energy deficits associated to a delayed establishment of fully-developed turbulence. The cell perturbation method has negligible computational cost, significantly accelerates the generation of realistic turbulence, and requires minimal parameter tuning, with the necessary information relatable to mean inflow conditions provided by the mesoscale solution.
17 WIND ENERGY↗
Self-consistent Kohn-Sham method based on the adiabatic-connection fluctuation-dissipation theorem and the exact-exchange kernel
A self-consistent Kohn-Sham method based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem, employing the frequency-dependent exact exchange kernel f{sub x} is presented. The resulting SC-exact-exchange-only (EXX)-ACFD method leads to even more accurate correlation potentials than those obtained within the direct random phase approximation (dRPA). In contrast to dRPA methods, not only the Coulomb kernel but also the exact exchange kernel f{sub x} is taken into account in the EXX-ACFD correlation which results in a method that, unlike dRPA methods, is free of self-correlations, i.e., a method that treats exactly all one-electron systems, like, e.g., the hydrogen atom. The self-consistent evaluation of EXX-ACFD total energies improves the accuracy compared to EXX-ACFD total energies evaluated non-self-consistently with EXX or dRPA orbitals and eigenvalues. Reaction energies of a set of small molecules, for which highly accurate experimental reference data are available, are calculated and compared to quantum chemistry methods like Møller-Plesset perturbation theory of second order (MP2) or coupled cluster methods [CCSD, coupled cluster singles, doubles, and perturbative triples (CCSD(T))]. Moreover, we compare our methods to other ACFD variants like dRPA combined with perturbative corrections such as the second order screened exchange corrections or a renormalized singles correction. Similarly, the performance of our EXX-ACFD methods is investigated for the non-covalently bonded dimers of the S22 reference set and for potential energy curves of noble gas, water, and benzene dimers. The computational effort of the SC-EXX-ACFD method exhibits the same scaling of N{sup 5} with respect to the system size N as the non-self-consistent evaluation of only the EXX-ACFD correlation energy; however, the prefactor increases significantly. Reaction energies from the SC-EXX-ACFD method deviate quite little from EXX-ACFD energies obtained non-self-consistently with dRPA orbitals and eigenvalues, and the deviation reduces even further if the Coulomb kernel is scaled by a factor of 0.75 in the dRPA to reduce self-correlations in the dRPA correlation potential. For larger systems, such a non-self-consistent EXX-ACFD method is a competitive alternative to high-level wave-function-based methods, yielding higher accuracy than MP2 and CCSD methods while exhibiting a better scaling of the computational effort than CCSD or CCSD(T) methods. Moreover, EXX-ACFD methods were shown to be applicable in situation characterized by static correlation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
SparseMaps—A systematic infrastructure for reduced-scaling electronic structure methods. III. Linear-scaling multireference domain-based pair natural orbital N-electron valence perturbation theory
Multi-reference (MR) electronic structure methods, such as MR configuration interaction or MR perturbation theory, can provide reliable energies and properties for many molecular phenomena like bond breaking, excited states, transition states or magnetic properties of transition metal complexes and clusters. However, owing to their inherent complexity, most MR methods are still too computationally expensive for large systems. Therefore the development of more computationally attractive MR approaches is necessary to enable routine application for large-scale chemical systems. Among the state-of-the-art MR methods, second-order N-electron valence state perturbation theory (NEVPT2) is an efficient, size-consistent, and intruder-state-free method. However, there are still two important bottlenecks in practical applications of NEVPT2 to large systems: (a) the high computational cost of NEVPT2 for large molecules, even with moderate active spaces and (b) the prohibitive cost for treating large active spaces. In this work, we address problem (a) by developing a linear scaling “partially contracted” NEVPT2 method. This development uses the idea of domain-based local pair natural orbitals (DLPNOs) to form a highly efficient algorithm. As shown previously in the framework of single-reference methods, the DLPNO concept leads to an enormous reduction in computational effort while at the same time providing high accuracy (approaching 99.9% of the correlation energy), robustness, and black-box character. In the DLPNO approach, the virtual space is spanned by pair natural orbitals that are expanded in terms of projected atomic orbitals in large orbital domains, while the inactive space is spanned by localized orbitals. The active orbitals are left untouched. Our implementation features a highly efficient “electron pair prescreening” that skips the negligible inactive pairs. The surviving pairs are treated using the partially contracted NEVPT2 formalism. A detailed comparison between the partial and strong contraction schemes is made, with conclusions that discourage the strong contraction scheme as a basis for local correlation methods due to its non-invariance with respect to rotations in the inactive and external subspaces. A minimal set of conservatively chosen truncation thresholds controls the accuracy of the method. With the default thresholds, about 99.9% of the canonical partially contracted NEVPT2 correlation energy is recovered while the crossover of the computational cost with the already very efficient canonical method occurs reasonably early; in linear chain type compounds at a chain length of around 80 atoms. Calculations are reported for systems with more than 300 atoms and 5400 basis functions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Comparison of XSUSA and "Two-Step" Approaches for Full Core Uncertainty Quantification
While there are multiple sources of error that are introduced into the standard computational regime for simulating reactor cores, rigorous uncertainty analysis methods are available primarily for quantifying the effects of cross section uncertainties. Two methods for propagating cross section uncertainties through core simulators are the XSUSA statistical approach and the 'Two-Step' method. The XSUSA approach, which is based on the SUSA code package, is fundamentally a stochastic sampling method. Alternatively, the Two-Step method utilizes generalized perturbation theory in the first step and stochastic sampling in the second step. The consistency of these two methods in quantifying uncertainties in the multiplication factor and in the core power distribution will be examined in the framework of phase I-3 of the UAM Benchmark. Using the TMI core as a base model for analysis, the XSUSA and Two-Step methods are applied with certain limitations and the results are compared to those produced by other stochastic sampling-based codes. Based on the uncertainty analysis results, conclusions are made for which method is currently a more viable option for computing uncertainties in burnup and transient calculations.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗