Quantum corrections to the generalized Proca theory via a matter field

NASA Astrophysics Data System (ADS)

Amado, André; Haghani, Zahra; Mohammadi, Azadeh; Shahidi, Shahab

2017-09-01

We study the quantum corrections to the generalized Proca theory via matter loops. We consider two types of interactions, linear and nonlinear in the vector field. Calculating the one-loop correction to the vector field propagator, three- and four-point functions, we show that the non-linear interactions are harmless, although they renormalize the theory. The linear matter-vector field interactions introduce ghost degrees of freedom to the generalized Proca theory. Treating the theory as an effective theory, we calculate the energy scale up to which the theory remains healthy.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory

NASA Astrophysics Data System (ADS)

Riplinger, Christoph; Pinski, Peter; Becker, Ute; Valeev, Edward F.; Neese, Frank

2016-01-01

Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate previous implementation.

Impulse-response functions and anthropogenic CO2

NASA Technical Reports Server (NTRS)

Tubiello, Francesco N.; Oppenheimer, Michael

1995-01-01

Non-linearities in the carbon cycle make the response to atmospheric CO2 perturbations dependent on emission history. We show that even when linear representations of the carbon cycle are used, the calculation of time scales characterizing the removal of excess CO2 depends on past emissions.

Auxiliary basis expansions for large-scale electronic structure calculations.

PubMed

Jung, Yousung; Sodt, Alex; Gill, Peter M W; Head-Gordon, Martin

2005-05-10

One way to reduce the computational cost of electronic structure calculations is to use auxiliary basis expansions to approximate four-center integrals in terms of two- and three-center integrals, usually by using the variationally optimum Coulomb metric to determine the expansion coefficients. However, the long-range decay behavior of the auxiliary basis expansion coefficients has not been characterized. We find that this decay can be surprisingly slow. Numerical experiments on linear alkanes and a toy model both show that the decay can be as slow as 1/r in the distance between the auxiliary function and the fitted charge distribution. The Coulomb metric fitting equations also involve divergent matrix elements for extended systems treated with periodic boundary conditions. An attenuated Coulomb metric that is short-range can eliminate these oddities without substantially degrading calculated relative energies. The sparsity of the fit coefficients is assessed on simple hydrocarbon molecules and shows quite early onset of linear growth in the number of significant coefficients with system size using the attenuated Coulomb metric. Hence it is possible to design linear scaling auxiliary basis methods without additional approximations to treat large systems.

Graph-based linear scaling electronic structure theory.

PubMed

Niklasson, Anders M N; Mniszewski, Susan M; Negre, Christian F A; Cawkwell, Marc J; Swart, Pieter J; Mohd-Yusof, Jamal; Germann, Timothy C; Wall, Michael E; Bock, Nicolas; Rubensson, Emanuel H; Djidjev, Hristo

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Graph-based linear scaling electronic structure theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Niklasson, Anders M. N., E-mail: amn@lanl.gov; Negre, Christian F. A.; Cawkwell, Marc J.

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Additive scales in degenerative disease--calculation of effect sizes and clinical judgment.

PubMed

Riepe, Matthias W; Wilkinson, David; Förstl, Hans; Brieden, Andreas

2011-12-16

The therapeutic efficacy of an intervention is often assessed in clinical trials by scales measuring multiple diverse activities that are added to produce a cumulative global score. Medical communities and health care systems subsequently use these data to calculate pooled effect sizes to compare treatments. This is done because major doubt has been cast over the clinical relevance of statistically significant findings relying on p values with the potential to report chance findings. Hence in an aim to overcome this pooling the results of clinical studies into a meta-analyses with a statistical calculus has been assumed to be a more definitive way of deciding of efficacy. We simulate the therapeutic effects as measured with additive scales in patient cohorts with different disease severity and assess the limitations of an effect size calculation of additive scales which are proven mathematically. We demonstrate that the major problem, which cannot be overcome by current numerical methods, is the complex nature and neurobiological foundation of clinical psychiatric endpoints in particular and additive scales in general. This is particularly relevant for endpoints used in dementia research. 'Cognition' is composed of functions such as memory, attention, orientation and many more. These individual functions decline in varied and non-linear ways. Here we demonstrate that with progressive diseases cumulative values from multidimensional scales are subject to distortion by the limitations of the additive scale. The non-linearity of the decline of function impedes the calculation of effect sizes based on cumulative values from these multidimensional scales. Statistical analysis needs to be guided by boundaries of the biological condition. Alternatively, we suggest a different approach avoiding the error imposed by over-analysis of cumulative global scores from additive scales.

Development of Computational Aeroacoustics Code for Jet Noise and Flow Prediction

NASA Astrophysics Data System (ADS)

Keith, Theo G., Jr.; Hixon, Duane R.

2002-07-01

Accurate prediction of jet fan and exhaust plume flow and noise generation and propagation is very important in developing advanced aircraft engines that will pass current and future noise regulations. In jet fan flows as well as exhaust plumes, two major sources of noise are present: large-scale, coherent instabilities and small-scale turbulent eddies. In previous work for the NASA Glenn Research Center, three strategies have been explored in an effort to computationally predict the noise radiation from supersonic jet exhaust plumes. In order from the least expensive computationally to the most expensive computationally, these are: 1) Linearized Euler equations (LEE). 2) Very Large Eddy Simulations (VLES). 3) Large Eddy Simulations (LES). The first method solves the linearized Euler equations (LEE). These equations are obtained by linearizing about a given mean flow and the neglecting viscous effects. In this way, the noise from large-scale instabilities can be found for a given mean flow. The linearized Euler equations are computationally inexpensive, and have produced good noise results for supersonic jets where the large-scale instability noise dominates, as well as for the tone noise from a jet engine blade row. However, these linear equations do not predict the absolute magnitude of the noise; instead, only the relative magnitude is predicted. Also, the predicted disturbances do not modify the mean flow, removing a physical mechanism by which the amplitude of the disturbance may be controlled. Recent research for isolated airfoils' indicates that this may not affect the solution greatly at low frequencies. The second method addresses some of the concerns raised by the LEE method. In this approach, called Very Large Eddy Simulation (VLES), the unsteady Reynolds averaged Navier-Stokes equations are solved directly using a high-accuracy computational aeroacoustics numerical scheme. With the addition of a two-equation turbulence model and the use of a relatively coarse grid, the numerical solution is effectively filtered into a directly calculated mean flow with the small-scale turbulence being modeled, and an unsteady large-scale component that is also being directly calculated. In this way, the unsteady disturbances are calculated in a nonlinear way, with a direct effect on the mean flow. This method is not as fast as the LEE approach, but does have many advantages to recommend it; however, like the LEE approach, only the effect of the largest unsteady structures will be captured. An initial calculation was performed on a supersonic jet exhaust plume, with promising results, but the calculation was hampered by the explicit time marching scheme that was employed. This explicit scheme required a very small time step to resolve the nozzle boundary layer, which caused a long run time. Current work is focused on testing a lower-order implicit time marching method to combat this problem.

Daubechies wavelets for linear scaling density functional theory.

PubMed

Mohr, Stephan; Ratcliff, Laura E; Boulanger, Paul; Genovese, Luigi; Caliste, Damien; Deutsch, Thierry; Goedecker, Stefan

2014-05-28

We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.

A Linear Electromagnetic Piston Pump

NASA Astrophysics Data System (ADS)

Hogan, Paul H.

Advancements in mobile hydraulics for human-scale applications have increased demand for a compact hydraulic power supply. Conventional designs couple a rotating electric motor to a hydraulic pump, which increases the package volume and requires several energy conversions. This thesis investigates the use of a free piston as the moving element in a linear motor to eliminate multiple energy conversions and decrease the overall package volume. A coupled model used a quasi-static magnetic equivalent circuit to calculate the motor inductance and the electromagnetic force acting on the piston. The force was an input to a time domain model to evaluate the mechanical and pressure dynamics. The magnetic circuit model was validated with finite element analysis and an experimental prototype linear motor. The coupled model was optimized using a multi-objective genetic algorithm to explore the parameter space and maximize power density and efficiency. An experimental prototype linear pump coupled pistons to an off-the-shelf linear motor to validate the mechanical and pressure dynamics models. The magnetic circuit force calculation agreed within 3% of finite element analysis, and within 8% of experimental data from the unoptimized prototype linear motor. The optimized motor geometry also had good agreement with FEA; at zero piston displacement, the magnetic circuit calculates optimized motor force within 10% of FEA in less than 1/1000 the computational time. This makes it well suited to genetic optimization algorithms. The mechanical model agrees very well with the experimental piston pump position data when tuned for additional unmodeled mechanical friction. Optimized results suggest that an improvement of 400% of the state of the art power density is attainable with as high as 85% net efficiency. This demonstrates that a linear electromagnetic piston pump has potential to serve as a more compact and efficient supply of fluid power for the human scale.

Power spectrum estimation from peculiar velocity catalogues

NASA Astrophysics Data System (ADS)

Macaulay, E.; Feldman, H. A.; Ferreira, P. G.; Jaffe, A. H.; Agarwal, S.; Hudson, M. J.; Watkins, R.

2012-09-01

The peculiar velocities of galaxies are an inherently valuable cosmological probe, providing an unbiased estimate of the distribution of matter on scales much larger than the depth of the survey. Much research interest has been motivated by the high dipole moment of our local peculiar velocity field, which suggests a large-scale excess in the matter power spectrum and can appear to be in some tension with the Λ cold dark matter (ΛCDM) model. We use a composite catalogue of 4537 peculiar velocity measurements with a characteristic depth of 33 h-1 Mpc to estimate the matter power spectrum. We compare the constraints with this method, directly studying the full peculiar velocity catalogue, to results by Macaulay et al., studying minimum variance moments of the velocity field, as calculated by Feldman, Watkins & Hudson. We find good agreement with the ΛCDM model on scales of k > 0.01 h Mpc-1. We find an excess of power on scales of k < 0.01 h Mpc-1 with a 1σ uncertainty which includes the ΛCDM model. We find that the uncertainty in excess at these scales is larger than an alternative result studying only moments of the velocity field, which is due to the minimum variance weights used to calculate the moments. At small scales, we are able to clearly discriminate between linear and non-linear clustering in simulated peculiar velocity catalogues and find some evidence (although less clear) for linear clustering in the real peculiar velocity data.

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory.

PubMed

Coriani, Sonia; Høst, Stinne; Jansík, Branislav; Thøgersen, Lea; Olsen, Jeppe; Jørgensen, Poul; Reine, Simen; Pawłowski, Filip; Helgaker, Trygve; Sałek, Paweł

2007-04-21

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

Auxiliary basis expansions for large-scale electronic structure calculations

PubMed Central

Jung, Yousung; Sodt, Alex; Gill, Peter M. W.; Head-Gordon, Martin

2005-01-01

One way to reduce the computational cost of electronic structure calculations is to use auxiliary basis expansions to approximate four-center integrals in terms of two- and three-center integrals, usually by using the variationally optimum Coulomb metric to determine the expansion coefficients. However, the long-range decay behavior of the auxiliary basis expansion coefficients has not been characterized. We find that this decay can be surprisingly slow. Numerical experiments on linear alkanes and a toy model both show that the decay can be as slow as 1/r in the distance between the auxiliary function and the fitted charge distribution. The Coulomb metric fitting equations also involve divergent matrix elements for extended systems treated with periodic boundary conditions. An attenuated Coulomb metric that is short-range can eliminate these oddities without substantially degrading calculated relative energies. The sparsity of the fit coefficients is assessed on simple hydrocarbon molecules and shows quite early onset of linear growth in the number of significant coefficients with system size using the attenuated Coulomb metric. Hence it is possible to design linear scaling auxiliary basis methods without additional approximations to treat large systems. PMID:15845767

Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations

NASA Astrophysics Data System (ADS)

Madsen, Niels Kristian; Godtliebsen, Ian H.; Losilla, Sergio A.; Christiansen, Ove

2018-01-01

A new implementation of vibrational coupled-cluster (VCC) theory is presented, where all amplitude tensors are represented in the canonical polyadic (CP) format. The CP-VCC algorithm solves the non-linear VCC equations without ever constructing the amplitudes or error vectors in full dimension but still formally includes the full parameter space of the VCC[n] model in question resulting in the same vibrational energies as the conventional method. In a previous publication, we have described the non-linear-equation solver for CP-VCC calculations. In this work, we discuss the general algorithm for evaluating VCC error vectors in CP format including the rank-reduction methods used during the summation of the many terms in the VCC amplitude equations. Benchmark calculations for studying the computational scaling and memory usage of the CP-VCC algorithm are performed on a set of molecules including thiadiazole and an array of polycyclic aromatic hydrocarbons. The results show that the reduced scaling and memory requirements of the CP-VCC algorithm allows for performing high-order VCC calculations on systems with up to 66 vibrational modes (anthracene), which indeed are not possible using the conventional VCC method. This paves the way for obtaining highly accurate vibrational spectra and properties of larger molecules.

Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library.

PubMed

Mohr, Stephan; Dawson, William; Wagner, Michael; Caliste, Damien; Nakajima, Takahito; Genovese, Luigi

2017-10-10

We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the density matrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selected interval. CheSS is able to exploit the sparsity of the matrices and scales linearly with respect to the number of nonzero entries, making it well-suited for large-scale calculations. The approach is particularly adapted for setups leading to small spectral widths of the involved matrices and outperforms alternative methods in this regime. By coupling CheSS to the DFT code BigDFT, we show that such a favorable setup is indeed possible in practice. In addition, the approach based on Chebyshev polynomials can be massively parallelized, and CheSS exhibits excellent scaling up to thousands of cores even for relatively small matrix sizes.

Elongation cutoff technique armed with quantum fast multipole method for linear scaling.

PubMed

Korchowiec, Jacek; Lewandowski, Jakub; Makowski, Marcin; Gu, Feng Long; Aoki, Yuriko

2009-11-30

A linear-scaling implementation of the elongation cutoff technique (ELG/C) that speeds up Hartree-Fock (HF) self-consistent field calculations is presented. The cutoff method avoids the known bottleneck of the conventional HF scheme, that is, diagonalization, because it operates within the low dimension subspace of the whole atomic orbital space. The efficiency of ELG/C is illustrated for two model systems. The obtained results indicate that the ELG/C is a very efficient sparse matrix algebra scheme. Copyright 2009 Wiley Periodicals, Inc.

The linearly scaling 3D fragment method for large scale electronic structure calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Zhengji; Meza, Juan; Lee, Byounghak

2009-07-28

The Linearly Scaling three-dimensional fragment (LS3DF) method is an O(N) ab initio electronic structure method for large-scale nano material simulations. It is a divide-and-conquer approach with a novel patching scheme that effectively cancels out the artificial boundary effects, which exist in all divide-and-conquer schemes. This method has made ab initio simulations of thousand-atom nanosystems feasible in a couple of hours, while retaining essentially the same accuracy as the direct calculation methods. The LS3DF method won the 2008 ACM Gordon Bell Prize for algorithm innovation. Our code has reached 442 Tflop/s running on 147,456 processors on the Cray XT5 (Jaguar) atmore » OLCF, and has been run on 163,840 processors on the Blue Gene/P (Intrepid) at ALCF, and has been applied to a system containing 36,000 atoms. In this paper, we will present the recent parallel performance results of this code, and will apply the method to asymmetric CdSe/CdS core/shell nanorods, which have potential applications in electronic devices and solar cells.« less

The Linearly Scaling 3D Fragment Method for Large Scale Electronic Structure Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Zhengji; Meza, Juan; Lee, Byounghak

2009-06-26

The Linearly Scaling three-dimensional fragment (LS3DF) method is an O(N) ab initio electronic structure method for large-scale nano material simulations. It is a divide-and-conquer approach with a novel patching scheme that effectively cancels out the artificial boundary effects, which exist in all divide-and-conquer schemes. This method has made ab initio simulations of thousand-atom nanosystems feasible in a couple of hours, while retaining essentially the same accuracy as the direct calculation methods. The LS3DF method won the 2008 ACM Gordon Bell Prize for algorithm innovation. Our code has reached 442 Tflop/s running on 147,456 processors on the Cray XT5 (Jaguar) atmore » OLCF, and has been run on 163,840 processors on the Blue Gene/P (Intrepid) at ALCF, and has been applied to a system containing 36,000 atoms. In this paper, we will present the recent parallel performance results of this code, and will apply the method to asymmetric CdSe/CdS core/shell nanorods, which have potential applications in electronic devices and solar cells.« less

Calculating Higher-Order Moments of Phylogenetic Stochastic Mapping Summaries in Linear Time.

PubMed

Dhar, Amrit; Minin, Vladimir N

2017-05-01

Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the evolutionary process on the phylogeny and, unlike parsimony-based mapping, conditions on the observed data to randomly draw substitution mappings that do not necessarily require the minimum number of events on a tree. Most stochastic mapping applications simulate substitution mappings only to estimate the mean and/or variance of two commonly used mapping summaries: the number of particular types of substitutions (labeled substitution counts) and the time spent in a particular group of states (labeled dwelling times) on the tree. Fast, simulation-free algorithms for calculating the mean of stochastic mapping summaries exist. Importantly, these algorithms scale linearly in the number of tips/leaves of the phylogenetic tree. However, to our knowledge, no such algorithm exists for calculating higher-order moments of stochastic mapping summaries. We present one such simulation-free dynamic programming algorithm that calculates prior and posterior mapping variances and scales linearly in the number of phylogeny tips. Our procedure suggests a general framework that can be used to efficiently compute higher-order moments of stochastic mapping summaries without simulations. We demonstrate the usefulness of our algorithm by extending previously developed statistical tests for rate variation across sites and for detecting evolutionarily conserved regions in genomic sequences.

Calculating Higher-Order Moments of Phylogenetic Stochastic Mapping Summaries in Linear Time

PubMed Central

Dhar, Amrit

2017-01-01

Abstract Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the evolutionary process on the phylogeny and, unlike parsimony-based mapping, conditions on the observed data to randomly draw substitution mappings that do not necessarily require the minimum number of events on a tree. Most stochastic mapping applications simulate substitution mappings only to estimate the mean and/or variance of two commonly used mapping summaries: the number of particular types of substitutions (labeled substitution counts) and the time spent in a particular group of states (labeled dwelling times) on the tree. Fast, simulation-free algorithms for calculating the mean of stochastic mapping summaries exist. Importantly, these algorithms scale linearly in the number of tips/leaves of the phylogenetic tree. However, to our knowledge, no such algorithm exists for calculating higher-order moments of stochastic mapping summaries. We present one such simulation-free dynamic programming algorithm that calculates prior and posterior mapping variances and scales linearly in the number of phylogeny tips. Our procedure suggests a general framework that can be used to efficiently compute higher-order moments of stochastic mapping summaries without simulations. We demonstrate the usefulness of our algorithm by extending previously developed statistical tests for rate variation across sites and for detecting evolutionarily conserved regions in genomic sequences. PMID:28177780

Linear and non-linear perturbations in dark energy models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Escamilla-Rivera, Celia; Casarini, Luciano; Fabris, Júlio C.

2016-11-01

In this work we discuss observational aspects of three time-dependent parameterisations of the dark energy equation of state w ( z ). In order to determine the dynamics associated with these models, we calculate their background evolution and perturbations in a scalar field representation. After performing a complete treatment of linear perturbations, we also show that the non-linear contribution of the selected w ( z ) parameterisations to the matter power spectra is almost the same for all scales, with no significant difference from the predictions of the standard ΛCDM model.

Non-Linear Cosmological Power Spectra in Real and Redshift Space

NASA Technical Reports Server (NTRS)

Taylor, A. N.; Hamilton, A. J. S.

1996-01-01

We present an expression for the non-linear evolution of the cosmological power spectrum based on Lagrangian trajectories. This is simplified using the Zel'dovich approximation to trace particle displacements, assuming Gaussian initial conditions. The model is found to exhibit the transfer of power from large to small scales expected in self-gravitating fields. Some exact solutions are found for power-law initial spectra. We have extended this analysis into red-shift space and found a solution for the non-linear, anisotropic redshift-space power spectrum in the limit of plane-parallel redshift distortions. The quadrupole-to-monopole ratio is calculated for the case of power-law initial spectra. We find that the shape of this ratio depends on the shape of the initial spectrum, but when scaled to linear theory depends only weakly on the redshift-space distortion parameter, beta. The point of zero-crossing of the quadrupole, kappa(sub o), is found to obey a simple scaling relation and we calculate this scale in the Zel'dovich approximation. This model is found to be in good agreement with a series of N-body simulations on scales down to the zero-crossing of the quadrupole, although the wavenumber at zero-crossing is underestimated. These results are applied to the quadrupole-to-monopole ratio found in the merged QDOT plus 1.2-Jy-IRAS redshift survey. Using a likelihood technique we have estimated that the distortion parameter is constrained to be beta greater than 0.5 at the 95 percent level. Our results are fairly insensitive to the local primordial spectral slope, but the likelihood analysis suggests n = -2 un the translinear regime. The zero-crossing scale of the quadrupole is k(sub 0) = 0.5 +/- 0.1 h Mpc(exp -1) and from this we infer that the amplitude of clustering is sigma(sub 8) = 0.7 +/- 0.05. We suggest that the success of this model is due to non-linear redshift-space effects arising from infall on to caustic and is not dominated by virialized cluster cores. The latter should start to dominate on scales below the zero-crossing of the quadrupole, where our model breaks down.

A Linearized Prognostic Cloud Scheme in NASAs Goddard Earth Observing System Data Assimilation Tools

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Errico, Ronald M.; Gelaro, Ronald; Kim, Jong G.; Mahajan, Rahul

2015-01-01

A linearized prognostic cloud scheme has been developed to accompany the linearized convection scheme recently implemented in NASA's Goddard Earth Observing System data assimilation tools. The linearization, developed from the nonlinear cloud scheme, treats cloud variables prognostically so they are subject to linearized advection, diffusion, generation, and evaporation. Four linearized cloud variables are modeled, the ice and water phases of clouds generated by large-scale condensation and, separately, by detraining convection. For each species the scheme models their sources, sublimation, evaporation, and autoconversion. Large-scale, anvil and convective species of precipitation are modeled and evaporated. The cloud scheme exhibits linearity and realistic perturbation growth, except around the generation of clouds through large-scale condensation. Discontinuities and steep gradients are widely used here and severe problems occur in the calculation of cloud fraction. For data assimilation applications this poor behavior is controlled by replacing this part of the scheme with a perturbation model. For observation impacts, where efficiency is less of a concern, a filtering is developed that examines the Jacobian. The replacement scheme is only invoked if Jacobian elements or eigenvalues violate a series of tuned constants. The linearized prognostic cloud scheme is tested by comparing the linear and nonlinear perturbation trajectories for 6-, 12-, and 24-h forecast times. The tangent linear model performs well and perturbations of clouds are well captured for the lead times of interest.

Accurate and Efficient Parallel Implementation of an Effective Linear-Scaling Direct Random Phase Approximation Method.

PubMed

Graf, Daniel; Beuerle, Matthias; Schurkus, Henry F; Luenser, Arne; Savasci, Gökcen; Ochsenfeld, Christian

2018-05-08

An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations ( Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016 , 144 , 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017 , 13 , 1647 - 1655 ) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of [Formula: see text]. Furthermore, we present a parallel implementation of our method, which not only leads to faster RPA correlation energy calculations but also to a scalable decrease in memory requirements, opening the door for investigations of large molecules even on small- to medium-sized computing clusters. Although it is known that AO methods are highly efficient for extended systems, where sparsity allows for reaching the linear-scaling regime, we show that our work also extends the applicability when considering highly delocalized systems for which no linear scaling can be achieved. As an example, the interlayer distance of two covalent organic framework pore fragments (comprising 384 atoms in total) is analyzed.

The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.

PubMed

Pang, Haotian; Liu, Han; Vanderbei, Robert

2014-02-01

We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L 1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

Pretest Predictions for Ventilation Tests

DOE Office of Scientific and Technical Information (OSTI.GOV)

Y. Sun; H. Yang; H.N. Kalia

The objective of this calculation is to predict the temperatures of the ventilating air, waste package surface, concrete pipe walls, and insulation that will be developed during the ventilation tests involving various test conditions. The results will be used as input to the following three areas: (1) Decisions regarding testing set-up and performance. (2) Assessing how best to scale the test phenomena measured. (3) Validating numerical approach for modeling continuous ventilation. The scope of the calculation is to identify the physical mechanisms and parameters related to thermal response in the ventilation tests, and develop and describe numerical methods that canmore » be used to calculate the effects of continuous ventilation. Sensitivity studies to assess the impact of variation of linear power densities (linear heat loads) and ventilation air flow rates are included. The calculation is limited to thermal effect only.« less

An accurate and linear-scaling method for calculating charge-transfer excitation energies and diabatic couplings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pavanello, Michele; Van Voorhis, Troy; Visscher, Lucas

2013-02-07

Quantum-mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those charge transfer excitations that take place between non-covalently bound molecules. In particular, we present a method that scales linearly with the number of non-covalently bound molecules in the system and is based on a two-pronged approach: The molecular electronic structure of broken-symmetry charge-localized states is obtained with the frozen density embedding formulation of subsystem density-functional theory; subsequently, in a post-SCF calculation, the full-electron Hamiltonian and overlapmore » matrix elements among the charge-localized states are evaluated with an algorithm which takes full advantage of the subsystem DFT density partitioning technique. The method is benchmarked against coupled-cluster calculations and achieves chemical accuracy for the systems considered for intermolecular separations ranging from hydrogen-bond distances to tens of Angstroms. Numerical examples are provided for molecular clusters comprised of up to 56 non-covalently bound molecules.« less

An accurate and linear-scaling method for calculating charge-transfer excitation energies and diabatic couplings.

PubMed

Pavanello, Michele; Van Voorhis, Troy; Visscher, Lucas; Neugebauer, Johannes

2013-02-07

Quantum-mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those charge transfer excitations that take place between non-covalently bound molecules. In particular, we present a method that scales linearly with the number of non-covalently bound molecules in the system and is based on a two-pronged approach: The molecular electronic structure of broken-symmetry charge-localized states is obtained with the frozen density embedding formulation of subsystem density-functional theory; subsequently, in a post-SCF calculation, the full-electron Hamiltonian and overlap matrix elements among the charge-localized states are evaluated with an algorithm which takes full advantage of the subsystem DFT density partitioning technique. The method is benchmarked against coupled-cluster calculations and achieves chemical accuracy for the systems considered for intermolecular separations ranging from hydrogen-bond distances to tens of Ångstroms. Numerical examples are provided for molecular clusters comprised of up to 56 non-covalently bound molecules.

The impact of using area-averaged land surface properties —topography, vegetation condition, soil wetness—in calculations of intermediate scale (approximately 10 km 2) surface-atmosphere heat and moisture fluxes

NASA Astrophysics Data System (ADS)

Sellers, Piers J.; Heiser, Mark D.; Hall, Forrest G.; Verma, Shashi B.; Desjardins, Raymond L.; Schuepp, Peter M.; Ian MacPherson, J.

1997-03-01

It is commonly assumed that biophysically based soil-vegetation-atmosphere transfer (SVAT) models are scale-invariant with respect to the initial boundary conditions of topography, vegetation condition and soil moisture. In practice, SVAT models that have been developed and tested at the local scale (a few meters or a few tens of meters) are applied almost unmodified within general circulation models (GCMs) of the atmosphere, which have grid areas of 50-500 km 2. This study, which draws much of its substantive material from the papers of Sellers et al. (1992c, J. Geophys. Res., 97(D17): 19033-19060) and Sellers et al. (1995, J. Geophys. Res., 100(D12): 25607-25629), explores the validity of doing this. The work makes use of the FIFE-89 data set which was collected over a 2 km × 15 km grassland area in Kansas. The site was characterized by high variability in soil moisture and vegetation condition during the late growing season of 1989. The area also has moderate topography. The 2 km × 15 km 'testbed' area was divided into 68 × 501 pixels of 30 m × 30 m spatial resolution, each of which could be assigned topographic, vegetation condition and soil moisture parameters from satellite and in situ observations gathered in FIFE-89. One or more of these surface fields was area-averaged in a series of simulation runs to determine the impact of using large-area means of these initial or boundary conditions on the area-integrated (aggregated) surface fluxes. The results of the study can be summarized as follows: 1. analyses and some of the simulations indicated that the relationships describing the effects of moderate topography on the surface radiation budget are near-linear and thus largely scale-invariant. The relationships linking the simple ratio vegetation index ( SR), the canopy conductance parameter (▽ F) and the canopy transpiration flux are also near-linear and similarly scale-invariant to first order. Because of this, it appears that simple area-averaging operations can be applied to these fields with relatively little impact on the calculated surface heat flux. 2. The relationships linking surface and root-zone soil wetness to the soil surface and canopy transpiration rates are non-linear. However, simulation results and observations indicate that soil moisture variability decreases significantly as an area dries out, which partially cancels out the effects of these non-linear functions.In conclusion, it appears that simple averages of topographic slope and vegetation parameters can be used to calculate surface energy and heat fluxes over a wide range of spatial scales, from a few meters up to many kilometers at least for grassland sites and areas with moderate topography. Although the relationships between soil moisture and evapotranspiration are non-linear for intermediate soil wetnesses, the dynamics of soil drying act to progressively reduce soil moisture variability and thus the impacts of these non-linearities on the area-averaged surface fluxes. These findings indicate that we may be able to use mean values of topography, vegetation condition and soil moisture to calculate the surface-atmosphere fluxes of energy, heat and moisture at larger length scales, to within an acceptable accuracy for climate modeling work. However, further tests over areas with different vegetation types, soils and more extreme topography are required to improve our confidence in this approach.

Quantum criticality of the two-channel pseudogap Anderson model: universal scaling in linear and non-linear conductance.

PubMed

Wu, Tsan-Pei; Wang, Xiao-Qun; Guo, Guang-Yu; Anders, Frithjof; Chung, Chung-Hou

2016-05-05

The quantum criticality of the two-lead two-channel pseudogap Anderson impurity model is studied. Based on the non-crossing approximation (NCA) and numerical renormalization group (NRG) approaches, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias and a power-law vanishing conduction electron density of states, ρc(ω) proportional |ω − μF|(r) (0 < r < 1) near the Fermi energy μF. At a fixed lead-impurity hybridization, a quantum phase transition from the two-channel Kondo (2CK) to the local moment (LM) phase is observed with increasing r from r = 0 to r = rc < 1. Surprisingly, in the 2CK phase, different power-law scalings from the well-known [Formula: see text] or [Formula: see text] form is found. Moreover, novel power-law scalings in conductances at the 2CK-LM quantum critical point are identified. Clear distinctions are found on the critical exponents between linear and non-linear conductance at criticality. The implications of these two distinct quantum critical properties for the non-equilibrium quantum criticality in general are discussed.

Scaled effective on-site Coulomb interaction in the DFT+U method for correlated materials

NASA Astrophysics Data System (ADS)

Nawa, Kenji; Akiyama, Toru; Ito, Tomonori; Nakamura, Kohji; Oguchi, Tamio; Weinert, M.

2018-01-01

The first-principles calculation of correlated materials within density functional theory remains challenging, but the inclusion of a Hubbard-type effective on-site Coulomb term (Ueff) often provides a computationally tractable and physically reasonable approach. However, the reported values of Ueff vary widely, even for the same ionic state and the same material. Since the final physical results can depend critically on the choice of parameter and the computational details, there is a need to have a consistent procedure to choose an appropriate one. We revisit this issue from constraint density functional theory, using the full-potential linearized augmented plane wave method. The calculated Ueff parameters for the prototypical transition-metal monoxides—MnO, FeO, CoO, and NiO—are found to depend significantly on the muffin-tin radius RMT, with variations of more than 2-3 eV as RMT changes from 2.0 to 2.7 aB. Despite this large variation in Ueff, the calculated valence bands differ only slightly. Moreover, we find an approximately linear relationship between Ueff(RMT) and the number of occupied localized electrons within the sphere, and give a simple scaling argument for Ueff; these results provide a rationalization for the large variation in reported values. Although our results imply that Ueff values are not directly transferable among different calculation methods (or even the same one with different input parameters such as RMT), use of this scaling relationship should help simplify the choice of Ueff.

Perturbations from cosmic strings in cold dark matter

NASA Technical Reports Server (NTRS)

Albrecht, Andreas; Stebbins, Albert

1992-01-01

A systematic linear analysis of the perturbations induced by cosmic strings in cold dark matter is presented. The power spectrum is calculated and it is found that the strings produce a great deal of power on small scales. It is shown that the perturbations on interesting scales are the result of many uncorrelated string motions, which indicates a much more Gaussian distribution than was previously supposed.

Perturbations from cosmic strings in cold dark matter

NASA Technical Reports Server (NTRS)

Albrecht, Andreas; Stebbins, Albert

1991-01-01

A systematic linear analysis of the perturbations induced by cosmic strings in cold dark matter is presented. The power spectrum is calculated and it is found that the strings produce a great deal of power on small scales. It is shown that the perturbations on interesting scales are the result of many uncorrelated string motions, which indicates a much more Gaussian distribution than was previously supposed.

A new scale of electronegativity based on electrophilicity index.

PubMed

Noorizadeh, Siamak; Shakerzadeh, Ehsan

2008-04-17

By calculating the energies of neutral and different ionic forms (M2+, M+, M, M-, and M2-) of 32 elements (using B3LYP/6-311++G** level of theory) and taking energy (E) to be a Morse-like function of the number of electrons (N), the electrophilicity values (omega) are calculated for these atoms. The obtained electrophilicities show a good linearity with some commonly used electronegativity scales such as Pauling and Allred-Rochow. Using these electrophilicities, the ionicities of some diatomic molecules are calculated, which are in good agreement with the experimental data. Therefore, these electrophilicities are introduced as a new scale for atomic electronegativity, chi(omega)0. The same procedure is also performed for some simple polyatomic molecules. It is shown that the new scale successfully obeys Sanderson's electronegativity equalization principle and for those molecules which have the same number of atoms, the ratio of the change in electronegativity during the formation of a molecule from its elements to the molecular electronegativity (Delta chi/chi omega) is the same.

Scaling of induction-cell transverse impedance: effect on accelerator design

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ekdahl, Carl August

2016-08-09

The strength of the dangerous beam breakup (BBU) instability in linear induction accelerators (LIAs) is characterized by the transverse coupling impedance Z ⊥. This note addresses the dimensional scaling of Z ⊥, which is important when comparing new LIA designs to existing accelerators with known i BBU growth. Moreover, it is shown that the scaling of Z ⊥ with the accelerating gap size relates BBU growth directly to high-voltage engineering considerations. It is proposed to firmly establish this scaling though a series of AMOS calculations.

A simplified method for power-law modelling of metabolic pathways from time-course data and steady-state flux profiles.

PubMed

Kitayama, Tomoya; Kinoshita, Ayako; Sugimoto, Masahiro; Nakayama, Yoichi; Tomita, Masaru

2006-07-17

In order to improve understanding of metabolic systems there have been attempts to construct S-system models from time courses. Conventionally, non-linear curve-fitting algorithms have been used for modelling, because of the non-linear properties of parameter estimation from time series. However, the huge iterative calculations required have hindered the development of large-scale metabolic pathway models. To solve this problem we propose a novel method involving power-law modelling of metabolic pathways from the Jacobian of the targeted system and the steady-state flux profiles by linearization of S-systems. The results of two case studies modelling a straight and a branched pathway, respectively, showed that our method reduced the number of unknown parameters needing to be estimated. The time-courses simulated by conventional kinetic models and those described by our method behaved similarly under a wide range of perturbations of metabolite concentrations. The proposed method reduces calculation complexity and facilitates the construction of large-scale S-system models of metabolic pathways, realizing a practical application of reverse engineering of dynamic simulation models from the Jacobian of the targeted system and steady-state flux profiles.

Relating Stellar Cycle Periods to Dynamo Calculations

NASA Technical Reports Server (NTRS)

Tobias, S. M.

1998-01-01

Stellar magnetic activity in slowly rotating stars is often cyclic, with the period of the magnetic cycle depending critically on the rotation rate and the convective turnover time of the star. Here we show that the interpretation of this law from dynamo models is not a simple task. It is demonstrated that the period is (unsurprisingly) sensitive to the precise type of non-linearity employed. Moreover the calculation of the wave-speed of plane-wave solutions does not (as was previously supposed) give an indication of the magnetic period in a more realistic dynamo model, as the changes in length-scale of solutions are not easily captured by this approach. Progress can be made, however, by considering a realistic two-dimensional model, in which the radial length-scale of waves is included. We show that it is possible in this case to derive a more robust relation between cycle period and dynamo number. For all the non-linearities considered in the most realistic model, the magnetic cycle period is a decreasing function of IDI (the amplitude of the dynamo number). However, discriminating between different non-linearities is difficult in this case and care must therefore be taken before advancing explanations for the magnetic periods of stars.

Thermal Conductivity of Liquid Water from Reverse Nonequilibrium Ab Initio Molecular Dynamics

NASA Astrophysics Data System (ADS)

Tsuchida, Eiji

2018-02-01

We report on a theoretical framework for calculating the thermal conductivity of liquid water from first principles with the aid of the linear scaling method. We also discuss the possibility of obtaining equilibrium properties from a nonequilibrium trajectory.

Linear Scaling of the Exciton Binding Energy versus the Band Gap of Two-Dimensional Materials

NASA Astrophysics Data System (ADS)

Choi, Jin-Ho; Cui, Ping; Lan, Haiping; Zhang, Zhenyu

2015-08-01

The exciton is one of the most crucial physical entities in the performance of optoelectronic and photonic devices, and widely varying exciton binding energies have been reported in different classes of materials. Using first-principles calculations within the G W -Bethe-Salpeter equation approach, here we investigate the excitonic properties of two recently discovered layered materials: phosphorene and graphene fluoride. We first confirm large exciton binding energies of, respectively, 0.85 and 2.03 eV in these systems. Next, by comparing these systems with several other representative two-dimensional materials, we discover a striking linear relationship between the exciton binding energy and the band gap and interpret the existence of the linear scaling law within a simple hydrogenic picture. The broad applicability of this novel scaling law is further demonstrated by using strained graphene fluoride. These findings are expected to stimulate related studies in higher and lower dimensions, potentially resulting in a deeper understanding of excitonic effects in materials of all dimensionalities.

Highly parallel demagnetization field calculation using the fast multipole method on tetrahedral meshes with continuous sources

NASA Astrophysics Data System (ADS)

Palmesi, P.; Exl, L.; Bruckner, F.; Abert, C.; Suess, D.

2017-11-01

The long-range magnetic field is the most time-consuming part in micromagnetic simulations. Computational improvements can relieve problems related to this bottleneck. This work presents an efficient implementation of the Fast Multipole Method [FMM] for the magnetic scalar potential as used in micromagnetics. The novelty lies in extending FMM to linearly magnetized tetrahedral sources making it interesting also for other areas of computational physics. We treat the near field directly and in use (exact) numerical integration on the multipole expansion in the far field. This approach tackles important issues like the vectorial and continuous nature of the magnetic field. By using FMM the calculations scale linearly in time and memory.

Plasmon mass scale and quantum fluctuations of classical fields on a real time lattice

NASA Astrophysics Data System (ADS)

Kurkela, Aleksi; Lappi, Tuomas; Peuron, Jarkko

2018-03-01

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Above the Debye scale the classical Yang-Mills (CYM) theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determining the plasmon mass of the system using 3 different methods. Then we argue that one needs a numerical calculation of a system of classical gauge fields and small linearized fluctuations, which correspond to quantum fluctuations, in a way that keeps the separation between the two manifest. We demonstrate and test an implementation of an algorithm with the linearized fluctuation showing that the linearization indeed works and that the Gauss's law is conserved.

Computation of indirect nuclear spin-spin couplings with reduced complexity in pure and hybrid density functional approximations.

PubMed

Luenser, Arne; Kussmann, Jörg; Ochsenfeld, Christian

2016-09-28

We present a (sub)linear-scaling algorithm to determine indirect nuclear spin-spin coupling constants at the Hartree-Fock and Kohn-Sham density functional levels of theory. Employing efficient integral algorithms and sparse algebra routines, an overall (sub)linear scaling behavior can be obtained for systems with a non-vanishing HOMO-LUMO gap. Calculations on systems with over 1000 atoms and 20 000 basis functions illustrate the performance and accuracy of our reference implementation. Specifically, we demonstrate that linear algebra dominates the runtime of conventional algorithms for 10 000 basis functions and above. Attainable speedups of our method exceed 6 × in total runtime and 10 × in the linear algebra steps for the tested systems. Furthermore, a convergence study of spin-spin couplings of an aminopyrazole peptide upon inclusion of the water environment is presented: using the new method it is shown that large solvent spheres are necessary to converge spin-spin coupling values.

Measuring the Power Spectrum with Peculiar Velocities

NASA Astrophysics Data System (ADS)

Macaulay, Edward; Feldman, H. A.; Ferreira, P. G.; Jaffe, A. H.; Agarwal, S.; Hudson, M. J.; Watkins, R.

2012-01-01

The peculiar velocities of galaxies are an inherently valuable cosmological probe, providing an unbiased estimate of the distribution of matter on scales much larger than the depth of the survey. Much research interest has been motivated by the high dipole moment of our local peculiar velocity field, which suggests a large scale excess in the matter power spectrum, and can appear to be in some tension with the LCDM model. We use a composite catalogue of 4,537 peculiar velocity measurements with a characteristic depth of 33 h-1 Mpc to estimate the matter power spectrum. We compare the constraints with this method, directly studying the full peculiar velocity catalogue, to results from Macaulay et al. (2011), studying minimum variance moments of the velocity field, as calculated by Watkins, Feldman & Hudson (2009) and Feldman, Watkins & Hudson (2010). We find good agreement with the LCDM model on scales of k > 0.01 h Mpc-1. We find an excess of power on scales of k < 0.01 h Mpc-1, although with a 1 sigma uncertainty which includes the LCDM model. We find that the uncertainty in the excess at these scales is larger than an alternative result studying only moments of the velocity field, which is due to the minimum variance weights used to calculate the moments. At small scales, we are able to clearly discriminate between linear and nonlinear clustering in simulated peculiar velocity catalogues, and find some evidence (although less clear) for linear clustering in the real peculiar velocity data.

Multiscale analysis of the gradient of linear polarization

NASA Astrophysics Data System (ADS)

Robitaille, J.-F.; Scaife, A. M. M.

2015-07-01

We propose a new multiscale method to calculate the amplitude of the gradient of the linear polarization vector, |∇ P|, using a wavelet-based formalism. We demonstrate this method using a field of the Canadian Galactic Plane Survey and show that the filamentary structure typically seen in |∇ P| maps depends strongly on the instrumental resolution. Our analysis reveals that different networks of filaments are present on different angular scales. The wavelet formalism allows us to calculate the power spectrum of the fluctuations seen in |∇ P| and to determine the scaling behaviour of this quantity. The power spectrum is found to follow a power law with γ ≈ 2.1. We identify a small drop in power between scales of 80 ≲ l ≲ 300 arcmin, which corresponds well to the overlap in the u-v plane between the Effelsberg 100-m telescope and the Dominion Radio Astrophysical Observatory 26-m telescope data. We suggest that this drop is due to undersampling present in the 26-m telescope data. In addition, the wavelet coefficient distributions show higher skewness on smaller scales than at larger scales. The spatial distribution of the outliers in the tails of these distributions creates a coherent subset of filaments correlated across multiple scales, which trace the sharpest changes in the polarization vector P within the field. We suggest that these structures may be associated with highly compressive shocks in the medium. The power spectrum of the field excluding these outliers shows a steeper power law with γ ≈ 2.5.

Dispersion interactions with linear scaling DFT: a study of planar molecules on charged polar surfaces

NASA Astrophysics Data System (ADS)

Andrinopoulos, Lampros; Hine, Nicholas; Haynes, Peter; Mostofi, Arash

2010-03-01

The placement of organic molecules such as CuPc (copper phthalocyanine) on wurtzite ZnO (zinc oxide) charged surfaces has been proposed as a way of creating photovoltaic solar cellsfootnotetextG.D. Sharma et al., Solar Energy Materials & Solar Cells 90, 933 (2006) ; optimising their performance may be aided by computational simulation. Electronic structure calculations provide high accuracy at modest computational cost but two challenges are encountered for such layered systems. First, the system size is at or beyond the limit of traditional cubic-scaling Density Functional Theory (DFT). Second, traditional exchange-correlation functionals do not account for van der Waals (vdW) interactions, crucial for determining the structure of weakly bonded systems. We present an implementation of recently developed approachesfootnotetextP.L. Silvestrelli, P.R.L. 100, 102 (2008) to include vdW in DFT within ONETEPfootnotetextC.-K. Skylaris, P.D. Haynes, A.A. Mostofi and M.C. Payne, J.C.P. 122, 084119 (2005) , a linear-scaling package for performing DFT calculations using a basis of localised functions. We have applied this methodology to simple planar organic molecules, such as benzene and pentacene, on ZnO surfaces.

Breaking the theoretical scaling limit for predicting quasiparticle energies: the stochastic GW approach.

PubMed

Neuhauser, Daniel; Gao, Yi; Arntsen, Christopher; Karshenas, Cyrus; Rabani, Eran; Baer, Roi

2014-08-15

We develop a formalism to calculate the quasiparticle energy within the GW many-body perturbation correction to the density functional theory. The occupied and virtual orbitals of the Kohn-Sham Hamiltonian are replaced by stochastic orbitals used to evaluate the Green function G, the polarization potential W, and, thereby, the GW self-energy. The stochastic GW (sGW) formalism relies on novel theoretical concepts such as stochastic time-dependent Hartree propagation, stochastic matrix compression, and spatial or temporal stochastic decoupling techniques. Beyond the theoretical interest, the formalism enables linear scaling GW calculations breaking the theoretical scaling limit for GW as well as circumventing the need for energy cutoff approximations. We illustrate the method for silicon nanocrystals of varying sizes with N_{e}>3000 electrons.

Mathematical Simulation for Integrated Linear Fresnel Spectrometer Chip

NASA Technical Reports Server (NTRS)

Park, Yeonjoon; Yoon, Hargoon; Lee, Uhn; King, Glen C.; Choi, Sang H.

2012-01-01

A miniaturized solid-state optical spectrometer chip was designed with a linear gradient-gap Fresnel grating which was mounted perpendicularly to a sensor array surface and simulated for its performance and functionality. Unlike common spectrometers which are based on Fraunhoffer diffraction with a regular periodic line grating, the new linear gradient grating Fresnel spectrometer chip can be miniaturized to a much smaller form-factor into the Fresnel regime exceeding the limit of conventional spectrometers. This mathematical calculation shows that building a tiny motionless multi-pixel microspectrometer chip which is smaller than 1 cubic millimter of optical path volume is possible. The new Fresnel spectrometer chip is proportional to the energy scale (hc/lambda), while the conventional spectrometers are proportional to the wavelength scale (lambda). We report the theoretical optical working principle and new data collection algorithm of the new Fresnel spectrometer to build a compact integrated optical chip.

Eigentime identities for on weighted polymer networks

NASA Astrophysics Data System (ADS)

Dai, Meifeng; Tang, Hualong; Zou, Jiahui; He, Di; Sun, Yu; Su, Weiyi

2018-01-01

In this paper, we first analytically calculate the eigenvalues of the transition matrix of a structure with very complex architecture and their multiplicities. We call this structure polymer network. Based on the eigenvalues obtained in the iterative manner, we then calculate the eigentime identity. We highlight two scaling behaviors (logarithmic and linear) for this quantity, strongly depending on the value of the weight factor. Finally, by making use of the obtained eigenvalues, we determine the weighted counting of spanning trees.

On the effects of tidal interaction on thin accretion disks: An analytic study

NASA Technical Reports Server (NTRS)

Dgani, R.; Livio, M.; Regev, O.

1994-01-01

We calculate tidal effects on two-dimensional thin accretion disks in binary systems. We apply a perturbation expansion to obtain an analytic solution of the tidally induced waves. We obtain spiral waves that are stronger at the inner parts of the disks, in addition to a local disturbance which scales like the strength of the local tidal force. Our results agree with recent calculations of the linear response of the disk to tidal interaction.

Continuum calculations of continental deformation in transcurrent environments

NASA Technical Reports Server (NTRS)

Sonder, L. J.; England, P. C.; Houseman, G. A.

1986-01-01

A thin viscous sheet approximation is used to investigate continental deformation near a strike-slip boundary. The vertically averaged velocity field is calculated for a medium characterized by a power law rheology with stress exponent n. Driving stresses include those applied along boundaries of the sheet and those arising from buoyancy forces related to lateral differences in crustal thickness. Exact and approximate analytic solutions for a region with a sinusoidal strike-slip boundary condition are compared with solutions for more geologically relevant boundary conditions obtained using a finite element technique. The across-strike length scale of the deformation is approximately 1/4pi x sq rt n times the dominant wavelength of the imposed strike-slip boundary condition for both the analytic and the numerical solutions; this result is consistent with length scales observed in continental regions of large-scale transcurrent faulting. An approximate, linear relationship between displacement and rotation is found that depends only on the deformation length scale and the rheology. Calculated displacements, finite rotations, and distribution of crustal thicknesses are consistent with those observed in the region of the Pacific-North America plate boundary in California.

Multigrid calculation of three-dimensional viscous cascade flows

NASA Technical Reports Server (NTRS)

Arnone, A.; Liou, M.-S.; Povinelli, L. A.

1991-01-01

A 3-D code for viscous cascade flow prediction was developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full multigrid method. The Baldwin-Lomax eddy viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Multigrid calculation of three-dimensional viscous cascade flows

NASA Technical Reports Server (NTRS)

Arnone, A.; Liou, M.-S.; Povinelli, L. A.

1991-01-01

A three-dimensional code for viscous cascade flow prediction has been developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large-scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Local unitary transformation method toward practical electron correlation calculations with scalar relativistic effect in large-scale molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seino, Junji; Nakai, Hiromi, E-mail: nakai@waseda.jp; Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555

In order to perform practical electron correlation calculations, the local unitary transformation (LUT) scheme at the spin-free infinite-order Douglas–Kroll–Hess (IODKH) level [J. Seino and H. Nakai, J. Chem. Phys.136, 244102 (2012); J. Seino and H. Nakai, J. Chem. Phys.137, 144101 (2012)], which is based on the locality of relativistic effects, has been combined with the linear-scaling divide-and-conquer (DC)-based Hartree–Fock (HF) and electron correlation methods, such as the second-order Møller–Plesset (MP2) and the coupled cluster theories with single and double excitations (CCSD). Numerical applications in hydrogen halide molecules, (HX){sub n} (X = F, Cl, Br, and I), coinage metal chain systems,more » M{sub n} (M = Cu and Ag), and platinum-terminated polyynediyl chain, trans,trans-((p-CH{sub 3}C{sub 6}H{sub 4}){sub 3}P){sub 2}(C{sub 6}H{sub 5})Pt(C≡C){sub 4}Pt(C{sub 6}H{sub 5})((p-CH{sub 3}C{sub 6}H{sub 4}){sub 3}P){sub 2}, clarified that the present methods, namely DC-HF, MP2, and CCSD with the LUT-IODKH Hamiltonian, reproduce the results obtained using conventional methods with small computational costs. The combination of both LUT and DC techniques could be the first approach that achieves overall quasi-linear-scaling with a small prefactor for relativistic electron correlation calculations.« less

A global traveling wave on Venus

NASA Technical Reports Server (NTRS)

Smith, Michael D.; Gierasch, Peter J.; Schinder, Paul J.

1993-01-01

The dominant large-scale pattern in the clouds of Venus has been described as a 'Y' or 'Psi' and tentatively identified by earlier workers as a Kelvin wave. A detailed calculation of linear wave modes in the Venus atmosphere verifies this identification. Cloud feedback by infrared heating fluctuations is a plausible excitation mechanism. Modulation of the large-scale pattern by the wave is a possible explanation for the Y. Momentum transfer by the wave could contribute to sustaining the general circulation.

Scaling results for the magnetic field line trajectories in the stochastic layer near the separatrix in divertor tokamaks with high magnetic shear using the higher shear map

NASA Astrophysics Data System (ADS)

Punjabi, Alkesh; Ali, Halima; Farhat, Hamidullah

2009-07-01

Extra terms are added to the generating function of the simple map (Punjabi et al 1992 Phys. Rev. Lett. 69 3322) to adjust shear of magnetic field lines in divertor tokamaks. From this new generating function, a higher shear map is derived from a canonical transformation. A continuous analog of the higher shear map is also derived. The method of maps (Punjabi et al 1994 J. Plasma Phys. 52 91) is used to calculate the average shear, stochastic broadening of the ideal separatrix near the X-point in the principal plane of the tokamak, loss of poloidal magnetic flux from inside the ideal separatrix, magnetic footprint on the collector plate, and its area, and the radial diffusion coefficient of magnetic field lines near the X-point. It is found that the width of the stochastic layer near the X-point and the loss of poloidal flux from inside the ideal separatrix scale linearly with average shear. The area of magnetic footprints scales roughly linearly with average shear. Linear scaling of the area is quite good when the average shear is greater than or equal to 1.25. When the average shear is in the range 1.1-1.25, the area of the footprint fluctuates (as a function of average shear) and scales faster than linear scaling. Radial diffusion of field lines near the X-point increases very rapidly by about four orders of magnitude as average shear increases from about 1.15 to 1.5. For higher values of average shear, diffusion increases linearly, and comparatively very slowly. The very slow scaling of the radial diffusion of the field can flatten the plasma pressure gradient near the separatrix, and lead to the elimination of type-I edge localized modes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Efimov, V.; Tkachenko, E.G.

It is shown that the well-known correlation between the triton binding energy and the nd doublet scattering length (the so-called Phillips line), which is observed in calculations, can be explained by smallness of the characteristic energies of the problem: the binding energies of the triton and deuteron: on the energy scale of nuclear forces. Equivalently, the Phillips line is a consequence of the diffuse structure of the triton and deuteron. These conclusions are obtained on the basis of qualitative consideration of the problem, calculation of the above correlation in the zero and linear approximation, and comparison of the calculated resultsmore » with the Phillips line.« less

Mixing of a passive scalar in isotropic and sheared homogeneous turbulence

NASA Technical Reports Server (NTRS)

Shirani, E.; Ferziger, J. H.; Reynolds, W. C.

1981-01-01

In order to calculate the velocity and scalar fields, the three dimensional, time-dependent equations of motion and the diffusion equation were solved numerically. The following cases were treated: isotropic, homogeneous turbulence with decay of a passive scalar; and homogeneous turbulent shear flow with a passive scalar whose mean varies linearly in the spanwise direction. The solutions were obtained at relatively low Reynolds numbers so that all of the turbulent scales could be resolved without modeling. Turbulent statistics such as integral length scales, Taylor microscales, Kolmogorov length scale, one- and two-point correlations of velocity-velocity and velocity-scalar, turbulent Prandtl/Schmidt number, r.m.s. values of velocities, the scalar quantity and pressure, skewness, decay rates, and decay exponents were calculated. The results are compared with the available expermental results, and good agreement is obtained.

Short-Term Memory in Orthogonal Neural Networks

NASA Astrophysics Data System (ADS)

White, Olivia L.; Lee, Daniel D.; Sompolinsky, Haim

2004-04-01

We study the ability of linear recurrent networks obeying discrete time dynamics to store long temporal sequences that are retrievable from the instantaneous state of the network. We calculate this temporal memory capacity for both distributed shift register and random orthogonal connectivity matrices. We show that the memory capacity of these networks scales with system size.

Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction

NASA Astrophysics Data System (ADS)

Song, Chenchen; Martínez, Todd J.

2017-01-01

In the first paper of the series [Paper I, C. Song and T. J. Martinez, J. Chem. Phys. 144, 174111 (2016)], we showed how tensor-hypercontracted (THC) SOS-MP2 could be accelerated by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs). This reduced the formal scaling of the SOS-MP2 energy calculation to cubic with respect to system size. The computational bottleneck then becomes the THC metric matrix inversion, which scales cubically with a large prefactor. In this work, the local THC approximation is proposed to reduce the computational cost of inverting the THC metric matrix to linear scaling with respect to molecular size. By doing so, we have removed the primary bottleneck to THC-SOS-MP2 calculations on large molecules with O(1000) atoms. The errors introduced by the local THC approximation are less than 0.6 kcal/mol for molecules with up to 200 atoms and 3300 basis functions. Together with the graphical processing unit techniques and locality-exploiting approaches introduced in previous work, the scaled opposite spin MP2 (SOS-MP2) calculations exhibit O(N2.5) scaling in practice up to 10 000 basis functions. The new algorithms make it feasible to carry out SOS-MP2 calculations on small proteins like ubiquitin (1231 atoms/10 294 atomic basis functions) on a single node in less than a day.

Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction.

PubMed

Song, Chenchen; Martínez, Todd J

2017-01-21

In the first paper of the series [Paper I, C. Song and T. J. Martinez, J. Chem. Phys. 144, 174111 (2016)], we showed how tensor-hypercontracted (THC) SOS-MP2 could be accelerated by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs). This reduced the formal scaling of the SOS-MP2 energy calculation to cubic with respect to system size. The computational bottleneck then becomes the THC metric matrix inversion, which scales cubically with a large prefactor. In this work, the local THC approximation is proposed to reduce the computational cost of inverting the THC metric matrix to linear scaling with respect to molecular size. By doing so, we have removed the primary bottleneck to THC-SOS-MP2 calculations on large molecules with O(1000) atoms. The errors introduced by the local THC approximation are less than 0.6 kcal/mol for molecules with up to 200 atoms and 3300 basis functions. Together with the graphical processing unit techniques and locality-exploiting approaches introduced in previous work, the scaled opposite spin MP2 (SOS-MP2) calculations exhibit O(N 2.5 ) scaling in practice up to 10 000 basis functions. The new algorithms make it feasible to carry out SOS-MP2 calculations on small proteins like ubiquitin (1231 atoms/10 294 atomic basis functions) on a single node in less than a day.

Relativistic initial conditions for N-body simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fidler, Christian; Tram, Thomas; Crittenden, Robert

2017-06-01

Initial conditions for (Newtonian) cosmological N-body simulations are usually set by re-scaling the present-day power spectrum obtained from linear (relativistic) Boltzmann codes to the desired initial redshift of the simulation. This back-scaling method can account for the effect of inhomogeneous residual thermal radiation at early times, which is absent in the Newtonian simulations. We analyse this procedure from a fully relativistic perspective, employing the recently-proposed Newtonian motion gauge framework. We find that N-body simulations for ΛCDM cosmology starting from back-scaled initial conditions can be self-consistently embedded in a relativistic space-time with first-order metric potentials calculated using a linear Boltzmann code.more » This space-time coincides with a simple ''N-body gauge'' for z < 50 for all observable modes. Care must be taken, however, when simulating non-standard cosmologies. As an example, we analyse the back-scaling method in a cosmology with decaying dark matter, and show that metric perturbations become large at early times in the back-scaling approach, indicating a breakdown of the perturbative description. We suggest a suitable ''forwards approach' for such cases.« less

Parametric resonance in the early Universe—a fitting analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Figueroa, Daniel G.; Torrentí, Francisco, E-mail: daniel.figueroa@cern.ch, E-mail: f.torrenti@csic.es

Particle production via parametric resonance in the early Universe, is a non-perturbative, non-linear and out-of-equilibrium phenomenon. Although it is a well studied topic, whenever a new scenario exhibits parametric resonance, a full re-analysis is normally required. To avoid this tedious task, many works present often only a simplified linear treatment of the problem. In order to surpass this circumstance in the future, we provide a fitting analysis of parametric resonance through all its relevant stages: initial linear growth, non-linear evolution, and relaxation towards equilibrium. Using lattice simulations in an expanding grid in 3+1 dimensions, we parametrize the dynamics' outcome scanningmore » over the relevant ingredients: role of the oscillatory field, particle coupling strength, initial conditions, and background expansion rate. We emphasize the inaccuracy of the linear calculation of the decay time of the oscillatory field, and propose a more appropriate definition of this scale based on the subsequent non-linear dynamics. We provide simple fits to the relevant time scales and particle energy fractions at each stage. Our fits can be applied to post-inflationary preheating scenarios, where the oscillatory field is the inflaton, or to spectator-field scenarios, where the oscillatory field can be e.g. a curvaton, or the Standard Model Higgs.« less

Redshift-space distortions with the halo occupation distribution - II. Analytic model

NASA Astrophysics Data System (ADS)

Tinker, Jeremy L.

2007-01-01

We present an analytic model for the galaxy two-point correlation function in redshift space. The cosmological parameters of the model are the matter density Ωm, power spectrum normalization σ8, and velocity bias of galaxies αv, circumventing the linear theory distortion parameter β and eliminating nuisance parameters for non-linearities. The model is constructed within the framework of the halo occupation distribution (HOD), which quantifies galaxy bias on linear and non-linear scales. We model one-halo pairwise velocities by assuming that satellite galaxy velocities follow a Gaussian distribution with dispersion proportional to the virial dispersion of the host halo. Two-halo velocity statistics are a combination of virial motions and host halo motions. The velocity distribution function (DF) of halo pairs is a complex function with skewness and kurtosis that vary substantially with scale. Using a series of collisionless N-body simulations, we demonstrate that the shape of the velocity DF is determined primarily by the distribution of local densities around a halo pair, and at fixed density the velocity DF is close to Gaussian and nearly independent of halo mass. We calibrate a model for the conditional probability function of densities around halo pairs on these simulations. With this model, the full shape of the halo velocity DF can be accurately calculated as a function of halo mass, radial separation, angle and cosmology. The HOD approach to redshift-space distortions utilizes clustering data from linear to non-linear scales to break the standard degeneracies inherent in previous models of redshift-space clustering. The parameters of the occupation function are well constrained by real-space clustering alone, separating constraints on bias and cosmology. We demonstrate the ability of the model to separately constrain Ωm,σ8 and αv in models that are constructed to have the same value of β at large scales as well as the same finger-of-god distortions at small scales.

General relativistic corrections to the weak lensing convergence power spectrum

NASA Astrophysics Data System (ADS)

Giblin, John T.; Mertens, James B.; Starkman, Glenn D.; Zentner, Andrew R.

2017-11-01

We compute the weak lensing convergence power spectrum, Cℓκκ, in a dust-filled universe using fully nonlinear general relativistic simulations. The spectrum is then compared to more standard, approximate calculations by computing the Bardeen (Newtonian) potentials in linearized gravity and partially utilizing the Born approximation. We find corrections to the angular power spectrum amplitude of order ten percent at very large angular scales, ℓ˜2 - 3 , and percent-level corrections at intermediate angular scales of ℓ˜20 - 30 .

Communication: Standard surface hopping predicts incorrect scaling for Marcus' golden-rule rate: The decoherence problem cannot be ignored

NASA Astrophysics Data System (ADS)

Landry, Brian R.; Subotnik, Joseph E.

2011-11-01

We evaluate the accuracy of Tully's surface hopping algorithm for the spin-boson model for the case of a small diabatic coupling parameter (V). We calculate the transition rates between diabatic surfaces, and we compare our results to the expected Marcus rates. We show that standard surface hopping yields an incorrect scaling with diabatic coupling (linear in V), which we demonstrate is due to an incorrect treatment of decoherence. By modifying standard surface hopping to include decoherence events, we recover the correct scaling (˜V2).

Stabilization of electron-scale turbulence by electron density gradient in national spherical torus experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ruiz Ruiz, J.; White, A. E.; Ren, Y.

2015-12-15

Theory and experiments have shown that electron temperature gradient (ETG) turbulence on the electron gyro-scale, k{sub ⊥}ρ{sub e} ≲ 1, can be responsible for anomalous electron thermal transport in NSTX. Electron scale (high-k) turbulence is diagnosed in NSTX with a high-k microwave scattering system [D. R. Smith et al., Rev. Sci. Instrum. 79, 123501 (2008)]. Here we report on stabilization effects of the electron density gradient on electron-scale density fluctuations in a set of neutral beam injection heated H-mode plasmas. We found that the absence of high-k density fluctuations from measurements is correlated with large equilibrium density gradient, which ismore » shown to be consistent with linear stabilization of ETG modes due to the density gradient using the analytical ETG linear threshold in F. Jenko et al. [Phys. Plasmas 8, 4096 (2001)] and linear gyrokinetic simulations with GS2 [M. Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1995)]. We also found that the observed power of electron-scale turbulence (when it exists) is anti-correlated with the equilibrium density gradient, suggesting density gradient as a nonlinear stabilizing mechanism. Higher density gradients give rise to lower values of the plasma frame frequency, calculated based on the Doppler shift of the measured density fluctuations. Linear gyrokinetic simulations show that higher values of the electron density gradient reduce the value of the real frequency, in agreement with experimental observation. Nonlinear electron-scale gyrokinetic simulations show that high electron density gradient reduces electron heat flux and stiffness, and increases the ETG nonlinear threshold, consistent with experimental observations.« less

Calculation of excitation energies from the CC2 linear response theory using Cholesky decomposition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baudin, Pablo, E-mail: baudin.pablo@gmail.com; qLEAP – Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C; Marín, José Sánchez

2014-03-14

A new implementation of the approximate coupled cluster singles and doubles CC2 linear response model is reported. It employs a Cholesky decomposition of the two-electron integrals that significantly reduces the computational cost and the storage requirements of the method compared to standard implementations. Our algorithm also exploits a partitioning form of the CC2 equations which reduces the dimension of the problem and avoids the storage of doubles amplitudes. We present calculation of excitation energies of benzene using a hierarchy of basis sets and compare the results with conventional CC2 calculations. The reduction of the scaling is evaluated as well asmore » the effect of the Cholesky decomposition parameter on the quality of the results. The new algorithm is used to perform an extrapolation to complete basis set investigation on the spectroscopically interesting benzylallene conformers. A set of calculations on medium-sized molecules is carried out to check the dependence of the accuracy of the results on the decomposition thresholds. Moreover, CC2 singlet excitation energies of the free base porphin are also presented.« less

Laser pulsing in linear Compton scattering

DOE PAGES

Krafft, G. A.; Johnson, E.; Deitrick, K.; ...

2016-12-16

Previous work on calculating energy spectra from Compton scattering events has either neglected considering the pulsed structure of the incident laser beam, or has calculated these effects in an approximate way subject to criticism. In this paper, this problem has been reconsidered within a linear plane wave model for the incident laser beam. By performing the proper Lorentz transformation of the Klein-Nishina scattering cross section, a spectrum calculation can be created which allows the electron beam energy spread and emittance effects on the spectrum to be accurately calculated, essentially by summing over the emission of each individual electron. Such anmore » approach has the obvious advantage that it is easily integrated with a particle distribution generated by particle tracking, allowing precise calculations of spectra for realistic particle distributions in collision. The method is used to predict the energy spectrum of radiation passing through an aperture for the proposed Old Dominion University inverse Compton source. In addition, as discussed in the body of the paper, many of the results allow easy scaling estimates to be made of the expected spectrum. A misconception in the literature on Compton scattering of circularly polarized beams is corrected and recorded.« less

Quinone 1 e – and 2 e – /2 H + Reduction Potentials: Identification and Analysis of Deviations from Systematic Scaling Relationships

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huynh, Mioy T.; Anson, Colin W.; Cavell, Andrew C.

Quinones participate in diverse electron transfer and proton-coupled electron transfer processes in chemistry and biology. An experimental study of common quinones reveals a non-linear correlation between the 1 e – and 2 e –/2 H + reduction potentials. This unexpected observation prompted a computational study of 128 different quinones, probing their 1 e – reduction potentials, pKa values, and 2 e –/2 H + reduction potentials. The density functional theory calculations reveal an approximately linear correlation between these three properties and an effective Hammett constant associated with the quinone substituent(s). However, deviations from this linear scaling relationship are evident formore » quinones that feature halogen substituents, charged substituents, intramolecular hydrogen bonding in the hydroquinone, and/or sterically bulky substituents. These results, particularly the different substituent effects on the 1 e – versus 2 e – /2 H + reduction potentials, have important implications for designing quinones with tailored redox properties.« less

Energy Decomposition Analysis Based on Absolutely Localized Molecular Orbitals for Large-Scale Density Functional Theory Calculations in Drug Design.

PubMed

Phipps, M J S; Fox, T; Tautermann, C S; Skylaris, C-K

2016-07-12

We report the development and implementation of an energy decomposition analysis (EDA) scheme in the ONETEP linear-scaling electronic structure package. Our approach is hybrid as it combines the localized molecular orbital EDA (Su, P.; Li, H. J. Chem. Phys., 2009, 131, 014102) and the absolutely localized molecular orbital EDA (Khaliullin, R. Z.; et al. J. Phys. Chem. A, 2007, 111, 8753-8765) to partition the intermolecular interaction energy into chemically distinct components (electrostatic, exchange, correlation, Pauli repulsion, polarization, and charge transfer). Limitations shared in EDA approaches such as the issue of basis set dependence in polarization and charge transfer are discussed, and a remedy to this problem is proposed that exploits the strictly localized property of the ONETEP orbitals. Our method is validated on a range of complexes with interactions relevant to drug design. We demonstrate the capabilities for large-scale calculations with our approach on complexes of thrombin with an inhibitor comprised of up to 4975 atoms. Given the capability of ONETEP for large-scale calculations, such as on entire proteins, we expect that our EDA scheme can be applied in a large range of biomolecular problems, especially in the context of drug design.

Hybrid MPI-OpenMP Parallelism in the ONETEP Linear-Scaling Electronic Structure Code: Application to the Delamination of Cellulose Nanofibrils.

PubMed

Wilkinson, Karl A; Hine, Nicholas D M; Skylaris, Chris-Kriton

2014-11-11

We present a hybrid MPI-OpenMP implementation of Linear-Scaling Density Functional Theory within the ONETEP code. We illustrate its performance on a range of high performance computing (HPC) platforms comprising shared-memory nodes with fast interconnect. Our work has focused on applying OpenMP parallelism to the routines which dominate the computational load, attempting where possible to parallelize different loops from those already parallelized within MPI. This includes 3D FFT box operations, sparse matrix algebra operations, calculation of integrals, and Ewald summation. While the underlying numerical methods are unchanged, these developments represent significant changes to the algorithms used within ONETEP to distribute the workload across CPU cores. The new hybrid code exhibits much-improved strong scaling relative to the MPI-only code and permits calculations with a much higher ratio of cores to atoms. These developments result in a significantly shorter time to solution than was possible using MPI alone and facilitate the application of the ONETEP code to systems larger than previously feasible. We illustrate this with benchmark calculations from an amyloid fibril trimer containing 41,907 atoms. We use the code to study the mechanism of delamination of cellulose nanofibrils when undergoing sonification, a process which is controlled by a large number of interactions that collectively determine the structural properties of the fibrils. Many energy evaluations were needed for these simulations, and as these systems comprise up to 21,276 atoms this would not have been feasible without the developments described here.

CMB hemispherical asymmetry from non-linear isocurvature perturbations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Assadullahi, Hooshyar; Wands, David; Firouzjahi, Hassan

2015-04-01

We investigate whether non-adiabatic perturbations from inflation could produce an asymmetric distribution of temperature anisotropies on large angular scales in the cosmic microwave background (CMB). We use a generalised non-linear δ N formalism to calculate the non-Gaussianity of the primordial density and isocurvature perturbations due to the presence of non-adiabatic, but approximately scale-invariant field fluctuations during multi-field inflation. This local-type non-Gaussianity leads to a correlation between very long wavelength inhomogeneities, larger than our observable horizon, and smaller scale fluctuations in the radiation and matter density. Matter isocurvature perturbations contribute primarily to low CMB multipoles and hence can lead to a hemisphericalmore » asymmetry on large angular scales, with negligible asymmetry on smaller scales. In curvaton models, where the matter isocurvature perturbation is partly correlated with the primordial density perturbation, we are unable to obtain a significant asymmetry on large angular scales while respecting current observational constraints on the observed quadrupole. However in the axion model, where the matter isocurvature and primordial density perturbations are uncorrelated, we find it may be possible to obtain a significant asymmetry due to isocurvature modes on large angular scales. Such an isocurvature origin for the hemispherical asymmetry would naturally give rise to a distinctive asymmetry in the CMB polarisation on large scales.« less

A unified stochastic formulation of dissipative quantum dynamics. II. Beyond linear response of spin baths

NASA Astrophysics Data System (ADS)

Hsieh, Chang-Yu; Cao, Jianshu

2018-01-01

We use the "generalized hierarchical equation of motion" proposed in Paper I [C.-Y. Hsieh and J. Cao, J. Chem. Phys. 148, 014103 (2018)] to study decoherence in a system coupled to a spin bath. The present methodology allows a systematic incorporation of higher-order anharmonic effects of the bath in dynamical calculations. We investigate the leading order corrections to the linear response approximations for spin bath models. Two kinds of spin-based environments are considered: (1) a bath of spins discretized from a continuous spectral density and (2) a bath of localized nuclear or electron spins. The main difference resides with how the bath frequency and the system-bath coupling parameters are distributed in an environment. When discretized from a continuous spectral density, the system-bath coupling typically scales as ˜1 /√{NB } where NB is the number of bath spins. This scaling suppresses the non-Gaussian characteristics of the spin bath and justifies the linear response approximations in the thermodynamic limit. For the nuclear/electron spin bath models, system-bath couplings are directly deduced from spin-spin interactions and do not necessarily obey the 1 /√{NB } scaling. It is not always possible to justify the linear response approximations in this case. Furthermore, if the spin-spin Hamiltonian is highly symmetrical, there exist additional constraints that generate highly non-Markovian and persistent dynamics that is beyond the linear response treatments.

Exciton Absorption Spectra by Linear Response Methods:Application to Conjugated Polymers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mosquera, Martin A.; Jackson, Nicholas E.; Fauvell, Thomas J.

The theoretical description of the timeevolution of excitons requires, as an initial step, the calculation of their spectra, which has been inaccessible to most users due to the high computational scaling of conventional algorithms and accuracy issues caused by common density functionals. Previously (J. Chem. Phys. 2016, 144, 204105), we developed a simple method that resolves these issues. Our scheme is based on a two-step calculation in which a linear-response TDDFT calculation is used to generate orbitals perturbed by the excitonic state, and then a second linear-response TDDFT calculation is used to determine the spectrum of excitations relative to themore » excitonic state. Herein, we apply this theory to study near-infrared absorption spectra of excitons in oligomers of the ubiquitous conjugated polymers poly(3-hexylthiophene) (P3HT), poly(2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene) (MEH-PPV), and poly(benzodithiophene-thieno[3,4-b]thiophene) (PTB7). For P3HT and MEH-PPV oligomers, the calculated intense absorption bands converge at the longest wavelengths for 10 monomer units, and show strong consistency with experimental measurements. The calculations confirm that the exciton spectral features in MEH-PPV overlap with those of the bipolaron formation. In addition, our calculations identify the exciton absorption bands in transient absorption spectra measured by our group for oligomers (1, 2, and 3 units) of PTB7. For all of the cases studied, we report the dominant orbital excitations contributing to the optically active excited state-excited state transitions, and suggest a simple rule to identify absorption peaks at the longest wavelengths. We suggest our methodology could be considered for further evelopments in theoretical transient spectroscopy to include nonadiabatic effects, coherences, and to describe the formation of species such as charge-transfer states and polaron pairs.« less

Surface Oscillations of a Free-Falling Droplet of an Ideal Fluid

NASA Astrophysics Data System (ADS)

Kistovich, A. V.; Chashechkin, Yu. D.

2018-03-01

According to observations, drops freely falling in the air under the action of gravity are deformed and oscillate in a wide range of frequencies and scales. A technique for calculating surface axisymmetric oscillations of a deformed droplet in the linear approximation under the assumption that the amplitude and wavelength are small when compared to the droplet diameter is proposed. The basic form of an axisymmetric droplet is chosen from observations. The calculation results for surface oscillations agree with recorded data on the varying shape of water droplets falling in the air.

On-field study of anaerobic digestion full-scale plants (part I): an on-field methodology to determine mass, carbon and nutrients balance.

PubMed

Schievano, Andrea; D'Imporzano, Giuliana; Salati, Silvia; Adani, Fabrizio

2011-09-01

The mass balance (input/output mass flows) of full-scale anaerobic digestion (AD) processes should be known for a series of purposes, e.g. to understand carbon and nutrients balances, to evaluate the contribution of AD processes to elemental cycles, especially when digestates are applied to agricultural land and to measure the biodegradation yields and the process efficiency. In this paper, three alternative methods were studied, to determine the mass balance in full-scale processes, discussing their reliability and applicability. Through a 1-year survey on three full-scale AD plants and through 38 laboratory-scale batch digesters, the congruency of the considered methods was demonstrated and a linear equation was provided that allows calculating the wet weight losses (WL) from the methane produced (MP) by the plant (WL=41.949*MP+20.853, R(2)=0.950, p<0.01). Additionally, this new tool was used to calculate carbon, nitrogen, phosphorous and potassium balances of the three observed AD plants. Copyright © 2011 Elsevier Ltd. All rights reserved.

Slowly-rotating neutron stars in massive bigravity

NASA Astrophysics Data System (ADS)

Sullivan, A.; Yunes, N.

2018-02-01

We study slowly-rotating neutron stars in ghost-free massive bigravity. This theory modifies general relativity by introducing a second, auxiliary but dynamical tensor field that couples to matter through the physical metric tensor through non-linear interactions. We expand the field equations to linear order in slow rotation and numerically construct solutions in the interior and exterior of the star with a set of realistic equations of state. We calculate the physical mass function with respect to observer radius and find that, unlike in general relativity, this function does not remain constant outside the star; rather, it asymptotes to a constant a distance away from the surface, whose magnitude is controlled by the ratio of gravitational constants. The Vainshtein-like radius at which the physical and auxiliary mass functions asymptote to a constant is controlled by the graviton mass scaling parameter, and outside this radius, bigravity modifications are suppressed. We also calculate the frame-dragging metric function and find that bigravity modifications are typically small in the entire range of coupling parameters explored. We finally calculate both the mass-radius and the moment of inertia-mass relations for a wide range of coupling parameters and find that both the graviton mass scaling parameter and the ratio of the gravitational constants introduce large modifications to both. These results could be used to place future constraints on bigravity with electromagnetic and gravitational-wave observations of isolated and binary neutron stars.

FT-IR, UV-vis, 1H and 13C NMR spectra and the equilibrium structure of organic dye molecule disperse red 1 acrylate: a combined experimental and theoretical analysis.

PubMed

Cinar, Mehmet; Coruh, Ali; Karabacak, Mehmet

2011-12-01

This study reports the characterization of disperse red 1 acrylate compound by spectral techniques and quantum chemical calculations. The spectroscopic properties were analyzed by FT-IR, UV-vis, (1)H NMR and (13)C NMR techniques. FT-IR spectrum in solid state was recorded in the region 4000-400 cm(-1). The UV-vis absorption spectrum of the compound that dissolved in methanol was recorded in the range of 200-800 nm. The (1)H and (13)C NMR spectra were recorded in CDCl(3) solution. The structural and spectroscopic data of the molecule in the ground state were calculated using density functional theory (DFT) employing B3LYP exchange correlation and the 6-311++G(d,p) basis set. The vibrational wavenumbers were calculated and scaled values were compared with experimental FT-IR spectrum. A satisfactory consistency between the experimental and theoretical spectra was obtained and it shows that the hybrid DFT method is very useful in predicting accurate vibrational structure, especially for high-frequency region. The complete assignments were performed on the basis of the experimental results and total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. Isotropic chemical shifts were calculated using the gauge-invariant atomic orbital (GIAO) method. A study on the electronic properties were performed by timedependent DFT (TD-DFT) and CIS(D) approach. To investigate non linear optical properties, the electric dipole moment μ, polarizability α, anisotropy of polarizability Δα and molecular first hyperpolarizability β were computed. The linear polarizabilities and first hyperpolarizabilities of the studied molecule indicate that the compound can be a good candidate of nonlinear optical materials. Copyright © 2011 Elsevier B.V. All rights reserved.

Local unitary transformation method for large-scale two-component relativistic calculations: case for a one-electron Dirac Hamiltonian.

PubMed

Seino, Junji; Nakai, Hiromi

2012-06-28

An accurate and efficient scheme for two-component relativistic calculations at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level is presented. The present scheme, termed local unitary transformation (LUT), is based on the locality of the relativistic effect. Numerical assessments of the LUT scheme were performed in diatomic molecules such as HX and X(2) (X = F, Cl, Br, I, and At) and hydrogen halide clusters, (HX)(n) (X = F, Cl, Br, and I). Total energies obtained by the LUT method agree well with conventional IODKH results. The computational costs of the LUT method are drastically lower than those of conventional methods since in the former there is linear-scaling with respect to the system size and a small prefactor.

Is the Jeffreys' scale a reliable tool for Bayesian model comparison in cosmology?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nesseris, Savvas; García-Bellido, Juan, E-mail: savvas.nesseris@uam.es, E-mail: juan.garciabellido@uam.es

2013-08-01

We are entering an era where progress in cosmology is driven by data, and alternative models will have to be compared and ruled out according to some consistent criterium. The most conservative and widely used approach is Bayesian model comparison. In this paper we explicitly calculate the Bayes factors for all models that are linear with respect to their parameters. We do this in order to test the so called Jeffreys' scale and determine analytically how accurate its predictions are in a simple case where we fully understand and can calculate everything analytically. We also discuss the case of nestedmore » models, e.g. one with M{sub 1} and another with M{sub 2} superset of M{sub 1} parameters and we derive analytic expressions for both the Bayes factor and the figure of Merit, defined as the inverse area of the model parameter's confidence contours. With all this machinery and the use of an explicit example we demonstrate that the threshold nature of Jeffreys' scale is not a ''one size fits all'' reliable tool for model comparison and that it may lead to biased conclusions. Furthermore, we discuss the importance of choosing the right basis in the context of models that are linear with respect to their parameters and how that basis affects the parameter estimation and the derived constraints.« less

Efficient parallel linear scaling construction of the density matrix for Born-Oppenheimer molecular dynamics.

PubMed

Mniszewski, S M; Cawkwell, M J; Wall, M E; Mohd-Yusof, J; Bock, N; Germann, T C; Niklasson, A M N

2015-10-13

We present an algorithm for the calculation of the density matrix that for insulators scales linearly with system size and parallelizes efficiently on multicore, shared memory platforms with small and controllable numerical errors. The algorithm is based on an implementation of the second-order spectral projection (SP2) algorithm [ Niklasson, A. M. N. Phys. Rev. B 2002 , 66 , 155115 ] in sparse matrix algebra with the ELLPACK-R data format. We illustrate the performance of the algorithm within self-consistent tight binding theory by total energy calculations of gas phase poly(ethylene) molecules and periodic liquid water systems containing up to 15,000 atoms on up to 16 CPU cores. We consider algorithm-specific performance aspects, such as local vs nonlocal memory access and the degree of matrix sparsity. Comparisons to sparse matrix algebra implementations using off-the-shelf libraries on multicore CPUs, graphics processing units (GPUs), and the Intel many integrated core (MIC) architecture are also presented. The accuracy and stability of the algorithm are illustrated with long duration Born-Oppenheimer molecular dynamics simulations of 1000 water molecules and a 303 atom Trp cage protein solvated by 2682 water molecules.

Time-sliced perturbation theory for large scale structure I: general formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blas, Diego; Garny, Mathias; Sibiryakov, Sergey

2016-07-01

We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution ofmore » the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.« less

Calibration sets and the accuracy of vibrational scaling factors: A case study with the X3LYP hybrid functional

NASA Astrophysics Data System (ADS)

Teixeira, Filipe; Melo, André; Cordeiro, M. Natália D. S.

2010-09-01

A linear least-squares methodology was used to determine the vibrational scaling factors for the X3LYP density functional. Uncertainties for these scaling factors were calculated according to the method devised by Irikura et al. [J. Phys. Chem. A 109, 8430 (2005)]. The calibration set was systematically partitioned according to several of its descriptors and the scaling factors for X3LYP were recalculated for each subset. The results show that the scaling factors are only significant up to the second digit, irrespective of the calibration set used. Furthermore, multivariate statistical analysis allowed us to conclude that the scaling factors and the associated uncertainties are independent of the size of the calibration set and strongly suggest the practical impossibility of obtaining vibrational scaling factors with more than two significant digits.

Calibration sets and the accuracy of vibrational scaling factors: a case study with the X3LYP hybrid functional.

PubMed

Teixeira, Filipe; Melo, André; Cordeiro, M Natália D S

2010-09-21

A linear least-squares methodology was used to determine the vibrational scaling factors for the X3LYP density functional. Uncertainties for these scaling factors were calculated according to the method devised by Irikura et al. [J. Phys. Chem. A 109, 8430 (2005)]. The calibration set was systematically partitioned according to several of its descriptors and the scaling factors for X3LYP were recalculated for each subset. The results show that the scaling factors are only significant up to the second digit, irrespective of the calibration set used. Furthermore, multivariate statistical analysis allowed us to conclude that the scaling factors and the associated uncertainties are independent of the size of the calibration set and strongly suggest the practical impossibility of obtaining vibrational scaling factors with more than two significant digits.

Numerical prediction of turbulent flame stability in premixed/prevaporized (HSCT) combustors

NASA Technical Reports Server (NTRS)

Winowich, Nicholas S.

1990-01-01

A numerical analysis of combustion instabilities that induce flashback in a lean, premixed, prevaporized dump combustor is performed. KIVA-II, a finite volume CFD code for the modeling of transient, multidimensional, chemically reactive flows, serves as the principal analytical tool. The experiment of Proctor and T'ien is used as a reference for developing the computational model. An experimentally derived combustion instability mechanism is presented on the basis of the observations of Proctor and T'ien and other investigators of instabilities in low speed (M less than 0.1) dump combustors. The analysis comprises two independent procedures that begin from a calculated stable flame: The first is a linear increase of the equivalence ratio and the second is the linear decrease of the inflow velocity. The objective is to observe changes in the aerothermochemical features of the flow field prior to flashback. It was found that only the linear increase of the equivalence ratio elicits a calculated flashback result. Though this result did not exhibit large scale coherent vortices in the turbulent shear layer coincident with a flame flickering mode as was observed experimentally, there were interesting acoustic effects which were resolved quite well in the calculation. A discussion of the k-e turbulence model used by KIVA-II is prompted by the absence of combustion instabilities in the model as the inflow velocity is linearly decreased. Finally, recommendations are made for further numerical analysis that may improve correlation with experimentally observed combustion instabilities.

Electron correlations in L-subshell photoionization of intermediate-Z elements (47<=Z<=51)

NASA Astrophysics Data System (ADS)

Jitschin, W.; Stötzel, R.

1998-08-01

The x-ray mass attenuation of 48Cd, 49In, 50Sn, and 51Sb in the energy regime of the L-subshell edges has been measured. For a comparison of the data of neighboring elements, these were scaled to 47Ag. The scaled data were compared with theoretical calculations of photoionization cross sections by Scofield, which use the common single electron approach. The comparison reveals minor but significant deviations between measurement and calculation: The measured cross sections are smaller than the prediction in the regime between the L3 and L2 edges, they have a flatter slope in the regime between the L2 and L1 edges, and they exhibit a decrease just above the L3 and L2 edges. All observed deviations can be explained as electron correlation effects originating from a polarization of the whole electron cloud by the ionizing radiation, since they are qualitatively reproduced by comparative calculations of the ionization process either omitting (independent particle approach) or including (in the linear response approximation) the electron correlations. However, the comparative calculations quantitatively overestimate the electron correlation effects.

Repopulation Kinetics and the Linear-Quadratic Model

NASA Astrophysics Data System (ADS)

O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.

2009-08-01

The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Liang; Abild-Pedersen, Frank

On the basis of an extensive set of density functional theory calculations, it is shown that a simple scheme provides a fundamental understanding of variations in the transition state energies and structures of reaction intermediates on transition metal surfaces across the periodic table. The scheme is built on the bond order conservation principle and requires a limited set of input data, still achieving transition state energies as a function of simple descriptors with an error smaller than those of approaches based on linear fits to a set of calculated transition state energies. Here, we have applied this approach together withmore » linear scaling of adsorption energies to obtain the energetics of the NH 3 decomposition reaction on a series of stepped fcc(211) transition metal surfaces. Moreover, this information is used to establish a microkinetic model for the formation of N 2 and H 2, thus providing insight into the components of the reaction that determines the activity.« less

DL_MG: A Parallel Multigrid Poisson and Poisson-Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution.

PubMed

Womack, James C; Anton, Lucian; Dziedzic, Jacek; Hasnip, Phil J; Probert, Matt I J; Skylaris, Chris-Kriton

2018-03-13

The solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential-a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the Poisson equation, featuring nonhomogeneous dielectric permittivities, ionic concentrations with nonlinear dependencies, and diverse boundary conditions. The analytic solutions generally used to solve the Poisson equation in vacuum (or with homogeneous permittivity) are not applicable in these circumstances, and numerical methods must be used. In this work, we present DL_MG, a flexible, scalable, and accurate solver library, developed specifically to tackle the challenges of solving the Poisson equation in modern large-scale electronic structure calculations on parallel computers. Our solver is based on the multigrid approach and uses an iterative high-order defect correction method to improve the accuracy of solutions. Using two chemically relevant model systems, we tested the accuracy and computational performance of DL_MG when solving the generalized Poisson and Poisson-Boltzmann equations, demonstrating excellent agreement with analytic solutions and efficient scaling to ∼10 9 unknowns and 100s of CPU cores. We also applied DL_MG in actual large-scale electronic structure calculations, using the ONETEP linear-scaling electronic structure package to study a 2615 atom protein-ligand complex with routinely available computational resources. In these calculations, the overall execution time with DL_MG was not significantly greater than the time required for calculations using a conventional FFT-based solver.

Extending the length and time scales of Gram-Schmidt Lyapunov vector computations

NASA Astrophysics Data System (ADS)

Costa, Anthony B.; Green, Jason R.

2013-08-01

Lyapunov vectors have found growing interest recently due to their ability to characterize systems out of thermodynamic equilibrium. The computation of orthogonal Gram-Schmidt vectors requires multiplication and QR decomposition of large matrices, which grow as N2 (with the particle count). This expense has limited such calculations to relatively small systems and short time scales. Here, we detail two implementations of an algorithm for computing Gram-Schmidt vectors. The first is a distributed-memory message-passing method using Scalapack. The second uses the newly-released MAGMA library for GPUs. We compare the performance of both codes for Lennard-Jones fluids from N=100 to 1300 between Intel Nahalem/Infiniband DDR and NVIDIA C2050 architectures. To our best knowledge, these are the largest systems for which the Gram-Schmidt Lyapunov vectors have been computed, and the first time their calculation has been GPU-accelerated. We conclude that Lyapunov vector calculations can be significantly extended in length and time by leveraging the power of GPU-accelerated linear algebra.

Parallel scalability of Hartree-Fock calculations

NASA Astrophysics Data System (ADS)

Chow, Edmond; Liu, Xing; Smelyanskiy, Mikhail; Hammond, Jeff R.

2015-03-01

Quantum chemistry is increasingly performed using large cluster computers consisting of multiple interconnected nodes. For a fixed molecular problem, the efficiency of a calculation usually decreases as more nodes are used, due to the cost of communication between the nodes. This paper empirically investigates the parallel scalability of Hartree-Fock calculations. The construction of the Fock matrix and the density matrix calculation are analyzed separately. For the former, we use a parallelization of Fock matrix construction based on a static partitioning of work followed by a work stealing phase. For the latter, we use density matrix purification from the linear scaling methods literature, but without using sparsity. When using large numbers of nodes for moderately sized problems, density matrix computations are network-bandwidth bound, making purification methods potentially faster than eigendecomposition methods.

LSMS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eisenbach, Markus; Li, Ying Wai; Liu, Xianglin

2017-12-01

LSMS is a first principles, Density Functional theory based, electronic structure code targeted mainly at materials applications. LSMS calculates the local spin density approximation to the diagonal part of the electron Green's function. The electron/spin density and energy are easily determined once the Green's function is known. Linear scaling with system size is achieved in the LSMS by using several unique properties of the real space multiple scattering approach to the Green's function.

Effect of lensing non-Gaussianity on the CMB power spectra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewis, Antony; Pratten, Geraint, E-mail: antony@cosmologist.info, E-mail: geraint.pratten@gmail.com

2016-12-01

Observed CMB anisotropies are lensed, and the lensed power spectra can be calculated accurately assuming the lensing deflections are Gaussian. However, the lensing deflections are actually slightly non-Gaussian due to both non-linear large-scale structure growth and post-Born corrections. We calculate the leading correction to the lensed CMB power spectra from the non-Gaussianity, which is determined by the lensing bispectrum. Assuming no primordial non-Gaussianity, the lowest-order result gives ∼ 0.3% corrections to the BB and EE polarization spectra on small-scales. However we show that the effect on EE is reduced by about a factor of two by higher-order Gaussian lensing smoothing,more » rendering the total effect safely negligible for the foreseeable future. We give a simple analytic model for the signal expected from skewness of the large-scale lensing field; the effect is similar to a net demagnification and hence a small change in acoustic scale (and therefore out of phase with the dominant lensing smoothing that predominantly affects the peaks and troughs of the power spectrum).« less

Scaling properties of ballistic nano-transistors

PubMed Central

2011-01-01

Recently, we have suggested a scale-invariant model for a nano-transistor. In agreement with experiments a close-to-linear thresh-old trace was found in the calculated ID - VD-traces separating the regimes of classically allowed transport and tunneling transport. In this conference contribution, the relevant physical quantities in our model and its range of applicability are discussed in more detail. Extending the temperature range of our studies it is shown that a close-to-linear thresh-old trace results at room temperatures as well. In qualitative agreement with the experiments the ID - VG-traces for small drain voltages show thermally activated transport below the threshold gate voltage. In contrast, at large drain voltages the gate-voltage dependence is weaker. As can be expected in our relatively simple model, the theoretical drain current is larger than the experimental one by a little less than a decade. PMID:21711899

Beam-driven acceleration in ultra-dense plasma media

DOE PAGES

Shin, Young-Min

2014-09-15

Accelerating parameters of beam-driven wakefield acceleration in an extremely dense plasma column has been analyzed with the dynamic framed particle-in-cell plasma simulator, and compared with analytic calculations. In the model, a witness beam undergoes a TeV/m scale alternating potential gradient excited by a micro-bunched drive beam in a 10 25 m -3 and 1.6 x 10 28 m -3 plasma column. The acceleration gradient, energy gain, and transformer ratio have been extensively studied in quasi-linear, linear-, and blowout-regimes. The simulation analysis indicated that in the beam-driven acceleration system a hollow plasma channel offers 20 % higher acceleration gradient by enlargingmore » the channel radius (r) from 0.2 Ap to 0.6 .Ap in a blowout regime. This paper suggests a feasibility of TeV/m scale acceleration with a hollow crystalline structure (e.g. nanotubes) of high electron plasma density.« less

Average receiving scaling of the weighted polygon Koch networks with the weight-dependent walk

NASA Astrophysics Data System (ADS)

Ye, Dandan; Dai, Meifeng; Sun, Yanqiu; Shao, Shuxiang; Xie, Qi

2016-09-01

Based on the weighted Koch networks and the self-similarity of fractals, we present a family of weighted polygon Koch networks with a weight factor r(0 < r ≤ 1) . We study the average receiving time (ART) on weight-dependent walk (i.e., the walker moves to any of its neighbors with probability proportional to the weight of edge linking them), whose key step is to calculate the sum of mean first-passage times (MFPTs) for all nodes absorpt at a hub node. We use a recursive division method to divide the weighted polygon Koch networks in order to calculate the ART scaling more conveniently. We show that the ART scaling exhibits a sublinear or linear dependence on network order. Thus, the weighted polygon Koch networks are more efficient than expended Koch networks in receiving information. Finally, compared with other previous studies' results (i.e., Koch networks, weighted Koch networks), we find out that our models are more general.

Density scaling of phantom materials for a 3D dose verification system.

PubMed

Tani, Kensuke; Fujita, Yukio; Wakita, Akihisa; Miyasaka, Ryohei; Uehara, Ryuzo; Kodama, Takumi; Suzuki, Yuya; Aikawa, Ako; Mizuno, Norifumi; Kawamori, Jiro; Saitoh, Hidetoshi

2018-05-21

In this study, the optimum density scaling factors of phantom materials for a commercially available three-dimensional (3D) dose verification system (Delta4) were investigated in order to improve the accuracy of the calculated dose distributions in the phantom materials. At field sizes of 10 × 10 and 5 × 5 cm 2 with the same geometry, tissue-phantom ratios (TPRs) in water, polymethyl methacrylate (PMMA), and Plastic Water Diagnostic Therapy (PWDT) were measured, and TPRs in various density scaling factors of water were calculated by Monte Carlo simulation, Adaptive Convolve (AdC, Pinnacle 3 ), Collapsed Cone Convolution (CCC, RayStation), and AcurosXB (AXB, Eclipse). Effective linear attenuation coefficients (μ eff ) were obtained from the TPRs. The ratios of μ eff in phantom and water ((μ eff ) pl,water ) were compared between the measurements and calculations. For each phantom material, the density scaling factor proposed in this study (DSF) was set to be the value providing a match between the calculated and measured (μ eff ) pl,water . The optimum density scaling factor was verified through the comparison of the dose distributions measured by Delta4 and calculated with three different density scaling factors: the nominal physical density (PD), nominal relative electron density (ED), and DSF. Three plans were used for the verifications: a static field of 10 × 10 cm 2 and two intensity modulated radiation therapy (IMRT) treatment plans. DSF were determined to be 1.13 for PMMA and 0.98 for PWDT. DSF for PMMA showed good agreement for AdC and CCC with 6 MV x ray, and AdC for 10 MV x ray. DSF for PWDT showed good agreement regardless of the dose calculation algorithms and x-ray energy. DSF can be considered one of the references for the density scaling factor of Delta4 phantom materials and may help improve the accuracy of the IMRT dose verification using Delta4. © 2018 The Authors. Journal of Applied Clinical Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine.

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals.

PubMed

Przybytek, Michal; Helgaker, Trygve

2013-08-07

We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions.

Linear static structural and vibration analysis on high-performance computers

NASA Technical Reports Server (NTRS)

Baddourah, M. A.; Storaasli, O. O.; Bostic, S. W.

1993-01-01

Parallel computers offer the oppurtunity to significantly reduce the computation time necessary to analyze large-scale aerospace structures. This paper presents algorithms developed for and implemented on massively-parallel computers hereafter referred to as Scalable High-Performance Computers (SHPC), for the most computationally intensive tasks involved in structural analysis, namely, generation and assembly of system matrices, solution of systems of equations and calculation of the eigenvalues and eigenvectors. Results on SHPC are presented for large-scale structural problems (i.e. models for High-Speed Civil Transport). The goal of this research is to develop a new, efficient technique which extends structural analysis to SHPC and makes large-scale structural analyses tractable.

Scale-Invariant Forms of Conservation Equations in Reactive Fields and a Modified Hydro-Thermo-Diffusive Theory of Laminar Flames

NASA Technical Reports Server (NTRS)

Sohrab, Siavash H.; Piltch, Nancy (Technical Monitor)

2000-01-01

A scale-invariant model of statistical mechanics is applied to present invariant forms of mass, energy, linear, and angular momentum conservation equations in reactive fields. The resulting conservation equations at molecular-dynamic scale are solved by the method of large activation energy asymptotics to describe the hydro-thermo-diffusive structure of laminar premixed flames. The predicted temperature and velocity profiles are in agreement with the observations. Also, with realistic physico-chemical properties and chemical-kinetic parameters for a single-step overall combustion of stoichiometric methane-air premixed flame, the laminar flame propagation velocity of 42.1 cm/s is calculated in agreement with the experimental value.

Macroweather Predictions and Climate Projections using Scaling and Historical Observations

NASA Astrophysics Data System (ADS)

Hébert, R.; Lovejoy, S.; Del Rio Amador, L.

2017-12-01

There are two fundamental time scales that are pertinent to decadal forecasts and multidecadal projections. The first is the lifetime of planetary scale structures, about 10 days (equal to the deterministic predictability limit), and the second is - in the anthropocene - the scale at which the forced anthropogenic variability exceeds the internal variability (around 16 - 18 years). These two time scales define three regimes of variability: weather, macroweather and climate that are respectively characterized by increasing, decreasing and then increasing varibility with scale.We discuss how macroweather temperature variability can be skilfully predicted to its theoretical stochastic predictability limits by exploiting its long-range memory with the Stochastic Seasonal and Interannual Prediction System (StocSIPS). At multi-decadal timescales, the temperature response to forcing is approximately linear and this can be exploited to make projections with a Green's function, or Climate Response Function (CRF). To make the problem tractable, we exploit the temporal scaling symmetry and restrict our attention to global mean forcing and temperature response using a scaling CRF characterized by the scaling exponent H and an inner scale of linearity τ. An aerosol linear scaling factor α and a non-linear volcanic damping exponent ν were introduced to account for the large uncertainty in these forcings. We estimate the model and forcing parameters by Bayesian inference using historical data and these allow us to analytically calculate a median (and likely 66% range) for the transient climate response, and for the equilibrium climate sensitivity: 1.6K ([1.5,1.8]K) and 2.4K ([1.9,3.4]K) respectively. Aerosol forcing typically has large uncertainty and we find a modern (2005) forcing very likely range (90%) of [-1.0, -0.3] Wm-2 with median at -0.7 Wm-2. Projecting to 2100, we find that to keep the warming below 1.5 K, future emissions must undergo cuts similar to Representative Concentration Pathway (RCP) 2.6 for which the probability to remain under 1.5 K is 48%. RCP 4.5 and RCP 8.5-like futures overshoot with very high probability. This underscores that over the next century, the state of the environment will be strongly influenced by past, present and future economical policies.

Concise calculation of the scaling function, exponents, and probability functional of the Edwards-Wilkinson equation with correlated noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Y.; Pang, N.; Halpin-Healy, T.

1994-12-01

The linear Langevin equation proposed by Edwards and Wilkinson [Proc. R. Soc. London A 381, 17 (1982)] is solved in closed form for noise of arbitrary space and time correlation. Furthermore, the temporal development of the full probability functional describing the height fluctuations is derived exactly, exhibiting an interesting evolution between two distinct Gaussian forms. We determine explicitly the dynamic scaling function for the interfacial width for any given initial condition, isolate the early-time behavior, and discover an invariance that was unsuspected in this problem of arbitrary spatiotemporal noise.

Natural Covariant Planck Scale Cutoffs and the Cosmic Microwave Background Spectrum.

PubMed

Chatwin-Davies, Aidan; Kempf, Achim; Martin, Robert T W

2017-07-21

We calculate the impact of quantum gravity-motivated ultraviolet cutoffs on inflationary predictions for the cosmic microwave background spectrum. We model the ultraviolet cutoffs fully covariantly to avoid possible artifacts of covariance breaking. Imposing these covariant cutoffs results in the production of small, characteristically k-dependent oscillations in the spectrum. The size of the effect scales linearly with the ratio of the Planck to Hubble lengths during inflation. Consequently, the relative size of the effect could be as large as one part in 10^{5}; i.e., eventual observability may not be ruled out.

A program for calculating photonic band structures, Green's functions and transmission/reflection coefficients using a non-orthogonal FDTD method

NASA Astrophysics Data System (ADS)

Ward, A. J.; Pendry, J. B.

2000-06-01

In this paper we present an updated version of our ONYX program for calculating photonic band structures using a non-orthogonal finite difference time domain method. This new version employs the same transparent formalism as the first version with the same capabilities for calculating photonic band structures or causal Green's functions but also includes extra subroutines for the calculation of transmission and reflection coefficients. Both the electric and magnetic fields are placed onto a discrete lattice by approximating the spacial and temporal derivatives with finite differences. This results in discrete versions of Maxwell's equations which can be used to integrate the fields forwards in time. The time required for a calculation using this method scales linearly with the number of real space points used in the discretization so the technique is ideally suited to handling systems with large and complicated unit cells.

Application of the Extended Completeness Relation to the Absorbing Boundary Condition

NASA Astrophysics Data System (ADS)

Iwasaki, Masataka; Otani, Reiji; Ito, Makoto

The strength function of the linear response by the external field is calculated in the formalism of the absorbing boundary condition (ABC). The dipole excitation of a schematic two-body system is treated in the present study. The extended completeness relation, which is assumed on the analogy of the formulation in the complex scaling method (CSM), is applied to the calculation of the strength function. The calculation of the strength function is successful in the present formalism and hence, the extended completeness relation seems to work well in the ABC formalism. The contributions from the resonance and the non-resonant continuum are also analyzed according to the decomposition of the energy levels in the extended completeness relation.

Elastic and viscoelastic mechanical properties of brain tissues on the implanting trajectory of sub-thalamic nucleus stimulation.

PubMed

Li, Yan; Deng, Jianxin; Zhou, Jun; Li, Xueen

2016-11-01

Corresponding to pre-puncture and post-puncture insertion, elastic and viscoelastic mechanical properties of brain tissues on the implanting trajectory of sub-thalamic nucleus stimulation are investigated, respectively. Elastic mechanical properties in pre-puncture are investigated through pre-puncture needle insertion experiments using whole porcine brains. A linear polynomial and a second order polynomial are fitted to the average insertion force in pre-puncture. The Young's modulus in pre-puncture is calculated from the slope of the two fittings. Viscoelastic mechanical properties of brain tissues in post-puncture insertion are investigated through indentation stress relaxation tests for six interested regions along a planned trajectory. A linear viscoelastic model with a Prony series approximation is fitted to the average load trace of each region using Boltzmann hereditary integral. Shear relaxation moduli of each region are calculated using the parameters of the Prony series approximation. The results show that, in pre-puncture insertion, needle force almost increases linearly with needle displacement. Both fitting lines can perfectly fit the average insertion force. The Young's moduli calculated from the slope of the two fittings are worthy of trust to model linearly or nonlinearly instantaneous elastic responses of brain tissues, respectively. In post-puncture insertion, both region and time significantly affect the viscoelastic behaviors. Six tested regions can be classified into three categories in stiffness. Shear relaxation moduli decay dramatically in short time scales but equilibrium is never truly achieved. The regional and temporal viscoelastic mechanical properties in post-puncture insertion are valuable for guiding probe insertion into each region on the implanting trajectory.

Scale-free network provides an optimal pattern for knowledge transfer

NASA Astrophysics Data System (ADS)

Lin, Min; Li, Nan

2010-02-01

We study numerically the knowledge innovation and diffusion process on four representative network models, such as regular networks, small-world networks, random networks and scale-free networks. The average knowledge stock level as a function of time is measured and the corresponding growth diffusion time, τ is defined and computed. On the four types of networks, the growth diffusion times all depend linearly on the network size N as τ∼N, while the slope for scale-free network is minimal indicating the fastest growth and diffusion of knowledge. The calculated variance and spatial distribution of knowledge stock illustrate that optimal knowledge transfer performance is obtained on scale-free networks. We also investigate the transient pattern of knowledge diffusion on the four networks, and a qualitative explanation of this finding is proposed.

Higher-order finite-difference formulation of periodic Orbital-free Density Functional Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Swarnava; Suryanarayana, Phanish, E-mail: phanish.suryanarayana@ce.gatech.edu

2016-02-15

We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we develop a generalized framework for performing OF-DFT simulations with different variants of the electronic kinetic energy. In particular, we propose a self-consistent field (SCF) type fixed-point method for calculations involving linear-response kinetic energy functionals. In this framework, evaluation of both the electronic ground-state and forces on the nuclei are amenable to computations that scale linearly with the number of atoms. We develop a parallel implementation of this formulation using the finite-difference discretization.more » We demonstrate that higher-order finite-differences can achieve relatively large convergence rates with respect to mesh-size in both the energies and forces. Additionally, we establish that the fixed-point iteration converges rapidly, and that it can be further accelerated using extrapolation techniques like Anderson's mixing. We validate the accuracy of the results by comparing the energies and forces with plane-wave methods for selected examples, including the vacancy formation energy in Aluminum. Overall, the suitability of the proposed formulation for scalable high performance computing makes it an attractive choice for large-scale OF-DFT calculations consisting of thousands of atoms.« less

Calculating Soil Wetness, Evapotranspiration and Carbon Cycle Processes Over Large Grid Areas Using a New Scaling Technique

NASA Technical Reports Server (NTRS)

Sellers, Piers

2012-01-01

Soil wetness typically shows great spatial variability over the length scales of general circulation model (GCM) grid areas (approx 100 km ), and the functions relating evapotranspiration and photosynthetic rate to local-scale (approx 1 m) soil wetness are highly non-linear. Soil respiration is also highly dependent on very small-scale variations in soil wetness. We therefore expect significant inaccuracies whenever we insert a single grid area-average soil wetness value into a function to calculate any of these rates for the grid area. For the particular case of evapotranspiration., this method - use of a grid-averaged soil wetness value - can also provoke severe oscillations in the evapotranspiration rate and soil wetness under some conditions. A method is presented whereby the probability distribution timction(pdf) for soil wetness within a grid area is represented by binning. and numerical integration of the binned pdf is performed to provide a spatially-integrated wetness stress term for the whole grid area, which then permits calculation of grid area fluxes in a single operation. The method is very accurate when 10 or more bins are used, can deal realistically with spatially variable precipitation, conserves moisture exactly and allows for precise modification of the soil wetness pdf after every time step. The method could also be applied to other ecological problems where small-scale processes must be area-integrated, or upscaled, to estimate fluxes over large areas, for example in treatments of the terrestrial carbon budget or trace gas generation.

Local Fitting of the Kohn-Sham Density in a Gaussian and Plane Waves Scheme for Large-Scale Density Functional Theory Simulations.

PubMed

Golze, Dorothea; Iannuzzi, Marcella; Hutter, Jürg

2017-05-09

A local resolution-of-the-identity (LRI) approach is introduced in combination with the Gaussian and plane waves (GPW) scheme to enable large-scale Kohn-Sham density functional theory calculations. In GPW, the computational bottleneck is typically the description of the total charge density on real-space grids. Introducing the LRI approximation, the linear scaling of the GPW approach with respect to system size is retained, while the prefactor for the grid operations is reduced. The density fitting is an O(N) scaling process implemented by approximating the atomic pair densities by an expansion in one-center fit functions. The computational cost for the grid-based operations becomes negligible in LRIGPW. The self-consistent field iteration is up to 30 times faster for periodic systems dependent on the symmetry of the simulation cell and on the density of grid points. However, due to the overhead introduced by the local density fitting, single point calculations and complete molecular dynamics steps, including the calculation of the forces, are effectively accelerated by up to a factor of ∼10. The accuracy of LRIGPW is assessed for different systems and properties, showing that total energies, reaction energies, intramolecular and intermolecular structure parameters are well reproduced. LRIGPW yields also high quality results for extended condensed phase systems such as liquid water, ice XV, and molecular crystals.

Simulated quantum computation of molecular energies.

PubMed

Aspuru-Guzik, Alán; Dutoi, Anthony D; Love, Peter J; Head-Gordon, Martin

2005-09-09

The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the readout register from about 20 to 4. Mappings of the molecular wave function to the quantum bits are described. An adiabatic method for the preparation of a good approximate ground-state wave function is described and demonstrated for a stretched hydrogen molecule. The number of quantum bits required scales linearly with the number of basis functions, and the number of gates required grows polynomially with the number of quantum bits.

Self-Consistent Field Theories for the Role of Large Length-Scale Architecture in Polymers

NASA Astrophysics Data System (ADS)

Wu, David

At large length-scales, the architecture of polymers can be described by a coarse-grained specification of the distribution of branch points and monomer types within a molecule. This includes molecular topology (e.g., cyclic or branched) as well as distances between branch points or chain ends. Design of large length-scale molecular architecture is appealing because it offers a universal strategy, independent of monomer chemistry, to tune properties. Non-linear analogs of linear chains differ in molecular-scale properties, such as mobility, entanglements, and surface segregation in blends that are well-known to impact rheological, dynamical, thermodynamic and surface properties including adhesion and wetting. We have used Self-Consistent Field (SCF) theories to describe a number of phenomena associated with large length-scale polymer architecture. We have predicted the surface composition profiles of non-linear chains in blends with linear chains. These predictions are in good agreement with experimental results, including from neutron scattering, on a range of well-controlled branched (star, pom-pom and end-branched) and cyclic polymer architectures. Moreover, the theory allows explanation of the segregation and conformations of branched polymers in terms of effective surface potentials acting on the end and branch groups. However, for cyclic chains, which have no end or junction points, a qualitatively different topological mechanism based on conformational entropy drives cyclic chains to a surface, consistent with recent neutron reflectivity experiments. We have also used SCF theory to calculate intramolecular and intermolecular correlations for polymer chains in the bulk, dilute solution, and trapped at a liquid-liquid interface. Predictions of chain swelling in dilute star polymer solutions compare favorably with existing PRISM theory and swelling at an interface helps explain recent measurements of chain mobility at an oil-water interface. In collaboration with: Renfeng Hu, Colorado School of Mines, and Mark Foster, University of Akron. This work was supported by NSF Grants No. CBET- 0730692 and No. CBET-0731319.

Parallel computation of fluid-structural interactions using high resolution upwind schemes

NASA Astrophysics Data System (ADS)

Hu, Zongjun

An efficient and accurate solver is developed to simulate the non-linear fluid-structural interactions in turbomachinery flutter flows. A new low diffusion E-CUSP scheme, Zha CUSP scheme, is developed to improve the efficiency and accuracy of the inviscid flux computation. The 3D unsteady Navier-Stokes equations with the Baldwin-Lomax turbulence model are solved using the finite volume method with the dual-time stepping scheme. The linearized equations are solved with Gauss-Seidel line iterations. The parallel computation is implemented using MPI protocol. The solver is validated with 2D cases for its turbulence modeling, parallel computation and unsteady calculation. The Zha CUSP scheme is validated with 2D cases, including a supersonic flat plate boundary layer, a transonic converging-diverging nozzle and a transonic inlet diffuser. The Zha CUSP2 scheme is tested with 3D cases, including a circular-to-rectangular nozzle, a subsonic compressor cascade and a transonic channel. The Zha CUSP schemes are proved to be accurate, robust and efficient in these tests. The steady and unsteady separation flows in a 3D stationary cascade under high incidence and three inlet Mach numbers are calculated to study the steady state separation flow patterns and their unsteady oscillation characteristics. The leading edge vortex shedding is the mechanism behind the unsteady characteristics of the high incidence separated flows. The separation flow characteristics is affected by the inlet Mach number. The blade aeroelasticity of a linear cascade with forced oscillating blades is studied using parallel computation. A simplified two-passage cascade with periodic boundary condition is first calculated under a medium frequency and a low incidence. The full scale cascade with 9 blades and two end walls is then studied more extensively under three oscillation frequencies and two incidence angles. The end wall influence and the blade stability are studied and compared under different frequencies and incidence angles. The Zha CUSP schemes are the first time to be applied in moving grid systems and 2D and 3D calculations. The implicit Gauss-Seidel iteration with dual time stepping is the first time to be used for moving grid systems. The NASA flutter cascade is the first time to be calculated in full scale.

A Scaling Model for the Anthropocene Climate Variability with Projections to 2100

NASA Astrophysics Data System (ADS)

Hébert, Raphael; Lovejoy, Shaun

2017-04-01

The determination of the climate sensitivity to radiative forcing is a fundamental climate science problem with important policy implications. We use a scaling model, with a limited set of parameters, which can directly calculate the forced globally-average surface air temperature response to anthropogenic and natural forcings. At timescales larger than an inner scale τ, which we determine as the ocean-atmosphere coupling scale at around 2 years, the global system responds, approximately, linearly, so that the variability may be decomposed into additive forced and internal components. The Ruelle response theory extends the classical linear response theory for small perturbations to systems far from equilibrium. Our model thus relates radiative forcings to a forced temperature response by convolution with a suitable Green's function, or climate response function. Motivated by scaling symmetries which allow for long range dependence, we assume a general scaling form, a scaling climate response function (SCRF) which is able to produce a wide range of responses: a power-law truncated at τ. This allows us to analytically calculate the climate sensitivity at different time scales, yielding a one-to-one relation from the transient climate response to the equilibrium climate sensitivity which are estimated, respectively, as 1.6+0.3-0.2K and 2.4+1.3-0.6K at the 90 % confidence level. The model parameters are estimated within a Bayesian framework, with a fractional Gaussian noise error model as the internal variability, from forcing series, instrumental surface temperature datasets and CMIP5 GCMs Representative Concentration Pathways (RCP) scenario runs. This observation based model is robust and projections for the coming century are made following the RCP scenario 2.6, 4.5 and 8.5, yielding in the year 2100, respectively : 1.5 +0.3)_{-0.2K, 2.3 ± 0.4 K and 4.0 ± 0.6 K at the 90 % confidence level. For comparison, the associated projections from a CMIP5 multi-model ensemble(MME) (32 models) are: 1.7 ± 0.8 K, 2.6 ± 0.8 K and 4.8 ± 1.3 K. Therefore, our projection uncertainty is less than half the structural uncertainty of this CMIP5 MME.

Large scale EMF in current sheets induced by tearing modes

NASA Astrophysics Data System (ADS)

Mizerski, Krzysztof A.

2018-02-01

An extension of the analysis of resistive instabilities of a sheet pinch from a famous work by Furth et al (1963 Phys. Fluids 6 459) is presented here, to study the mean electromotive force (EMF) generated by the developing instability. In a Cartesian configuration and in the presence of a current sheet first the boundary layer technique is used to obtain global, matched asymptotic solutions for the velocity and magnetic field and then the solutions are used to calculate the large-scale EMF in the system. It is reported, that in the bulk the curl of the mean EMF is linear in {{j}}0\\cdot {{B}}0, a simple pseudo-scalar quantity constructed from the large-scale quantities.

A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma

NASA Astrophysics Data System (ADS)

Rosin, M. S.; Schekochihin, A. A.; Rincon, F.; Cowley, S. C.

2011-05-01

Weakly collisional magnetized cosmic plasmas have a dynamical tendency to develop pressure anisotropies with respect to the local direction of the magnetic field. These anisotropies trigger plasma instabilities at scales just above the ion Larmor radius ρi and much below the mean free path λmfp. They have growth rates of a fraction of the ion cyclotron frequency, which is much faster than either the global dynamics or even local turbulence. Despite their microscopic nature, these instabilities dramatically modify the transport properties and, therefore, the macroscopic dynamics of the plasma. The non-linear evolution of these instabilities is expected to drive pressure anisotropies towards marginal stability values, controlled by the plasma beta βi. Here this non-linear evolution is worked out in an ab initio kinetic calculation for the simplest analytically tractable example - the parallel (k⊥= 0) firehose instability in a high-beta plasma. An asymptotic theory is constructed, based on a particular physical ordering and leading to a closed non-linear equation for the firehose turbulence. In the non-linear regime, both the analytical theory and the numerical solution predict secular (∝t) growth of magnetic fluctuations. The fluctuations develop a k-3∥ spectrum, extending from scales somewhat larger than ρi to the maximum scale that grows secularly with time (∝t1/2); the relative pressure anisotropy (p⊥-p∥)/p∥ tends to the marginal value -2/βi. The marginal state is achieved via changes in the magnetic field, not particle scattering. When a parallel ion heat flux is present, the parallel firehose mutates into the new gyrothermal instability (GTI), which continues to exist up to firehose-stable values of pressure anisotropy, which can be positive and are limited by the magnitude of the ion heat flux. The non-linear evolution of the GTI also features secular growth of magnetic fluctuations, but the fluctuation spectrum is eventually dominated by modes around a maximal scale ˜ρilT/λmfp, where lT is the scale of the parallel temperature variation. Implications for momentum and heat transport are speculated about. This study is motivated by our interest in the dynamics of galaxy cluster plasmas (which are used as the main astrophysical example), but its relevance to solar wind and accretion flow plasmas is also briefly discussed.

Iterative-method performance evaluation for multiple vectors associated with a large-scale sparse matrix

NASA Astrophysics Data System (ADS)

Imamura, Seigo; Ono, Kenji; Yokokawa, Mitsuo

2016-07-01

Ensemble computing, which is an instance of capacity computing, is an effective computing scenario for exascale parallel supercomputers. In ensemble computing, there are multiple linear systems associated with a common coefficient matrix. We improve the performance of iterative solvers for multiple vectors by solving them at the same time, that is, by solving for the product of the matrices. We implemented several iterative methods and compared their performance. The maximum performance on Sparc VIIIfx was 7.6 times higher than that of a naïve implementation. Finally, to deal with the different convergence processes of linear systems, we introduced a control method to eliminate the calculation of already converged vectors.

Bond Order Conservation Strategies in Catalysis Applied to the NH 3 Decomposition Reaction

DOE PAGES

Yu, Liang; Abild-Pedersen, Frank

2016-12-14

On the basis of an extensive set of density functional theory calculations, it is shown that a simple scheme provides a fundamental understanding of variations in the transition state energies and structures of reaction intermediates on transition metal surfaces across the periodic table. The scheme is built on the bond order conservation principle and requires a limited set of input data, still achieving transition state energies as a function of simple descriptors with an error smaller than those of approaches based on linear fits to a set of calculated transition state energies. Here, we have applied this approach together withmore » linear scaling of adsorption energies to obtain the energetics of the NH 3 decomposition reaction on a series of stepped fcc(211) transition metal surfaces. Moreover, this information is used to establish a microkinetic model for the formation of N 2 and H 2, thus providing insight into the components of the reaction that determines the activity.« less

[Computer-assisted phonetography as a diagnostic aid in functional dysphonia].

PubMed

Airainer, R; Klingholz, F

1991-07-01

A total of 160 voice-trained and untrained subjects with functional dysphonia were given a "clinical rating" according to their clinical findings. This was a certain value on a scale that recorded the degree of functional voice disorder ranging from a marked hypofunction to an extreme hyperfunction. The phonetograms of these patients were approximated by ellipses, whereby the definition and quantitative recording of several phonetogram parameters were rendered possible. By means of a linear combination of phonetogram parameters, a "calculated assessment" was obtained for each patient that was expected to tally with the "clinical rating". This paper demonstrates that a graduation of the dysphonic clinical picture with regard to the presence of hypofunctional or hyperfunctional components is possible via computerised phonetogram evaluation. In this case, the "calculated assessments" for both male and female singers and non-singers must be computed using different linear combinations. The method can be introduced as a supplementary diagnostic procedure in the diagnosis of functional dysphonia.

Conductivity and transit time estimates of a soil liner

USGS Publications Warehouse

Krapac, I.G.; Cartwright, K.; Panno, S.V.; Hensel, B.R.; Rehfeldt, K.H.; Herzog, B.L.

1990-01-01

A field-scale soil linear was built to assess the feasibilty of constructing a liner to meet the saturated hydraulic conductivity requirement of the U.S. EPA (i.e., less than 1 ?? 10-7 cm/s), and to determine the breakthrough and transit times of water and tracers through the liner. The liner, 8 ?? 15 ?? 0.9 m, was constructed in 15-cm compacted lifts using a 20,037-kg pad-foot compactor and standard engineering practices. Estimated saturated hydraulic conductivities were 2.4 ?? 10-9 cm/s, based on data from large-ring infiltrometers; 4.0 ?? 10-8 cm/s from small-ring infiltrometers; and 5.0 ?? 10-8 cm/s from a water-balance analysis. These estimates were derived from 1 year of monitoring water infiltration into the linear. Breakthrough of tracers at the base of the liner was estimated to be between 2 and 13 years, depending on the method of calculation and the assumptions used in the calculation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Jong-Won; Hirao, Kimihiko

Long-range corrected density functional theory (LC-DFT) attracts many chemists’ attentions as a quantum chemical method to be applied to large molecular system and its property calculations. However, the expensive time cost to evaluate the long-range HF exchange is a big obstacle to be overcome to be applied to the large molecular systems and the solid state materials. Upon this problem, we propose a linear-scaling method of the HF exchange integration, in particular, for the LC-DFT hybrid functional.

Scale Up Considerations for Sediment Microbial Fuel Cells

DTIC Science & Technology

2013-01-01

density calculations were made once WPs stabilized for each system. Linear sweep voltametry was then used on these systems to generate polarization and...power density curves. The systems were allowed to equilibrate under open circuit conditions (about 12 h) before a potential sweep was performed with a...reference. The potential sweep was set to begin at the anode potential under open circuit conditions (20.4 V vs. Ag/AgCl) and was raised to the

Extending the length and time scales of Gram–Schmidt Lyapunov vector computations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Costa, Anthony B., E-mail: acosta@northwestern.edu; Green, Jason R., E-mail: jason.green@umb.edu; Department of Chemistry, University of Massachusetts Boston, Boston, MA 02125

Lyapunov vectors have found growing interest recently due to their ability to characterize systems out of thermodynamic equilibrium. The computation of orthogonal Gram–Schmidt vectors requires multiplication and QR decomposition of large matrices, which grow as N{sup 2} (with the particle count). This expense has limited such calculations to relatively small systems and short time scales. Here, we detail two implementations of an algorithm for computing Gram–Schmidt vectors. The first is a distributed-memory message-passing method using Scalapack. The second uses the newly-released MAGMA library for GPUs. We compare the performance of both codes for Lennard–Jones fluids from N=100 to 1300 betweenmore » Intel Nahalem/Infiniband DDR and NVIDIA C2050 architectures. To our best knowledge, these are the largest systems for which the Gram–Schmidt Lyapunov vectors have been computed, and the first time their calculation has been GPU-accelerated. We conclude that Lyapunov vector calculations can be significantly extended in length and time by leveraging the power of GPU-accelerated linear algebra.« less

Treecode-based generalized Born method

NASA Astrophysics Data System (ADS)

Xu, Zhenli; Cheng, Xiaolin; Yang, Haizhao

2011-02-01

We have developed a treecode-based O(Nlog N) algorithm for the generalized Born (GB) implicit solvation model. Our treecode-based GB (tGB) is based on the GBr6 [J. Phys. Chem. B 111, 3055 (2007)], an analytical GB method with a pairwise descreening approximation for the R6 volume integral expression. The algorithm is composed of a cutoff scheme for the effective Born radii calculation, and a treecode implementation of the GB charge-charge pair interactions. Test results demonstrate that the tGB algorithm can reproduce the vdW surface based Poisson solvation energy with an average relative error less than 0.6% while providing an almost linear-scaling calculation for a representative set of 25 proteins with different sizes (from 2815 atoms to 65456 atoms). For a typical system of 10k atoms, the tGB calculation is three times faster than the direct summation as implemented in the original GBr6 model. Thus, our tGB method provides an efficient way for performing implicit solvent GB simulations of larger biomolecular systems at longer time scales.

Generating log-normal mock catalog of galaxies in redshift space

NASA Astrophysics Data System (ADS)

Agrawal, Aniket; Makiya, Ryu; Chiang, Chi-Ting; Jeong, Donghui; Saito, Shun; Komatsu, Eiichiro

2017-10-01

We present a public code to generate a mock galaxy catalog in redshift space assuming a log-normal probability density function (PDF) of galaxy and matter density fields. We draw galaxies by Poisson-sampling the log-normal field, and calculate the velocity field from the linearised continuity equation of matter fields, assuming zero vorticity. This procedure yields a PDF of the pairwise velocity fields that is qualitatively similar to that of N-body simulations. We check fidelity of the catalog, showing that the measured two-point correlation function and power spectrum in real space agree with the input precisely. We find that a linear bias relation in the power spectrum does not guarantee a linear bias relation in the density contrasts, leading to a cross-correlation coefficient of matter and galaxies deviating from unity on small scales. We also find that linearising the Jacobian of the real-to-redshift space mapping provides a poor model for the two-point statistics in redshift space. That is, non-linear redshift-space distortion is dominated by non-linearity in the Jacobian. The power spectrum in redshift space shows a damping on small scales that is qualitatively similar to that of the well-known Fingers-of-God (FoG) effect due to random velocities, except that the log-normal mock does not include random velocities. This damping is a consequence of non-linearity in the Jacobian, and thus attributing the damping of the power spectrum solely to FoG, as commonly done in the literature, is misleading.

Protein linear indices of the 'macromolecular pseudograph alpha-carbon atom adjacency matrix' in bioinformatics. Part 1: prediction of protein stability effects of a complete set of alanine substitutions in Arc repressor.

PubMed

Marrero-Ponce, Yovani; Medina-Marrero, Ricardo; Castillo-Garit, Juan A; Romero-Zaldivar, Vicente; Torrens, Francisco; Castro, Eduardo A

2005-04-15

A novel approach to bio-macromolecular design from a linear algebra point of view is introduced. A protein's total (whole protein) and local (one or more amino acid) linear indices are a new set of bio-macromolecular descriptors of relevance to protein QSAR/QSPR studies. These amino-acid level biochemical descriptors are based on the calculation of linear maps on Rn[f k(xmi):Rn-->Rn] in canonical basis. These bio-macromolecular indices are calculated from the kth power of the macromolecular pseudograph alpha-carbon atom adjacency matrix. Total linear indices are linear functional on Rn. That is, the kth total linear indices are linear maps from Rn to the scalar R[f k(xm):Rn-->R]. Thus, the kth total linear indices are calculated by summing the amino-acid linear indices of all amino acids in the protein molecule. A study of the protein stability effects for a complete set of alanine substitutions in the Arc repressor illustrates this approach. A quantitative model that discriminates near wild-type stability alanine mutants from the reduced-stability ones in a training series was obtained. This model permitted the correct classification of 97.56% (40/41) and 91.67% (11/12) of proteins in the training and test set, respectively. It shows a high Matthews correlation coefficient (MCC=0.952) for the training set and an MCC=0.837 for the external prediction set. Additionally, canonical regression analysis corroborated the statistical quality of the classification model (Rcanc=0.824). This analysis was also used to compute biological stability canonical scores for each Arc alanine mutant. On the other hand, the linear piecewise regression model compared favorably with respect to the linear regression one on predicting the melting temperature (tm) of the Arc alanine mutants. The linear model explains almost 81% of the variance of the experimental tm (R=0.90 and s=4.29) and the LOO press statistics evidenced its predictive ability (q2=0.72 and scv=4.79). Moreover, the TOMOCOMD-CAMPS method produced a linear piecewise regression (R=0.97) between protein backbone descriptors and tm values for alanine mutants of the Arc repressor. A break-point value of 51.87 degrees C characterized two mutant clusters and coincided perfectly with the experimental scale. For this reason, we can use the linear discriminant analysis and piecewise models in combination to classify and predict the stability of the mutant Arc homodimers. These models also permitted the interpretation of the driving forces of such folding process, indicating that topologic/topographic protein backbone interactions control the stability profile of wild-type Arc and its alanine mutants.

Run-up of Tsunamis in the Gulf of Mexico caused by the Chicxulub Impact Event

NASA Astrophysics Data System (ADS)

Weisz, R.; Wünnenmann, K.; Bahlburg, H.

2003-04-01

The Chicxulub impact event can be investigated on (1) local, (2) regional and in (3) global scales. Our investigations focus on the regional scale, especially on the run-up of tsunami waves on the coast around the Gulf of Mexico caused by the impact. An impact produces two types of tsunami waves: (1) the rim wave, (2) the collapse wave. Both waves propagate over long distances and reach coastal areas. Depending on the tsunami wave characteristics, they have a potentionally large influence on the coastal areas. Run-up distance and run-up height can be used as parameters for assessing this influence. To calculate these parameters, we are using a multi-material hydrocode (SALE) to simulate the generation of the tsunami wave, a non-linear shallow water approach for the propagation, and we implemented a special open boundary for considering the run-up of tsunami waves. With the help of the one-dimensional shallow water approach, we will give run-up heights and distances for the coastal area around the Gulf of Mexico. The calculations are done along several sections from the impact site towards the coast. These are a first approximation to run-up calculations for the entire coast of the Gulf of Mexico. The bathymetric data along the sections, used in the wave propagation and run-up, correspond to a linearized bathymetry of the recent Gulf of Mexico. Additionally, we will present preliminary results from our first two-dimensional experiments of propagation and run-up. These results will be compared with the one-dimensional approach.

Linear actuation using milligram quantities of CL-20 and TAGDNAT.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Snedigar, Shane; Salton, Jonathan Robert; Tappan, Alexander Smith

2009-07-01

There are numerous applications for small-scale actuation utilizing pyrotechnics and explosives. In certain applications, especially when multiple actuation strokes are needed, or actuator reuse is required, it is desirable to have all gaseous combustion products with no condensed residue in the actuator cylinder. Toward this goal, we have performed experiments on utilizing milligram quantities of high explosives to drive a millimeter-diameter actuator with a stroke of 30 mm. Calculations were performed to select proper material quantities to provide 0.5 J of actuation energy. This was performed utilizing the thermochemical code Cheetah to calculate the impetus for numerous propellants and tomore » select quantities based on estimated efficiencies of these propellants at small scales. Milligram quantities of propellants were loaded into a small-scale actuator and ignited with an ignition increment and hot wire ignition. Actuator combustion chamber pressure was monitored with a pressure transducer and actuator stroke was monitored using a laser displacement meter. Total actuation energy was determined by calculating the kinetic energy of reaction mass motion against gravity. Of the materials utilized, the best performance was obtained with a mixture of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) and bis-triaminoguanidinium(3,3{prime}dinitroazotriazolate) (TAGDNAT).« less

Molecular structure, vibrational spectra, NBO analysis, first hyperpolarizability, and HOMO-LUMO studies of 2-amino-4-hydroxypyrimidine by density functional method

NASA Astrophysics Data System (ADS)

Jeyavijayan, S.

2015-04-01

This study is a comparative analysis of FTIR and FT-Raman spectra of 2-amino-4-hydroxypyrimidine. The total energies of different conformations have been obtained from DFT (B3LYP) method with 6-31+G(d,p) and 6-311++G(d,p) basis sets. The barrier of planarity between the most stable and planar form is also predicted. The molecular structure, vibrational wavenumbers, infrared intensities, Raman scattering activities were calculated for the molecule using the B3LYP density functional theory (DFT) method. The computed values of frequencies are scaled using multiple scaling factors to yield good coherence with the observed values. Reliable vibrational assignments were made on the basis of total energy distribution (TED) along with scaled quantum mechanical (SQM) method. The stability of the molecule arising from hyperconjugative interactions, charge delocalization has been analyzed using natural bond orbital (NBO) analysis. Non-linear properties such as electric dipole moment (μ), polarizability (α), and hyperpolarizability (β) values of the investigated molecule have been computed using B3LYP quantum chemical calculation. The calculated HOMO and LUMO energies show that charge transfer occurs within the molecule. Besides, molecular electrostatic potential (MEP), Mulliken's charges analysis, and several thermodynamic properties were performed by the DFT method.

Highly efficient implementation of pseudospectral time-dependent density-functional theory for the calculation of excitation energies of large molecules.

PubMed

Cao, Yixiang; Hughes, Thomas; Giesen, Dave; Halls, Mathew D; Goldberg, Alexander; Vadicherla, Tati Reddy; Sastry, Madhavi; Patel, Bhargav; Sherman, Woody; Weisman, Andrew L; Friesner, Richard A

2016-06-15

We have developed and implemented pseudospectral time-dependent density-functional theory (TDDFT) in the quantum mechanics package Jaguar to calculate restricted singlet and restricted triplet, as well as unrestricted excitation energies with either full linear response (FLR) or the Tamm-Dancoff approximation (TDA) with the pseudospectral length scales, pseudospectral atomic corrections, and pseudospectral multigrid strategy included in the implementations to improve the chemical accuracy and to speed the pseudospectral calculations. The calculations based on pseudospectral time-dependent density-functional theory with full linear response (PS-FLR-TDDFT) and within the Tamm-Dancoff approximation (PS-TDA-TDDFT) for G2 set molecules using B3LYP/6-31G*(*) show mean and maximum absolute deviations of 0.0015 eV and 0.0081 eV, 0.0007 eV and 0.0064 eV, 0.0004 eV and 0.0022 eV for restricted singlet excitation energies, restricted triplet excitation energies, and unrestricted excitation energies, respectively; compared with the results calculated from the conventional spectral method. The application of PS-FLR-TDDFT to OLED molecules and organic dyes, as well as the comparisons for results calculated from PS-FLR-TDDFT and best estimations demonstrate that the accuracy of both PS-FLR-TDDFT and PS-TDA-TDDFT. Calculations for a set of medium-sized molecules, including Cn fullerenes and nanotubes, using the B3LYP functional and 6-31G(**) basis set show PS-TDA-TDDFT provides 19- to 34-fold speedups for Cn fullerenes with 450-1470 basis functions, 11- to 32-fold speedups for nanotubes with 660-3180 basis functions, and 9- to 16-fold speedups for organic molecules with 540-1340 basis functions compared to fully analytic calculations without sacrificing chemical accuracy. The calculations on a set of larger molecules, including the antibiotic drug Ramoplanin, the 46-residue crambin protein, fullerenes up to C540 and nanotubes up to 14×(6,6), using the B3LYP functional and 6-31G(**) basis set with up to 8100 basis functions show that PS-FLR-TDDFT CPU time scales as N(2.05) with the number of basis functions. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Iterative initial condition reconstruction

NASA Astrophysics Data System (ADS)

Schmittfull, Marcel; Baldauf, Tobias; Zaldarriaga, Matias

2017-07-01

Motivated by recent developments in perturbative calculations of the nonlinear evolution of large-scale structure, we present an iterative algorithm to reconstruct the initial conditions in a given volume starting from the dark matter distribution in real space. In our algorithm, objects are first moved back iteratively along estimated potential gradients, with a progressively reduced smoothing scale, until a nearly uniform catalog is obtained. The linear initial density is then estimated as the divergence of the cumulative displacement, with an optional second-order correction. This algorithm should undo nonlinear effects up to one-loop order, including the higher-order infrared resummation piece. We test the method using dark matter simulations in real space. At redshift z =0 , we find that after eight iterations the reconstructed density is more than 95% correlated with the initial density at k ≤0.35 h Mpc-1 . The reconstruction also reduces the power in the difference between reconstructed and initial fields by more than 2 orders of magnitude at k ≤0.2 h Mpc-1 , and it extends the range of scales where the full broadband shape of the power spectrum matches linear theory by a factor of 2-3. As a specific application, we consider measurements of the baryonic acoustic oscillation (BAO) scale that can be improved by reducing the degradation effects of large-scale flows. In our idealized dark matter simulations, the method improves the BAO signal-to-noise ratio by a factor of 2.7 at z =0 and by a factor of 2.5 at z =0.6 , improving standard BAO reconstruction by 70% at z =0 and 30% at z =0.6 , and matching the optimal BAO signal and signal-to-noise ratio of the linear density in the same volume. For BAO, the iterative nature of the reconstruction is the most important aspect.

A model for tides and currents in the English Channel and southern North Sea

USGS Publications Warehouse

Walters, Roy A.

1987-01-01

The amplitude and phase of 11 tidal constituents for the English Channel and southern North Sea are calculated using a frequency domain, finite element model. The governing equations - the shallow water equations - are modifed such that sea level is calculated using an elliptic equation of the Helmholz type followed by a back-calculation of velocity using the primitive momentum equations. Triangular elements with linear basis functions are used. The modified form of the governing equations provides stable solutions with little numerical noise. In this field-scale test problem, the model was able to produce the details of the structure of 11 tidal constituents including O1, K1, M2, S2, N2, K2, M4, MS4, MN4, M6, and 2MS6.

Influence of Turbulent Flow and Fractal Scaling on Effective Permeability of Fracture Network

NASA Astrophysics Data System (ADS)

Zhu, J.

2017-12-01

A new approach is developed to calculate hydraulic gradient dependent effective permeability of a fractal fracture network where both laminar and turbulent flows may occur in individual fractures. A critical fracture length is used to distinguish flow characteristics in individual fractures. The developed new solutions can be used for the case of a general scaling relationship, an extension to the linear scaling. We examine the impact on the effective permeability of the network of fractal fracture network characteristics, which include the fractal scaling coefficient and exponent, fractal dimension, ratio of minimum over maximum fracture lengths. Results demonstrate that the developed solution can explain more variations of the effective permeability in relation to the fractal dimensions estimated from the field observations. At high hydraulic gradient the effective permeability decreases with the fractal scaling exponent, but increases with the fractal scaling exponent at low gradient. The effective permeability increases with the scaling coefficient, fractal dimension, fracture length ratio and maximum fracture length.

Representation of the exact relativistic electronic Hamiltonian within the regular approximation

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2003-12-01

The exact relativistic Hamiltonian for electronic states is expanded in terms of energy-independent linear operators within the regular approximation. An effective relativistic Hamiltonian has been obtained, which yields in lowest order directly the infinite-order regular approximation (IORA) rather than the zeroth-order regular approximation method. Further perturbational expansion of the exact relativistic electronic energy utilizing the effective Hamiltonian leads to new methods based on ordinary (IORAn) or double [IORAn(2)] perturbation theory (n: order of expansion), which provide improved energies in atomic calculations. Energies calculated with IORA4 and IORA3(2) are accurate up to c-20. Furthermore, IORA is improved by using the IORA wave function to calculate the Rayleigh quotient, which, if minimized, leads to the exact relativistic energy. The outstanding performance of this new IORA method coined scaled IORA is documented in atomic and molecular calculations.

An efficient linear-scaling CCSD(T) method based on local natural orbitals.

PubMed

Rolik, Zoltán; Szegedy, Lóránt; Ladjánszki, István; Ladóczki, Bence; Kállay, Mihály

2013-09-07

An improved version of our general-order local coupled-cluster (CC) approach [Z. Rolik and M. Kállay, J. Chem. Phys. 135, 104111 (2011)] and its efficient implementation at the CC singles and doubles with perturbative triples [CCSD(T)] level is presented. The method combines the cluster-in-molecule approach of Li and co-workers [J. Chem. Phys. 131, 114109 (2009)] with frozen natural orbital (NO) techniques. To break down the unfavorable fifth-power scaling of our original approach a two-level domain construction algorithm has been developed. First, an extended domain of localized molecular orbitals (LMOs) is assembled based on the spatial distance of the orbitals. The necessary integrals are evaluated and transformed in these domains invoking the density fitting approximation. In the second step, for each occupied LMO of the extended domain a local subspace of occupied and virtual orbitals is constructed including approximate second-order Mo̸ller-Plesset NOs. The CC equations are solved and the perturbative corrections are calculated in the local subspace for each occupied LMO using a highly-efficient CCSD(T) code, which was optimized for the typical sizes of the local subspaces. The total correlation energy is evaluated as the sum of the individual contributions. The computation time of our approach scales linearly with the system size, while its memory and disk space requirements are independent thereof. Test calculations demonstrate that currently our method is one of the most efficient local CCSD(T) approaches and can be routinely applied to molecules of up to 100 atoms with reasonable basis sets.

Development of WRF-CO2 4DVAR Data Assimilation System

NASA Astrophysics Data System (ADS)

Zheng, T.; French, N. H. F.

2016-12-01

Four dimensional variational (4DVar) assimilation systems have been widely used for CO2 inverse modeling at global scale. At regional scale, however, 4DVar assimilation systems have been lacking. At present, most regional CO2 inverse models use Lagrangian particle backward trajectory tools to compute influence function in an analytical/synthesis framework. To provide a 4DVar based alternative, we developed WRF-CO2 4DVAR based on Weather Research and Forecasting (WRF), its chemistry extension (WRF-Chem), and its data assimilation system (WRFDA/WRFPLUS). Different from WRFDA, WRF-CO2 4DVAR does not optimize meteorology initial condition, instead it solves for the optimized CO2 surface fluxes (sources/sink) constrained by atmospheric CO2 observations. Based on WRFPLUS, we developed tangent linear and adjoint code for CO2 emission, advection, vertical mixing in boundary layer, and convective transport. Furthermore, we implemented an incremental algorithm to solve for optimized CO2 emission scaling factors by iteratively minimizing the cost function in a Bayes framework. The model sensitivity (of atmospheric CO2 with respect to emission scaling factor) calculated by tangent linear and adjoint model agrees well with that calculated by finite difference, indicating the validity of the newly developed code. The effectiveness of WRF-CO2 4DVar for inverse modeling is tested using forward-model generated pseudo-observation data in two experiments: first-guess CO2 fluxes has a 50% overestimation in the first case and 50% underestimation in the second. In both cases, WRF-CO2 4DVar reduces cost function to less than 10-4 of its initial values in less than 20 iterations and successfully recovers the true values of emission scaling factors. We expect future applications of WRF-CO2 4DVar with satellite observations will provide insights for CO2 regional inverse modeling, including the impacts of model transport error in vertical mixing.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pinski, Peter; Riplinger, Christoph; Neese, Frank, E-mail: evaleev@vt.edu, E-mail: frank.neese@cec.mpg.de

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implementsmore » sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.« less

Rapid sampling of stochastic displacements in Brownian dynamics simulations

NASA Astrophysics Data System (ADS)

Fiore, Andrew M.; Balboa Usabiaga, Florencio; Donev, Aleksandar; Swan, James W.

2017-03-01

We present a new method for sampling stochastic displacements in Brownian Dynamics (BD) simulations of colloidal scale particles. The method relies on a new formulation for Ewald summation of the Rotne-Prager-Yamakawa (RPY) tensor, which guarantees that the real-space and wave-space contributions to the tensor are independently symmetric and positive-definite for all possible particle configurations. Brownian displacements are drawn from a superposition of two independent samples: a wave-space (far-field or long-ranged) contribution, computed using techniques from fluctuating hydrodynamics and non-uniform fast Fourier transforms; and a real-space (near-field or short-ranged) correction, computed using a Krylov subspace method. The combined computational complexity of drawing these two independent samples scales linearly with the number of particles. The proposed method circumvents the super-linear scaling exhibited by all known iterative sampling methods applied directly to the RPY tensor that results from the power law growth of the condition number of tensor with the number of particles. For geometrically dense microstructures (fractal dimension equal three), the performance is independent of volume fraction, while for tenuous microstructures (fractal dimension less than three), such as gels and polymer solutions, the performance improves with decreasing volume fraction. This is in stark contrast with other related linear-scaling methods such as the force coupling method and the fluctuating immersed boundary method, for which performance degrades with decreasing volume fraction. Calculations for hard sphere dispersions and colloidal gels are illustrated and used to explore the role of microstructure on performance of the algorithm. In practice, the logarithmic part of the predicted scaling is not observed and the algorithm scales linearly for up to 4 ×106 particles, obtaining speed ups of over an order of magnitude over existing iterative methods, and making the cost of computing Brownian displacements comparable to the cost of computing deterministic displacements in BD simulations. A high-performance implementation employing non-uniform fast Fourier transforms implemented on graphics processing units and integrated with the software package HOOMD-blue is used for benchmarking.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals.

PubMed

Pinski, Peter; Riplinger, Christoph; Valeev, Edward F; Neese, Frank

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.

Simulations of nanocrystals under pressure: combining electronic enthalpy and linear-scaling density-functional theory.

PubMed

Corsini, Niccolò R C; Greco, Andrea; Hine, Nicholas D M; Molteni, Carla; Haynes, Peter D

2013-08-28

We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure. Based on a definition of the system volume as that enclosed within an electronic density isosurface [M. Cococcioni, F. Mauri, G. Ceder, and N. Marzari, Phys. Rev. Lett. 94, 145501 (2005)], it supports both geometry optimizations and molecular dynamics simulations. We introduce an approach for calibrating the parameters defining the volume in the context of geometry optimizations and discuss their significance. Results in good agreement with simulations using explicit solvents are obtained, validating our approach. Size-dependent pressure-induced structural transformations and variations in the energy gap of hydrogenated silicon nanocrystals are investigated, including one comparable in size to recent experiments. A detailed analysis of the polyamorphic transformations reveals three types of amorphous structures and their persistence on depressurization is assessed.

Simulations of nanocrystals under pressure: Combining electronic enthalpy and linear-scaling density-functional theory

NASA Astrophysics Data System (ADS)

Corsini, Niccolò R. C.; Greco, Andrea; Hine, Nicholas D. M.; Molteni, Carla; Haynes, Peter D.

2013-08-01

We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure. Based on a definition of the system volume as that enclosed within an electronic density isosurface [M. Cococcioni, F. Mauri, G. Ceder, and N. Marzari, Phys. Rev. Lett. 94, 145501 (2005)], 10.1103/PhysRevLett.94.145501, it supports both geometry optimizations and molecular dynamics simulations. We introduce an approach for calibrating the parameters defining the volume in the context of geometry optimizations and discuss their significance. Results in good agreement with simulations using explicit solvents are obtained, validating our approach. Size-dependent pressure-induced structural transformations and variations in the energy gap of hydrogenated silicon nanocrystals are investigated, including one comparable in size to recent experiments. A detailed analysis of the polyamorphic transformations reveals three types of amorphous structures and their persistence on depressurization is assessed.

Next Generation Extended Lagrangian Quantum-based Molecular Dynamics

NASA Astrophysics Data System (ADS)

Negre, Christian

2017-06-01

A new framework for extended Lagrangian first-principles molecular dynamics simulations is presented, which overcomes shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while maintaining important advantages of the unified extended Lagrangian formulation of density functional theory pioneered by Car and Parrinello three decades ago. The new framework allows, for the first time, energy conserving, linear-scaling Born-Oppenheimer molecular dynamics simulations, which is necessary to study larger and more realistic systems over longer simulation times than previously possible. Expensive, self-consinstent-field optimizations are avoided and normal integration time steps of regular, direct Born-Oppenheimer molecular dynamics can be used. Linear scaling electronic structure theory is presented using a graph-based approach that is ideal for parallel calculations on hybrid computer platforms. For the first time, quantum based Born-Oppenheimer molecular dynamics simulation is becoming a practically feasible approach in simulations of +100,000 atoms-representing a competitive alternative to classical polarizable force field methods. In collaboration with: Anders Niklasson, Los Alamos National Laboratory.

Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.

PubMed

Meair, Jonathan; Jacquod, Philippe

2013-02-27

We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance.

Linear-scaling generation of potential energy surfaces using a double incremental expansion

DOE Office of Scientific and Technical Information (OSTI.GOV)

König, Carolin, E-mail: carolink@kth.se; Christiansen, Ove, E-mail: ove@chem.au.dk

We present a combination of the incremental expansion of potential energy surfaces (PESs), known as n-mode expansion, with the incremental evaluation of the electronic energy in a many-body approach. The application of semi-local coordinates in this context allows the generation of PESs in a very cost-efficient way. For this, we employ the recently introduced flexible adaptation of local coordinates of nuclei (FALCON) coordinates. By introducing an additional transformation step, concerning only a fraction of the vibrational degrees of freedom, we can achieve linear scaling of the accumulated cost of the single point calculations required in the PES generation. Numerical examplesmore » of these double incremental approaches for oligo-phenyl examples show fast convergence with respect to the maximum number of simultaneously treated fragments and only a modest error introduced by the additional transformation step. The approach, presented here, represents a major step towards the applicability of vibrational wave function methods to sizable, covalently bound systems.« less

The Determination of the Large-Scale Circulation of the Pacific Ocean from Satellite Altimetry using Model Green's Functions

NASA Technical Reports Server (NTRS)

Stammer, Detlef; Wunsch, Carl

1996-01-01

A Green's function method for obtaining an estimate of the ocean circulation using both a general circulation model and altimetric data is demonstrated. The fundamental assumption is that the model is so accurate that the differences between the observations and the model-estimated fields obey a linear dynamics. In the present case, the calculations are demonstrated for model/data differences occurring on very a large scale, where the linearization hypothesis appears to be a good one. A semi-automatic linearization of the Bryan/Cox general circulation model is effected by calculating the model response to a series of isolated (in both space and time) geostrophically balanced vortices. These resulting impulse responses or 'Green's functions' then provide the kernels for a linear inverse problem. The method is first demonstrated with a set of 'twin experiments' and then with real data spanning the entire model domain and a year of TOPEX/POSEIDON observations. Our present focus is on the estimate of the time-mean and annual cycle of the model. Residuals of the inversion/assimilation are largest in the western tropical Pacific, and are believed to reflect primarily geoid error. Vertical resolution diminishes with depth with 1 year of data. The model mean is modified such that the subtropical gyre is weakened by about 1 cm/s and the center of the gyre shifted southward by about 10 deg. Corrections to the flow field at the annual cycle suggest that the dynamical response is weak except in the tropics, where the estimated seasonal cycle of the low-latitude current system is of the order of 2 cm/s. The underestimation of observed fluctuations can be related to the inversion on the coarse spatial grid, which does not permit full resolution of the tropical physics. The methodology is easily extended to higher resolution, to use of spatially correlated errors, and to other data types.

TU-EF-304-06: A Comparison of CT Number to Relative Linear Stopping Power Conversion Curves Used by Proton Therapy Centers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Taylor, P; Lowenstein, J; Kry, S

Purpose: To compare the CT Number (CTN) to Relative Linear Stopping Power (RLSP) conversion curves used by 14 proton institutions in their dose calculations. Methods: The proton institution’s CTN to RLSP conversion curves were collected by the Imaging and Radiation Oncology Core (IROC) Houston QA Center during its on-site dosimetry review audits. The CTN values were converted to scaled CT Numbers. The scaling assigns a CTN of 0 to air and 1000 to water to allow intercomparison. The conversion curves were compared and the mean curve was calculated based on institutions’ predicted RLSP values for air (CTN 0), lung (CTNmore » 250), fat (CTN 950), water (1000), liver (CTN 1050), and bone (CTN 2000) points. Results: One institution’s curve was found to have a unique curve shape between the scaled CTN of 1025 to 1225. This institution modified its curve based on the findings. Another institution had higher RLSP values than expected for both low and high CTNs. This institution recalibrated their two CT scanners and the new data placed their curve closer to the mean of all institutions. After corrections were made to several conversion curves, four institutions still fall outside 2 standard deviations at very low CTNs (100–200), and two institutions fall outside between CTN 850–900. The largest percent difference in RLSP values between institutions for the specific tissues reviewed was 22% for the lung point. Conclusion: The review and comparison of CTN to RLSP conversion curves allows IROC Houston to identify any outliers and make recommendations for improvement. Several institutions improved their clinical dose calculation accuracy as a Result of this review. There is still area for improvement, particularly in the lung area of the curve. The IROC Houston QA Center is supported by NCI grant CA180803.« less

Investigation of scale effects in the TRF determined by VLBI

NASA Astrophysics Data System (ADS)

Wahl, Daniel; Heinkelmann, Robert; Schuh, Harald

2017-04-01

The improvement of the International Terrestrial Reference Frame (ITRF) is of great significance for Earth sciences and one of the major tasks in geodesy. The translation, rotation and the scale-factor, as well as their linear rates, are solved in a 14-parameter transformation between individual frames of each space geodetic technique and the combined frame. In ITRF2008, as well as in the current release ITRF2014, the scale-factor is provided by Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging (SLR) in equal shares. Since VLBI measures extremely precise group delays that are transformed to baseline lengths by the velocity of light, a natural constant, VLBI is the most suitable method for providing the scale. The aim of the current work is to identify possible shortcomings in the VLBI scale contribution to ITRF2008. For developing recommendations for an enhanced estimation, scale effects in the Terrestrial Reference Frame (TRF) determined with VLBI are considered in detail and compared to ITRF2008. In contrast to station coordinates, where the scale is defined by a geocentric position vector, pointing from the origin of the reference frame to the station, baselines are not related to the origin. They are describing the absolute scale independently from the datum. The more accurate a baseline length, and consequently the scale, is estimated by VLBI, the better the scale contribution to the ITRF. Considering time series of baseline length between different stations, a non-linear periodic signal can clearly be recognized, caused by seasonal effects at observation sites. Modeling these seasonal effects and subtracting them from the original data enhances the repeatability of single baselines significantly. Other effects influencing the scale strongly, are jumps in the time series of baseline length, mainly evoked by major earthquakes. Co- and post-seismic effects can be identified in the data, having a non-linear character likewise. Modeling the non-linear motion or completely excluding affected stations is another important step for an improved scale determination. In addition to the investigation of single baseline repeatabilities also the spatial transformation, which is performed for determining parameters of the ITRF2008, are considered. Since the reliability of the resulting transformation parameters is higher the more identical points are used in the transformation, an approach where all possible stations are used as control points is comprehensible. Experiments that examine the scale-factor and its spatial behavior between control points in ITRF2008 and coordinates determined by VLBI only showed that the network geometry has a large influence on the outcome as well. Introducing an unequally distributed network for the datum configuration, the correlations between translation parameters and the scale-factor can become remarkably high. Only a homogeneous spatial distribution of participating stations yields a maximally uncorrelated scale-factor that can be interpreted independent from other parameters. In the current release of the ITRF, the ITRF2014, for the first time, non-linear effects in the time series of station coordinates are taken into account. The present work shows the importance and the right direction of the modification of the ITRF calculation. But also further improvements were found which lead to an enhanced scale determination.

Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hardy, David J., E-mail: dhardy@illinois.edu; Schulten, Klaus; Wolff, Matthew A.

2016-03-21

The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation methodmore » (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle–mesh Ewald method falls short.« less

Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations.

PubMed

Hardy, David J; Wolff, Matthew A; Xia, Jianlin; Schulten, Klaus; Skeel, Robert D

2016-03-21

The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle-mesh Ewald method falls short.

Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Hardy, David J.; Wolff, Matthew A.; Xia, Jianlin; Schulten, Klaus; Skeel, Robert D.

2016-03-01

The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle-mesh Ewald method falls short.

Large-Scale Cubic-Scaling Random Phase Approximation Correlation Energy Calculations Using a Gaussian Basis.

PubMed

Wilhelm, Jan; Seewald, Patrick; Del Ben, Mauro; Hutter, Jürg

2016-12-13

We present an algorithm for computing the correlation energy in the random phase approximation (RPA) in a Gaussian basis requiring [Formula: see text] operations and [Formula: see text] memory. The method is based on the resolution of the identity (RI) with the overlap metric, a reformulation of RI-RPA in the Gaussian basis, imaginary time, and imaginary frequency integration techniques, and the use of sparse linear algebra. Additional memory reduction without extra computations can be achieved by an iterative scheme that overcomes the memory bottleneck of canonical RPA implementations. We report a massively parallel implementation that is the key for the application to large systems. Finally, cubic-scaling RPA is applied to a thousand water molecules using a correlation-consistent triple-ζ quality basis.

Synthesis, spectroscopic characterization and quantum chemical computational studies of (S)-N-benzyl-1-phenyl-5-(pyridin-2-yl)-pent-4-yn-2-amine

NASA Astrophysics Data System (ADS)

Kose, Etem; Atac, Ahmet; Karabacak, Mehmet; Karaca, Caglar; Eskici, Mustafa; Karanfil, Abdullah

2012-11-01

The synthesis and characterization of a novel compound (S)-N-benzyl-1-phenyl-5-(pyridin-2-yl)-pent-4-yn-2-amine (abbreviated as BPPPYA) was presented in this study. The spectroscopic properties of the compound were investigated by FT-IR, NMR and UV spectroscopy experimentally and theoretically. The molecular geometry and vibrational frequencies of the BPPPYA in the ground state were calculated by using density functional theory (DFT) B3LYP method invoking 6-311++G(d,p) basis set. The geometry of the BPPPYA was fully optimized, vibrational spectra were calculated and fundamental vibrations were assigned on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method and PQS program. The results of the energy and oscillator strength calculated by time-dependent density functional theory (TD-DFT) and CIS approach complement with the experimental findings. Total and partial density of state (TDOS and PDOS) and also overlap population density of state (COOP or OPDOS) diagrams analysis were presented. The theoretical NMR chemical shifts (1H and 13C) complement with experimentally measured ones. The dipole moment, linear polarizability and first hyperpolarizability values were also computed. The linear polarizabilities and first hyper polarizabilities of the studied molecule indicate that the compound is a good candidate of nonlinear optical materials. The calculated vibrational wavenumbers, absorption wavelengths and chemical shifts showed the best agreement with the experimental results.

First principles electron-correlated calculations of optical absorption in magnesium clusters★

NASA Astrophysics Data System (ADS)

Shinde, Ravindra; Shukla, Alok

2017-11-01

In this paper, we report large-scale configuration interaction (CI) calculations of linear optical absorption spectra of various isomers of magnesium clusters Mgn (n = 2-5), corresponding to valence transitions. Geometry optimization of several low-lying isomers of each cluster was carried out using coupled-cluster singles doubles (CCSD) approach, and these geometries were subsequently employed to perform ground and excited state calculations using either the full-CI (FCI) or the multi-reference singles-doubles configuration interaction (MRSDCI) approach, within the frozen-core approximation. Our calculated photoabsorption spectrum of magnesium dimer (Mg2) is in excellent agreement with the experiments both for peak positions, and intensities. Owing to the sufficiently inclusive electron-correlation effects, these results can serve as benchmarks against which future experiments, as well as calculations performed using other theoretical approaches, can be tested. Supplementary material in the form of one pdf fille available from the Journal web page at http://https://doi.org/10.1140/epjd/e2017-80356-6.

The contour-buildup algorithm to calculate the analytical molecular surface.

PubMed

Totrov, M; Abagyan, R

1996-01-01

A new algorithm is presented to calculate the analytical molecular surface defined as a smooth envelope traced out by the surface of a probe sphere rolled over the molecule. The core of the algorithm is the sequential build up of multi-arc contours on the van der Waals spheres. This algorithm yields substantial reduction in both memory and time requirements of surface calculations. Further, the contour-buildup principle is intrinsically "local", which makes calculations of the partial molecular surfaces even more efficient. Additionally, the algorithm is equally applicable not only to convex patches, but also to concave triangular patches which may have complex multiple intersections. The algorithm permits the rigorous calculation of the full analytical molecular surface for a 100-residue protein in about 2 seconds on an SGI indigo with R4400++ processor at 150 Mhz, with the performance scaling almost linearly with the protein size. The contour-buildup algorithm is faster than the original Connolly algorithm an order of magnitude.

Local elasticity map and plasticity in a model Lennard-Jones glass.

PubMed

Tsamados, Michel; Tanguy, Anne; Goldenberg, Chay; Barrat, Jean-Louis

2009-08-01

In this work we calculate the local elastic moduli in a weakly polydispersed two-dimensional Lennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse-grained microscopic expressions for the strain, displacement, and stress fields. This method allows us to calculate the local elasticity tensor and to quantify the deviation from linear elasticity (local Hooke's law) at different coarse-graining scales. From the results a clear picture emerges of an amorphous material with strongly spatially heterogeneous elastic moduli that simultaneously satisfies Hooke's law at scales larger than a characteristic length scale of the order of five interatomic distances. At this scale, the glass appears as a composite material composed of a rigid scaffolding and of soft zones. Only recently calculated in nonhomogeneous materials, the local elastic structure plays a crucial role in the elastoplastic response of the amorphous material. For a small macroscopic shear strain, the structures associated with the nonaffine displacement field appear directly related to the spatial structure of the elastic moduli. Moreover, for a larger macroscopic shear strain we show that zones of low shear modulus concentrate most of the strain in the form of plastic rearrangements. The spatiotemporal evolution of this local elasticity map and its connection with long term dynamical heterogeneity as well as with the plasticity in the material is quantified. The possibility to use this local parameter as a predictor of subsequent local plastic activity is also discussed.

Rapid solution of large-scale systems of equations

NASA Technical Reports Server (NTRS)

Storaasli, Olaf O.

1994-01-01

The analysis and design of complex aerospace structures requires the rapid solution of large systems of linear and nonlinear equations, eigenvalue extraction for buckling, vibration and flutter modes, structural optimization and design sensitivity calculation. Computers with multiple processors and vector capabilities can offer substantial computational advantages over traditional scalar computer for these analyses. These computers fall into two categories: shared memory computers and distributed memory computers. This presentation covers general-purpose, highly efficient algorithms for generation/assembly or element matrices, solution of systems of linear and nonlinear equations, eigenvalue and design sensitivity analysis and optimization. All algorithms are coded in FORTRAN for shared memory computers and many are adapted to distributed memory computers. The capability and numerical performance of these algorithms will be addressed.

Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals.

PubMed

Zuehlsdorff, T J; Hine, N D M; Payne, M C; Haynes, P D

2015-11-28

We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.

Linear and nonlinear spectroscopy from quantum master equations.

PubMed

Fetherolf, Jonathan H; Berkelbach, Timothy C

2017-12-28

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.

Linear and nonlinear spectroscopy from quantum master equations

NASA Astrophysics Data System (ADS)

Fetherolf, Jonathan H.; Berkelbach, Timothy C.

2017-12-01

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.

Accurate potential energy surface for the 1(2)A' state of NH(2): scaling of external correlation versus extrapolation to the complete basis set limit.

PubMed

Li, Y Q; Varandas, A J C

2010-09-16

An accurate single-sheeted double many-body expansion potential energy surface is reported for the title system which is suitable for dynamics and kinetics studies of the reactions of N(2D) + H2(X1Sigmag+) NH(a1Delta) + H(2S) and their isotopomeric variants. It is obtained by fitting ab initio energies calculated at the multireference configuration interaction level with the aug-cc-pVQZ basis set, after slightly correcting semiempirically the dynamical correlation using the double many-body expansion-scaled external correlation method. The function so obtained is compared in detail with a potential energy surface of the same family obtained by extrapolating the calculated raw energies to the complete basis set limit. The topographical features of the novel global potential energy surface are examined in detail and found to be in general good agreement with those calculated directly from the raw ab initio energies, as well as previous calculations available in the literature. The novel function has been built so as to become degenerate at linear geometries with the ground-state potential energy surface of A'' symmetry reported by our group, where both form a Renner-Teller pair.

Power Laws, Scale Invariance and the Generalized Frobenius Series:

NASA Astrophysics Data System (ADS)

Visser, Matt; Yunes, Nicolas

We present a self-contained formalism for calculating the background solution, the linearized solutions and a class of generalized Frobenius-like solutions to a system of scale-invariant differential equations. We first cast the scale-invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background solutions. After linearizing about these fixed points, we find a second linearized solution, which provides a distinct collection of power laws characterizing the deviations from the fixed point. We prove that generically there will be a region surrounding the fixed point in which the complete general solution can be represented as a generalized Frobenius-like power series with exponents that are integer multiples of the exponents arising in the linearized problem. While discussions of the linearized system are common, and one can often find a discussion of power-series with integer exponents, power series with irrational (indeed complex) exponents are much rarer in the extant literature. The Frobenius-like series we encounter can be viewed as a variant of the rarely-discussed Liapunov expansion theorem (not to be confused with the more commonly encountered Liapunov functions and Liapunov exponents). As specific examples we apply these ideas to Newtonian and relativistic isothermal stars and construct two separate power series with the overlapping radius of convergence. The second of these power series solutions represents an expansion around "spatial infinity," and in realistic models it is this second power series that gives information about the stellar core, and the damped oscillations in core mass and core radius as the central pressure goes to infinity. The power-series solutions we obtain extend classical results; as exemplified for instance by the work of Lane, Emden, and Chandrasekhar in the Newtonian case, and that of Harrison, Thorne, Wakano, and Wheeler in the relativistic case. We also indicate how to extend these ideas to situations where fixed points may not exist — either due to "monotone" flow or due to the presence of limit cycles. Monotone flow generically leads to logarithmic deviations from scaling, while limit cycles generally lead to discrete self-similar solutions.

A model for tides and currents in the English Channel and southern North Sea

NASA Astrophysics Data System (ADS)

Walters, Roy. A.

The amplitude and phase of 11 tidal constituents for the English Channel and southern North Sea are calculated using a frequency domain, finite element model. The governing equations — the shallow water equations — are modifed such that sea level is calculated using an elliptic equation of the Helmholz type followed by a back-calculation of velocity using the primitive momentum equations. Triangular elements with linear basis functions are used. The modified form of the governing equations provides stable solutions with little numerical noise. In this field-scale test problem, the model was able to produce the details of the structure of 11 tidal constituents including O 1, K 1, M 2, S 2, N 2, K 2, M 4, MS 4, MN 4, M 6, and 2MS 6.

Development of social capital scale from a national longitudinal survey and examination of its validity and reliability.

PubMed

Aiba, Miyuki; Tachikawa, Hirokazu; Nakamine, Shin; Takahashi, Sho; Noguchi, Haruko; Takahashi, Hideto; Tamiya, Nanako

2017-01-01

Objectives　Social capital consists of two subordinate concepts; first one is structural formal, structural informal, or cognitive and second one is bonding or bridging. This study was designed to develop a social capital scale using samples from a national longitudinal survey and evaluate the validity and test-retest reliability of the scale.Methods　Data were collected from a nationwide panel survey, the "Longitudinal Survey of Middle-aged and Elderly Persons." Individuals aged 50-59 years living in Japan were selected by stratified random sampling in the first wave conducted in 2005. The first (n=34,240) and second (n=32,285) sets of data were used for Phase 1, and the sixth (n=26,220) and seventh (n=25,321) sets of data were used for Phase 2. In regard to first subordinate concept, the occurrence of six selected social activities with "neighborhood association" and "NPOs, or Public Interest Corporations" were calculated as the structural formal index, and the occurrence of six selected social activities with "families or friends" and "colleagues" were calculated as the structural informal index. Moreover, satisfaction with social activities (community activities, support for the elderly, and others) was used as the cognitive index. In regard to second subordinate concept, the bonding index was calculated using "families or friends," "colleagues," and "neighborhood association;" the bridging index was calculated using "NPOs or Public Interest Corporations." The diagnoses of heart disease, stroke, and cancer (yes=1, no=0) and self-rated health (1 item, 6-point scale) were used as variables for determining validity.Results　We categorized social capital indices into subordinate concepts based on the construct of social capital defined by professional agreement to assess content validity. The results showed that this survey questionnaire was constructed using items that assessed all the subordinate concepts. Hierarchical Linear Modeling examined the relationship between social capital and health as assessed by diagnoses of physical disease and self-rated health to examine convergent validity, which indicated that all social capital indices had significant positive effects on self-rated health at an individual or group level. However, the diagnosis of a stroke was negatively influenced by cognitive and formal social capital indices at a group level, whereas heart disease and cancer were not significantly affected.　Multilevel correlation analyses of Phase 1 (the first and second) and Phase 2 (sixth and seventh) were conducted to assess test-retest reliability, which indicated correlation coefficients of 0.392 to 0.999.Conclusion　The findings of this study indicated the content validity of the scale that was developed from the national longitudinal survey. Moreover, results of Hierarchical Linear Modeling confirmed the partial convergent validity of the scale. Furthermore, multilevel correlation analyses demonstrated the adequate test-retest reliability of the scale at the group level.

Generating log-normal mock catalog of galaxies in redshift space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agrawal, Aniket; Makiya, Ryu; Saito, Shun

We present a public code to generate a mock galaxy catalog in redshift space assuming a log-normal probability density function (PDF) of galaxy and matter density fields. We draw galaxies by Poisson-sampling the log-normal field, and calculate the velocity field from the linearised continuity equation of matter fields, assuming zero vorticity. This procedure yields a PDF of the pairwise velocity fields that is qualitatively similar to that of N-body simulations. We check fidelity of the catalog, showing that the measured two-point correlation function and power spectrum in real space agree with the input precisely. We find that a linear biasmore » relation in the power spectrum does not guarantee a linear bias relation in the density contrasts, leading to a cross-correlation coefficient of matter and galaxies deviating from unity on small scales. We also find that linearising the Jacobian of the real-to-redshift space mapping provides a poor model for the two-point statistics in redshift space. That is, non-linear redshift-space distortion is dominated by non-linearity in the Jacobian. The power spectrum in redshift space shows a damping on small scales that is qualitatively similar to that of the well-known Fingers-of-God (FoG) effect due to random velocities, except that the log-normal mock does not include random velocities. This damping is a consequence of non-linearity in the Jacobian, and thus attributing the damping of the power spectrum solely to FoG, as commonly done in the literature, is misleading.« less

Transport Coefficients in weakly compressible turbulence

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Erlebacher, Gordon

1996-01-01

A theory of transport coefficients in weakly compressible turbulence is derived by applying Yoshizawa's two-scale direct interaction approximation to the compressible equations of motion linearized about a state of incompressible turbulence. The result is a generalization of the eddy viscosity representation of incompressible turbulence. In addition to the usual incompressible eddy viscosity, the calculation generates eddy diffusivities for entropy and pressure, and an effective bulk viscosity acting on the mean flow. The compressible fluctuations also generate an effective turbulent mean pressure and corrections to the speed of sound. Finally, a prediction unique to Yoshizawa's two-scale approximation is that terms containing gradients of incompressible turbulence quantities also appear in the mean flow equations. The form these terms take is described.

Approximating natural connectivity of scale-free networks based on largest eigenvalue

NASA Astrophysics Data System (ADS)

Tan, S.-Y.; Wu, J.; Li, M.-J.; Lu, X.

2016-06-01

It has been recently proposed that natural connectivity can be used to efficiently characterize the robustness of complex networks. The natural connectivity has an intuitive physical meaning and a simple mathematical formulation, which corresponds to an average eigenvalue calculated from the graph spectrum. However, as a network model close to the real-world system that widely exists, the scale-free network is found difficult to obtain its spectrum analytically. In this article, we investigate the approximation of natural connectivity based on the largest eigenvalue in both random and correlated scale-free networks. It is demonstrated that the natural connectivity of scale-free networks can be dominated by the largest eigenvalue, which can be expressed asymptotically and analytically to approximate natural connectivity with small errors. Then we show that the natural connectivity of random scale-free networks increases linearly with the average degree given the scaling exponent and decreases monotonically with the scaling exponent given the average degree. Moreover, it is found that, given the degree distribution, the more assortative a scale-free network is, the more robust it is. Experiments in real networks validate our methods and results.

Reliability measures in item response theory: manifest versus latent correlation functions.

PubMed

Milanzi, Elasma; Molenberghs, Geert; Alonso, Ariel; Verbeke, Geert; De Boeck, Paul

2015-02-01

For item response theory (IRT) models, which belong to the class of generalized linear or non-linear mixed models, reliability at the scale of observed scores (i.e., manifest correlation) is more difficult to calculate than latent correlation based reliability, but usually of greater scientific interest. This is not least because it cannot be calculated explicitly when the logit link is used in conjunction with normal random effects. As such, approximations such as Fisher's information coefficient, Cronbach's α, or the latent correlation are calculated, allegedly because it is easy to do so. Cronbach's α has well-known and serious drawbacks, Fisher's information is not meaningful under certain circumstances, and there is an important but often overlooked difference between latent and manifest correlations. Here, manifest correlation refers to correlation between observed scores, while latent correlation refers to correlation between scores at the latent (e.g., logit or probit) scale. Thus, using one in place of the other can lead to erroneous conclusions. Taylor series based reliability measures, which are based on manifest correlation functions, are derived and a careful comparison of reliability measures based on latent correlations, Fisher's information, and exact reliability is carried out. The latent correlations are virtually always considerably higher than their manifest counterparts, Fisher's information measure shows no coherent behaviour (it is even negative in some cases), while the newly introduced Taylor series based approximations reflect the exact reliability very closely. Comparisons among the various types of correlations, for various IRT models, are made using algebraic expressions, Monte Carlo simulations, and data analysis. Given the light computational burden and the performance of Taylor series based reliability measures, their use is recommended. © 2014 The British Psychological Society.

Effect of ploidy on scale-cover pattern in linear ornamental (koi) common carp Cyprinus carpio.

PubMed

Gomelsky, B; Schneider, K J; Glennon, R P; Plouffe, D A

2012-09-01

The effect of ploidy on scale-cover pattern in linear ornamental (koi) common carp Cyprinus carpio was investigated. To obtain diploid and triploid linear fish, eggs taken from a leather C. carpio female (genotype ssNn) and sperm taken from a scaled C. carpio male (genotype SSnn) were used for the production of control (no shock) and heat-shocked progeny. In heat-shocked progeny, the 2 min heat shock (40° C) was applied 6 min after insemination. Diploid linear fish (genotype SsNn) demonstrated a scale-cover pattern typical for this category with one even row of scales along lateral line and few scales located near operculum and at bases of fins. The majority (97%) of triploid linear fish (genotype SssNnn) exhibited non-typical scale patterns which were characterized by the appearance of additional scales on the body. The extent of additional scales in triploid linear fish was variable; some fish had large scales, which covered almost the entire body. Apparently, the observed difference in scale-cover pattern between triploid and diploid linear fish was caused by different phenotypic expression of gene N/n. Due to incomplete dominance of allele N, triploids Nnn demonstrate less profound reduction of scale cover compared with diploids Nn. © 2012 The Authors. Journal of Fish Biology © 2012 The Fisheries Society of the British Isles.

Fast Combinatorial Algorithm for the Solution of Linearly Constrained Least Squares Problems

DOEpatents

Van Benthem, Mark H.; Keenan, Michael R.

2008-11-11

A fast combinatorial algorithm can significantly reduce the computational burden when solving general equality and inequality constrained least squares problems with large numbers of observation vectors. The combinatorial algorithm provides a mathematically rigorous solution and operates at great speed by reorganizing the calculations to take advantage of the combinatorial nature of the problems to be solved. The combinatorial algorithm exploits the structure that exists in large-scale problems in order to minimize the number of arithmetic operations required to obtain a solution.

A random distribution reacting mixing layer model

NASA Technical Reports Server (NTRS)

Jones, Richard A.; Marek, C. John; Myrabo, Leik N.; Nagamatsu, Henry T.

1994-01-01

A methodology for simulation of molecular mixing, and the resulting velocity and temperature fields has been developed. The ideas are applied to the flow conditions present in the NASA Lewis Research Center Planar Reacting Shear Layer (PRSL) facility, and results compared to experimental data. A gaussian transverse turbulent velocity distribution is used in conjunction with a linearly increasing time scale to describe the mixing of different regions of the flow. Equilibrium reaction calculations are then performed on the mix to arrive at a new species composition and temperature. Velocities are determined through summation of momentum contributions. The analysis indicates a combustion efficiency of the order of 80 percent for the reacting mixing layer, and a turbulent Schmidt number of 2/3. The success of the model is attributed to the simulation of large-scale transport of fluid. The favorable comparison shows that a relatively quick and simple PC calculation is capable of simulating the basic flow structure in the reacting and nonreacting shear layer present in the facility given basic assumptions about turbulence properties.

Structural response calculations for a reverse ballistics test of an earth penetrator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alves, D.F.; Goudreau, G.L.

1976-08-01

A dynamic response calculation has been performed on a half-scale earth penetrator to be tested on a reverse ballistics test in Aug. 1976. In this test a 14 in. dia sandstone target is fired at the EP at 1800 ft/sec at normal impact. Basically two types of calculations were made. The first utilized an axisymmetric, finite element code DTVIS2 in the dynamic mode and with materials having linear elastic properties. CRT's radial and axial force histories were smoothed to eliminate grid encounter frequency and applied to the nodal points along the nose of the penetrator. Given these inputs DTVIS2 thenmore » calculated the internal dynamic response. Secondly, SAP4, a structural analysis code, is utilized to calculate axial frequencies and mode shapes of the structure. A special one dimensional display facilitates interpretation of the mode shape. DTVIS2 and SAP4 use a common mesh description. Special considerations in the calculation are the assessment of the effect of gaps and preload and the internal axial sliding of components.« less

SU-F-T-428: An Optimization-Based Commissioning Tool for Finite Size Pencil Beam Dose Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Y; Tian, Z; Song, T

Purpose: Finite size pencil beam (FSPB) algorithms are commonly used to pre-calculate the beamlet dose distribution for IMRT treatment planning. FSPB commissioning, which usually requires fine tuning of the FSPB kernel parameters, is crucial to the dose calculation accuracy and hence the plan quality. Yet due to the large number of beamlets, FSPB commissioning could be very tedious. This abstract reports an optimization-based FSPB commissioning tool we have developed in MatLab to facilitate the commissioning. Methods: A FSPB dose kernel generally contains two types of parameters: the profile parameters determining the dose kernel shape, and a 2D scaling factors accountingmore » for the longitudinal and off-axis corrections. The former were fitted using the penumbra of a reference broad beam’s dose profile with Levenberg-Marquardt algorithm. Since the dose distribution of a broad beam is simply a linear superposition of the dose kernel of each beamlet calculated with the fitted profile parameters and scaled using the scaling factors, these factors could be determined by solving an optimization problem which minimizes the discrepancies between the calculated dose of broad beams and the reference dose. Results: We have commissioned a FSPB algorithm for three linac photon beams (6MV, 15MV and 6MVFFF). Dose of four field sizes (6*6cm2, 10*10cm2, 15*15cm2 and 20*20cm2) were calculated and compared with the reference dose exported from Eclipse TPS system. For depth dose curves, the differences are less than 1% of maximum dose after maximum dose depth for most cases. For lateral dose profiles, the differences are less than 2% of central dose at inner-beam regions. The differences of the output factors are within 1% for all the three beams. Conclusion: We have developed an optimization-based commissioning tool for FSPB algorithms to facilitate the commissioning, providing sufficient accuracy of beamlet dose calculation for IMRT optimization.« less

A "Stepping Stone" Approach for Obtaining Quantum Free Energies of Hydration.

PubMed

Sampson, Chris; Fox, Thomas; Tautermann, Christofer S; Woods, Christopher; Skylaris, Chris-Kriton

2015-06-11

We present a method which uses DFT (quantum, QM) calculations to improve free energies of binding computed with classical force fields (classical, MM). To overcome the incomplete overlap of configurational spaces between MM and QM, we use a hybrid Monte Carlo approach to generate quickly correct ensembles of structures of intermediate states between a MM and a QM/MM description, hence taking into account a great fraction of the electronic polarization of the quantum system, while being able to use thermodynamic integration to compute the free energy of transition between the MM and QM/MM. Then, we perform a final transition from QM/MM to full QM using a one-step free energy perturbation approach. By using QM/MM as a stepping stone toward the full QM description, we find very small convergence errors (<1 kJ/mol) in the transition to full QM. We apply this method to compute hydration free energies, and we obtain consistent improvements over the MM values for all molecules we used in this study. This approach requires large-scale DFT calculations as the full QM systems involved the ligands and all waters in their simulation cells, so the linear-scaling DFT code ONETEP was used for these calculations.

Local unitary transformation method for large-scale two-component relativistic calculations. II. Extension to two-electron Coulomb interaction.

PubMed

Seino, Junji; Nakai, Hiromi

2012-10-14

The local unitary transformation (LUT) scheme at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level [J. Seino and H. Nakai, J. Chem. Phys. 136, 244102 (2012)], which is based on the locality of relativistic effects, has been extended to a four-component Dirac-Coulomb Hamiltonian. In the previous study, the LUT scheme was applied only to a one-particle IODKH Hamiltonian with non-relativistic two-electron Coulomb interaction, termed IODKH/C. The current study extends the LUT scheme to a two-particle IODKH Hamiltonian as well as one-particle one, termed IODKH/IODKH, which has been a real bottleneck in numerical calculation. The LUT scheme with the IODKH/IODKH Hamiltonian was numerically assessed in the diatomic molecules HX and X(2) and hydrogen halide molecules, (HX)(n) (X = F, Cl, Br, and I). The total Hartree-Fock energies calculated by the LUT method agree well with conventional IODKH/IODKH results. The computational cost of the LUT method is reduced drastically compared with that of the conventional method. In addition, the LUT method achieves linear-scaling with respect to the system size and a small prefactor.

Polarizabilities and van der Waals C{sub 6} coefficients of fullerenes from an atomistic electrodynamics model: Anomalous scaling with number of carbon atoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saidi, Wissam A., E-mail: alsaidi@pitt.edu; Norman, Patrick

2016-07-14

The van der Waals C{sub 6} coefficients of fullerenes are shown to exhibit an anomalous dependence on the number of carbon atoms N such that C{sub 6} ∝ N{sup 2.2} as predicted using state-of-the-art quantum mechanical calculations based on fullerenes with small sizes, and N{sup 2.75} as predicted using a classical-metallic spherical-shell approximation of the fullerenes. We use an atomistic electrodynamics model where each carbon atom is described by a polarizable object to extend the quantum mechanical calculations to larger fullerenes. The parameters of this model are optimized to describe accurately the static and complex polarizabilities of the fullerenes bymore » fitting against accurate ab initio calculations. This model shows that C{sub 6} ∝ N{sup 2.8}, which is supportive of the classical-metallic spherical-shell approximation. Additionally, we show that the anomalous dependence of the polarizability on N is attributed to the electric charge term, while the dipole–dipole term scales almost linearly with the number of carbon atoms.« less

Swimming of a linear chain with a cargo in an incompressible viscous fluid with inertia

NASA Astrophysics Data System (ADS)

Felderhof, B. U.

2017-01-01

An approximation to the added mass matrix of an assembly of spheres is constructed on the basis of potential flow theory for situations where one sphere is much larger than the others. In the approximation, the flow potential near a small sphere is assumed to be dipolar, but near the large sphere it involves all higher order multipoles. The analysis is based on an exact result for the potential of a magnetic dipole in the presence of a superconducting sphere. Subsequently, the approximate added mass hydrodynamic interactions are used in a calculation of the swimming velocity and rate of dissipation of linear chain structures consisting of a number of small spheres and a single large one, with account also of frictional hydrodynamic interactions. The results derived for periodic swimming on the basis of a kinematic approach are compared with the bilinear theory, valid for small amplitude of stroke, and with the numerical solution of the approximate equations of motion. The calculations interpolate over the whole range of scale number between the friction-dominated Stokes limit and the inertia-dominated regime.

Percolation Thresholds in Angular Grain media: Drude Directed Infiltration

NASA Astrophysics Data System (ADS)

Priour, Donald

Pores in many realistic systems are not well delineated channels, but are void spaces among grains impermeable to charge or fluid flow which comprise the medium. Sparse grain concentrations lead to permeable systems, while concentrations in excess of a critical density block bulk fluid flow. We calculate percolation thresholds in porous materials made up of randomly placed (and oriented) disks, tetrahedrons, and cubes. To determine if randomly generated finite system samples are permeable, we deploy virtual tracer particles which are scattered (e.g. specularly) by collisions with impenetrable angular grains. We hasten the rate of exploration (which would otherwise scale as ncoll1 / 2 where ncoll is the number of collisions with grains if the tracers followed linear trajectories) by considering the tracer particles to be charged in conjunction with a randomly directed uniform electric field. As in the Drude treatment, where a succession of many scattering events leads to a constant drift velocity, tracer displacements on average grow linearly in ncoll. By averaging over many disorder realizations for a variety of systems sizes, we calculate the percolation threshold and critical exponent which characterize the phase transition.

Multidecadal Variability in Surface Albedo Feedback Across CMIP5 Models

NASA Astrophysics Data System (ADS)

Schneider, Adam; Flanner, Mark; Perket, Justin

2018-02-01

Previous studies quantify surface albedo feedback (SAF) in climate change, but few assess its variability on decadal time scales. Using the Coupled Model Intercomparison Project Version 5 (CMIP5) multimodel ensemble data set, we calculate time evolving SAF in multiple decades from surface albedo and temperature linear regressions. Results are meaningful when temperature change exceeds 0.5 K. Decadal-scale SAF is strongly correlated with century-scale SAF during the 21st century. Throughout the 21st century, multimodel ensemble mean SAF increases from 0.37 to 0.42 W m-2 K-1. These results suggest that models' mean decadal-scale SAFs are good estimates of their century-scale SAFs if there is at least 0.5 K temperature change. Persistent SAF into the late 21st century indicates ongoing capacity for Arctic albedo decline despite there being less sea ice. If the CMIP5 multimodel ensemble results are representative of the Earth, we cannot expect decreasing Arctic sea ice extent to suppress SAF in the 21st century.

Poster — Thur Eve — 28: Enabling trajectory-based radiotherapy on a TrueBeam accelerator with the Eclipse treatment planning system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mullins, J; Asiev, K; DeBlois, F

2014-08-15

The TrueBeam linear accelerator platform has a developer's mode which permits the user dynamic control over many of the machine's mechanical and radiation systems. Using this research tool, synchronous couch and gantry motion can be programmed to simulate isocentric treatment with a shortened SAD, with benefits such as smaller projected MLC leaf widths and an increased dose rate. In this work, water tank measurements were used to commission a virtual linear accelerator with an 85 cm SAD in Eclipse, from which several arc-based radiotherapy treatments were generated, including an inverse optimized VMAT delivery. For each plan, the pertinent treatment deliverymore » information was extracted from control points specified in the Eclipse-exported DICOM files using the pydicom package in Python, allowing construction of an XML control file. The dimensions of the jaws and MLC positions, defined for an 85 cm SAD in Eclipse, were scaled for delivery on a conventional SAD linear accelerator, and translational couch motion was added as a function of gantry angle to simulate delivery at 85 cm SAD. Ionization chamber and Gafchromic film measurements were used to compare the radiation delivery to dose calculations in Eclipse. With the exception of the VMAT delivery, ionization chamber measurements agreed within 3.3% of the Eclipse calculations. For the VMAT delivery, the ionization chamber was located in an inhomogeneous region, but gamma evaluation of the Gafchromic film plane resulted in a 94.5% passing rate using criteria of 3 mm/3%. The results indicate that Eclipse calculation infrastructure can be used.« less

On the estimation and detection of the Rees-Sciama effect

NASA Astrophysics Data System (ADS)

Fullana, M. J.; Arnau, J. V.; Thacker, R. J.; Couchman, H. M. P.; Sáez, D.

2017-02-01

Maps of the Rees-Sciama (RS) effect are simulated using the parallel N-body code, HYDRA, and a run-time ray-tracing procedure. A method designed for the analysis of small, square cosmic microwave background (CMB) maps is applied to our RS maps. Each of these techniques has been tested and successfully applied in previous papers. Within a range of angular scales, our estimate of the RS angular power spectrum due to variations in the peculiar gravitational potential on scales smaller than 42/h megaparsecs is shown to be robust. An exhaustive study of the redshifts and spatial scales relevant for the production of RS anisotropy is developed for the first time. Results from this study demonstrate that (I) to estimate the full integrated RS effect, the initial redshift for the calculations (integration) must be greater than 25, (II) the effect produced by strongly non-linear structures is very small and peaks at angular scales close to 4.3 arcmin, and (III) the RS anisotropy cannot be detected either directly-in temperature CMB maps-or by looking for cross-correlations between these maps and tracers of the dark matter distribution. To estimate the RS effect produced by scales larger than 42/h megaparsecs, where the density contrast is not strongly non-linear, high accuracy N-body simulations appear unnecessary. Simulations based on approximations such as the Zel'dovich approximation and adhesion prescriptions, for example, may be adequate. These results can be used to guide the design of future RS simulations.

Assessing variance components in multilevel linear models using approximate Bayes factors: A case study of ethnic disparities in birthweight

PubMed Central

Saville, Benjamin R.; Herring, Amy H.; Kaufman, Jay S.

2013-01-01

Racial/ethnic disparities in birthweight are a large source of differential morbidity and mortality worldwide and have remained largely unexplained in epidemiologic models. We assess the impact of maternal ancestry and census tract residence on infant birth weights in New York City and the modifying effects of race and nativity by incorporating random effects in a multilevel linear model. Evaluating the significance of these predictors involves the test of whether the variances of the random effects are equal to zero. This is problematic because the null hypothesis lies on the boundary of the parameter space. We generalize an approach for assessing random effects in the two-level linear model to a broader class of multilevel linear models by scaling the random effects to the residual variance and introducing parameters that control the relative contribution of the random effects. After integrating over the random effects and variance components, the resulting integrals needed to calculate the Bayes factor can be efficiently approximated with Laplace’s method. PMID:24082430

Non-linearities in Holocene floodplain sediment storage

NASA Astrophysics Data System (ADS)

Notebaert, Bastiaan; Nils, Broothaerts; Jean-François, Berger; Gert, Verstraeten

2013-04-01

Floodplain sediment storage is an important part of the sediment cascade model, buffering sediment delivery between hillslopes and oceans, which is hitherto not fully quantified in contrast to other global sediment budget components. Quantification and dating of floodplain sediment storage is data and financially demanding, limiting contemporary estimates for larger spatial units to simple linear extrapolations from a number of smaller catchments. In this paper we will present non-linearities in both space and time for floodplain sediment budgets in three different catchments. Holocene floodplain sediments of the Dijle catchment in the Belgian loess region, show a clear distinction between morphological stages: early Holocene peat accumulation, followed by mineral floodplain aggradation from the start of the agricultural period on. Contrary to previous assumptions, detailed dating of this morphological change at different shows an important non-linearity in geomorphologic changes of the floodplain, both between and within cross sections. A second example comes from the Pre-Alpine French Valdaine region, where non-linearities and complex system behavior exists between (temporal) patterns of soil erosion and floodplain sediment deposition. In this region Holocene floodplain deposition is characterized by different cut-and-fill phases. The quantification of these different phases shows a complicated image of increasing and decreasing floodplain sediment storage, which hampers the image of increasing sediment accumulation over time. Although fill stages may correspond with large quantities of deposited sediment and traditionally calculated sedimentation rates for such stages are high, they do not necessary correspond with a long-term net increase in floodplain deposition. A third example is based on the floodplain sediment storage in the Amblève catchment, located in the Belgian Ardennes uplands. Detailed floodplain sediment quantification for this catchments shows that a strong multifractality is present in the scaling relationship between sediment storage and catchment area, depending on geomorphic landscape properties. Extrapolation of data from one spatial scale to another inevitably leads to large errors: when only the data of the upper floodplains are considered, a regression analysis results in an overestimation of total floodplain deposition for the entire catchment of circa 115%. This example demonstrates multifractality and related non-linearity in scaling relationships, which influences extrapolations beyond the initial range of measurements. These different examples indicate how traditional extrapolation techniques and assumptions in sediment budget studies can be challenged by field data, further complicating our understanding of these systems. Although simplifications are often necessary when working on large spatial scale, such non-linearities may form challenges for a better understanding of system behavior.

Mechanistic insights into heterogeneous methane activation

DOE PAGES

Latimer, Allegra A.; Aljama, Hassan; Kakekhani, Arvin; ...

2017-01-11

While natural gas is an abundant chemical fuel, its low volumetric energy density has prompted a search for catalysts able to transform methane into more useful chemicals. This search has often been aided through the use of transition state (TS) scaling relationships, which estimate methane activation TS energies as a linear function of a more easily calculated descriptor, such as final state energy, thus avoiding tedious TS energy calculations. It has been shown that methane can be activated via a radical or surface-stabilized pathway, both of which possess a unique TS scaling relationship. Herein, we present a simple model tomore » aid in the prediction of methane activation barriers on heterogeneous catalysts. Analogous to the universal radical TS scaling relationship introduced in a previous publication, we show that a universal TS scaling relationship that transcends catalysts classes also seems to exist for surface-stabilized methane activation if the relevant final state energy is used. We demonstrate that this scaling relationship holds for several reducible and irreducible oxides, promoted metals, and sulfides. By combining the universal scaling relationships for both radical and surface-stabilized methane activation pathways, we show that catalyst reactivity must be considered in addition to catalyst geometry to obtain an accurate estimation for the TS energy. Here, this model can yield fast and accurate predictions of methane activation barriers on a wide range of catalysts, thus accelerating the discovery of more active catalysts for methane conversion.« less

Mechanistic insights into heterogeneous methane activation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Latimer, Allegra A.; Aljama, Hassan; Kakekhani, Arvin

While natural gas is an abundant chemical fuel, its low volumetric energy density has prompted a search for catalysts able to transform methane into more useful chemicals. This search has often been aided through the use of transition state (TS) scaling relationships, which estimate methane activation TS energies as a linear function of a more easily calculated descriptor, such as final state energy, thus avoiding tedious TS energy calculations. It has been shown that methane can be activated via a radical or surface-stabilized pathway, both of which possess a unique TS scaling relationship. Herein, we present a simple model tomore » aid in the prediction of methane activation barriers on heterogeneous catalysts. Analogous to the universal radical TS scaling relationship introduced in a previous publication, we show that a universal TS scaling relationship that transcends catalysts classes also seems to exist for surface-stabilized methane activation if the relevant final state energy is used. We demonstrate that this scaling relationship holds for several reducible and irreducible oxides, promoted metals, and sulfides. By combining the universal scaling relationships for both radical and surface-stabilized methane activation pathways, we show that catalyst reactivity must be considered in addition to catalyst geometry to obtain an accurate estimation for the TS energy. Here, this model can yield fast and accurate predictions of methane activation barriers on a wide range of catalysts, thus accelerating the discovery of more active catalysts for methane conversion.« less

Predicting survival time in noncurative patients with advanced cancer: a prospective study in China.

PubMed

Cui, Jing; Zhou, Lingjun; Wee, B; Shen, Fengping; Ma, Xiuqiang; Zhao, Jijun

2014-05-01

Accurate prediction of prognosis for cancer patients is important for good clinical decision making in therapeutic and care strategies. The application of prognostic tools and indicators could improve prediction accuracy. This study aimed to develop a new prognostic scale to predict survival time of advanced cancer patients in China. We prospectively collected items that we anticipated might influence survival time of advanced cancer patients. Participants were recruited from 12 hospitals in Shanghai, China. We collected data including demographic information, clinical symptoms and signs, and biochemical test results. Log-rank tests, Cox regression, and linear regression were performed to develop a prognostic scale. Three hundred twenty patients with advanced cancer were recruited. Fourteen prognostic factors were included in the prognostic scale: Karnofsky Performance Scale (KPS) score, pain, ascites, hydrothorax, edema, delirium, cachexia, white blood cell (WBC) count, hemoglobin, sodium, total bilirubin, direct bilirubin, aspartate aminotransferase (AST), and alkaline phosphatase (ALP) values. The score was calculated by summing the partial scores, ranging from 0 to 30. When using the cutoff points of 7-day, 30-day, 90-day, and 180-day survival time, the scores were calculated as 12, 10, 8, and 6, respectively. We propose a new prognostic scale including KPS, pain, ascites, hydrothorax, edema, delirium, cachexia, WBC count, hemoglobin, sodium, total bilirubin, direct bilirubin, AST, and ALP values, which may help guide physicians in predicting the likely survival time of cancer patients more accurately. More studies are needed to validate this scale in the future.

EvArnoldi: A New Algorithm for Large-Scale Eigenvalue Problems.

PubMed

Tal-Ezer, Hillel

2016-05-19

Eigenvalues and eigenvectors are an essential theme in numerical linear algebra. Their study is mainly motivated by their high importance in a wide range of applications. Knowledge of eigenvalues is essential in quantum molecular science. Solutions of the Schrödinger equation for the electrons composing the molecule are the basis of electronic structure theory. Electronic eigenvalues compose the potential energy surfaces for nuclear motion. The eigenvectors allow calculation of diople transition matrix elements, the core of spectroscopy. The vibrational dynamics molecule also requires knowledge of the eigenvalues of the vibrational Hamiltonian. Typically in these problems, the dimension of Hilbert space is huge. Practically, only a small subset of eigenvalues is required. In this paper, we present a highly efficient algorithm, named EvArnoldi, for solving the large-scale eigenvalues problem. The algorithm, in its basic formulation, is mathematically equivalent to ARPACK ( Sorensen , D. C. Implicitly Restarted Arnoldi/Lanczos Methods for Large Scale Eigenvalue Calculations ; Springer , 1997 ; Lehoucq , R. B. ; Sorensen , D. C. SIAM Journal on Matrix Analysis and Applications 1996 , 17 , 789 ; Calvetti , D. ; Reichel , L. ; Sorensen , D. C. Electronic Transactions on Numerical Analysis 1994 , 2 , 21 ) (or Eigs of Matlab) but significantly simpler.

An area-preserving mapping in natural canonical coordinates for magnetic field line trajectories in the DIII-D tokamak

NASA Astrophysics Data System (ADS)

Punjabi, Alkesh

2009-11-01

The new approach of integrating magnetic field line trajectories in natural canonical coordinates (Punjabi and Ali 2008 Phys. Plasmas 15 122502) in divertor tokamaks is used for the DIII-D tokamak (Luxon and Davis1985 Fusion Technol. 8 441). The equilibrium EFIT data (Evans et al 2004 Phys. Rev. Lett. 92 235003, Lao et al 2005 Fusion Sci. Technol. 48 968) for the DIII-D tokamak shot 115467 at 3000 ms is used to construct the equilibrium generating function (EGF) for the DIII-D in natural canonical coordinates. The EGF gives quite an accurate representation of the closed and open equilibrium magnetic surfaces near the separatrix, the separatrix, the position of the X-point and the poloidal magnetic flux inside the ideal separatrix in the DIII-D. The equilibrium safety factor q from the EGF is somewhat smaller than the DIII-D EFIT q profile. The equilibrium safety factor is calculated from EGF as described in the previous paper (Punjabi and Ali 2008 Phys. Plasmas 15 122502). Here the safety factor for the open surfaces in the DIII-D is calculated. A canonical transformation is used to construct a symplectic mapping for magnetic field line trajectories in the DIII-D in natural canonical coordinates. The map is explored in more detail in this work, and is used to calculate field line trajectories in the DIII-D tokamak. The continuous analogue of the map does not distort the DIII-D magnetic surfaces in different toroidal planes between successive iterations of the map. The map parameter k can represent effects of magnetic asymmetries in the DIII-D. These effects in the DIII-D are illustrated. The DIII-D map is then used to calculate stochastic broadening of the ideal separatrix from the topological noise and field errors, the low mn, the high mn and peeling-ballooning magnetic perturbations in the DIII-D. The width of the stochastic layer scales as 1/2 power of amplitude with a maximum deviation of 6% from the Boozer-Rechester scaling (Boozer and Rechester 1978 Phys. Fluids 21 682). The loss of poloidal flux scales linearly with the amplitude of perturbation with a maximum deviation of 10% from linearity. Perturbations with higher mode numbers result in higher stochasticity. The higher the complexity and coupling in the equilibrium magnetic geometry, the closer is the scaling to the Boozer-Rechester scaling of width. The comparison of the EGF for the simple map (Punjabi et al 1992 Phys. Rev. Lett. 69 3322) with that of the DIII-D shows that the more complex the magnetic geometry and the more coupling of modes in equilibrium, the more robust or resilient is the system against the chaos-inducing, symmetry-breaking perturbations.

SU-F-T-111: Investigation of the Attila Deterministic Solver as a Supplement to Monte Carlo for Calculating Out-Of-Field Radiotherapy Dose

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mille, M; Lee, C; Failla, G

Purpose: To use the Attila deterministic solver as a supplement to Monte Carlo for calculating out-of-field organ dose in support of epidemiological studies looking at the risks of second cancers. Supplemental dosimetry tools are needed to speed up dose calculations for studies involving large-scale patient cohorts. Methods: Attila is a multi-group discrete ordinates code which can solve the 3D photon-electron coupled linear Boltzmann radiation transport equation on a finite-element mesh. Dose is computed by multiplying the calculated particle flux in each mesh element by a medium-specific energy deposition cross-section. The out-of-field dosimetry capability of Attila is investigated by comparing averagemore » organ dose to that which is calculated by Monte Carlo simulation. The test scenario consists of a 6 MV external beam treatment of a female patient with a tumor in the left breast. The patient is simulated by a whole-body adult reference female computational phantom. Monte Carlo simulations were performed using MCNP6 and XVMC. Attila can export a tetrahedral mesh for MCNP6, allowing for a direct comparison between the two codes. The Attila and Monte Carlo methods were also compared in terms of calculation speed and complexity of simulation setup. A key perquisite for this work was the modeling of a Varian Clinac 2100 linear accelerator. Results: The solid mesh of the torso part of the adult female phantom for the Attila calculation was prepared using the CAD software SpaceClaim. Preliminary calculations suggest that Attila is a user-friendly software which shows great promise for our intended application. Computational performance is related to the number of tetrahedral elements included in the Attila calculation. Conclusion: Attila is being explored as a supplement to the conventional Monte Carlo radiation transport approach for performing retrospective patient dosimetry. The goal is for the dosimetry to be sufficiently accurate for use in retrospective epidemiological investigations.« less

Phase transitions in coupled map lattices and in associated probabilistic cellular automata.

PubMed

Just, Wolfram

2006-10-01

Analytical tools are applied to investigate piecewise linear coupled map lattices in terms of probabilistic cellular automata. The so-called disorder condition of probabilistic cellular automata is closely related with attracting sets in coupled map lattices. The importance of this condition for the suppression of phase transitions is illustrated by spatially one-dimensional systems. Invariant densities and temporal correlations are calculated explicitly. Ising type phase transitions are found for one-dimensional coupled map lattices acting on repelling sets and for a spatially two-dimensional Miller-Huse-like system with stable long time dynamics. Critical exponents are calculated within a finite size scaling approach. The relevance of detailed balance of the resulting probabilistic cellular automaton for the critical behavior is pointed out.

Linear Inverse Modeling and Scaling Analysis of Drainage Inventories.

NASA Astrophysics Data System (ADS)

O'Malley, C.; White, N. J.

2016-12-01

It is widely accepted that the stream power law can be used to describe the evolution of longitudinal river profiles. Over the last 5 years, this phenomenological law has been used to develop non-linear and linear inversion algorithms that enable uplift rate histories to be calculated by minimizing the misfit between observed and calculated river profiles. Substantial, continent-wide inventories of river profiles have been successfully inverted to yield uplift as a function of time and space. Erosional parameters can be determined by independent geological calibration. Our results help to illuminate empirical scaling laws that are well known to the geomorphological community. Here we present an analysis of river profiles from Asia. The timing and magnitude of uplift events across Asia, including the Himalayas and Tibet, have long been debated. River profile analyses have played an important role in clarifying the timing of uplift events. However, no attempt has yet been made to invert a comprehensive database of river profiles from the entire region. Asian rivers contain information which allows us to investigate putative uplift events quantitatively and to determine a cumulative uplift history for Asia. Long wavelength shapes of river profiles are governed by regional uplift and moderated by erosional processes. These processes are parameterised using the stream power law in the form of an advective-diffusive equation. Our non-negative, least-squares inversion scheme was applied to an inventory of 3722 Asian river profiles. We calibrate the key erosional parameters by predicting solid sedimentary flux for a set of Asian rivers and by comparing the flux predictions against published depositional histories for major river deltas. The resultant cumulative uplift history is compared with a range of published geological constraints for uplift and palaeoelevation. We have found good agreement for many regions across Asia. Surprisingly, single values of erosional constants can be shown to produce reliable uplift histories. However, these erosional constants appear to vary from continent to continent. Future work will investigate the global relationship between our inversion results, scaling laws, climate models, lithological variation and sedimentary flux.

Scaling up stomatal conductance from leaf to canopy using a dual-leaf model for estimating crop evapotranspiration.

PubMed

Ding, Risheng; Kang, Shaozhong; Du, Taisheng; Hao, Xinmei; Zhang, Yanqun

2014-01-01

The dual-source Shuttleworth-Wallace model has been widely used to estimate and partition crop evapotranspiration (λET). Canopy stomatal conductance (Gsc), an essential parameter of the model, is often calculated by scaling up leaf stomatal conductance, considering the canopy as one single leaf in a so-called "big-leaf" model. However, Gsc can be overestimated or underestimated depending on leaf area index level in the big-leaf model, due to a non-linear stomatal response to light. A dual-leaf model, scaling up Gsc from leaf to canopy, was developed in this study. The non-linear stomata-light relationship was incorporated by dividing the canopy into sunlit and shaded fractions and calculating each fraction separately according to absorbed irradiances. The model includes: (1) the absorbed irradiance, determined by separately integrating the sunlit and shaded leaves with consideration of both beam and diffuse radiation; (2) leaf area for the sunlit and shaded fractions; and (3) a leaf conductance model that accounts for the response of stomata to PAR, vapor pressure deficit and available soil water. In contrast to the significant errors of Gsc in the big-leaf model, the predicted Gsc using the dual-leaf model had a high degree of data-model agreement; the slope of the linear regression between daytime predictions and measurements was 1.01 (R2 = 0.98), with RMSE of 0.6120 mm s-1 for four clear-sky days in different growth stages. The estimates of half-hourly λET using the dual-source dual-leaf model (DSDL) agreed well with measurements and the error was within 5% during two growing seasons of maize with differing hydrometeorological and management strategies. Moreover, the estimates of soil evaporation using the DSDL model closely matched actual measurements. Our results indicate that the DSDL model can produce more accurate estimation of Gsc and λET, compared to the big-leaf model, and thus is an effective alternative approach for estimating and partitioning λET.

Scaling Up Stomatal Conductance from Leaf to Canopy Using a Dual-Leaf Model for Estimating Crop Evapotranspiration

PubMed Central

Ding, Risheng; Kang, Shaozhong; Du, Taisheng; Hao, Xinmei; Zhang, Yanqun

2014-01-01

The dual-source Shuttleworth-Wallace model has been widely used to estimate and partition crop evapotranspiration (λET). Canopy stomatal conductance (Gsc), an essential parameter of the model, is often calculated by scaling up leaf stomatal conductance, considering the canopy as one single leaf in a so-called “big-leaf” model. However, Gsc can be overestimated or underestimated depending on leaf area index level in the big-leaf model, due to a non-linear stomatal response to light. A dual-leaf model, scaling up Gsc from leaf to canopy, was developed in this study. The non-linear stomata-light relationship was incorporated by dividing the canopy into sunlit and shaded fractions and calculating each fraction separately according to absorbed irradiances. The model includes: (1) the absorbed irradiance, determined by separately integrating the sunlit and shaded leaves with consideration of both beam and diffuse radiation; (2) leaf area for the sunlit and shaded fractions; and (3) a leaf conductance model that accounts for the response of stomata to PAR, vapor pressure deficit and available soil water. In contrast to the significant errors of Gsc in the big-leaf model, the predicted Gsc using the dual-leaf model had a high degree of data-model agreement; the slope of the linear regression between daytime predictions and measurements was 1.01 (R2 = 0.98), with RMSE of 0.6120 mm s−1 for four clear-sky days in different growth stages. The estimates of half-hourly λET using the dual-source dual-leaf model (DSDL) agreed well with measurements and the error was within 5% during two growing seasons of maize with differing hydrometeorological and management strategies. Moreover, the estimates of soil evaporation using the DSDL model closely matched actual measurements. Our results indicate that the DSDL model can produce more accurate estimation of Gsc and λET, compared to the big-leaf model, and thus is an effective alternative approach for estimating and partitioning λET. PMID:24752329

Mapping the Dark Matter with 6dFGS

NASA Astrophysics Data System (ADS)

Mould, Jeremy R.; Magoulas, C.; Springob, C.; Colless, M.; Jones, H.; Lucey, J.; Erdogdu, P.; Campbell, L.

2012-05-01

Fundamental plane distances from the 6dF Galaxy Redshift Survey are fitted to a model of the density field within 200/h Mpc. Likelihood is maximized for a single value of the local galaxy density, as expected in linear theory for the relation between overdensity and peculiar velocity. The dipole of the inferred southern hemisphere early type galaxy peculiar velocities is calculated within 150/h Mpc, before and after correction for the individual galaxy velocities predicted by the model. The former agrees with that obtained by other peculiar velocity studies (e.g. SFI++). The latter is only of order 150 km/sec and consistent with the expectations of the standard cosmological model and recent forecasts of the cosmic mach number, which show linearly declining bulk flow with increasing scale.

Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions

NASA Astrophysics Data System (ADS)

Ziegler, Benjamin; Rauhut, Guntram

2016-03-01

The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multimode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory requirements as the potfit approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.

Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions.

PubMed

Ziegler, Benjamin; Rauhut, Guntram

2016-03-21

The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multimode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory requirements as the potfit approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.

Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response

DOE PAGES

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory; ...

2015-02-25

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

Calculating hyperfine couplings in large ionic crystals containing hundreds of QM atoms: subsystem DFT is the key.

PubMed

Kevorkyants, Ruslan; Wang, Xiqiao; Close, David M; Pavanello, Michele

2013-11-14

We present an application of the linear scaling frozen density embedding (FDE) formulation of subsystem DFT to the calculation of isotropic hyperfine coupling constants (hfcc's) of atoms belonging to a guanine radical cation embedded in a guanine hydrochloride monohydrate crystal. The model systems range from an isolated guanine to a 15,000 atom QM/MM cluster where the QM region is comprised of 36 protonated guanine cations, 36 chlorine anions, and 42 water molecules. Our calculations show that the embedding effects of the surrounding crystal cannot be reproduced by small model systems nor by a pure QM/MM procedure. Instead, a large QM region is needed to fully capture the complicated nature of the embedding effects in this system. The unprecedented system size for a relativistic all-electron isotropic hfcc calculation can be approached in this work because the local nature of the electronic structure of the organic crystals considered is fully captured by the FDE approach.

Massively parallel sparse matrix function calculations with NTPoly

NASA Astrophysics Data System (ADS)

Dawson, William; Nakajima, Takahito

2018-04-01

We present NTPoly, a massively parallel library for computing the functions of sparse, symmetric matrices. The theory of matrix functions is a well developed framework with a wide range of applications including differential equations, graph theory, and electronic structure calculations. One particularly important application area is diagonalization free methods in quantum chemistry. When the input and output of the matrix function are sparse, methods based on polynomial expansions can be used to compute matrix functions in linear time. We present a library based on these methods that can compute a variety of matrix functions. Distributed memory parallelization is based on a communication avoiding sparse matrix multiplication algorithm. OpenMP task parallellization is utilized to implement hybrid parallelization. We describe NTPoly's interface and show how it can be integrated with programs written in many different programming languages. We demonstrate the merits of NTPoly by performing large scale calculations on the K computer.

Numerical study on wave-induced beam ion prompt losses in DIII-D tokamak

DOE PAGES

Feng, Zhichen; Zhu, Jia; Fu, Guo -Yong; ...

2017-08-30

A numerical study is performed on the coherent beam ion prompt losses driven by Alfven eigenmodes (AEs) in DIII-D plasmas using realistic parameters and beam ion deposition profiles. The synthetic signal of a fast-ion loss detector (FILD) is calculated for a single AE mode. The first harmonic of the calculated FILD signal is linearly proportional to the AE amplitude with the same AE frequency in agreement with the experimental measurement. The calculated second harmonic is proportional to the square of the first harmonic for typical AE amplitudes. The coefficient of quadratic scaling is found to be sensitive to the AEmore » mode width. The second part of this work considers the AE drive due to coherent prompt loss. As a result, it is shown that the loss-induced mode drive is much smaller than the previous estimate and can be ignored for mode stability.« less

Stability properties and fast ion confinement of hybrid tokamak plasma configurations

NASA Astrophysics Data System (ADS)

Graves, J. P.; Brunetti, D.; Pfefferle, D.; Faustin, J. M. P.; Cooper, W. A.; Kleiner, A.; Lanthaler, S.; Patten, H. W.; Raghunathan, M.

2015-11-01

In hybrid scenarios with flat q just above unity, extremely fast growing tearing modes are born from toroidal sidebands of the near resonant ideal internal kink mode. New scalings of the growth rate with the magnetic Reynolds number arise from two fluid effects and sheared toroidal flow. Non-linear saturated 1/1 dominant modes obtained from initial value stability calculation agree with the amplitude of the 1/1 component of a 3D VMEC equilibrium calculation. Viable and realistic equilibrium representation of such internal kink modes allow fast ion studies to be accurately established. Calculations of MAST neutral beam ion distributions using the VENUS-LEVIS code show very good agreement of observed impaired core fast ion confinement when long lived modes occur. The 3D ICRH code SCENIC also enables the establishment of minority RF distributions in hybrid plasmas susceptible to saturated near resonant internal kink modes.

Is there a stable B2Π state for the CNO molecule?

NASA Astrophysics Data System (ADS)

Marian, Christel; Hess, Bernd A.; Schöttke, Sigrid; Buenker, Robert J.

1987-07-01

We report MRD-CI calculations on the ground state X2Π and the excited states A2Σ + and B2Π of the CNO molecule in linear geometry. The surfaces for oxygen and carbon extraction are calculated using a limited CI expansion of 47 configuration state functions; in the vicinity of the minima obtained with this procedure large-scale CI calculations are carried out including deter-mination of the spin-orbit splitting of the 2Π states of the minima. We find that the B2Π state will be difficult to detect spectroscopically due to an avoided crossing just at the equilibrium geometry of the ground state at RCN = 2.25 a.u., RNO = 2.30 a.u. Accordingly we find two shallow minima for B2Π at RCN = 2.33 a.u., RNO = 2.91 a.u. and RCN = 2.78 a.u., RNO = 2.28 a.u., respectively.

The Zeldovich approximation and wide-angle redshift-space distortions

NASA Astrophysics Data System (ADS)

Castorina, Emanuele; White, Martin

2018-06-01

The contribution of line-of-sight peculiar velocities to the observed redshift of objects breaks the translational symmetry of the underlying theory, modifying the predicted 2-point functions. These `wide angle effects' have mostly been studied using linear perturbation theory in the context of the multipoles of the correlation function and power spectrum . In this work we present the first calculation of wide angle terms in the Zeldovich approximation, which is known to be more accurate than linear theory on scales probed by the next generation of galaxy surveys. We present the exact result for dark matter and perturbatively biased tracers as well as the small angle expansion of the configuration- and Fourier-space two-point functions and the connection to the multi-frequency angular power spectrum. We compare different definitions of the line-of-sight direction and discuss how to translate between them. We show that wide angle terms can reach tens of percent of the total signal in a measurement at low redshift in some approximations, and that a generic feature of wide angle effects is to slightly shift the Baryon Acoustic Oscillation scale.

Computational investigation of large-scale vortex interaction with flexible bodies

NASA Astrophysics Data System (ADS)

Connell, Benjamin; Yue, Dick K. P.

2003-11-01

The interaction of large-scale vortices with flexible bodies is examined with particular interest paid to the energy and momentum budgets of the system. Finite difference direct numerical simulation of the Navier-Stokes equations on a moving curvilinear grid is coupled with a finite difference structural solver of both a linear membrane under tension and linear Euler-Bernoulli beam. The hydrodynamics and structural dynamics are solved simultaneously using an iterative procedure with the external structural forcing calculated from the hydrodynamics at the surface and the flow-field velocity boundary condition given by the structural motion. We focus on an investigation into the canonical problem of a vortex-dipole impinging on a flexible membrane. It is discovered that the structural properties of the membrane direct the interaction in terms of the flow evolution and the energy budget. Pressure gradients associated with resonant membrane response are shown to sustain the oscillatory motion of the vortex pair. Understanding how the key mechanisms in vortex-body interactions are guided by the structural properties of the body is a prerequisite to exploiting these mechanisms.

A linear framework for time-scale separation in nonlinear biochemical systems.

PubMed

Gunawardena, Jeremy

2012-01-01

Cellular physiology is implemented by formidably complex biochemical systems with highly nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale separation has been one of the few theoretical methods for distilling general principles from such complexity. It has provided essential insights in areas such as enzyme kinetics, allosteric enzymes, G-protein coupled receptors, ion channels, gene regulation and post-translational modification. In each case, internal molecular complexity has been eliminated, leading to rational algebraic expressions among the remaining components. This has yielded familiar formulas such as those of Michaelis-Menten in enzyme kinetics, Monod-Wyman-Changeux in allostery and Ackers-Johnson-Shea in gene regulation. Here we show that these calculations are all instances of a single graph-theoretic framework. Despite the biochemical nonlinearity to which it is applied, this framework is entirely linear, yet requires no approximation. We show that elimination of internal complexity is feasible when the relevant graph is strongly connected. The framework provides a new methodology with the potential to subdue combinatorial explosion at the molecular level.

Cost-effectiveness analysis of the diarrhea alleviation through zinc and oral rehydration therapy (DAZT) program in rural Gujarat India: an application of the net-benefit regression framework.

PubMed

Shillcutt, Samuel D; LeFevre, Amnesty E; Fischer-Walker, Christa L; Taneja, Sunita; Black, Robert E; Mazumder, Sarmila

2017-01-01

This study evaluates the cost-effectiveness of the DAZT program for scaling up treatment of acute child diarrhea in Gujarat India using a net-benefit regression framework. Costs were calculated from societal and caregivers' perspectives and effectiveness was assessed in terms of coverage of zinc and both zinc and Oral Rehydration Salt. Regression models were tested in simple linear regression, with a specified set of covariates, and with a specified set of covariates and interaction terms using linear regression with endogenous treatment effects was used as the reference case. The DAZT program was cost-effective with over 95% certainty above $5.50 and $7.50 per appropriately treated child in the unadjusted and adjusted models respectively, with specifications including interaction terms being cost-effective with 85-97% certainty. Findings from this study should be combined with other evidence when considering decisions to scale up programs such as the DAZT program to promote the use of ORS and zinc to treat child diarrhea.

Another look at zonal flows: Resonance, shearing, and frictionless saturation

NASA Astrophysics Data System (ADS)

Li, J. C.; Diamond, P. H.

2018-04-01

We show that shear is not the exclusive parameter that represents all aspects of flow structure effects on turbulence. Rather, wave-flow resonance enters turbulence regulation, both linearly and nonlinearly. Resonance suppresses the linear instability by wave absorption. Flow shear can weaken the resonance, and thus destabilize drift waves, in contrast to the near-universal conventional shear suppression paradigm. Furthermore, consideration of wave-flow resonance resolves the long-standing problem of how zonal flows (ZFs) saturate in the limit of weak or zero frictional drag, and also determines the ZF scale. We show that resonant vorticity mixing, which conserves potential enstrophy, enables ZF saturation in the absence of drag, and so is effective at regulating the Dimits up-shift regime. Vorticity mixing is incorporated as a nonlinear, self-regulation effect in an extended 0D predator-prey model of drift-ZF turbulence. This analysis determines the saturated ZF shear and shows that the mesoscopic ZF width scales as LZ F˜f3 /16(1-f ) 1 /8ρs5/8l03 /8 in the (relevant) adiabatic limit (i.e., τckk‖2D‖≫1 ). f is the fraction of turbulence energy coupled to ZF and l0 is the base state mixing length, absent ZF shears. We calculate and compare the stationary flow and turbulence level in frictionless, weakly frictional, and strongly frictional regimes. In the frictionless limit, the results differ significantly from conventionally quoted scalings derived for frictional regimes. To leading order, the flow is independent of turbulence intensity. The turbulence level scales as E ˜(γL/εc) 2 , which indicates the extent of the "near-marginal" regime to be γL<εc , for the case of avalanche-induced profile variability. Here, εc is the rate of dissipation of potential enstrophy and γL is the characteristic linear growth rate of fluctuations. The implications for dynamics near marginality of the strong scaling of saturated E with γL are discussed.

Dispersion interactions in Density Functional Theory

NASA Astrophysics Data System (ADS)

Andrinopoulos, Lampros; Hine, Nicholas; Mostofi, Arash

2012-02-01

Semilocal functionals in Density Functional Theory (DFT) achieve high accuracy simulating a wide range of systems, but miss the effect of dispersion (vdW) interactions, important in weakly bound systems. We study two different methods to include vdW in DFT: First, we investigate a recent approach [1] to evaluate the vdW contribution to the total energy using maximally-localized Wannier functions. Using a set of simple dimers, we show that it has a number of shortcomings that hamper its predictive power; we then develop and implement a series of improvements [2] and obtain binding energies and equilibrium geometries in closer agreement to quantum-chemical coupled-cluster calculations. Second, we implement the vdW-DF functional [3], using Soler's method [4], within ONETEP [5], a linear-scaling DFT code, and apply it to a range of systems. This method within a linear-scaling DFT code allows the simulation of weakly bound systems of larger scale, such as organic/inorganic interfaces, biological systems and implicit solvation models. [1] P. Silvestrelli, JPC A 113, 5224 (2009). [2] L. Andrinopoulos et al, JCP 135, 154105 (2011). [3] M. Dion et al, PRL 92, 246401 (2004). [4] G. Rom'an-P'erez, J.M. Soler, PRL 103, 096102 (2009). [5] C. Skylaris et al, JCP 122, 084119 (2005).

Long-lived light mediator to dark matter and primordial small scale spectrum

DOE PAGES

Zhang, Yue

2015-05-01

We calculate the early universe evolution of perturbations in the dark matter energy density in the context of simple dark sector models containing a GeV scale light mediator. We consider the case that the mediator is long-lived, with lifetime up to a second, and before decaying it temporarily dominates the energy density of the universe. We show that for primordial perturbations that enter the horizon around this period, the interplay between linear growth during matter domination and collisional damping can generically lead to a sharp peak in the spectrum of dark matter density perturbation. Finally, as a result, the populationmore » of the smallest DM halos gets enhanced. Possible implications of this scenario are discussed.« less

Non-linear non-local molecular electrodynamics with nano-optical fields.

PubMed

Chernyak, Vladimir Y; Saurabh, Prasoon; Mukamel, Shaul

2015-10-28

The interaction of optical fields sculpted on the nano-scale with matter may not be described by the dipole approximation since the fields may vary appreciably across the molecular length scale. Rather than incrementally adding higher multipoles, it is advantageous and more physically transparent to describe the optical process using non-local response functions that intrinsically include all multipoles. We present a semi-classical approach for calculating non-local response functions based on the minimal coupling Hamiltonian. The first, second, and third order response functions are expressed in terms of correlation functions of the charge and the current densities. This approach is based on the gauge invariant current rather than the polarization, and on the vector potential rather than the electric and magnetic fields.

A controls engineering approach for analyzing airplane input-output characteristics

NASA Technical Reports Server (NTRS)

Arbuckle, P. Douglas

1991-01-01

An engineering approach for analyzing airplane control and output characteristics is presented. State-space matrix equations describing the linear perturbation dynamics are transformed from physical coordinates into scaled coordinates. The scaling is accomplished by applying various transformations to the system to employ prior engineering knowledge of the airplane physics. Two different analysis techniques are then explained. Modal analysis techniques calculate the influence of each system input on each fundamental mode of motion and the distribution of each mode among the system outputs. The optimal steady state response technique computes the blending of steady state control inputs that optimize the steady state response of selected system outputs. Analysis of an example airplane model is presented to demonstrate the described engineering approach.

Relating Ab Initio Mechanical Behavior of Intergranular Glassy Films in Γ-Si3N4 to Continuum Scales

NASA Astrophysics Data System (ADS)

Ouyang, L.; Chen, J.; Ching, W.; Misra, A.

2006-05-01

Nanometer thin intergranular glassy films (IGFs) form in polycrystalline ceramics during sintering at high temperatures. The structure and properties of these IGFs are significantly changed by doping with rare earth elements. We have performed highly accurate large-scale ab initio calculations of the mechanical properties of both undoped and Yittria doped (Y-IGF) model by theoretical uniaxial tensile experiments. Uniaxial strain was applied by incrementally stretching the super cell in one direction, while the other two dimensions were kept constant. At each strain, all atoms in the model were fully relaxed using Vienna Ab initio Simulation Package VASP. The relaxed model at a given strain serves as the starting position for the next increment of strain. This process is carried on until the total energy (TE) and stress data show that the "sample" is fully fractured. Interesting differences are seen between the stress-strain response of undoped and Y-doped models. For the undoped model, the stress-strain behavior indicates that the initial atomic structure of the IGF is such that there is negligible coupling between the x- and the y-z directions. However, once the behavior becomes non- linear the lateral stresses increase, indicating that the atomic structure evolves with loading [1]. To relate the ab initio calculations to the continuum scales we analyze the atomic-scale deformation field under this uniaxial loading [1]. The applied strain in the x-direction is mostly accommodated by the IGF part of the model and the crystalline part experiences almost negligible strain. As the overall strain on the sample is incrementally increased, the local strain field evolves such that locations proximal to the softer spots attract higher strains. As the load progresses, the strain concentration spots coalesce and eventually form persistent strain localization zone across the IGF. The deformation pattern obtained through ab initio calculations indicates that it is possible to construct discrete grain-scale models that may be used to bridge these calculations to the continuum scale for finite element analysis. Reference: 1. J. Chen, L. Ouyang, P. Rulis, A. Misra, W. Y. Ching, Phys. Rev. Lett. 95, 256103 (2005)

Implementation and performance of FDPS: a framework for developing parallel particle simulation codes

NASA Astrophysics Data System (ADS)

Iwasawa, Masaki; Tanikawa, Ataru; Hosono, Natsuki; Nitadori, Keigo; Muranushi, Takayuki; Makino, Junichiro

2016-08-01

We present the basic idea, implementation, measured performance, and performance model of FDPS (Framework for Developing Particle Simulators). FDPS is an application-development framework which helps researchers to develop simulation programs using particle methods for large-scale distributed-memory parallel supercomputers. A particle-based simulation program for distributed-memory parallel computers needs to perform domain decomposition, exchange of particles which are not in the domain of each computing node, and gathering of the particle information in other nodes which are necessary for interaction calculation. Also, even if distributed-memory parallel computers are not used, in order to reduce the amount of computation, algorithms such as the Barnes-Hut tree algorithm or the Fast Multipole Method should be used in the case of long-range interactions. For short-range interactions, some methods to limit the calculation to neighbor particles are required. FDPS provides all of these functions which are necessary for efficient parallel execution of particle-based simulations as "templates," which are independent of the actual data structure of particles and the functional form of the particle-particle interaction. By using FDPS, researchers can write their programs with the amount of work necessary to write a simple, sequential and unoptimized program of O(N2) calculation cost, and yet the program, once compiled with FDPS, will run efficiently on large-scale parallel supercomputers. A simple gravitational N-body program can be written in around 120 lines. We report the actual performance of these programs and the performance model. The weak scaling performance is very good, and almost linear speed-up was obtained for up to the full system of the K computer. The minimum calculation time per timestep is in the range of 30 ms (N = 107) to 300 ms (N = 109). These are currently limited by the time for the calculation of the domain decomposition and communication necessary for the interaction calculation. We discuss how we can overcome these bottlenecks.

New Method for Solving Inductive Electric Fields in the Ionosphere

NASA Astrophysics Data System (ADS)

Vanhamäki, H.

2005-12-01

We present a new method for calculating inductive electric fields in the ionosphere. It is well established that on large scales the ionospheric electric field is a potential field. This is understandable, since the temporal variations of large scale current systems are generally quite slow, in the timescales of several minutes, so inductive effects should be small. However, studies of Alfven wave reflection have indicated that in some situations inductive phenomena could well play a significant role in the reflection process, and thus modify the nature of ionosphere-magnetosphere coupling. The input to our calculation method are the time series of the potential part of the ionospheric electric field together with the Hall and Pedersen conductances. The output is the time series of the induced rotational part of the ionospheric electric field. The calculation method works in the time-domain and can be used with non-uniform, time-dependent conductances. In addition no particular symmetry requirements are imposed on the input potential electric field. The presented method makes use of special non-local vector basis functions called Cartesian Elementary Current Systems (CECS). This vector basis offers a convenient way of representing curl-free and divergence-free parts of 2-dimensional vector fields and makes it possible to solve the induction problem using simple linear algebra. The new calculation method is validated by comparing it with previously published results for Alfven wave reflection from uniformly conducting ionosphere.

Spectroscopic (FT-IR, FT-Raman and UV) investigation, NLO, NBO, molecular orbital and MESP analysis of 2-{2-[(2,6-dichlorophenyl)amino]phenyl}acetic acid

NASA Astrophysics Data System (ADS)

Govindasamy, P.; Gunasekaran, S.

2015-02-01

In this work, FT-IR and FT-Raman spectra of 2-{2-[(2,6-dichlorophenyl)amino]phenyl}acetic acid (abbreviated as 2DCPAPAA) have been reported in the regions 4000-450 cm-1 and 4000-50 cm-1, respectively. The molecular structure, geometry optimization, intensities, vibrational frequencies were obtained by the ab initio and DFT levels of theory B3LYP with 6-311++G(d,p) standard basis set and a different scaling of the calculated wave numbers. The complete vibrational assignments were performed on the basis of the potential energy distribution (PED) of the vibrational modes calculated using vibrational energy distribution analysis (VEDA 4) program. The harmonic frequencies were calculated and the scaled values were compared with experimental FT-IR and FT-Raman data. The observed and the calculated frequencies are found to be in good agreement. Stability of the molecule arising from hyper conjugative interactions, charge delocalization has been analyzed using natural bond orbital (NBO) analysis. The thermodynamic properties of the title compound at different temperature reveal the correlations between standard heat capacities (C) standard entropies (S) standard enthalpy changes (ΔH). The important non-linear optical properties such as electric dipole momentum, polarizability and first hyperpolarizability of 2DCPAPAA have been computed using B3LYP/6-311++G(d,p) quantum chemical calculations. The Natural charges, HOMO, LUMO, chemical hardness (η), chemical potential (μ), Electro negativity (χ) and electrophilicity values (ω) are calculated and reported. The oscillator's strength, wave length, and energy calculated by TD-DFT and 2DCPAPAA is approach complement with the experimental findings. The molecular electrostatic potential (MESP) surfaces of the molecule were constructed.

Spectroscopic (FT-IR, FT-Raman and UV) investigation, NLO, NBO, molecular orbital and MESP analysis of 2-{2-[(2,6-dichlorophenyl)amino]phenyl}acetic acid.

PubMed

Govindasamy, P; Gunasekaran, S

2015-02-05

In this work, FT-IR and FT-Raman spectra of 2-{2-[(2,6-dichlorophenyl)amino]phenyl}acetic acid (abbreviated as 2DCPAPAA) have been reported in the regions 4000-450cm(-1) and 4000-50cm(-1), respectively. The molecular structure, geometry optimization, intensities, vibrational frequencies were obtained by the ab initio and DFT levels of theory B3LYP with 6-311++G(d,p) standard basis set and a different scaling of the calculated wave numbers. The complete vibrational assignments were performed on the basis of the potential energy distribution (PED) of the vibrational modes calculated using vibrational energy distribution analysis (VEDA 4) program. The harmonic frequencies were calculated and the scaled values were compared with experimental FT-IR and FT-Raman data. The observed and the calculated frequencies are found to be in good agreement. Stability of the molecule arising from hyper conjugative interactions, charge delocalization has been analyzed using natural bond orbital (NBO) analysis. The thermodynamic properties of the title compound at different temperature reveal the correlations between standard heat capacities (C) standard entropies (S) standard enthalpy changes (ΔH). The important non-linear optical properties such as electric dipole momentum, polarizability and first hyperpolarizability of 2DCPAPAA have been computed using B3LYP/6-311++G(d,p) quantum chemical calculations. The Natural charges, HOMO, LUMO, chemical hardness (η), chemical potential (μ), Electro negativity (χ) and electrophilicity values (ω) are calculated and reported. The oscillator's strength, wave length, and energy calculated by TD-DFT and 2DCPAPAA is approach complement with the experimental findings. The molecular electrostatic potential (MESP) surfaces of the molecule were constructed. Copyright © 2014 Elsevier B.V. All rights reserved.

Cosmic-string-induced hot dark matter perturbations

NASA Technical Reports Server (NTRS)

Van Dalen, Anthony

1990-01-01

This paper investigates the evolution of initially relativistic matter, radiation, and baryons around cosmic string seed perturbations. A detailed analysis of the linear evolution of spherical perturbations in a universe is carried out, and this formalism is used to study the evolution of perturbations around a sphere of uniform density and fixed radius, approximating a loop of cosmic string. It was found that, on scales less than a few megaparsec, the results agree with the nonrelativistic calculation of previous authors. On greater scales, there is a deviation approaching a factor of 2-3 in the perturbation mass. It is shown that a scenario with cosmic strings, hot dark matter, and a Hubble constant greater than 75 km/sec per Mpc can generally produce structure on the observed mass scales and at the appropriate time: 1 + z = about 4 for galaxies and 1 + z = about 1.5 for Abell clusters.

Cosmic background radiation anisotropies in universes dominated by nonbaryonic dark matter

NASA Technical Reports Server (NTRS)

Bond, J. R.; Efstathiou, G.

1984-01-01

Detailed calculations of the temperature fluctuations in the cosmic background radiation for universes dominated by massive collisionless relics of the big bang are presented. An initially adiabatic constant curvature perturbation spectrum is assumed. In models with cold dark matter, the simplest hypothesis - that galaxies follow the mass distribution leads to small-scale anisotropies which exceed current observational limits if omega is less than 0.2 h to the -4/3. Since low values of omega are indicated by dynamical studies of galaxy clustering, cold particle models in which light traces mass are probably incorrect. Reheating of the pregalactic medium is unlikely to modify this conclusion. In cold particle or neutrino-dominated universes with omega = 1, presented predictions for small-scale and quadrupole anisotropies are below current limits. In all cases, the small-scale fluctuations are predicted to be about 10 percent linearly polarized.

Basin-scale estimates of oceanic primary production by remote sensing - The North Atlantic

NASA Technical Reports Server (NTRS)

Platt, Trevor; Caverhill, Carla; Sathyendranath, Shubha

1991-01-01

The monthly averaged CZCS data for 1979 are used to estimate annual primary production at ocean basin scales in the North Atlantic. The principal supplementary data used were 873 vertical profiles of chlorophyll and 248 sets of parameters derived from photosynthesis-light experiments. Four different procedures were tested for calculation of primary production. The spectral model with nonuniform biomass was considered as the benchmark for comparison against the other three models. The less complete models gave results that differed by as much as 50 percent from the benchmark. Vertically uniform models tended to underestimate primary production by about 20 percent compared to the nonuniform models. At horizontal scale, the differences between spectral and nonspectral models were negligible. The linear correlation between biomass and estimated production was poor outside the tropics, suggesting caution against the indiscriminate use of biomass as a proxy variable for primary production.

Simulation of Shock-Shock Interaction in Parsec-Scale Jets

NASA Astrophysics Data System (ADS)

Fromm, Christian M.; Perucho, Manel; Ros, Eduardo; Mimica, Petar; Savolainen, Tuomas; Lobanov, Andrei P.; Zensus, J. Anton

The analysis of the radio light curves of the blazar CTA 102 during its 2006 flare revealed a possible interaction between a standing shock wave and a traveling one. In order to better understand this highly non-linear process, we used a relativistic hydrodynamic code to simulate the high energy interaction and its related emission. The calculated synchrotron emission from these simulations showed an increase in turnover flux density, Sm, and turnover frequency, νm, during the interaction and decrease to its initial values after the passage of the traveling shock wave.

The Finite-Size Scaling Relation for the Order-Parameter Probability Distribution of the Six-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Merdan, Ziya; Karakuş, Özlem

2016-11-01

The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.

Modeling Primary Atomization of Liquid Fuels using a Multiphase DNS/LES Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arienti, Marco; Oefelein, Joe; Doisneau, Francois

2016-08-01

As part of a Laboratory Directed Research and Development project, we are developing a modeling-and-simulation capability to study fuel direct injection in automotive engines. Predicting mixing and combustion at realistic conditions remains a challenging objective of energy science. And it is a research priority in Sandia’s mission-critical area of energy security, being also relevant to many flows in defense and climate. High-performance computing applied to this non-linear multi-scale problem is key to engine calculations with increased scientific reliability.

A 3D Ginibre Point Field

NASA Astrophysics Data System (ADS)

Kargin, Vladislav

2018-06-01

We introduce a family of three-dimensional random point fields using the concept of the quaternion determinant. The kernel of each field is an n-dimensional orthogonal projection on a linear space of quaternionic polynomials. We find explicit formulas for the basis of the orthogonal quaternion polynomials and for the kernel of the projection. For number of particles n → ∞, we calculate the scaling limits of the point field in the bulk and at the center of coordinates. We compare our construction with the previously introduced Fermi-sphere point field process.

Communication: A reduced scaling J-engine based reformulation of SOS-MP2 using graphics processing units.

PubMed

Maurer, S A; Kussmann, J; Ochsenfeld, C

2014-08-07

We present a low-prefactor, cubically scaling scaled-opposite-spin second-order Møller-Plesset perturbation theory (SOS-MP2) method which is highly suitable for massively parallel architectures like graphics processing units (GPU). The scaling is reduced from O(N⁵) to O(N³) by a reformulation of the MP2-expression in the atomic orbital basis via Laplace transformation and the resolution-of-the-identity (RI) approximation of the integrals in combination with efficient sparse algebra for the 3-center integral transformation. In contrast to previous works that employ GPUs for post Hartree-Fock calculations, we do not simply employ GPU-based linear algebra libraries to accelerate the conventional algorithm. Instead, our reformulation allows to replace the rate-determining contraction step with a modified J-engine algorithm, that has been proven to be highly efficient on GPUs. Thus, our SOS-MP2 scheme enables us to treat large molecular systems in an accurate and efficient manner on a single GPU-server.

Who Will Win?: Predicting the Presidential Election Using Linear Regression

ERIC Educational Resources Information Center

Lamb, John H.

2007-01-01

This article outlines a linear regression activity that engages learners, uses technology, and fosters cooperation. Students generated least-squares linear regression equations using TI-83 Plus[TM] graphing calculators, Microsoft[C] Excel, and paper-and-pencil calculations using derived normal equations to predict the 2004 presidential election.…

A Method for Calculating Strain Energy Release Rates in Preliminary Design of Composite Skin/Stringer Debonding Under Multi-Axial Loading

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Minguet, Pierre J.; OBrien, T. Kevin

1999-01-01

Three simple procedures were developed to determine strain energy release rates, G, in composite skin/stringer specimens for various combinations of unaxial and biaxial (in-plane/out-of-plane) loading conditions. These procedures may be used for parametric design studies in such a way that only a few finite element computations will be necessary for a study of many load combinations. The results were compared with mixed mode strain energy release rates calculated directly from nonlinear two-dimensional plane-strain finite element analyses using the virtual crack closure technique. The first procedure involved solving three unknown parameters needed to determine the energy release rates. Good agreement was obtained when the external loads were used in the expression derived. This superposition technique was only applicable if the structure exhibits a linear load/deflection behavior. Consequently, a second technique was derived which was applicable in the case of nonlinear load/deformation behavior. The technique involved calculating six unknown parameters from a set of six simultaneous linear equations with data from six nonlinear analyses to determine the energy release rates. This procedure was not time efficient, and hence, less appealing. A third procedure was developed to calculate mixed mode energy release rates as a function of delamination lengths. This procedure required only one nonlinear finite element analysis of the specimen with a single delamination length to obtain a reference solution for the energy release rates and the scale factors. The delamination was extended in three separate linear models of the local area in the vicinity of the delamination subjected to unit loads to obtain the distribution of G with delamination lengths. This set of sub-problems was Although additional modeling effort is required to create the sub- models, this local technique is efficient for parametric studies.

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

DOE PAGES

Woodward, Carol S.; Gardner, David J.; Evans, Katherine J.

2015-01-01

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but thismore » Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.« less

Perturbation theory for BAO reconstructed fields: One-loop results in the real-space matter density field

NASA Astrophysics Data System (ADS)

Hikage, Chiaki; Koyama, Kazuya; Heavens, Alan

2017-08-01

We compute the power spectrum at one-loop order in standard perturbation theory for the matter density field to which a standard Lagrangian baryonic acoustic oscillation (BAO) reconstruction technique is applied. The BAO reconstruction method corrects the bulk motion associated with the gravitational evolution using the inverse Zel'dovich approximation (ZA) for the smoothed density field. We find that the overall amplitude of one-loop contributions in the matter power spectrum substantially decreases after reconstruction. The reconstructed power spectrum thereby approaches the initial linear spectrum when the smoothed density field is close enough to linear, i.e., the smoothing scale Rs≳10 h-1 Mpc . On smaller Rs, however, the deviation from the linear spectrum becomes significant on large scales (k ≲Rs-1 ) due to the nonlinearity in the smoothed density field, and the reconstruction is inaccurate. Compared with N-body simulations, we show that the reconstructed power spectrum at one-loop order agrees with simulations better than the unreconstructed power spectrum. We also calculate the tree-level bispectrum in standard perturbation theory to investigate non-Gaussianity in the reconstructed matter density field. We show that the amplitude of the bispectrum significantly decreases for small k after reconstruction and that the tree-level bispectrum agrees well with N-body results in the weakly nonlinear regime.

HT-FRTC: a fast radiative transfer code using kernel regression

NASA Astrophysics Data System (ADS)

Thelen, Jean-Claude; Havemann, Stephan; Lewis, Warren

2016-09-01

The HT-FRTC is a principal component based fast radiative transfer code that can be used across the electromagnetic spectrum from the microwave through to the ultraviolet to calculate transmittance, radiance and flux spectra. The principal components cover the spectrum at a very high spectral resolution, which allows very fast line-by-line, hyperspectral and broadband simulations for satellite-based, airborne and ground-based sensors. The principal components are derived during a code training phase from line-by-line simulations for a diverse set of atmosphere and surface conditions. The derived principal components are sensor independent, i.e. no extra training is required to include additional sensors. During the training phase we also derive the predictors which are required by the fast radiative transfer code to determine the principal component scores from the monochromatic radiances (or fluxes, transmittances). These predictors are calculated for each training profile at a small number of frequencies, which are selected by a k-means cluster algorithm during the training phase. Until recently the predictors were calculated using a linear regression. However, during a recent rewrite of the code the linear regression was replaced by a Gaussian Process (GP) regression which resulted in a significant increase in accuracy when compared to the linear regression. The HT-FRTC has been trained with a large variety of gases, surface properties and scatterers. Rayleigh scattering as well as scattering by frozen/liquid clouds, hydrometeors and aerosols have all been included. The scattering phase function can be fully accounted for by an integrated line-by-line version of the Edwards-Slingo spherical harmonics radiation code or approximately by a modification to the extinction (Chou scaling).

Experimental and theoretical study of p-nitroacetanilide

NASA Astrophysics Data System (ADS)

Gnanasambandan, T.; Gunasekaran, S.; Seshadri, S.

2014-01-01

The spectroscopic properties of the p-nitroacetanilide (PNA) were examined by FT-IR, FT-Raman and UV-Vis techniques. FT-IR and FT-Raman spectra in solid state were observed in the region 4000-400 cm-1 and 3500-100 cm-1, respectively. The UV-Vis absorption spectrum of the compound that dissolved in ethanol was recorded in the range of 200-400 nm. The structural and spectroscopic data of the molecule in the ground state were calculated by using density functional theory (DFT) employing B3LYP methods with the 6-31G(d,p) and 6-311+G(d,p) basis sets. The geometry of the molecule was fully optimized, vibrational spectra were calculated and fundamental vibrations were assigned on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. Thermodynamic properties like entropy, heat capacity and enthalpy have been calculated for the molecule. HOMO-LUMO energy gap has been calculated. The intramolecular contacts have been interpreted using natural bond orbital (NBO) and natural localized molecular orbital (NLMO) analysis. Important non-linear optical (NLO) properties such as electric dipole moment and first hyperpolarizability have been computed using B3LYP quantum chemical calculation.

Simulations of neutral wind shear effect on the equatorial ionosphere irregularities

NASA Astrophysics Data System (ADS)

Kim, J.; Chagelishvili, G.; Horton, W.

2005-12-01

We present numerical calculations of the large-scale electron density driven by the gradient drift instability in the daytime equatorial electrojet. Under two-fluid theory the linear analysis for kilometer scale waves lead to the result that all the perturbations are transformed to small scales through linear convection by shear and then damped by diffusion. The inclusion of the nonlinearity enables inverse energy cascade to provide energy to long scale. The feedback between velocity shear and nonlinearity keeps waves growing and leads to the turbulence. In strongly turbulent regime, the nonlinear states are saturated [1]. Since the convective nonlinearities are isotropic while the interactions of velocity shear with waves are anisotropic, the feedback do not necessarily enable waves to grow. The growth of waves are highly variable on k-space configuration [2]. Our simulations show that the directional relationship between vorticity of irregularities and shear are one of key factors. Thus during the transient period, the irregularities show the anisotropy of the vorticity power spectrum. We report the evolution of the power spectrum of the vorticity and density of irregularties and its anistropic nature as observed. The work was supported in part by the Department of NSF Grant ATM-0229863 and ISTC Grant G-553. C. Ronchi, R.N. Sudan, and D.T. Farley. Numerical simulations of large-scale plasma turbulece in teh day time equatorial electrojet. J. Geophys. Res., 96:21263--21279, 1991. G.D. Chagelishvili, R.G. Chanishvili, T.S. Hristov, and J.G. Lominadze. A turbulence model in unbounded smooth shear flows : The weak turbulence approach. JETP, 94(2):434--445, 2002.

Shapes of strong shock fronts in an inhomogeneous solar wind

NASA Technical Reports Server (NTRS)

Heinemann, M. A.; Siscoe, G. L.

1974-01-01

The shapes expected for solar-flare-produced strong shock fronts in the solar wind have been calculated, large-scale variations in the ambient medium being taken into account. It has been shown that for reasonable ambient solar wind conditions the mean and the standard deviation of the east-west shock normal angle are in agreement with experimental observations including shocks of all strengths. The results further suggest that near a high-speed stream it is difficult to distinguish between corotating shocks and flare-associated shocks on the basis of the shock normal alone. Although the calculated shapes are outside the range of validity of the linear approximation, these results indicate that the variations in the ambient solar wind may account for large deviations of shock normals from the radial direction.

Electrostatic attraction between overall neutral surfaces.

PubMed

Adar, Ram M; Andelman, David; Diamant, Haim

2016-08-01

Two overall neutral surfaces with positively and negatively charged domains ("patches") have been shown in recent experiments to exhibit long-range attraction when immersed in an ionic solution. Motivated by the experiments, we calculate analytically the osmotic pressure between such surfaces within the Poisson-Boltzmann framework, using a variational principle for the surface-averaged free energy. The electrostatic potential, calculated beyond the linear Debye-Hückel theory, yields an overall attraction at large intersurface separations, over a wide range of the system's controlled length scales. In particular, the attraction is stronger and occurs at smaller separations for surface patches of larger size and charge density. In this large patch limit, we find that the attraction-repulsion crossover separation is inversely proportional to the square of the patch-charge density and to the Debye screening length.

Verification of GENE and GYRO with L-mode and I-mode plasmas in Alcator C-Mod

DOE PAGES

Mikkelsen, D. R.; Howard, N. T.; White, A. E.; ...

2018-04-25

Here, verification comparisons are carried out for L-mode and I-mode plasma conditions in Alcator C-Mod. We compare linear and nonlinear ion-scale calculations by the gyrokinetic codes GENE and GYRO to each other and to the experimental power balance analysis. The two gyrokinetic codes' linear growth rates and real frequencies are in good agreement throughout all the ion temperature gradient mode branches and most of the trapped electron mode branches of the kyρs spectra at r/a = 0.65, 0.7, and 0.8. The shapes of the toroidal mode spectra of heat fluxes in nonlinear simulations are very similar for k yρ smore » ≤ 0.5, but in most cases GENE has a relatively higher heat flux than GYRO at higher mode numbers.« less

The Power Spectrum of Ionic Nanopore Currents: The Role of Ion Correlations.

PubMed

Zorkot, Mira; Golestanian, Ramin; Bonthuis, Douwe Jan

2016-04-13

We calculate the power spectrum of electric-field-driven ion transport through nanometer-scale membrane pores using both linearized mean-field theory and Langevin dynamics simulations. Remarkably, the linearized mean-field theory predicts a plateau in the power spectral density at low frequency ω, which is confirmed by the simulations at low ion concentration. At high ion concentration, however, the power spectral density follows a power law that is reminiscent of the 1/ω(α) dependence found experimentally at low frequency. On the basis of simulations with and without ion-ion interactions, we attribute the low-frequency power-law dependence to ion-ion correlations. We show that neither a static surface charge density, nor an increased pore length, nor an increased ion valency have a significant effect on the shape of the power spectral density at low frequency.

Verification of GENE and GYRO with L-mode and I-mode plasmas in Alcator C-Mod

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mikkelsen, D. R.; Howard, N. T.; White, A. E.

Here, verification comparisons are carried out for L-mode and I-mode plasma conditions in Alcator C-Mod. We compare linear and nonlinear ion-scale calculations by the gyrokinetic codes GENE and GYRO to each other and to the experimental power balance analysis. The two gyrokinetic codes' linear growth rates and real frequencies are in good agreement throughout all the ion temperature gradient mode branches and most of the trapped electron mode branches of the kyρs spectra at r/a = 0.65, 0.7, and 0.8. The shapes of the toroidal mode spectra of heat fluxes in nonlinear simulations are very similar for k yρ smore » ≤ 0.5, but in most cases GENE has a relatively higher heat flux than GYRO at higher mode numbers.« less

Simple scale interpolator facilitates reading of graphs

NASA Technical Reports Server (NTRS)

Fazio, A.; Henry, B.; Hood, D.

1966-01-01

Set of cards with scale divisions and a scale finder permits accurate reading of the coordinates of points on linear or logarithmic graphs plotted on rectangular grids. The set contains 34 different scales for linear plotting and 28 single cycle scales for log plots.

3D CSEM inversion based on goal-oriented adaptive finite element method

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.

2016-12-01

We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with complex geological scenarios by applying it to the inversion of synthetic marine controlled source EM data generated for a complex 3D offshore model with significant seafloor topography.

Patient and Societal Value Functions for the Testing Morbidities Index

PubMed Central

Swan, John Shannon; Kong, Chung Yin; Lee, Janie M.; Akinyemi, Omosalewa; Halpern, Elkan F.; Lee, Pablo; Vavinskiy, Sergey; Williams, Olubunmi; Zoltick, Emilie S.; Donelan, Karen

2013-01-01

Background We developed preference-based and summated scale scoring for the Testing Morbidities Index (TMI) classification, which addresses short-term effects on quality of life from diagnostic testing before, during and after a testing procedure. Methods The two TMI value functions utilize multiattribute value techniques; one is patient-based and the other has a societal perspective. 206 breast biopsy patients and 466 (societal) subjects informed the models. Due to a lack of standard short-term methods for this application, we utilized the visual analog scale (VAS). Waiting trade-off (WTO) tolls provided an additional option for linear transformation of the TMI. We randomized participants to one of three surveys: the first derived weights for generic testing morbidity attributes and levels of severity with the VAS; a second developed VAS values and WTO tolls for linear transformation of the TMI to a death-healthy scale; the third addressed initial validation in a specific test (breast biopsy). 188 patients and 425 community subjects participated in initial validation, comparing direct VAS and WTO values to the TMI. Alternative TMI scoring as a non-preference summated scale was included, given evidence of construct and content validity. Results The patient model can use an additive function, while the societal model is multiplicative. Direct VAS and the VAS-scaled TMI were correlated across modeling groups (r=0.45 to 0.62) and agreement was comparable to the value function validation of the Health Utilities Index 2. Mean Absolute Difference (MAD) calculations showed a range of 0.07–0.10 in patients and 0.11–0.17 in subjects. MAD for direct WTO tolls compared to the WTO-scaled TMI varied closely around one quality-adjusted life day. Conclusions The TMI shows initial promise in measuring short-term testing-related health states. PMID:23689044

Modeling time-coincident ultrafast electron transfer and solvation processes at molecule-semiconductor interfaces

NASA Astrophysics Data System (ADS)

Li, Lesheng; Giokas, Paul G.; Kanai, Yosuke; Moran, Andrew M.

2014-06-01

Kinetic models based on Fermi's Golden Rule are commonly employed to understand photoinduced electron transfer dynamics at molecule-semiconductor interfaces. Implicit in such second-order perturbative descriptions is the assumption that nuclear relaxation of the photoexcited electron donor is fast compared to electron injection into the semiconductor. This approximation breaks down in systems where electron transfer transitions occur on 100-fs time scale. Here, we present a fourth-order perturbative model that captures the interplay between time-coincident electron transfer and nuclear relaxation processes initiated by light absorption. The model consists of a fairly small number of parameters, which can be derived from standard spectroscopic measurements (e.g., linear absorbance, fluorescence) and/or first-principles electronic structure calculations. Insights provided by the model are illustrated for a two-level donor molecule coupled to both (i) a single acceptor level and (ii) a density of states (DOS) calculated for TiO2 using a first-principles electronic structure theory. These numerical calculations show that second-order kinetic theories fail to capture basic physical effects when the DOS exhibits narrow maxima near the energy of the molecular excited state. Overall, we conclude that the present fourth-order rate formula constitutes a rigorous and intuitive framework for understanding photoinduced electron transfer dynamics that occur on the 100-fs time scale.

Fragment approach to constrained density functional theory calculations using Daubechies wavelets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ratcliff, Laura E.; Genovese, Luigi; Mohr, Stephan

2015-06-21

In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix ofmore » the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.« less

Probabilistic measurement of non-physical constructs during early childhood: Epistemological implications for advancing psychosocial science

NASA Astrophysics Data System (ADS)

Bezruczko, N.; Fatani, S. S.

2010-07-01

Social researchers commonly compute ordinal raw scores and ratings to quantify human aptitudes, attitudes, and abilities but without a clear understanding of their limitations for scientific knowledge. In this research, common ordinal measures were compared to higher order linear (equal interval) scale measures to clarify implications for objectivity, precision, ontological coherence, and meaningfulness. Raw score gains, residualized raw gains, and linear gains calculated with a Rasch model were compared between Time 1 and Time 2 for observations from two early childhood learning assessments. Comparisons show major inconsistencies between ratings and linear gains. When gain distribution was dense, relatively compact, and initial status near item mid-range, linear measures and ratings were indistinguishable. When Time 1 status was distributed more broadly and magnitude of change variable, ratings were unrelated to linear gain, which emphasizes problematic implications of ordinal measures. Surprisingly, residualized gain scores did not significantly improve ordinal measurement of change. In general, raw scores and ratings may be meaningful in specific samples to establish order and high/low rank, but raw score differences suffer from non-uniform units. Even meaningfulness of sample comparisons, as well as derived proportions and percentages, are seriously affected by rank order distortions and should be avoided.

Synchronous fluorescence spectroscopic study of solvatochromic curcumin dye

NASA Astrophysics Data System (ADS)

Patra, Digambara; Barakat, Christelle

2011-09-01

Curcumin, the main yellow bioactive component of turmeric, has recently acquired attention by chemists due its wide range of potential biological applications as an antioxidant, an anti-inflammatory, and an anti-carcinogenic agent. This molecule fluoresces weakly and poorly soluble in water. In this detailed study of curcumin in thirteen different solvents, both the absorption and fluorescence spectra of curcumin was found to be broad, however, a narrower and simple synchronous fluorescence spectrum of curcumin was obtained at Δ λ = 10-20 nm. Lippert-Mataga plot of curcumin in different solvents illustrated two sets of linearity which is consistent with the plot of Stokes' shift vs. the ET30. When Stokes's shift in wavenumber scale was replaced by synchronous fluorescence maximum in nanometer scale, the solvent polarity dependency measured by λSFSmax vs. Lippert-Mataga plot or ET30 values offered similar trends as measured via Stokes' shift for protic and aprotic solvents for curcumin. Better linear correlation of λSFSmax vs. π* scale of solvent polarity was found compared to λabsmax or λemmax or Stokes' shift measurements. In Stokes' shift measurement both absorption/excitation as well as emission (fluorescence) spectra are required to compute the Stokes' shift in wavenumber scale, but measurement could be done in a very fast and simple way by taking a single scan of SFS avoiding calculation and obtain information about polarity of the solvent. Curcumin decay properties in all the solvents could be fitted well to a double-exponential decay function.

The Magnetic Reconnection Code: an AMR-based fully implicit simulation suite

NASA Astrophysics Data System (ADS)

Germaschewski, K.; Bhattacharjee, A.; Ng, C.-S.

2006-12-01

Extended MHD models, which incorporate two-fluid effects, are promising candidates to enhance understanding of collisionless reconnection phenomena in laboratory, space and astrophysical plasma physics. In this paper, we introduce two simulation codes in the Magnetic Reconnection Code suite which integrate reduced and full extended MHD models. Numerical integration of these models comes with two challenges: Small-scale spatial structures, e.g. thin current sheets, develop and must be well resolved by the code. Adaptive mesh refinement (AMR) is employed to provide high resolution where needed while maintaining good performance. Secondly, the two-fluid effects in extended MHD give rise to dispersive waves, which lead to a very stringent CFL condition for explicit codes, while reconnection happens on a much slower time scale. We use a fully implicit Crank--Nicholson time stepping algorithm. Since no efficient preconditioners are available for our system of equations, we instead use a direct solver to handle the inner linear solves. This requires us to actually compute the Jacobian matrix, which is handled by a code generator that calculates the derivative symbolically and then outputs code to calculate it.

MATLAB Stability and Control Toolbox Trim and Static Stability Module

NASA Technical Reports Server (NTRS)

Kenny, Sean P.; Crespo, Luis

2012-01-01

MATLAB Stability and Control Toolbox (MASCOT) utilizes geometric, aerodynamic, and inertial inputs to calculate air vehicle stability in a variety of critical flight conditions. The code is based on fundamental, non-linear equations of motion and is able to translate results into a qualitative, graphical scale useful to the non-expert. MASCOT was created to provide the conceptual aircraft designer accurate predictions of air vehicle stability and control characteristics. The code takes as input mass property data in the form of an inertia tensor, aerodynamic loading data, and propulsion (i.e. thrust) loading data. Using fundamental nonlinear equations of motion, MASCOT then calculates vehicle trim and static stability data for the desired flight condition(s). Available flight conditions include six horizontal and six landing rotation conditions with varying options for engine out, crosswind, and sideslip, plus three take-off rotation conditions. Results are displayed through a unique graphical interface developed to provide the non-stability and control expert conceptual design engineer a qualitative scale indicating whether the vehicle has acceptable, marginal, or unacceptable static stability characteristics. If desired, the user can also examine the detailed, quantitative results.

Synchronicity in predictive modelling: a new view of data assimilation

NASA Astrophysics Data System (ADS)

Duane, G. S.; Tribbia, J. J.; Weiss, J. B.

2006-11-01

The problem of data assimilation can be viewed as one of synchronizing two dynamical systems, one representing "truth" and the other representing "model", with a unidirectional flow of information between the two. Synchronization of truth and model defines a general view of data assimilation, as machine perception, that is reminiscent of the Jung-Pauli notion of synchronicity between matter and mind. The dynamical systems paradigm of the synchronization of a pair of loosely coupled chaotic systems is expected to be useful because quasi-2D geophysical fluid models have been shown to synchronize when only medium-scale modes are coupled. The synchronization approach is equivalent to standard approaches based on least-squares optimization, including Kalman filtering, except in highly non-linear regions of state space where observational noise links regimes with qualitatively different dynamics. The synchronization approach is used to calculate covariance inflation factors from parameters describing the bimodality of a one-dimensional system. The factors agree in overall magnitude with those used in operational practice on an ad hoc basis. The calculation is robust against the introduction of stochastic model error arising from unresolved scales.

A Method of Calculating Motion Error in a Linear Motion Bearing Stage

PubMed Central

Khim, Gyungho; Park, Chun Hong; Oh, Jeong Seok

2015-01-01

We report a method of calculating the motion error of a linear motion bearing stage. The transfer function method, which exploits reaction forces of individual bearings, is effective for estimating motion errors; however, it requires the rail-form errors. This is not suitable for a linear motion bearing stage because obtaining the rail-form errors is not straightforward. In the method described here, we use the straightness errors of a bearing block to calculate the reaction forces on the bearing block. The reaction forces were compared with those of the transfer function method. Parallelism errors between two rails were considered, and the motion errors of the linear motion bearing stage were measured and compared with the results of the calculations, revealing good agreement. PMID:25705715

Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zuehlsdorff, T. J., E-mail: tjz21@cam.ac.uk; Payne, M. C.; Hine, N. D. M.

2015-11-28

We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on amore » small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.« less

Design of an ignition target for the laser megajoule, mitigating parametric instabilities

NASA Astrophysics Data System (ADS)

Laffite, S.; Loiseau, P.

2010-10-01

Laser plasma interaction (LPI) is a critical issue in ignition target design. Based on both scaling laws and two-dimensional calculations, this article describes how we can constrain a laser megajoule (LMJ) [J. Ebrardt and J. M. Chaput, J. Phys.: Conf. Ser. 112, 032005 (2008)] target design by mitigating LPI. An ignition indirect drive target has been designed for the 2/3 LMJ step. It requires 0.9 MJ and 260 TW of laser energy and power, to achieve a temperature of 300 eV in a rugby-shaped Hohlraum and give a yield of about 20 MJ. The study focuses on the analysis of linear gain for stimulated Raman and Brillouin scatterings. Enlarging the focal spot is an obvious way to reduce linear gains. We show that this reduction is nonlinear with the focal spot size. For relatively small focal spot area, linear gains are significantly reduced by enlarging the focal spot. However, there is no benefit in too large focal spots because of necessary larger laser entrance holes, which require more laser energy. Furthermore, this leads to the existence, for a given design, of a minimum value for linear gains for which we cannot go below.

Atomic-scale friction modulated by potential corrugation in multi-layered graphene materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhuang, Chunqiang, E-mail: chunqiang.zhuang@bjut.edu.cn; Liu, Lei

2015-03-21

Friction is an important issue that has to be carefully treated for the fabrication of graphene-based nano-scale devices. So far, the friction mechanism of graphene materials on the atomic scale has not yet been clearly presented. Here, first-principles calculations were employed to unveil the friction behaviors and their atomic-scale mechanism. We found that potential corrugations on sliding surfaces dominate the friction force and the friction anisotropy of graphene materials. Higher friction forces correspond to larger corrugations of potential energy, which are tuned by the number of graphene layers. The friction anisotropy is determined by the regular distributions of potential energy.more » The sliding along a fold-line path (hollow-atop-hollow) has a relatively small potential energy barrier. Thus, the linear sliding observed in macroscopic friction experiments may probably be attributed to the fold-line sliding mode on the atomic scale. These findings can also be extended to other layer-structure materials, such as molybdenum disulfide (MoS{sub 2}) and graphene-like BN sheets.« less

Differential pencil beam dose computation model for photons.

PubMed

Mohan, R; Chui, C; Lidofsky, L

1986-01-01

Differential pencil beam (DPB) is defined as the dose distribution relative to the position of the first collision, per unit collision density, for a monoenergetic pencil beam of photons in an infinite homogeneous medium of unit density. We have generated DPB dose distribution tables for a number of photon energies in water using the Monte Carlo method. The three-dimensional (3D) nature of the transport of photons and electrons is automatically incorporated in DPB dose distributions. Dose is computed by evaluating 3D integrals of DPB dose. The DPB dose computation model has been applied to calculate dose distributions for 60Co and accelerator beams. Calculations for the latter are performed using energy spectra generated with the Monte Carlo program. To predict dose distributions near the beam boundaries defined by the collimation system as well as blocks, we utilize the angular distribution of incident photons. Inhomogeneities are taken into account by attenuating the primary photon fluence exponentially utilizing the average total linear attenuation coefficient of intervening tissue, by multiplying photon fluence by the linear attenuation coefficient to yield the number of collisions in the scattering volume, and by scaling the path between the scattering volume element and the computation point by an effective density.

New algorithms for field-theoretic block copolymer simulations: Progress on using adaptive-mesh refinement and sparse matrix solvers in SCFT calculations

NASA Astrophysics Data System (ADS)

Sides, Scott; Jamroz, Ben; Crockett, Robert; Pletzer, Alexander

2012-02-01

Self-consistent field theory (SCFT) for dense polymer melts has been highly successful in describing complex morphologies in block copolymers. Field-theoretic simulations such as these are able to access large length and time scales that are difficult or impossible for particle-based simulations such as molecular dynamics. The modified diffusion equations that arise as a consequence of the coarse-graining procedure in the SCF theory can be efficiently solved with a pseudo-spectral (PS) method that uses fast-Fourier transforms on uniform Cartesian grids. However, PS methods can be difficult to apply in many block copolymer SCFT simulations (eg. confinement, interface adsorption) in which small spatial regions might require finer resolution than most of the simulation grid. Progress on using new solver algorithms to address these problems will be presented. The Tech-X Chompst project aims at marrying the best of adaptive mesh refinement with linear matrix solver algorithms. The Tech-X code PolySwift++ is an SCFT simulation platform that leverages ongoing development in coupling Chombo, a package for solving PDEs via block-structured AMR calculations and embedded boundaries, with PETSc, a toolkit that includes a large assortment of sparse linear solvers.

Energy conserving, linear scaling Born-Oppenheimer molecular dynamics.

PubMed

Cawkwell, M J; Niklasson, Anders M N

2012-10-07

Born-Oppenheimer molecular dynamics simulations with long-term conservation of the total energy and a computational cost that scales linearly with system size have been obtained simultaneously. Linear scaling with a low pre-factor is achieved using density matrix purification with sparse matrix algebra and a numerical threshold on matrix elements. The extended Lagrangian Born-Oppenheimer molecular dynamics formalism [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] yields microcanonical trajectories with the approximate forces obtained from the linear scaling method that exhibit no systematic drift over hundreds of picoseconds and which are indistinguishable from trajectories computed using exact forces.

Determining polarizable force fields with electrostatic potentials from quantum mechanical linear response theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Hao; Yang, Weitao, E-mail: weitao.yang@duke.edu; Department of Physics, Duke University, Durham, North Carolina 27708

We developed a new method to calculate the atomic polarizabilities by fitting to the electrostatic potentials (ESPs) obtained from quantum mechanical (QM) calculations within the linear response theory. This parallels the conventional approach of fitting atomic charges based on electrostatic potentials from the electron density. Our ESP fitting is combined with the induced dipole model under the perturbation of uniform external electric fields of all orientations. QM calculations for the linear response to the external electric fields are used as input, fully consistent with the induced dipole model, which itself is a linear response model. The orientation of the uniformmore » external electric fields is integrated in all directions. The integration of orientation and QM linear response calculations together makes the fitting results independent of the orientations and magnitudes of the uniform external electric fields applied. Another advantage of our method is that QM calculation is only needed once, in contrast to the conventional approach, where many QM calculations are needed for many different applied electric fields. The molecular polarizabilities obtained from our method show comparable accuracy with those from fitting directly to the experimental or theoretical molecular polarizabilities. Since ESP is directly fitted, atomic polarizabilities obtained from our method are expected to reproduce the electrostatic interactions better. Our method was used to calculate both transferable atomic polarizabilities for polarizable molecular mechanics’ force fields and nontransferable molecule-specific atomic polarizabilities.« less

Theoretical and spectroscopic studies of a tricyclic antidepressant, imipramine hydrochloride

NASA Astrophysics Data System (ADS)

Sagdinc, S. G.; Azkeskin, Caner; Eşme, A.

2018-06-01

Imipramine hydrochloride ([H-IMI]Cl), C19H24N2.HCl, is the prototypic tricyclic antidepressant (TCA) inhibitor of norepinephrine and serotonin neuronal reuptake. The molecular structure, molecular electrostatic potential (MEP), natural bond orbital (NBO) analysis, linear and non-linear optical (NLO) properties of [H-IMI]Cl have been investigated using the density functional theory (DFT) calculations with the B3LYP level at the 6‒311++G(d,p) basis set. The UV-Vis spectra for [H-IMI]Cl were experimentally studied in water and methanol. TD‒DFT calculations in water and methanol were employed to investigate the absorption wavelengths (λ), excitation energies (E), and oscillator strengths (f) for the UV-Vis analysis and the major contributions to the electronic transitions. From NBO analysis, the orbitals with the stabilization energy E(2) of 192.15 kcal/mol are π*(C5sbnd C18) as donor NBO and π*(C19sbnd C20) as acceptor NBO. The FT‒IR (4000‒400 cm-1) and FT‒Raman (3500-50 cm-1) spectra have been measured and analyzed. The assignment of bands observed vibrational spectra have been made by comparison of its calculated theoretical vibrational frequencies obtained using the DFT/B3LYP/6‒311++G(d,p) method. The detailed vibrational assignments were performed with the DFT calculation, and the potential energy distribution (PED) of [H-IMI]Cl was obtained by the Vibrational Energy Distribution Analysis 4 (VEDA4) program. The scaled frequencies resulted in good agreement with the observed spectral patterns.

Calculations of absorbed fractions in small water spheres for low-energy monoenergetic electrons and the Auger-emitting radionuclides (123)Ι and (125)Ι.

PubMed

Bousis, Christos; Emfietzoglou, Dimitris; Nikjoo, Hooshang

2012-12-01

To calculate the absorbed fraction (AF) of low energy electrons in small tissue-equivalent spherical volumes by Monte Carlo (MC) track structure simulation and assess the influence of phase (liquid water versus density-scaled water vapor) and of the continuous-slowing-down approximation (CSDA) used in semi-analytic calculations. An event-by-event MC code simulating the transport of electrons in both the vapor and liquid phase of water using appropriate electron-water interaction cross sections was used to quantify the energy deposition of low-energy electrons in spherical volumes. Semi-analytic calculations within the CSDA using a convolution integral of the Howell range-energy expressions are also presented for comparison. The AF for spherical volumes of radii from 10-1000 nm are presented for monoenergetic electrons over the energy range 100-10,000 eV and the two Auger-emitting radionuclides (125)I and (123)I. The MC calculated AF for the liquid phase are found to be smaller than those of the (density scaled) gas phase by up to 10-20% for the monoenergetic electrons and 10% for the two Auger-emitters. Differences between the liquid-phase MC results and the semi-analytic CSDA calculations are up to ∼ 55% for the monoenergetic electrons and up to ∼ 35% for the two Auger-emitters. Condensed-phase effects in the inelastic interaction of low-energy electrons with water have a noticeable but relatively small impact on the AF for the energy range and target sizes examined. Depending on the electron energies, the semi-analytic approach may lead to sizeable errors for target sizes with linear dimensions below 1 micron.

The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Staebler, G. M.; Candy, J.; Howard, N. T.

2016-06-15

The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the thresholdmore » for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. The zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ion-scale gyrokinetic simulations.« less

A Simple and Convenient Method of Multiple Linear Regression to Calculate Iodine Molecular Constants

ERIC Educational Resources Information Center

Cooper, Paul D.

2010-01-01

A new procedure using a student-friendly least-squares multiple linear-regression technique utilizing a function within Microsoft Excel is described that enables students to calculate molecular constants from the vibronic spectrum of iodine. This method is advantageous pedagogically as it calculates molecular constants for ground and excited…

Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)].

PubMed

Guo, Yang; Riplinger, Christoph; Becker, Ute; Liakos, Dimitrios G; Minenkov, Yury; Cavallo, Luigi; Neese, Frank

2018-01-07

In this communication, an improved perturbative triples correction (T) algorithm for domain based local pair-natural orbital singles and doubles coupled cluster (DLPNO-CCSD) theory is reported. In our previous implementation, the semi-canonical approximation was used and linear scaling was achieved for both the DLPNO-CCSD and (T) parts of the calculation. In this work, we refer to this previous method as DLPNO-CCSD(T 0 ) to emphasize the semi-canonical approximation. It is well-established that the DLPNO-CCSD method can predict very accurate absolute and relative energies with respect to the parent canonical CCSD method. However, the (T 0 ) approximation may introduce significant errors in absolute energies as the triples correction grows up in magnitude. In the majority of cases, the relative energies from (T 0 ) are as accurate as the canonical (T) results of themselves. Unfortunately, in rare cases and in particular for small gap systems, the (T 0 ) approximation breaks down and relative energies show large deviations from the parent canonical CCSD(T) results. To address this problem, an iterative (T) algorithm based on the previous DLPNO-CCSD(T 0 ) algorithm has been implemented [abbreviated here as DLPNO-CCSD(T)]. Using triples natural orbitals to represent the virtual spaces for triples amplitudes, storage bottlenecks are avoided. Various carefully designed approximations ease the computational burden such that overall, the increase in the DLPNO-(T) calculation time over DLPNO-(T 0 ) only amounts to a factor of about two (depending on the basis set). Benchmark calculations for the GMTKN30 database show that compared to DLPNO-CCSD(T 0 ), the errors in absolute energies are greatly reduced and relative energies are moderately improved. The particularly problematic case of cumulene chains of increasing lengths is also successfully addressed by DLPNO-CCSD(T).

Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)

NASA Astrophysics Data System (ADS)

Guo, Yang; Riplinger, Christoph; Becker, Ute; Liakos, Dimitrios G.; Minenkov, Yury; Cavallo, Luigi; Neese, Frank

2018-01-01

In this communication, an improved perturbative triples correction (T) algorithm for domain based local pair-natural orbital singles and doubles coupled cluster (DLPNO-CCSD) theory is reported. In our previous implementation, the semi-canonical approximation was used and linear scaling was achieved for both the DLPNO-CCSD and (T) parts of the calculation. In this work, we refer to this previous method as DLPNO-CCSD(T0) to emphasize the semi-canonical approximation. It is well-established that the DLPNO-CCSD method can predict very accurate absolute and relative energies with respect to the parent canonical CCSD method. However, the (T0) approximation may introduce significant errors in absolute energies as the triples correction grows up in magnitude. In the majority of cases, the relative energies from (T0) are as accurate as the canonical (T) results of themselves. Unfortunately, in rare cases and in particular for small gap systems, the (T0) approximation breaks down and relative energies show large deviations from the parent canonical CCSD(T) results. To address this problem, an iterative (T) algorithm based on the previous DLPNO-CCSD(T0) algorithm has been implemented [abbreviated here as DLPNO-CCSD(T)]. Using triples natural orbitals to represent the virtual spaces for triples amplitudes, storage bottlenecks are avoided. Various carefully designed approximations ease the computational burden such that overall, the increase in the DLPNO-(T) calculation time over DLPNO-(T0) only amounts to a factor of about two (depending on the basis set). Benchmark calculations for the GMTKN30 database show that compared to DLPNO-CCSD(T0), the errors in absolute energies are greatly reduced and relative energies are moderately improved. The particularly problematic case of cumulene chains of increasing lengths is also successfully addressed by DLPNO-CCSD(T).

Quantifying Environmental Effects on the Decay of Hole Transfer Couplings in Biosystems.

PubMed

Ramos, Pablo; Pavanello, Michele

2014-06-10

In the past two decades, many research groups worldwide have tried to understand and categorize simple regimes in the charge transfer of such biological systems as DNA. Theoretically speaking, the lack of exact theories for electron-nuclear dynamics on one side and poor quality of the parameters needed by model Hamiltonians and nonadiabatic dynamics alike (such as couplings and site energies) on the other are the two main difficulties for an appropriate description of the charge transfer phenomena. In this work, we present an application of a previously benchmarked and linear-scaling subsystem density functional theory (DFT) method for the calculation of couplings, site energies, and superexchange decay factors (β) of several biological donor-acceptor dyads, as well as double stranded DNA oligomers composed of up to five base pairs. The calculations are all-electron and provide a clear view of the role of the environment on superexchange couplings in DNA-they follow experimental trends and confirm previous semiempirical calculations. The subsystem DFT method is proven to be an excellent tool for long-range, bridge-mediated coupling and site energy calculations of embedded molecular systems.

Full-wave and ray-based modeling of cross-beam energy transfer between laser beams with distributed phase plates and polarization smoothing

DOE PAGES

Follett, R. K.; Edgell, D. H.; Froula, D. H.; ...

2017-10-20

Radiation-hydrodynamic simulations of inertial confinement fusion (ICF) experiments rely on ray-based cross-beam energy transfer (CBET) models to calculate laser energy deposition. The ray-based models assume locally plane-wave laser beams and polarization averaged incoherence between laser speckles for beams with polarization smoothing. The impact of beam speckle and polarization smoothing on crossbeam energy transfer (CBET) are studied using the 3-D wave-based laser-plasma-interaction code LPSE. The results indicate that ray-based models under predict CBET when the assumption of spatially averaged longitudinal incoherence across the CBET interaction region is violated. A model for CBET between linearly-polarized speckled beams is presented that uses raymore » tracing to solve for the real speckle pattern of the unperturbed laser beams within the eikonal approximation and gives excellent agreement with the wavebased calculations. Lastly, OMEGA-scale 2-D LPSE calculations using ICF relevant plasma conditions suggest that the impact of beam speckle on laser absorption calculations in ICF implosions is small (< 1%).« less

Full-wave and ray-based modeling of cross-beam energy transfer between laser beams with distributed phase plates and polarization smoothing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Follett, R. K.; Edgell, D. H.; Froula, D. H.

Radiation-hydrodynamic simulations of inertial confinement fusion (ICF) experiments rely on ray-based cross-beam energy transfer (CBET) models to calculate laser energy deposition. The ray-based models assume locally plane-wave laser beams and polarization averaged incoherence between laser speckles for beams with polarization smoothing. The impact of beam speckle and polarization smoothing on crossbeam energy transfer (CBET) are studied using the 3-D wave-based laser-plasma-interaction code LPSE. The results indicate that ray-based models under predict CBET when the assumption of spatially averaged longitudinal incoherence across the CBET interaction region is violated. A model for CBET between linearly-polarized speckled beams is presented that uses raymore » tracing to solve for the real speckle pattern of the unperturbed laser beams within the eikonal approximation and gives excellent agreement with the wavebased calculations. Lastly, OMEGA-scale 2-D LPSE calculations using ICF relevant plasma conditions suggest that the impact of beam speckle on laser absorption calculations in ICF implosions is small (< 1%).« less

Towards a Comprehensive Model of Jet Noise Using an Acoustic Analogy and Steady RANS Solutions

NASA Technical Reports Server (NTRS)

Miller, Steven A. E.

2013-01-01

An acoustic analogy is developed to predict the noise from jet flows. It contains two source models that independently predict the noise from turbulence and shock wave shear layer interactions. The acoustic analogy is based on the Euler equations and separates the sources from propagation. Propagation effects are taken into account by calculating the vector Green's function of the linearized Euler equations. The sources are modeled following the work of Tam and Auriault, Morris and Boluriaan, and Morris and Miller. A statistical model of the two-point cross-correlation of the velocity fluctuations is used to describe the turbulence. The acoustic analogy attempts to take into account the correct scaling of the sources for a wide range of nozzle pressure and temperature ratios. It does not make assumptions regarding fine- or large-scale turbulent noise sources, self- or shear-noise, or convective amplification. The acoustic analogy is partially informed by three-dimensional steady Reynolds-Averaged Navier-Stokes solutions that include the nozzle geometry. The predictions are compared with experiments of jets operating subsonically through supersonically and at unheated and heated temperatures. Predictions generally capture the scaling of both mixing noise and BBSAN for the conditions examined, but some discrepancies remain that are due to the accuracy of the steady RANS turbulence model closure, the equivalent sources, and the use of a simplified vector Green's function solver of the linearized Euler equations.

Two-dimensional energy spectra in a high Reynolds number turbulent boundary layer

NASA Astrophysics Data System (ADS)

Chandran, Dileep; Baidya, Rio; Monty, Jason; Marusic, Ivan

2016-11-01

The current study measures the two-dimensional (2D) spectra of streamwise velocity component (u) in a high Reynolds number turbulent boundary layer for the first time. A 2D spectra shows the contribution of streamwise (λx) and spanwise (λy) length scales to the streamwise variance at a given wall height (z). 2D spectra could be a better tool to analyse spectral scaling laws as it is devoid of energy aliasing errors that could be present in one-dimensional spectra. A novel method is used to calculate the 2D spectra from the 2D correlation of u which is obtained by measuring velocity time series at various spanwise locations using hot-wire anemometry. At low Reynolds number, the shape of the 2D spectra at a constant energy level shows λy √{ zλx } behaviour at larger scales which is in agreement with the literature. However, at high Reynolds number, it is observed that the square-root relationship gradually transforms into a linear relationship (λy λx) which could be caused by the large packets of eddies whose length grows proportionately to the growth of its width. Additionally, we will show that this linear relationship observed at high Reynolds number is consistent with attached eddy predictions. The authors gratefully acknowledge the support from the Australian Research Council.

The allometry of coarse root biomass: log-transformed linear regression or nonlinear regression?

PubMed

Lai, Jiangshan; Yang, Bo; Lin, Dunmei; Kerkhoff, Andrew J; Ma, Keping

2013-01-01

Precise estimation of root biomass is important for understanding carbon stocks and dynamics in forests. Traditionally, biomass estimates are based on allometric scaling relationships between stem diameter and coarse root biomass calculated using linear regression (LR) on log-transformed data. Recently, it has been suggested that nonlinear regression (NLR) is a preferable fitting method for scaling relationships. But while this claim has been contested on both theoretical and empirical grounds, and statistical methods have been developed to aid in choosing between the two methods in particular cases, few studies have examined the ramifications of erroneously applying NLR. Here, we use direct measurements of 159 trees belonging to three locally dominant species in east China to compare the LR and NLR models of diameter-root biomass allometry. We then contrast model predictions by estimating stand coarse root biomass based on census data from the nearby 24-ha Gutianshan forest plot and by testing the ability of the models to predict known root biomass values measured on multiple tropical species at the Pasoh Forest Reserve in Malaysia. Based on likelihood estimates for model error distributions, as well as the accuracy of extrapolative predictions, we find that LR on log-transformed data is superior to NLR for fitting diameter-root biomass scaling models. More importantly, inappropriately using NLR leads to grossly inaccurate stand biomass estimates, especially for stands dominated by smaller trees.

Modelling climate change responses in tropical forests: similar productivity estimates across five models, but different mechanisms and responses

NASA Astrophysics Data System (ADS)

Rowland, L.; Harper, A.; Christoffersen, B. O.; Galbraith, D. R.; Imbuzeiro, H. M. A.; Powell, T. L.; Doughty, C.; Levine, N. M.; Malhi, Y.; Saleska, S. R.; Moorcroft, P. R.; Meir, P.; Williams, M.

2014-11-01

Accurately predicting the response of Amazonia to climate change is important for predicting changes across the globe. However, changes in multiple climatic factors simultaneously may result in complex non-linear responses, which are difficult to predict using vegetation models. Using leaf and canopy scale observations, this study evaluated the capability of five vegetation models (CLM3.5, ED2, JULES, SiB3, and SPA) to simulate the responses of canopy and leaf scale productivity to changes in temperature and drought in an Amazonian forest. The models did not agree as to whether gross primary productivity (GPP) was more sensitive to changes in temperature or precipitation. There was greater model-data consistency in the response of net ecosystem exchange to changes in temperature, than in the response to temperature of leaf area index (LAI), net photosynthesis (An) and stomatal conductance (gs). Modelled canopy scale fluxes are calculated by scaling leaf scale fluxes to LAI, and therefore in this study similarities in modelled ecosystem scale responses to drought and temperature were the result of inconsistent leaf scale and LAI responses among models. Across the models, the response of An to temperature was more closely linked to stomatal behaviour than biochemical processes. Consequently all the models predicted that GPP would be higher if tropical forests were 5 °C colder, closer to the model optima for gs. There was however no model consistency in the response of the An-gs relationship when temperature changes and drought were introduced simultaneously. The inconsistencies in the An-gs relationships amongst models were caused by to non-linear model responses induced by simultaneous drought and temperature change. To improve the reliability of simulations of the response of Amazonian rainforest to climate change the mechanistic underpinnings of vegetation models need more complete validation to improve accuracy and consistency in the scaling of processes from leaf to canopy.

Linear and nonlinear response in sheared soft spheres

NASA Astrophysics Data System (ADS)

Tighe, Brian

2013-11-01

Packings of soft spheres provide an idealized model of foams, emulsions, and grains, while also serving as the canonical example of a system undergoing a jamming transition. Packings' mechanical response has now been studied exhaustively in the context of ``strict linear response,'' i.e. by linearizing about a stable static packing and solving the resulting equations of motion. Both because the system is close to a critical point and because the soft sphere pair potential is non-analytic at the point of contact, it is reasonable to ask under what circumstances strict linear response provides a good approximation to the actual response. We simulate sheared soft sphere packings close to jamming and identify two distinct strain scales: (i) the scale on which strict linear response fails, coinciding with a topological change in the packing's contact network; and (ii) the scale on which linear superposition of the averaged stress-strain curve breaks down. This latter scale provides a ``weak linear response'' criterion and is likely to be more experimentally relevant.

Langmuir wave damping decreases slowly

NASA Astrophysics Data System (ADS)

Rose, Harvey

2006-10-01

The onset of stimulated Raman scatter in a single laser speckle occurs (D. S. Montgomery et al., Phys. Plasmas, 9, 2311 (2002)) at lower laser intensity, I, than predicted by linear theory based on classical Landau damping, νL, of the SRS daughter Langmuir wave. Does this imply that SRS onset in a speckled laser beam, propagating through long scale length plasma, is also at odds with linear theory? It has been shown (Harvey A. Rose and D. F. DuBois, Phys. Rev. Lett. 72, 2883 (1994)) that linear convective gain in speckles with large fluctuations of I about the average, , leads to onset at a value of , Ic, small compared to that for onset in a uniform beam. While nonlinear electron trapping effects may occur in very intense speckles, whether or not these effects are sufficient to lower the onset value of below Ic depends on how strongly electrons must be trapped before there is significant reduction in νL. As the amplitude of an SRS daughter Langmuir wave increases, its νL decreases by the factor ν/φb, due to the competition between electron trapping, with electron bounce frequency, φb, and escape of these trapped electrons by advection out of a speckle's side, at rate ν. This result (Harvey A. Rose and David A. Russell, Phys. Plasmas, 8, 4784 (2001)) is valid for ν/φb 1. In this talk I present a nonlinear, transit time damping, calculation of νL and find that reduction by a factor of two does not occur until φb/ν 5. This slow turn on of trapping effects suggests that the linear calculation of Ic is NIF relevant.