Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Teglas, Russell

1987-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Parenting, attention and externalizing problems: testing mediation longitudinally, repeatedly and reciprocally.

PubMed

Belsky, Jay; Pasco Fearon, R M; Bell, Brian

2007-12-01

Building on prior work, this paper tests, longitudinally and repeatedly, the proposition that attentional control processes mediate the effect of earlier parenting on later externalizing problems. Repeated independent measurements of all three constructs--observed parenting, computer-tested attentional control and adult-reported externalizing problems--were subjected to structural equation modeling using data from the large-scale American study of child care and youth development. Structural equation modeling indicated (a) that greater maternal sensitivity at two different ages (54 months, approximately 6 years) predicted better attentional control on the Continuous Performance Test (CPT) of attention regulation two later ages ( approximately 6/9 years); (2) that better attentional control at three different ages (54 months, approximately 6/9 years) predicted less teacher-reported externalizing problems at three later ages ( approximately 6/8/10 years); and (3) that attentional control partially mediated the effect of parenting on externalizing problems at two different lags (i.e., 54 months--> approximately 6 years--> approximately 8 years; approximately 6 years--> approximately 9 years--> approximately 10 years), though somewhat more strongly for the first. Additionally, (4) some evidence of reciprocal effects of attentional processes on parenting emerged (54 months--> approximately 6 years; approximately 6 years--> approximately 8 years), but not of problem behavior on attention. Because attention control partially mediates the effects of parenting on externalizing problems, intervention efforts could target both parenting and attentional processes.

75 FR 61371 - Proposed Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2010-10-05

... Black Creek Approximately 1.9 mile None +581 City of Trussville, downstream of Whites Town of Argo, Town.... Approximately 0.3 mile None +695 upstream of Kelly Creek Road. Little Black Creek Approximately 110 feet None... County. Approximately 2.5 miles None +860 upstream of the railroad. Middle Black Creek Approximately 1.0...

77 FR 26733 - Uinta-Wasatch-Cache National Forest; Evanston-Mountain View Ranger District; Utah; Smiths Fork...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-05-07

... mapped, is anticipated to involve approximately 3.1 miles of new specified road construction, approximately 10.7 miles of temporary road construction, approximately 6.7 miles of additional temporary road use on the existing road prism, and approximately 2.6 miles of road reconstruction. Approximately 3.8...

More on approximations of Poisson probabilities

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

Kao, C

1980-05-01

Calculation of Poisson probabilities frequently involves calculating high factorials, which becomes tedious and time-consuming with regular calculators. The usual way to overcome this difficulty has been to find approximations by making use of the table of the standard normal distribution. A new transformation proposed by Kao in 1978 appears to perform better for this purpose than traditional transformations. In the present paper several approximation methods are stated and compared numerically, including an approximation method that utilizes a modified version of Kao's transformation. An approximation based on a power transformation was found to outperform those based on the square-root type transformationsmore » as proposed in literature. The traditional Wilson-Hilferty approximation and Makabe-Morimura approximation are extremely poor compared with this approximation. 4 tables. (RWR)« less

An Approximate Approach to Automatic Kernel Selection.

PubMed

Ding, Lizhong; Liao, Shizhong

2016-02-02

Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.

Extractant composition including crown ether and calixarene extractants

DOEpatents

Meikrantz, David H.; Todd, Terry A.; Riddle, Catherine L.; Law, Jack D.; Peterman, Dean R.; Mincher, Bruce J.; McGrath, Christopher A.; Baker, John D.

2009-04-28

An extractant composition comprising a mixed extractant solvent consisting of calix[4] arene-bis-(tert-octylbenzo)-crown-6 ("BOBCalixC6"), 4',4',(5')-di-(t-butyldicyclo-hexano)-18-crown-6 ("DtBu18C6"), and at least one modifier dissolved in a diluent. The DtBu18C6 may be present at from approximately 0.01M to approximately 0.4M, such as at from approximately 0.086 M to approximately 0.108 M. The modifier may be 1-(2,2,3,3-tetrafluoropropoxy)-3-(4-sec-butylphenoxy)-2-propanol ("Cs-7SB") and may be present at from approximately 0.01M to approximately 0.8M. In one embodiment, the mixed extractant solvent includes approximately 0.15M DtBu18C6, approximately 0.007M BOBCalixC6, and approximately 0.75M Cs-7SB modifier dissolved in an isoparaffinic hydrocarbon diluent. The extractant composition further comprises an aqueous phase. The mixed extractant solvent may be used to remove cesium and strontium from the aqueous phase.

Minimal-Approximation-Based Distributed Consensus Tracking of a Class of Uncertain Nonlinear Multiagent Systems With Unknown Control Directions.

PubMed

Choi, Yun Ho; Yoo, Sung Jin

2017-03-28

A minimal-approximation-based distributed adaptive consensus tracking approach is presented for strict-feedback multiagent systems with unknown heterogeneous nonlinearities and control directions under a directed network. Existing approximation-based consensus results for uncertain nonlinear multiagent systems in lower-triangular form have used multiple function approximators in each local controller to approximate unmatched nonlinearities of each follower. Thus, as the follower's order increases, the number of the approximators used in its local controller increases. However, the proposed approach employs only one function approximator to construct the local controller of each follower regardless of the order of the follower. The recursive design methodology using a new error transformation is derived for the proposed minimal-approximation-based design. Furthermore, a bounding lemma on parameters of Nussbaum functions is presented to handle the unknown control direction problem in the minimal-approximation-based distributed consensus tracking framework and the stability of the overall closed-loop system is rigorously analyzed in the Lyapunov sense.

Characterization and depositional and evolutionary history of the Apollo 17 deep drill core

NASA Technical Reports Server (NTRS)

Morris, R. V.; Lauer, H. V., Jr.; Gose, W. A.

1979-01-01

With a depth resolution of about 0.5 cm, the stratigraphy of the approximately 3 m Apollo 17 deep drill core by measurement of the total FeO concentration is characterized along with the FMR surface exposure (maturity) index Is/FeO, the metallic iron concentration Fe-vsm, and the FMR linewidth delta-H. For stratigraphic characterization, the first two parameters are the most important. Most of the core is characterized by a FeO concentration of approximately 15.5 wt. %; there is a more mafic zone in the upper approximately 75 cm where the maximum FeO concentration is approximately 18.5 wt. %, and a more felsic zone between approximately 225 and 260 cm where the minimum FeO concentration is approximately 14.0%. As indicated by Is/FeO, most of the soil in the core is submature to mature; the only immature zone is located between approximately 20 and 60 cm and is one of the most distinctive features in the core. A two stage model for the depositional and evolutionary history of the Apollo 17 deep drill core is proposed: (1) deposition by one event approximately 110 m.y. ago or deposition by a sequence of closely spaced events initating a maximum of approximately 200 m.y. ago and terminating approximately 110 m.y. ago, (2) in situ reworking (gardening) to a depth of approximately 26 cm in the period between approximately 110 m.y. ago and the present day.

An accurate method for evaluating the kernel of the integral equation relating lift to downwash in unsteady potential flow

NASA Technical Reports Server (NTRS)

Desmarais, R. N.

1982-01-01

The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. The method can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

A rat osteogenic cell line (UMR 106-01) synthesizes a highly sulfated form of bone sialoprotein.

PubMed

Midura, R J; McQuillan, D J; Benham, K J; Fisher, L W; Hascall, V C

1990-03-25

The rat osteosarcoma cell line (UMR 106-01) synthesizes and secretes relatively large amounts of a sulfated glycoprotein into its culture medium (approximately 240 ng/10(6) cells/day). This glycoprotein was purified, and amino-terminal sequence analysis identified it as bone sialoprotein (BSP). [35S]Sulfate, [3H]glucosamine, and [3H]tyrosine were used as metabolic precursors to label the BSP. Sulfate esters were found on N- and O-linked oligosaccharides and on tyrosine residues, with about half of the total tyrosines in the BSP being sulfated. The proportion of 35S activity in tyrosine-O-sulfate (approximately 70%) was greater than that in N-linked (approximately 20%) and O-linked (approximately 10%) oligosaccharides. From the deduced amino acid sequence for rat BSP (Oldberg, A., Franzén, A., and Heinegård, D. (1988) J. Biol. Chem. 263, 19430-19432), the results indicate that on average approximately 12 tyrosine residues, approximately 3 N-linked, and approximately 2 O-linked oligosaccharides are sulfated/molecule. The carboxyl-terminal quarter of the BSP probably contains most, if not all, of the sulfated tyrosine residues because this region of the polypeptide contains the necessary requirements for tyrosine sulfation. Oligosaccharide analyses indicated that for every N-linked oligosaccharide on the BSP, there are also approximately 2 hexa-, approximately 5 tetra-, and approximately 2 trisaccharides O-linked to serine and threonine residues. On average, the BSP synthesized by UMR 106-01 cells would contain a total of approximately 3 N-linked and approximately 25 of the above O-linked oligosaccharides. This large number of oligosaccharides is in agreement with the known carbohydrate content (approximately 50%) of the BSP.

On a Solar Origin for the Cosmogenic Nuclide Event of 775 A.D.

NASA Technical Reports Server (NTRS)

Cliver, E. W.; Tylka, A. J.; Dietrich, W. F.; Ling, A. G.

2014-01-01

We explore requirements for a solar particle event (SPE) and flare capable of producing the cosmogenic nuclide event of 775 A.D., and review solar circumstances at that time. A solar source for 775 would require a greater than 1 GV spectrum approximately 45 times stronger than that of the intense high-energy SPE of 1956 February 23. This implies a greater than 30 MeV proton fluence (F(sub 30)) of approximately 8 × 10(exp 10) proton cm(exp -2), approximately 10 times larger than that of the strongest 3 month interval of SPE activity in the modern era. This inferred F(sub 30) value for the 775 SPE is inconsistent with the occurrence probability distribution for greater than 30 MeV solar proton events. The best guess value for the soft X-ray classification (total energy) of an associated flare is approximately X230 (approximately 9 × 10(exp 33) erg). For comparison, the flares on 2003 November 4 and 1859 September 1 had observed/inferred values of approximately X35 (approximately 10(exp 33) erg) and approximately X45 (approximately 2 × 10(exp 33) erg), respectively. The estimated size of the source active region for a approximately 10(exp 34) erg flare is approximately 2.5 times that of the largest region yet recorded. The 775 event occurred during a period of relatively low solar activity, with a peak smoothed amplitude about half that of the second half of the 20th century. The approximately 1945-1995 interval, the most active of the last approximately 2000 yr, failed to witness a SPE comparable to that required for the proposed solar event in 775. These considerations challenge a recent suggestion that the 775 event is likely of solar origin.

The complex variable boundary element method: Applications in determining approximative boundaries

USGS Publications Warehouse

Hromadka, T.V.

1984-01-01

The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary. ?? 1984.

A comparison of polynomial approximations and artificial neural nets as response surfaces

NASA Technical Reports Server (NTRS)

Carpenter, William C.; Barthelemy, Jean-Francois M.

1992-01-01

Artificial neural nets and polynomial approximations were used to develop response surfaces for several test problems. Based on the number of functional evaluations required to build the approximations and the number of undetermined parameters associated with the approximations, the performance of the two types of approximations was found to be comparable. A rule of thumb is developed for determining the number of nodes to be used on a hidden layer of an artificial neural net, and the number of designs needed to train an approximation is discussed.

High-Dimensional Function Approximation With Neural Networks for Large Volumes of Data.

PubMed

Andras, Peter

2018-02-01

Approximation of high-dimensional functions is a challenge for neural networks due to the curse of dimensionality. Often the data for which the approximated function is defined resides on a low-dimensional manifold and in principle the approximation of the function over this manifold should improve the approximation performance. It has been show that projecting the data manifold into a lower dimensional space, followed by the neural network approximation of the function over this space, provides a more precise approximation of the function than the approximation of the function with neural networks in the original data space. However, if the data volume is very large, the projection into the low-dimensional space has to be based on a limited sample of the data. Here, we investigate the nature of the approximation error of neural networks trained over the projection space. We show that such neural networks should have better approximation performance than neural networks trained on high-dimensional data even if the projection is based on a relatively sparse sample of the data manifold. We also find that it is preferable to use a uniformly distributed sparse sample of the data for the purpose of the generation of the low-dimensional projection. We illustrate these results considering the practical neural network approximation of a set of functions defined on high-dimensional data including real world data as well.

``Glue" approximation for the pairing interaction in the Hubbard model with next nearest neighbor hopping

NASA Astrophysics Data System (ADS)

Khatami, Ehsan; Macridin, Alexandru; Jarrell, Mark

2008-03-01

Recently, several authors have employed the ``glue" approximation for the Cuprates in which the full pairing vertex is approximated by the spin susceptibility. We study this approximation using Quantum Monte Carlo Dynamical Cluster Approximation methods on a 2D Hubbard model. By considering a reasonable finite value for the next nearest neighbor hopping, we find that this ``glue" approximation, in the current form, does not capture the correct pairing symmetry. Here, d-wave is not the leading pairing symmetry while it is the dominant symmetry using the ``exact" QMC results. We argue that the sensitivity of this approximation to the band structure changes leads to this inconsistency and that this form of interaction may not be the appropriate description of the pairing mechanism in Cuprates. We suggest improvements to this approximation which help to capture the the essential features of the QMC data.

A result about scale transformation families in approximation

NASA Astrophysics Data System (ADS)

Apprato, Dominique; Gout, Christian

2000-06-01

Scale transformations are common in approximation. In surface approximation from rapidly varying data, one wants to suppress, or at least dampen the oscillations of the approximation near steep gradients implied by the data. In that case, scale transformations can be used to give some control over overshoot when the surface has large variations of its gradient. Conversely, in image analysis, scale transformations are used in preprocessing to enhance some features present on the image or to increase jumps of grey levels before segmentation of the image. In this paper, we establish the convergence of an approximation method which allows some control over the behavior of the approximation. More precisely, we study the convergence of an approximation from a data set of , while using scale transformations on the values before and after classical approximation. In addition, the construction of scale transformations is also given. The algorithm is presented with some numerical examples.

Direct application of Padé approximant for solving nonlinear differential equations.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

2014-01-01

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

Born approximation in linear-time invariant system

NASA Astrophysics Data System (ADS)

Gumjudpai, Burin

2017-09-01

An alternative way of finding the LTI’s solution with the Born approximation, is investigated. We use Born approximation in the LTI and in the transformed LTI in form of Helmholtz equation. General solution are considered as infinite series or Feynman graph. Slow-roll approximation are explored. Transforming the LTI system into Helmholtz equation, approximated general solution can be found for any given forms of force with its initial value.

Analysis of corrections to the eikonal approximation

NASA Astrophysics Data System (ADS)

Hebborn, C.; Capel, P.

2017-11-01

Various corrections to the eikonal approximations are studied for two- and three-body nuclear collisions with the goal to extend the range of validity of this approximation to beam energies of 10 MeV/nucleon. Wallace's correction does not improve much the elastic-scattering cross sections obtained at the usual eikonal approximation. On the contrary, a semiclassical approximation that substitutes the impact parameter by a complex distance of closest approach computed with the projectile-target optical potential efficiently corrects the eikonal approximation. This opens the possibility to analyze data measured down to 10 MeV/nucleon within eikonal-like reaction models.

Sensitivity analysis and approximation methods for general eigenvalue problems

NASA Technical Reports Server (NTRS)

Murthy, D. V.; Haftka, R. T.

1986-01-01

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

A Subsonic Aircraft Design Optimization With Neural Network and Regression Approximators

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Guptill, James D.; Hopkins, Dale A.; Haller, William J.

2004-01-01

The Flight-Optimization-System (FLOPS) code encountered difficulty in analyzing a subsonic aircraft. The limitation made the design optimization problematic. The deficiencies have been alleviated through use of neural network and regression approximations. The insight gained from using the approximators is discussed in this paper. The FLOPS code is reviewed. Analysis models are developed and validated for each approximator. The regression method appears to hug the data points, while the neural network approximation follows a mean path. For an analysis cycle, the approximate model required milliseconds of central processing unit (CPU) time versus seconds by the FLOPS code. Performance of the approximators was satisfactory for aircraft analysis. A design optimization capability has been created by coupling the derived analyzers to the optimization test bed CometBoards. The approximators were efficient reanalysis tools in the aircraft design optimization. Instability encountered in the FLOPS analyzer was eliminated. The convergence characteristics were improved for the design optimization. The CPU time required to calculate the optimum solution, measured in hours with the FLOPS code was reduced to minutes with the neural network approximation and to seconds with the regression method. Generation of the approximators required the manipulation of a very large quantity of data. Design sensitivity with respect to the bounds of aircraft constraints is easily generated.

Warming and glacier recession in the Rakaia valley, Southern Alps of New Zealand, during Heinrich Stadial 1

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

Aaron E. Putnam; Joerg M. Schaefe; George H .Denton

2013-11-01

The termination of the last ice age featured a major reconfiguration of Earth's climate and cryosphere, yet the underlying causes of these massive changes continue to be debated. Documenting the spatial and temporal variations of atmospheric temperature during deglaciation can help discriminate among potential drivers. Here, we present a 10Be surface-exposure chronology and glaciological reconstruction of ice recession following the Last Glacial Maximum (LGM) in the Rakaia valley, Southern Alps of New Zealand. Innermost LGM moraines at Big Ben have an age of 17,840 +/- 240 yrs, whereas ice-marginal moraines or ice-molded bedrock surfaces at distances up-valley from Big Benmore » of 12.5 km (Lake Coleridge), approximately 25 km (Castle Hill), approximately 28 km (Double Hill), approximately 43 km (Prospect Hill), and approximately 58 km (Reischek knob) have ages of 17,020 +/- 70 yrs, 17,100 +/- 110 yrs, 16,960 +/- 370 yrs, 16,250 +/- 340 yrs, and 15,660 +/- 160 yrs, respectively. These results indicate extensive recession of the Rakaia glacier, which we attribute primarily to the effects of climatic warming. In conjunction with geomorphological maps and a glaciological reconstruction for the Rakaia valley, we use our chronology to infer timing and magnitude of past atmospheric temperature changes. Compared to an overall temperature rise of approximately 4.65?degrees C between the end of the LGM and the start of the Holocene, the glacier recession between approximately 17,840 and approximately 15,660 yrs ago is attributable to a net temperature increase of approximately 4.0?degrees C (from -6.25 to -2.25?degrees C), accounting for approximately 86% of the overall warming. Approximately 3.75?degrees C (approximately 70%) of the warming occurred between approximately 17,840 and approximately 16,250 yrs ago, with a further 0.75?degrees C (approximately 16%) increase between approximately 16,250 and approximately 15,660 yrs ago. A sustained southward shift of the Subtropical Front (STF) south of Australia between approximately 17,800 and approximately 16,000 yrs ago coincides with the warming over the Rakaia valley, and suggests a close link between Southern Ocean frontal boundary positions and southern mid-latitude climate. Most of the deglacial warming in the Southern Alps occurred during the early part of Heinrich Stadial 1 (HS1) of the North Atlantic region. Because the STF is associated with the position of the westerly wind belt, our findings support the concept that a southward shift of Earth's wind belts accompanied the early part of HS1 cooling in the North Atlantic, leading to warming and deglaciation in southern middle latitudes.« less

Comparison of dynamical approximation schemes for nonlinear gravitaional clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.

75 FR 62048 - Proposed Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2010-10-07

... Road. Approximately 105 feet None +1556 downstream of Evergreen Road. Paint Creek Approximately 0.47... Pettit Creek. Mill Creek Just upstream of None +270 City of Pocahontas, Ridgecrest Road. Unincorporated... Martin Road. Approximately 710 feet None +1923 upstream of Martin Road. Clearfield Creek Approximately...

Surface Segregation Energies of BCC Binaries from Ab Initio and Quantum Approximate Calculations

NASA Technical Reports Server (NTRS)

Good, Brian S.

2003-01-01

We compare dilute-limit segregation energies for selected BCC transition metal binaries computed using ab initio and quantum approximate energy method. Ab initio calculations are carried out using the CASTEP plane-wave pseudopotential computer code, while quantum approximate results are computed using the Bozzolo-Ferrante-Smith (BFS) method with the most recent parameterization. Quantum approximate segregation energies are computed with and without atomistic relaxation. The ab initio calculations are performed without relaxation for the most part, but predicted relaxations from quantum approximate calculations are used in selected cases to compute approximate relaxed ab initio segregation energies. Results are discussed within the context of segregation models driven by strain and bond-breaking effects. We compare our results with other quantum approximate and ab initio theoretical work, and available experimental results.

Approximate number and approximate time discrimination each correlate with school math abilities in young children.

PubMed

Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin

2016-01-01

What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright © 2015 Elsevier B.V. All rights reserved.

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

Broda, Jill Terese

The neutron flux across the nuclear reactor core is of interest to reactor designers and others. The diffusion equation, an integro-differential equation in space and energy, is commonly used to determine the flux level. However, the solution of a simplified version of this equation when automated is very time consuming. Since the flux level changes with time, in general, this calculation must be made repeatedly. Therefore solution techniques that speed the calculation while maintaining accuracy are desirable. One factor that contributes to the solution time is the spatial flux shape approximation used. It is common practice to use the samemore » order flux shape approximation in each energy group even though this method may not be the most efficient. The one-dimensional, two-energy group diffusion equation was solved, for the node average flux and core k-effective, using two sets of spatial shape approximations for each of three reactor types. A fourth-order approximation in both energy groups forms the first set of approximations used. The second set used combines a second-order approximation with a fourth-order approximation in energy group two. Comparison of the results from the two approximation sets show that the use of a different order spatial flux shape approximation results in considerable loss in accuracy for the pressurized water reactor modeled. However, the loss in accuracy is small for the heavy water and graphite reactors modeled. The use of different order approximations in each energy group produces mixed results. Further investigation into the accuracy and computing time is required before any quantitative advantage of the use of the second-order approximation in energy group one and the fourth-order approximation in energy group two can be determined.« less

On twelve types of covering-based rough sets.

PubMed

Safari, Samira; Hooshmandasl, Mohammad Reza

2016-01-01

Covering approximation spaces are a generalization of equivalence-based rough set theories. In this paper, we will consider twelve types of covering based approximation operators by combining four types of covering lower approximation operators and three types of covering upper approximation operators. Then, we will study the properties of these new pairs and show they have most of the common properties among existing covering approximation pairs. Finally, the relation between these new pairs is studied.

Energy conservation - A test for scattering approximations

NASA Technical Reports Server (NTRS)

Acquista, C.; Holland, A. C.

1980-01-01

The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method.

Pawlak Algebra and Approximate Structure on Fuzzy Lattice

PubMed Central

Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai

2014-01-01

The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties. PMID:25152922

Pawlak algebra and approximate structure on fuzzy lattice.

PubMed

Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai

2014-01-01

The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties.

HST images of very compact blue galaxies at z approximately 0.2

NASA Technical Reports Server (NTRS)

Koo, David C.; Bershady, Matthew A.; Wirth, Gregory D.; Stanford, S. Adam; Majewski, Steven R.

1994-01-01

We present the results of Hubble Space Telescope (HST) Wide-Field Camera (WFC) imaging of seven very compact, very blue galaxies with B less than or equal to 21 and redshifts z approximately 0.1 to 0.35. Based on deconvolved images, we estimate typical half-light diameters of approximately 0.65 sec, corresponding to approximately 1.4 h(exp -1) kpc at redshifts z approximately 0.2. The average rest frame surface brightness within this diameter is mu(sub v) approximately 20.5 mag arcsec(exp -2), approximately 1 mag brighter than that of typical late-type blue galaxies. Ground-based spectra show strong, narrow emission lines indicating high ionization; their very blue colors suggest recent bursts of star-formation; their typical luminosities are approximately 4 times fainter than that of field galaxies. These characteristics suggest H II galaxies as likely local counterparts of our sample, though our most luminous targets appear to be unusually compact for their luminosities.

Screening in ionic systems: simulations for the Lebowitz length.

PubMed

Kim, Young C; Luijten, Erik; Fisher, Michael E

2005-09-30

Simulations of the Lebowitz length, xiL (T, rho), are reported for the restricted primitive model hard-core (diameter a) 1:1 electrolyte for densities rho approximately < 4rho(c) and T(c) approximately < T approximately < 40T(c). Finite-size effects are elucidated for the charge fluctuations in various subdomains that serve to evaluate xiL. On extrapolation to the bulk limit for T approximately > 10T(c) the exact low-density expansions are seen to fail badly when rho > 1/10 rho(c) (with rho(c)a3 approximately = 0.08). At higher densities xiL rises above the Debye length, xiD proportional to square root(T/rho), by 10%-30% (up to rho approximately =1.3rho(c)); the variation is portrayed fairly well by the generalized Debye-Hückel theory. On approaching criticality at fixed rho or fixed T, xiL (T, rho) remains finite with xiL(c) approximately = 0.30a approximately = 1.3xiD(c) but displays a weak entropylike singularity.

Approximate Genealogies Under Genetic Hitchhiking

PubMed Central

Pfaffelhuber, P.; Haubold, B.; Wakolbinger, A.

2006-01-01

The rapid fixation of an advantageous allele leads to a reduction in linked neutral variation around the target of selection. The genealogy at a neutral locus in such a selective sweep can be simulated by first generating a random path of the advantageous allele's frequency and then a structured coalescent in this background. Usually the frequency path is approximated by a logistic growth curve. We discuss an alternative method that approximates the genealogy by a random binary splitting tree, a so-called Yule tree that does not require first constructing a frequency path. Compared to the coalescent in a logistic background, this method gives a slightly better approximation for identity by descent during the selective phase and a much better approximation for the number of lineages that stem from the founder of the selective sweep. In applications such as the approximation of the distribution of Tajima's D, the two approximation methods perform equally well. For relevant parameter ranges, the Yule approximation is faster. PMID:17182733

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. III. Cylindrical approximations for heat waves traveling inwards

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

Berkel, M. van; Fellow of the Japan Society for the Promotion of Science; FOM Institute DIFFER-Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM, Trilateral Euregio Cluster, P.O. Box 1207, 3430 BE Nieuwegein

In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on the heat equation in cylindrical geometry using the symmetry (Neumann) boundary condition at the plasma center. This means that the approximations derived here should be used only to estimate transport coefficients between the plasma center and the off-axis perturbative source. If the effect of cylindrical geometry is small, it is also possiblemore » to use semi-infinite domain approximations presented in Part I and Part II of this series. A number of new approximations are derived in this part, Part III, based upon continued fractions of the modified Bessel function of the first kind and the confluent hypergeometric function of the first kind. These approximations together with the approximations based on semi-infinite domains are compared for heat waves traveling towards the center. The relative error for the different derived approximations is presented for different values of the frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can be used to estimate the transport coefficients over a large parameter range for cases without convection and damping, cases with damping only, and cases with convection and damping. The relative error between the approximation and its underlying model is below 2% for the case, where only diffusivity and damping are considered. If also convectivity is considered, the diffusivity can be estimated well in a large region, but there is also a large region in which no suitable approximation is found. This paper is the third part (Part III) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In Part II, cylindrical approximations are treated for heat waves traveling towards the plasma edge assuming a semi-infinite domain.« less

Binary collision approximations for the memory function for density fluctuations in equilibrium atomic liquids

NASA Astrophysics Data System (ADS)

Noah, Joyce E.

Time correlation functions of density fluctuations of liquids at equilibrium can be used to relate the microscopic dynamics of a liquid to its macroscopic transport properties. Time correlation functions are especially useful since they can be generated in a variety of ways, from scattering experiments to computer simulation to analytic theory. The kinetic theory of fluctuations in equilibrium liquids is an analytic theory for calculating correlation functions using memory functions. In this work, we use a diagrammatic formulation of the kinetic theory to develop a series of binary collision approximations for the collisional part of the memory function. We define binary collisions as collisions between two distinct density fluctuations whose identities are fixed during the duration of a collsion. R approximations are for the short time part of the memory function, and build upon the work of Ranganathan and Andersen. These approximations have purely repulsive interactions between the fluctuations. The second type of approximation, RA approximations, is for the longer time part of the memory function, where the density fluctuations now interact via repulsive and attractive forces. Although RA approximations are a natural extension of R approximations, they permit two density fluctuations to become trapped in the wells of the interaction potential, leading to long-lived oscillatory behavior, which is unphysical. Therefore we consider S approximations which describe binary particles which experience the random effect of the surroundings while interacting via repulsive or repulsive and attractive interactions. For each of these approximations for the memory function we numerically solve the kinetic equation to generate correlation functions. These results are compared to molecular dynamics results for the correlation functions. Comparing the successes and failures of the different approximations, we conclude that R approximations give more accurate intermediate and long time results while RA and S approximations do particularly well at predicting the short time behavior. Lastly, we also develop a series of non-graphically derived approximations and use an optimization procedure to determine the underlying memory function from the simulation data. These approaches provide valuable information about the memory function that will be used in the development of future kinetic theories.

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

NASA Technical Reports Server (NTRS)

Klimas, A. J.; Sandri, G.; Scudder, J. D.; Howell, D. R.

1976-01-01

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.

Axicon based conical resonators with high power copper vapor laser.

PubMed

Singh, Bijendra; Subramaniam, V V; Daultabad, S R; Chakraborty, Ashim

2010-07-01

We report for the first time the performance of axicon based conical resonators (ABCRs) in a copper vapor laser, with novel results. The unstable conical resonator comprising of conical mirror (reflecting axicon) with axicon angle approximately pi/18, cone angle approximately 160 degrees, and a convex mirror of 60 cm radius of curvature was effective in reducing the average beam divergence to approximately 0.15 mrad (approximately 25 fold reduction compared to standard multimode plane-plane cavity) with output power of approximately 31 W. Extraction efficiency of approximately 50%-60% and beam divergence of <1 mrad was achieved in other stable ABCR configurations using flat and concave mirrors with the axicon. This is a significant improvement compared to 4-5 mrad normally observed in conventional stable resonators in copper vapor lasers. The conical resonators with copper vapor laser provide high misalignment tolerance beta approximately 4-5 mrad where beta is the tilt angle of the conical mirror from optimum position responsible for approximately 20% decline in laser power. The depth of focus d was approximately three times larger in case of conical resonator as compared to that of standard spherical unstable resonator under similar beam divergence and focusing conditions.

Spline approximation, Part 1: Basic methodology

NASA Astrophysics Data System (ADS)

Ezhov, Nikolaj; Neitzel, Frank; Petrovic, Svetozar

2018-04-01

In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of "irregularly" distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.

Some comparisons of complexity in dictionary-based and linear computational models.

PubMed

Gnecco, Giorgio; Kůrková, Věra; Sanguineti, Marcello

2011-03-01

Neural networks provide a more flexible approximation of functions than traditional linear regression. In the latter, one can only adjust the coefficients in linear combinations of fixed sets of functions, such as orthogonal polynomials or Hermite functions, while for neural networks, one may also adjust the parameters of the functions which are being combined. However, some useful properties of linear approximators (such as uniqueness, homogeneity, and continuity of best approximation operators) are not satisfied by neural networks. Moreover, optimization of parameters in neural networks becomes more difficult than in linear regression. Experimental results suggest that these drawbacks of neural networks are offset by substantially lower model complexity, allowing accuracy of approximation even in high-dimensional cases. We give some theoretical results comparing requirements on model complexity for two types of approximators, the traditional linear ones and so called variable-basis types, which include neural networks, radial, and kernel models. We compare upper bounds on worst-case errors in variable-basis approximation with lower bounds on such errors for any linear approximator. Using methods from nonlinear approximation and integral representations tailored to computational units, we describe some cases where neural networks outperform any linear approximator. Copyright © 2010 Elsevier Ltd. All rights reserved.

Cesium and strontium extraction using a mixed extractant solvent including crown ether and calixarene extractants

DOEpatents

Meikrantz, David H.; Todd, Terry A.; Riddle, Catherine L.; Law, Jack D.; Peterman, Dean R.; Mincher, Bruce J.; McGrath, Christopher A.; Baker, John D.

2007-11-06

A mixed extractant solvent including calix[4]arene-bis-(tert-octylbenzo)-crown-6 ("BOBCalixC6"), 4',4',(5')-di-(t-butyldicyclo-hexano)-18-crown-6 ("DtBu18C6"), and at least one modifier dissolved in a diluent. The mixed extractant solvent may be used to remove cesium and strontium from an acidic solution. The DtBu18C6 may be present from approximately 0.01 M to approximately 0.4M, such as from approximately 0.086 M to approximately 0.108 M. The modifier may be 1-(2,2,3,3-tetrafluoropropoxy)-3-(4-sec-butylphenoxy)-2-propanol ("Cs-7SB") and may be present from approximately 0.01M to approximately 0.8M. In one embodiment, the mixed extractant solvent includes approximately 0.15M DtBu18C6, approximately 0.007M BOBCalixC6, and approximately 0.75M Cs-7SB modifier dissolved in an isoparaffinic hydrocarbon diluent. The mixed extractant solvent may form an organic phase in an extraction system that also includes an aqueous phase. Methods of extracting cesium and strontium as well as strontium alone are also disclosed.

[Study of cefuroxime in pediatric field (author's transl)].

PubMed

Iwai, N; Sasaki, A; Miyazu, M; Osuga, T; Inaguma, K

1979-11-01

1. Cefuroxime (CXM) was studied for absorption and excretion in 4 pediatric patients given one shot intravenous injection of 20 approximately 25 mg/kg. The following serum levels were determined: 24.5 approximately 38.0 micrograms/ml at 30 minutes (mean 33.3 +/- 6.1 micrograms/ml), 10.0 approximately 17.0 micrograms/ml at 1 hours (mean 13.9 +/- 3.3 micrograms/ml), 3.4 approximately 7.6 micrograms/ml at 2 hours (mean 5.2 +/- 1.9 micrograms/ml, 0.7 approximately 2.1 micrograms/ml at 4 hours (mean 1.3 +/- 0.6 micrograms/ml, 0.1 approximately 0.3 microgram/ml at 6 hours (mean 0.2 +/- 0.1 microgram microgram/ml). Half-life (T 1/2) was 0.65 approximately 0.88 hour (mean 0.75 +/- 0.10 hour). Urinary levels were 1,280 approximately 7,100 micrograms/ml at 0 approximately 2 hours, 96 approximately 3,400 micrograms/ml at 2 approximately 4 hours, 68 approximately 250 micrograms/ml at 4 approximately 6 hours. Urinary recovery rate at 0 approximately 6 hours was 54.1 approximately 74.4% (mean 61.8 +/- 9.4%). 2. From the study on spinal fluid concentration in pediatric patients with Haemophilus influenzae-induced meningitis, the dose of CXM 52.2 mg/kg was given to 1 pediatric case with this disease by one shot intravenous injection. Spinal fluid levels were presumed as 9.0 micrograms/ml at 30 minutes, 6.8 micrograms/ml at 1 hour, 3.8 micrograms/ml at 2 hours and 1.2 micrograms/ml at 4 hours. 3. CXM was studied in 19 pediatric patients with bacterial infection for clinical efficacy, bacteriological effect and side effect. Clinical result was found good in 1 with purulent meningitis; excellent in 9 out of 15 with acute lobar pneumonia or acute bronchopneumonia, and good in remaining 6 cases; good in 2 with acute bronchitis; excellent in 1 with acute pyelonephritis. This represents efficacy ("excellent" plus "good") rate of 100%. Of 5 strains of H. influenzae presumed as causative organisms, 4 were disappeared and 1 was reduced. Two strains of Streptococcus pneumoniae and 1 strain of Escherichia coli were disappeared. No side effect was noted in terms of clinical symptom. Laboratory examination showed elevation of GOT and GPT in 1 case, but these elevated values returned to normal after the end of the CXM treatment.

78 FR 9831 - Final Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2013-02-12

... Drive. Wake County. Approximately 850 feet +345 upstream of Keighley Forest Drive. Richland Creek Approximately 850 feet +301 Town of Wake Forest. upstream of the confluence with Richland Creek Tributary 2... Approximately 750 feet +301 Town of Wake Forest. upstream of the confluence with Richland Creek. Approximately 0...

Soybean Breeding in the US

USDA-ARS?s Scientific Manuscript database

Soybean provides approximately 71% of the world’s protein meal and about 29% of the world’s vegetable oil. The U.S., Brazil, and Argentina supply approximately 80% of the world’s soybean production, accounting for approximately 88% of world soybean exports. In the U.S., approximately 30 million me...

Assimilation and subcellular partitioning of elements by grass shrimp collected along an impact gradient.

PubMed

Seebaugh, David R; Wallace, William G

2009-06-28

Chronic exposure to polluted field conditions can impact metal bioavailability in prey and may influence metal transfer to predators. The present study investigated the assimilation of Cd, Hg and organic carbon by grass shrimp Palaemonetes pugio, collected along an impact gradient within the New York/New Jersey Harbor Estuary. Adult shrimp were collected from five Staten Island, New York study sites, fed (109)Cd- or (203)Hg-labeled amphipods or (14)C-labeled meals and analyzed for assimilation efficiencies (AE). Subsamples of amphipods and shrimp were subjected to subcellular fractionation to isolate metal associated with a compartment presumed to contain trophically available metal (TAM) (metal associated with heat-stable proteins [HSP - e.g., metallothionein-like proteins], heat-denatured proteins [HDP - e.g., enzymes] and organelles [ORG]). TAM-(109)Cd% and TAM-(203)Hg% in radiolabeled amphipods were approximately 64% and approximately 73%, respectively. Gradients in AE-(109)Cd% ( approximately 54% to approximately 75%) and AE-(203)Hg% ( approximately 61% to approximately 78%) were observed for grass shrimp, with the highest values exhibited by shrimp collected from sites within the heavily polluted Arthur Kill complex. Population differences in AE-(14)C% were not observed. Assimilated (109)Cd% partitioned to the TAM compartment in grass shrimp varied between approximately 67% and approximately 75%. (109)Cd bound to HSP in shrimp varied between approximately 15% and approximately 47%, while (109)Cd associated with metal-sensitive HDP was approximately 17% to approximately 44%. Percentages of assimilated (109)Cd bound to ORG were constant at approximately 10%. Assimilated (203)Hg% associated with TAM in grass shrimp did not exhibit significant variation. Percentages of assimilated (203)Hg bound to HDP ( approximately 47%) and ORG ( approximately 11%) did not vary among populations and partitioning of (203)Hg to HSP was not observed. Using a simplified biokinetic model of metal accumulation from the diet, it is estimated that site-specific variability in Cd AE by shrimp and tissue Cd burdens in field-collected prey (polychaetes Nereis spp.) could potentially result in up to approximately 3.2-fold differences in the dose of Cd assimilated by shrimp from a meal in the field. The results of this study also suggest that chronic field exposure can impact mechanisms of metal transport across the gut epithelium that do not influence carbon assimilation. Differences in the assimilation and subcellular partitioning of metal may have important implications for metal toxicity in impacted shrimp populations.

An approximation technique for predicting the transient response of a second order nonlinear equation

NASA Technical Reports Server (NTRS)

Laurenson, R. M.; Baumgarten, J. R.

1975-01-01

An approximation technique has been developed for determining the transient response of a nonlinear dynamic system. The nonlinearities in the system which has been considered appear in the system's dissipation function. This function was expressed as a second order polynomial in the system's velocity. The developed approximation is an extension of the classic Kryloff-Bogoliuboff technique. Two examples of the developed approximation are presented for comparative purposes with other approximation methods.

VLBI observations of the nucleus of Centaurus A

NASA Technical Reports Server (NTRS)

Preston, R. A.; Wehrle, A. E.; Morabito, D. D.; Jauncey, D. L.; Batty, M. J.; Haynes, R. F.; Wright, A. E.; Nicolson, G. D.

1983-01-01

VLBI observations of the nucleus of Centaurus A made at 2.3 GHz on baselines with minimum fringe spacings of 0.15 and 0.0027 arcsec are presented. Results show that the nuclear component is elongated with a maximum extent of approximately 0.05 arcsec which is equivalent to a size of approximately 1 pc at the 5 Mpc distance of Centaurus A. The position angle of the nucleus is found to be 30 + or - 20 degrees, while the ratio of nuclear jet length to width is less than or approximately equal to 20. The nuclear flux density is determined to be 6.8 Jy, while no core component is found with an extent less than or approximately equal to 0.001 (less than or approximately equal to 0.02 pc) with a flux density of greater than or approximately equal to 20 mJy. A model of the Centaurus A nucleus composed of at least two components is developed on the basis of these results in conjunction with earlier VLBI and spectral data. The first component is an elongated source of approximately 0.05 arcsec (approximately 1 pc) size which contains most of the 2.3 GHz nuclear flux, while the second component is a source of approximately 0.0005 arcsec (approximately 0.01 pc) size which is nearly completely self-absorbed at 2.3 GHz but strengthens at higher frequencies.

On the origins of approximations for stochastic chemical kinetics.

PubMed

Haseltine, Eric L; Rawlings, James B

2005-10-22

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies.

Systems and Methods for Implementing High-Temperature Tolerant Supercapacitors

NASA Technical Reports Server (NTRS)

Bugga, Ratnakumar V. (Inventor); Brandon, Erik J. (Inventor); West, William C. (Inventor)

2016-01-01

Systems and methods in accordance with embodiments of the invention implement high-temperature tolerant supercapacitors. In one embodiment, a high-temperature tolerant super capacitor includes a first electrode that is thermally stable between at least approximately 80C and approximately 300C; a second electrode that is thermally stable between at least approximately 80C and approximately 300C; an ionically conductive separator that is thermally stable between at least approximately 80C and 300C; an electrolyte that is thermally stable between approximately at least 80C and approximately 300C; where the first electrode and second electrode are separated by the separator such that the first electrode and second electrode are not in physical contact; and where each of the first electrode and second electrode is at least partially immersed in the electrolyte solution.

Thorium-230 ages of corals and duration of the last interglacial sea-level high stand on Oahu, Hawaii

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

Szabo, B.J.; Ludwig, K.R.; Muhs, D.R.

1994-10-07

Thorium-230 ages of emergent marine deposits on Oahu, Hawaii, have a uniform distribution of ages from {approximately}114,000 to {approximately}131,000 years, indicating a duration for the last interglacial sea-level high stand of {approximately}17,000 years, in contrast to a duration of {approximately}8000 years inferred from the orbitally tuned marine oxygen isotope record. Sea level on Oahu rose to {>=}1 to 2 meters higher than present by 131,000 years ago or {approximately}6000 years earlier than inferred from the marine record. Although the latter record suggests a shift back to glacial conditions beginning at {approximately}119,000 years ago, the Oahu coral ages indicate a nearmore » present sea level until {approximately}114,000 years ago.« less

Precise analytic approximations for the Bessel function J1 (x)

NASA Astrophysics Data System (ADS)

Maass, Fernando; Martin, Pablo

2018-03-01

Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.

Theory and applications of a deterministic approximation to the coalescent model

PubMed Central

Jewett, Ethan M.; Rosenberg, Noah A.

2014-01-01

Under the coalescent model, the random number nt of lineages ancestral to a sample is nearly deterministic as a function of time when nt is moderate to large in value, and it is well approximated by its expectation E[nt]. In turn, this expectation is well approximated by simple deterministic functions that are easy to compute. Such deterministic functions have been applied to estimate allele age, effective population size, and genetic diversity, and they have been used to study properties of models of infectious disease dynamics. Although a number of simple approximations of E[nt] have been derived and applied to problems of population-genetic inference, the theoretical accuracy of the formulas and the inferences obtained using these approximations is not known, and the range of problems to which they can be applied is not well understood. Here, we demonstrate general procedures by which the approximation nt ≈ E[nt] can be used to reduce the computational complexity of coalescent formulas, and we show that the resulting approximations converge to their true values under simple assumptions. Such approximations provide alternatives to exact formulas that are computationally intractable or numerically unstable when the number of sampled lineages is moderate or large. We also extend an existing class of approximations of E[nt] to the case of multiple populations of time-varying size with migration among them. Our results facilitate the use of the deterministic approximation nt ≈ E[nt] for deriving functionally simple, computationally efficient, and numerically stable approximations of coalescent formulas under complicated demographic scenarios. PMID:24412419

Approximate number word knowledge before the cardinal principle.

PubMed

Gunderson, Elizabeth A; Spaepen, Elizabet; Levine, Susan C

2015-02-01

Approximate number word knowledge-understanding the relation between the count words and the approximate magnitudes of sets-is a critical piece of knowledge that predicts later math achievement. However, researchers disagree about when children first show evidence of approximate number word knowledge-before, or only after, they have learned the cardinal principle. In two studies, children who had not yet learned the cardinal principle (subset-knowers) produced sets in response to number words (verbal comprehension task) and produced number words in response to set sizes (verbal production task). As evidence of approximate number word knowledge, we examined whether children's numerical responses increased with increasing numerosity of the stimulus. In Study 1, subset-knowers (ages 3.0-4.2 years) showed approximate number word knowledge above their knower-level on both tasks, but this effect did not extend to numbers above 4. In Study 2, we collected data from a broader age range of subset-knowers (ages 3.1-5.6 years). In this sample, children showed approximate number word knowledge on the verbal production task even when only examining set sizes above 4. Across studies, children's age predicted approximate number word knowledge (above 4) on the verbal production task when controlling for their knower-level, study (1 or 2), and parents' education, none of which predicted approximation ability. Thus, children can develop approximate knowledge of number words up to 10 before learning the cardinal principle. Furthermore, approximate number word knowledge increases with age and might not be closely related to the development of exact number word knowledge. Copyright © 2014 Elsevier Inc. All rights reserved.

Explicitly solvable complex Chebyshev approximation problems related to sine polynomials

NASA Technical Reports Server (NTRS)

Freund, Roland

1989-01-01

Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.

76 FR 21695 - Proposed Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2011-04-18

... County. At the Betts Spring None +571 Branch and Bradford Creek confluence. Big Cove Creek Approximately.... Approximately 0.7 mile None +677 upstream of the Big Cove Creek confluence. Blue Spring Creek Approximately 400... Road. Approximately 450 feet None +748 upstream of Spragins Hollow Road Northwest. East Fork Pinhook...

From Lobatto Quadrature to the Euler Constant "e"

ERIC Educational Resources Information Center

Khattri, Sanjay Kumar

2010-01-01

Based on the Lobatto quadrature, we develop several new closed form approximations to the mathematical constant "e." For validating effectiveness of our approximations, a comparison of our results to the existing approximations is also presented. Another objective of our work is to inspire students to formulate other better approximations by using…

Meta-Regression Approximations to Reduce Publication Selection Bias

ERIC Educational Resources Information Center

Stanley, T. D.; Doucouliagos, Hristos

2014-01-01

Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with…

Better approximation guarantees for job-shop scheduling

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

Goldberg, L.A.; Paterson, M.; Srinivasan, A.

1997-06-01

Job-shop scheduling is a classical NP-hard problem. Shmoys, Stein & Wein presented the first polynomial-time approximation algorithm for this problem that has a good (polylogarithmic) approximation guarantee. We improve the approximation guarantee of their work, and present further improvements for some important NP-hard special cases of this problem (e.g., in the preemptive case where machines can suspend work on operations and later resume). We also present NC algorithms with improved approximation guarantees for some NP-hard special cases.

Effect of design selection on response surface performance

NASA Technical Reports Server (NTRS)

Carpenter, William C.

1993-01-01

Artificial neural nets and polynomial approximations were used to develop response surfaces for several test problems. Based on the number of functional evaluations required to build the approximations and the number of undetermined parameters associated with the approximations, the performance of the two types of approximations was found to be comparable. A rule of thumb is developed for determining the number of nodes to be used on a hidden layer of an artificial neural net and the number of designs needed to train an approximation is discussed.

Thin-wall approximation in vacuum decay: A lemma

NASA Astrophysics Data System (ADS)

Brown, Adam R.

2018-05-01

The "thin-wall approximation" gives a simple estimate of the decay rate of an unstable quantum field. Unfortunately, the approximation is uncontrolled. In this paper I show that there are actually two different thin-wall approximations and that they bracket the true decay rate: I prove that one is an upper bound and the other a lower bound. In the thin-wall limit, the two approximations converge. In the presence of gravity, a generalization of this lemma provides a simple sufficient condition for nonperturbative vacuum instability.

Constrained Chebyshev approximations to some elementary functions suitable for evaluation with floating point arithmetic

NASA Technical Reports Server (NTRS)

Manos, P.; Turner, L. R.

1972-01-01

Approximations which can be evaluated with precision using floating-point arithmetic are presented. The particular set of approximations thus far developed are for the function TAN and the functions of USASI FORTRAN excepting SQRT and EXPONENTIATION. These approximations are, furthermore, specialized to particular forms which are especially suited to a computer with a small memory, in that all of the approximations can share one general purpose subroutine for the evaluation of a polynomial in the square of the working argument.

Properties of the Boltzmann equation in the classical approximation

DOE PAGES

Epelbaum, Thomas; Gelis, François; Tanji, Naoto; ...

2014-12-30

We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since onemore » has also access to the non-approximated result for comparison.« less

Laplace approximation for Bessel functions of matrix argument

NASA Astrophysics Data System (ADS)

Butler, Ronald W.; Wood, Andrew T. A.

2003-06-01

We derive Laplace approximations to three functions of matrix argument which arise in statistics and elsewhere: matrix Bessel A[nu]; matrix Bessel B[nu]; and the type II confluent hypergeometric function of matrix argument, [Psi]. We examine the theoretical and numerical properties of the approximations. On the theoretical side, it is shown that the Laplace approximations to A[nu], B[nu] and [Psi] given here, together with the Laplace approximations to the matrix argument functions 1F1 and 2F1 presented in Butler and Wood (Laplace approximations to hyper-geometric functions with matrix argument, Ann. Statist. (2002)), satisfy all the important confluence relations and symmetry relations enjoyed by the original functions.

Polybenzoxazole-filled nitrile butadiene rubber compositions

NASA Technical Reports Server (NTRS)

Gajiwala, Himansu M. (Inventor); Guillot, David G. (Inventor)

2008-01-01

An insulation composition that comprises at least one nitrile butadiene rubber (NBR) having an acrylonitrile content that ranges from approximately 26% by weight to approximately 35% by weight and polybenzoxazole (PBO) fibers. The NBR may be a copolymer of acrylonitrile and butadiene and may be present in the insulation composition in a range of from approximately 45% by weight to approximately 56% by weight of a total weight of the insulation composition. The PBO fibers may be present in a range of from approximately 3% by weight to approximately 10% by weight of a total weight of the insulation composition. A rocket motor including the insulation composition and a method of insulating a rocket motor are also disclosed.

Recent advances in approximation concepts for optimum structural design

NASA Technical Reports Server (NTRS)

Barthelemy, Jean-Francois M.; Haftka, Raphael T.

1991-01-01

The basic approximation concepts used in structural optimization are reviewed. Some of the most recent developments in that area since the introduction of the concept in the mid-seventies are discussed. The paper distinguishes between local, medium-range, and global approximations; it covers functions approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It also appears that some new methodologies are emerging which could greatly benefit from the introduction of new computer architecture.

Compaction by impact of unconsolidated lunar fines

NASA Technical Reports Server (NTRS)

Ahrens, T. J.

1975-01-01

New Hugoniot and release adiabat data for 1.8 g/cu cm lunar fines in the approximately 2 to 70 kbar range demonstrate that upon shock compression intrinsic crystal density (approximately 3.1 g/cu cm) is achieved under shock stress of 15 to 20 kbar. Release adiabat determinations indicate that measurable irreversible compaction occurs upon achieving shock pressures above approximately 4 kbar. For shocks in the approximately 7 to 15 kbar range, the inferred post-shock specific volumes observed decrease nearly linearly with increasing peak shock pressures. Upon shocking to approximately 15 kbar the post-shock density is approximately that of the intrinsic minerals. If the present data are taken to be representative of the response to impact of unconsolidated regolith material on the moon, it is inferred that the formation of appreciable quantities of soil breccia can be associated with the impact of meteoroids or ejecta at speeds as low as approximately 1 km/sec.

Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.

PubMed

Wei, Qinglai; Li, Benkai; Song, Ruizhuo

2018-04-01

In this paper, a generalized policy iteration (GPI) algorithm with approximation errors is developed for solving infinite horizon optimal control problems for nonlinear systems. The developed stable GPI algorithm provides a general structure of discrete-time iterative adaptive dynamic programming algorithms, by which most of the discrete-time reinforcement learning algorithms can be described using the GPI structure. It is for the first time that approximation errors are explicitly considered in the GPI algorithm. The properties of the stable GPI algorithm with approximation errors are analyzed. The admissibility of the approximate iterative control law can be guaranteed if the approximation errors satisfy the admissibility criteria. The convergence of the developed algorithm is established, which shows that the iterative value function is convergent to a finite neighborhood of the optimal performance index function, if the approximate errors satisfy the convergence criterion. Finally, numerical examples and comparisons are presented.

Comparison of Response Surface and Kriging Models in the Multidisciplinary Design of an Aerospike Nozzle

NASA Technical Reports Server (NTRS)

Simpson, Timothy W.

1998-01-01

The use of response surface models and kriging models are compared for approximating non-random, deterministic computer analyses. After discussing the traditional response surface approach for constructing polynomial models for approximation, kriging is presented as an alternative statistical-based approximation method for the design and analysis of computer experiments. Both approximation methods are applied to the multidisciplinary design and analysis of an aerospike nozzle which consists of a computational fluid dynamics model and a finite element analysis model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations. Four optimization problems are formulated and solved using both approximation models. While neither approximation technique consistently outperforms the other in this example, the kriging models using only a constant for the underlying global model and a Gaussian correlation function perform as well as the second order polynomial response surface models.

Extending generalized Kubelka-Munk to three-dimensional radiative transfer.

PubMed

Sandoval, Christopher; Kim, Arnold D

2015-08-10

The generalized Kubelka-Munk (gKM) approximation is a linear transformation of the double spherical harmonics of order one (DP₁) approximation of the radiative transfer equation. Here, we extend the gKM approximation to study problems in three-dimensional radiative transfer. In particular, we derive the gKM approximation for the problem of collimated beam propagation and scattering in a plane-parallel slab composed of a uniform absorbing and scattering medium. The result is an 8×8 system of partial differential equations that is much easier to solve than the radiative transfer equation. We compare the solutions of the gKM approximation with Monte Carlo simulations of the radiative transfer equation to identify the range of validity for this approximation. We find that the gKM approximation is accurate for isotropic scattering media that are sufficiently thick and much less accurate for anisotropic, forward-peaked scattering media.

A filament of energetic particles near the high-latitude dawn magnetopause

NASA Technical Reports Server (NTRS)

Lui, A. T. Y.; Williams, D. J.; Mcentire, R. W.; Christon, S. P.; Jacquey, C.; Angelopoulos, V.; Yamamoto, T.; Kokubun, S.; Frank, L. A.; Ackerson, K. L.

1994-01-01

The Geotail satelite detected a filament of tailward-streaming energetic particles spatially separated from the boundary layer of energetic particles at the high-latitude dawn magnetopause at a downstream distance of approximately 80 R(sub E) on October 27, 1992. During this event, the composition and charge states of energetic ions at energies above approximately 10 keV show significant intermix of ions from solar wind and ionospheric sources. Detailed analysis leads to the deduction that the filament was moving southward towards the neutral sheet at an average speed of approximately 80 km/s, implying an average duskward electric field of approximately 1 mV/m. Its north-south dimension was approximately 1 R(sub E) and it was associated with an earthward directed field-aligned current of approximately 5 mA/m. The filament was separated from the energetic particle boundary layer straddling the magnetopause by approximately 0.8 R(sub E) and was inferred to be detached from the boundary layer at downstream distance beyond approximately 70 R(sub E) in the distant tail.

Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units

NASA Astrophysics Data System (ADS)

Franović, Igor; Todorović, Kristina; Vasović, Nebojša; Burić, Nikola

2014-02-01

We consider the approximations behind the typical mean-field model derived for a class of systems made up of type II excitable units influenced by noise and coupling delays. The formulation of the two approximations, referred to as the Gaussian and the quasi-independence approximation, as well as the fashion in which their validity is verified, are adapted to reflect the essential properties of the underlying system. It is demonstrated that the failure of the mean-field model associated with the breakdown of the quasi-independence approximation can be predicted by the noise-induced bistability in the dynamics of the mean-field system. As for the Gaussian approximation, its violation is related to the increase of noise intensity, but the actual condition for failure can be cast in qualitative, rather than quantitative terms. We also discuss how the fulfillment of the mean-field approximations affects the statistics of the first return times for the local and global variables, further exploring the link between the fulfillment of the quasi-independence approximation and certain forms of synchronization between the individual units.

A test of the adhesion approximation for gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.

1993-01-01

We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

A test of the adhesion approximation for gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.; Shandarin, Sergei F.; Weinberg, David H.

1994-01-01

We quantitatively compare a particle implementation of the adhesion approximation to fully nonlinear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel'dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel'dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate that that from ZA to TZA, (b) the error in the phase angle of Fourier components is worse that that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.

PubMed

Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E

2018-06-01

An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.

Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion

NASA Astrophysics Data System (ADS)

Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.

2017-10-01

Over the recent decades, a number of fast approximate solutions of Lippmann-Schwinger equation, which are more accurate than classic Born and Rytov approximations, were proposed in the field of electromagnetic modeling. Those developments could be naturally extended to acoustic and elastic fields; however, until recently, they were almost unknown in seismology. This paper presents several solutions of this kind applied to acoustic modeling for both lossy and lossless media. We evaluated the numerical merits of those methods and provide an estimation of their numerical complexity. In our numerical realization we use the matrix-free implementation of the corresponding integral operator. We study the accuracy of those approximate solutions and demonstrate, that the quasi-analytical approximation is more accurate, than the Born approximation. Further, we apply the quasi-analytical approximation to the solution of the inverse problem. It is demonstrated that, this approach improves the estimation of the data gradient, comparing to the Born approximation. The developed inversion algorithm is based on the conjugate-gradient type optimization. Numerical model study demonstrates that the quasi-analytical solution significantly reduces computation time of the seismic full-waveform inversion. We also show how the quasi-analytical approximation can be extended to the case of elastic wavefield.

Prostatic origin of a zinc binding high molecular weight protein complex in human seminal plasma.

PubMed

Siciliano, L; De Stefano, C; Petroni, M F; Vivacqua, A; Rago, V; Carpino, A

2000-03-01

The profile of the zinc ligand high molecular weight proteins was investigated in the seminal plasma of 55 normozoospermic subjects by size exclusion high performance liquid chromatography (HPLC). The proteins were recovered from Sephadex G-75 gel filtration of seminal plasma in three zinc-containing fractions which were then submitted to HPLC analysis. The results were, that in all the samples, the protein profiles showed two peaks with apparent molecular weight of approximately 660 and approximately 250 kDa. Dialysis experiments revealed that both approximately 660 and approximately 250 kDa proteins were able to uptake zinc against gradient indicating their zinc binding capacity. The HPLC analysis of the whole seminal plasma evidenced only the approximately 660 kDa protein complex as a single well quantifying peak, furthermore a positive correlation between its peak area and the seminal zinc values (P < 0.001) was observed. This suggested a prostatic origin of the approximately 660 kDa protein complex which was then confirmed by the seminal plasma HPLC analysis of a subject with agenesis of the Wolffian ducts. Finally the study demonstrated the presence of two zinc binding proteins, approximately 660 and approximately 250 kDa respectively, in human seminal plasma and the prostatic origin of the approximately 660 kDa.

Opacity, metallicity, and Cepheid period ratios in the galaxy and Magellanic Clouds

NASA Technical Reports Server (NTRS)

Simon, Norman R.; Kanbur, Shashi M.

1994-01-01

Linear pulsation calculations are employed to reproduce the bump Cepheid resonance (P(sub 2)/P(sub 0) = 0.5 at P(sub 0) approximately equal to 10 days) and to model, individually, the P(sub 1)/P(sub 0) period ratios for the dozen known Galactic beat Cepheids. Convection is ignored. The results point to a range of metallicity among the Cepheids, perhaps as large as 0.01 approximately less than Z approximately less than 0.02, with no evidence for any star exceeding Z = 0.02. We find masses and luminosities which range from M approximately less than 4 solar mass, log(base 10) approximately less than 3.0 at P(sub 0) approximately equal to 3 days to M approximately less than 6 solar mass, log(base 10) L approximately greater than 3.5 at P(sub 0) approximately equal to 10 days. Similar parameters are indicated for the P(sub 0) approximately equal to 10 days Cepheids in the LMC and SMC, provided that the resonance for these stars occurs at a slightly longer period, P(sub 0) days, as has been suggested in the literature. Our calculations were performed mainly using OPAL opacities, but also with new opacities from the Opacity project (OP). Only small differences were found between the OPAL results and those from OP. Finally, some suggestions are made for possible future work, including evolution and pulsation calculations, and more precise observations of Cepheids in the Magellanic Clouds.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers

PubMed Central

Szkudlarek, Emily; Brannon, Elizabeth M.

2018-01-01

Recent studies suggest that practice with approximate and non-symbolic arithmetic problems improves the math performance of adults, school aged children, and preschoolers. However, the relative effectiveness of approximate arithmetic training compared to available educational games, and the type of math skills that approximate arithmetic targets are unknown. The present study was designed to (1) compare the effectiveness of approximate arithmetic training to two commercially available numeral and letter identification tablet applications and (2) to examine the specific type of math skills that benefit from approximate arithmetic training. Preschool children (n = 158) were pseudo-randomly assigned to one of three conditions: approximate arithmetic, letter identification, or numeral identification. All children were trained for 10 short sessions and given pre and post tests of informal and formal math, executive function, short term memory, vocabulary, alphabet knowledge, and number word knowledge. We found a significant interaction between initial math performance and training condition, such that children with low pretest math performance benefited from approximate arithmetic training, and children with high pretest math performance benefited from symbol identification training. This effect was restricted to informal, and not formal, math problems. There were also effects of gender, socio-economic status, and age on post-test informal math score after intervention. A median split on pretest math ability indicated that children in the low half of math scores in the approximate arithmetic training condition performed significantly better than children in the letter identification training condition on post-test informal math problems when controlling for pretest, age, gender, and socio-economic status. Our results support the conclusion that approximate arithmetic training may be especially effective for children with low math skills, and that approximate arithmetic training improves early informal, but not formal, math skills. PMID:29867624

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers.

PubMed

Szkudlarek, Emily; Brannon, Elizabeth M

2018-01-01

Recent studies suggest that practice with approximate and non-symbolic arithmetic problems improves the math performance of adults, school aged children, and preschoolers. However, the relative effectiveness of approximate arithmetic training compared to available educational games, and the type of math skills that approximate arithmetic targets are unknown. The present study was designed to (1) compare the effectiveness of approximate arithmetic training to two commercially available numeral and letter identification tablet applications and (2) to examine the specific type of math skills that benefit from approximate arithmetic training. Preschool children ( n = 158) were pseudo-randomly assigned to one of three conditions: approximate arithmetic, letter identification, or numeral identification. All children were trained for 10 short sessions and given pre and post tests of informal and formal math, executive function, short term memory, vocabulary, alphabet knowledge, and number word knowledge. We found a significant interaction between initial math performance and training condition, such that children with low pretest math performance benefited from approximate arithmetic training, and children with high pretest math performance benefited from symbol identification training. This effect was restricted to informal, and not formal, math problems. There were also effects of gender, socio-economic status, and age on post-test informal math score after intervention. A median split on pretest math ability indicated that children in the low half of math scores in the approximate arithmetic training condition performed significantly better than children in the letter identification training condition on post-test informal math problems when controlling for pretest, age, gender, and socio-economic status. Our results support the conclusion that approximate arithmetic training may be especially effective for children with low math skills, and that approximate arithmetic training improves early informal, but not formal, math skills.

Embedding impedance approximations in the analysis of SIS mixers

NASA Technical Reports Server (NTRS)

Kerr, A. R.; Pan, S.-K.; Withington, S.

1992-01-01

Future millimeter-wave radio astronomy instruments will use arrays of many SIS receivers, either as focal plane arrays on individual radio telescopes, or as individual receivers on the many antennas of radio interferometers. Such applications will require broadband integrated mixers without mechanical tuners. To produce such mixers, it will be necessary to improve present mixer design techniques, most of which use the three-frequency approximation to Tucker's quantum mixer theory. This paper examines the adequacy of three approximations to Tucker's theory: (1) the usual three-frequency approximation which assumes a sinusoidal LO voltage at the junction, and a short-circuit at all frequencies above the upper sideband; (2) a five-frequency approximation which allows two LO voltage harmonics and five small-signal sidebands; and (3) a quasi five-frequency approximation in which five small-signal sidebands are allowed, but the LO voltage is assumed sinusoidal. These are compared with a full harmonic-Newton solution of Tucker's equations, including eight LO harmonics and their corresponding sidebands, for realistic SIS mixer circuits. It is shown that the accuracy of the three approximations depends strongly on the value of omega R(sub N)C for the SIS junctions used. For large omega R(sub N)C, all three approximations approach the eight-harmonic solution. For omega R(sub N)C values in the range 0.5 to 10, the range of most practical interest, the quasi five-frequency approximation is a considerable improvement over the three-frequency approximation, and should be suitable for much design work. For the realistic SIS mixers considered here, the five-frequency approximation gives results very close to those of the eight-harmonic solution. Use of these approximations, where appropriate, considerably reduces the computational effort needed to analyze an SIS mixer, and allows the design and optimization of mixers using a personal computer.

Plasma observations near saturn: initial results from voyager 2.

PubMed

Bridge, H S; Bagenal, F; Belcher, J W; Lazarus, A J; McNutt, R L; Sullivan, J D; Gazis, P R; Hartle, R E; Ogilvie, K W; Scudder, J D; Sittler, E C; Eviatar, A; Siscoe, G L; Goertz, C K; Vasyliunas, V M

1982-01-29

Results of measurements of plasma electrons and poitive ions made during the Voyager 2 encounter with Saturn have been combined with measurements from Voyager 1 and Pioneer 11 to define more clearly the configuration of plasma in the Saturnian magnetosphere. The general morphology is well represented by four regions: (i) the shocked solar wind plasma in the magnetosheath, observed between about 30 and 22 Saturn radii (RS) near the noon meridian; (ii) a variable density region between approximately 17 RS and the magnetopause; (iii) an extended thick plasma sheet between approximately 17 and approximately 7 RS symmetrical with respect to Saturn's equatorial plane and rotation axis; and (iv) an inner plasma torus that probably originates from local sources and extends inward from L approximately 7 to less than L approximately 2.7 (L is the magnetic shell parameter). In general, the heavy ions, probably O(+), are more closely confined to the equatorial plane than H(+), so that the ratio of heavy to light ions varies along the trajectory according to the distance of the spacecraft from the equatorial plane. The general configuration of the plasma sheet at Saturn found by Voyager 1 is confirmed, with some notable differences and additions. The "extended plasma sheet," observed between L approximately 7 and L approximately 15 by Voyager 1 is considerably thicker as observed by Voyager 2. Inward of L approximately 4, the plasma sheet collapses to a thin region about the equatorial plane. At the ring plane crossing, L approximately 2.7, the observations are consistent with a density of O(+) of approximately 100 per cubic centimeter, with a temperature of approximately 10 electron volts. The location of the bow shock and magnetopause crossings were consistent with those previously observed. The entire magnetosphere was larger during the outbound passage of Voyager 2 than had been previously observed; however, a magnetosphere of this size or larger is expected approximately 3 percent of the time.

Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions

PubMed Central

Onufriev, Alexey V.

2013-01-01

We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance the extent of the charge distribution–the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Å from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Å ) is half that of the point multipole expansion up to the octupole order. PMID:23861790

The NuSTAR Extragalactic Survey: A First Sensitive Look at the High-Energy Cosmic X-Ray Background Population

NASA Technical Reports Server (NTRS)

Alexander, D. M.; Stern, D.; DelMoro, A.; Lansbury, G. B.; Assef, R. J.; Aird, J.; Ajello, M.; Ballantyne, D. R.; Bauer, F. E.; Boggs, S. E.;

Robust Approximations to the Non-Null Distribution of the Product Moment Correlation Coefficient I: The Phi Coefficient.

ERIC Educational Resources Information Center

Edwards, Lynne K.; Meyers, Sarah A.

Correlation coefficients are frequently reported in educational and psychological research. The robustness properties and optimality among practical approximations when phi does not equal 0 with moderate sample sizes are not well documented. Three major approximations and their variations are examined: (1) a normal approximation of Fisher's Z,…

Certain approximation problems for functions on the infinite-dimensional torus: Lipschitz spaces

NASA Astrophysics Data System (ADS)

Platonov, S. S.

2018-02-01

We consider some questions about the approximation of functions on the infinite-dimensional torus by trigonometric polynomials. Our main results are analogues of the direct and inverse theorems in the classical theory of approximation of periodic functions and a description of the Lipschitz spaces on the infinite-dimensional torus in terms of the best approximation.

Legendre-tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1986-01-01

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

Legendre-Tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1983-01-01

The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.

A comparison of finite element and analytic models of acoustic scattering from rough poroelastic interfaces.

PubMed

Bonomo, Anthony L; Isakson, Marcia J; Chotiros, Nicholas P

2015-04-01

The finite element method is used to model acoustic scattering from rough poroelastic surfaces. Both monostatic and bistatic scattering strengths are calculated and compared with three analytic models: Perturbation theory, the Kirchhoff approximation, and the small-slope approximation. It is found that the small-slope approximation is in very close agreement with the finite element results for all cases studied and that perturbation theory and the Kirchhoff approximation can be considered valid in those instances where their predictions match those given by the small-slope approximation.

Eigenvalue and eigenvector sensitivity and approximate analysis for repeated eigenvalue problems

NASA Technical Reports Server (NTRS)

Hou, Gene J. W.; Kenny, Sean P.

1991-01-01

A set of computationally efficient equations for eigenvalue and eigenvector sensitivity analysis are derived, and a method for eigenvalue and eigenvector approximate analysis in the presence of repeated eigenvalues is presented. The method developed for approximate analysis involves a reparamaterization of the multivariable structural eigenvalue problem in terms of a single positive-valued parameter. The resulting equations yield first-order approximations of changes in both the eigenvalues and eigenvectors associated with the repeated eigenvalue problem. Examples are given to demonstrate the application of such equations for sensitivity and approximate analysis.

Monotonically improving approximate answers to relational algebra queries

NASA Technical Reports Server (NTRS)

Smith, Kenneth P.; Liu, J. W. S.

1989-01-01

We present here a query processing method that produces approximate answers to queries posed in standard relational algebra. This method is monotone in the sense that the accuracy of the approximate result improves with the amount of time spent producing the result. This strategy enables us to trade the time to produce the result for the accuracy of the result. An approximate relational model that characterizes appromimate relations and a partial order for comparing them is developed. Relational operators which operate on and return approximate relations are defined.

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

On the convergence of local approximations to pseudodifferential operators with applications

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas

1994-01-01

We consider the approximation of a class pseudodifferential operators by sequences of operators which can be expressed as compositions of differential operators and their inverses. We show that the error in such approximations can be bounded in terms of L(1) error in approximating a convolution kernel, and use this fact to develop convergence results. Our main result is a finite time convergence analysis of the Engquist-Majda Pade approximants to the square root of the d'Alembertian. We also show that no spatially local approximation to this operator can be convergent uniformly in time. We propose some temporally local but spatially nonlocal operators with better long time behavior. These are based on Laguerre and exponential series.

New approximate orientation averaging of the water molecule interacting with the thermal neutron

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

Markovic, M.I.; Minic, D.M.; Rakic, A.D.

1992-02-01

This paper reports that exactly describing the time of thermal neutron collisions with water molecules, orientation averaging is performed by an exact method (EOA{sub k}) and four approximate methods (two well known and two less known). Expressions for the microscopic scattering kernel are developed. The two well-known approximate orientation averaging methods are Krieger-Nelkin (K-N) and Koppel-Young (K-Y). The results obtained by one of the two proposed approximate orientation averaging methods agree best with the corresponding results obtained by EOA{sub k}. The largest discrepancies between the EOA{sub k} results and the results of the approximate methods are obtained using the well-knowmore » K-N approximate orientation averaging method.« less

A Generalization of the Karush-Kuhn-Tucker Theorem for Approximate Solutions of Mathematical Programming Problems Based on Quadratic Approximation

NASA Astrophysics Data System (ADS)

Voloshinov, V. V.

2018-03-01

In computations related to mathematical programming problems, one often has to consider approximate, rather than exact, solutions satisfying the constraints of the problem and the optimality criterion with a certain error. For determining stopping rules for iterative procedures, in the stability analysis of solutions with respect to errors in the initial data, etc., a justified characteristic of such solutions that is independent of the numerical method used to obtain them is needed. A necessary δ-optimality condition in the smooth mathematical programming problem that generalizes the Karush-Kuhn-Tucker theorem for the case of approximate solutions is obtained. The Lagrange multipliers corresponding to the approximate solution are determined by solving an approximating quadratic programming problem.

Dynamic approximate entropy electroanatomic maps detect rotors in a simulated atrial fibrillation model.

PubMed

Ugarte, Juan P; Orozco-Duque, Andrés; Tobón, Catalina; Kremen, Vaclav; Novak, Daniel; Saiz, Javier; Oesterlein, Tobias; Schmitt, Clauss; Luik, Armin; Bustamante, John

2014-01-01

There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multi-center databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping.

Resumming the large-N approximation for time evolving quantum systems

NASA Astrophysics Data System (ADS)

Mihaila, Bogdan; Dawson, John F.; Cooper, Fred

2001-05-01

In this paper we discuss two methods of resumming the leading and next to leading order in 1/N diagrams for the quartic O(N) model. These two approaches have the property that they preserve both boundedness and positivity for expectation values of operators in our numerical simulations. These approximations can be understood either in terms of a truncation to the infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a particular two-particle irreducible vacuum energy graph in the effective action of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the case of quantum mechanics where the Lagrangian is L(x,ẋ)=(12)∑Ni=1x˙2i-(g/8N)[∑Ni=1x2i- r20]2. The key to these approximations is to treat both the x propagator and the x2 propagator on similar footing which leads to a theory whose graphs have the same topology as QED with the x2 propagator playing the role of the photon. The bare vertex approximation is obtained by replacing the exact vertex function by the bare one in the exact Schwinger-Dyson equations for the one and two point functions. The second approximation, which we call the dynamic Debye screening approximation, makes the further approximation of replacing the exact x2 propagator by its value at leading order in the 1/N expansion. These two approximations are compared with exact numerical simulations for the quantum roll problem. The bare vertex approximation captures the physics at large and modest N better than the dynamic Debye screening approximation.

Revisiting the time until fixation of a neutral mutant in a finite population - A coalescent theory approach.

PubMed

Greenbaum, Gili

2015-09-07

Evaluation of the time scale of the fixation of neutral mutations is crucial to the theoretical understanding of the role of neutral mutations in evolution. Diffusion approximations of the Wright-Fisher model are most often used to derive analytic formulations of genetic drift, as well as for the time scales of the fixation of neutral mutations. These approximations require a set of assumptions, most notably that genetic drift is a stochastic process in a continuous allele-frequency space, an assumption appropriate for large populations. Here equivalent approximations are derived using a coalescent theory approach which relies on a different set of assumptions than the diffusion approach, and adopts a discrete allele-frequency space. Solutions for the mean and variance of the time to fixation of a neutral mutation derived from the two approaches converge for large populations but slightly differ for small populations. A Markov chain analysis of the Wright-Fisher model for small populations is used to evaluate the solutions obtained, showing that both the mean and the variance are better approximated by the coalescent approach. The coalescence approximation represents a tighter upper-bound for the mean time to fixation than the diffusion approximation, while the diffusion approximation and coalescence approximation form an upper and lower bound, respectively, for the variance. The converging solutions and the small deviations of the two approaches strongly validate the use of diffusion approximations, but suggest that coalescent theory can provide more accurate approximations for small populations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Genome duplication events and functional reduction of ploidy levels in sturgeon (Acipenser, Huso and Scaphirhynchus).

PubMed

Ludwig, A; Belfiore, N M; Pitra, C; Svirsky, V; Jenneckens, I

2001-07-01

Sturgeon (order Acipenserformes) provide an ideal taxonomic context for examination of genome duplication events. Multiple levels of ploidy exist among these fish. In a novel microsatellite approach, data from 962 fish from 20 sturgeon species were used for analysis of ploidy in sturgeon. Allele numbers in a sample of individuals were assessed at six microsatellite loci. Species with approximately 120 chromosomes are classified as functional diploid species, species with approximately 250 chromosomes as functional tetraploid species, and with approximately 500 chromosomes as functional octaploids. A molecular phylogeny of the sturgeon was determined on the basis of sequences of the entire mitochondrial cytochrome b gene. By mapping the estimated levels of ploidy on this proposed phylogeny we demonstrate that (I) polyploidization events independently occurred in the acipenseriform radiation; (II) the process of functional genome reduction is nearly finished in species with approximately 120 chromosomes and more active in species with approximately 250 chromosomes and approximately 500 chromosomes; and (III) species with approximately 250 and approximately 500 chromosomes arose more recently than those with approximately 120 chromosomes. These results suggest that gene silencing, chromosomal rearrangements, and transposition events played an important role in the acipenseriform genome formation. Furthermore, this phylogeny is broadly consistent with previous hypotheses but reveals a highly supported oceanic (Atlantic-Pacific) subdivision within the Acipenser/Huso complex.

Genome duplication events and functional reduction of ploidy levels in sturgeon (Acipenser, Huso and Scaphirhynchus).

PubMed Central

Ludwig, A; Belfiore, N M; Pitra, C; Svirsky, V; Jenneckens, I

2001-01-01

Sturgeon (order Acipenserformes) provide an ideal taxonomic context for examination of genome duplication events. Multiple levels of ploidy exist among these fish. In a novel microsatellite approach, data from 962 fish from 20 sturgeon species were used for analysis of ploidy in sturgeon. Allele numbers in a sample of individuals were assessed at six microsatellite loci. Species with approximately 120 chromosomes are classified as functional diploid species, species with approximately 250 chromosomes as functional tetraploid species, and with approximately 500 chromosomes as functional octaploids. A molecular phylogeny of the sturgeon was determined on the basis of sequences of the entire mitochondrial cytochrome b gene. By mapping the estimated levels of ploidy on this proposed phylogeny we demonstrate that (I) polyploidization events independently occurred in the acipenseriform radiation; (II) the process of functional genome reduction is nearly finished in species with approximately 120 chromosomes and more active in species with approximately 250 chromosomes and approximately 500 chromosomes; and (III) species with approximately 250 and approximately 500 chromosomes arose more recently than those with approximately 120 chromosomes. These results suggest that gene silencing, chromosomal rearrangements, and transposition events played an important role in the acipenseriform genome formation. Furthermore, this phylogeny is broadly consistent with previous hypotheses but reveals a highly supported oceanic (Atlantic-Pacific) subdivision within the Acipenser/Huso complex. PMID:11454768

Padé approximant for normal stress differences in large-amplitude oscillatory shear flow

NASA Astrophysics Data System (ADS)

Poungthong, P.; Saengow, C.; Giacomin, A. J.; Kolitawong, C.; Merger, D.; Wilhelm, M.

2018-04-01

Analytical solutions for the normal stress differences in large-amplitude oscillatory shear flow (LAOS), for continuum or molecular models, normally take the inexact form of the first few terms of a series expansion in the shear rate amplitude. Here, we improve the accuracy of these truncated expansions by replacing them with rational functions called Padé approximants. The recent advent of exact solutions in LAOS presents an opportunity to identify accurate and useful Padé approximants. For this identification, we replace the truncated expansion for the corotational Jeffreys fluid with its Padé approximants for the normal stress differences. We uncover the most accurate and useful approximant, the [3,4] approximant, and then test its accuracy against the exact solution [C. Saengow and A. J. Giacomin, "Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow," Phys. Fluids 29, 121601 (2017)]. We use Ewoldt grids to show the stunning accuracy of our [3,4] approximant in LAOS. We quantify this accuracy with an objective function and then map it onto the Pipkin space. Our two applications illustrate how to use our new approximant reliably. For this, we use the Spriggs relations to generalize our best approximant to multimode, and then, we compare with measurements on molten high-density polyethylene and on dissolved polyisobutylene in isobutylene oligomer.

Function approximation using combined unsupervised and supervised learning.

PubMed

Andras, Peter

2014-03-01

Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data.

Convergence Rates of Finite Difference Stochastic Approximation Algorithms

DTIC Science & Technology

2016-06-01

dfferences as gradient approximations. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the...descent algorithm, under various updating schemes using finite dfferences as gradient approximations. It is shown that the convergence of these...the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes using finite differences as gradient approximations. It

Spline smoothing of histograms by linear programming

NASA Technical Reports Server (NTRS)

Bennett, J. O.

1972-01-01

An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.

A hybrid Pade-Galerkin technique for differential equations

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1993-01-01

A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated.

Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics

PubMed Central

2017-01-01

We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics. PMID:28932256

Effect of design selection on response surface performance

NASA Technical Reports Server (NTRS)

Carpenter, William C.

1993-01-01

The mathematical formulation of the engineering optimization problem is given. Evaluation of the objective function and constraint equations can be very expensive in a computational sense. Thus, it is desirable to use as few evaluations as possible in obtaining its solution. In solving the equation, one approach is to develop approximations to the objective function and/or restraint equations and then to solve the equation using the approximations in place of the original functions. These approximations are referred to as response surfaces. The desirability of using response surfaces depends upon the number of functional evaluations required to build the response surfaces compared to the number required in the direct solution of the equation without approximations. The present study is concerned with evaluating the performance of response surfaces so that a decision can be made as to their effectiveness in optimization applications. In particular, this study focuses on how the quality of approximations is effected by design selection. Polynomial approximations and neural net approximations are considered.

Structural optimization with approximate sensitivities

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Hopkins, D. A.; Coroneos, R.

1994-01-01

Computational efficiency in structural optimization can be enhanced if the intensive computations associated with the calculation of the sensitivities, that is, gradients of the behavior constraints, are reduced. Approximation to gradients of the behavior constraints that can be generated with small amount of numerical calculations is proposed. Structural optimization with these approximate sensitivities produced correct optimum solution. Approximate gradients performed well for different nonlinear programming methods, such as the sequence of unconstrained minimization technique, method of feasible directions, sequence of quadratic programming, and sequence of linear programming. Structural optimization with approximate gradients can reduce by one third the CPU time that would otherwise be required to solve the problem with explicit closed-form gradients. The proposed gradient approximation shows potential to reduce intensive computation that has been associated with traditional structural optimization.

Big geo data surface approximation using radial basis functions: A comparative study

NASA Astrophysics Data System (ADS)

Majdisova, Zuzana; Skala, Vaclav

2017-12-01

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in n-dimensional space. It is a non-separable approximation, as it is based on the distance between two points. This method leads to the solution of an overdetermined linear system of equations. In this paper the RBF approximation methods are briefly described, a new approach to the RBF approximation of big datasets is presented, and a comparison for different Compactly Supported RBFs (CS-RBFs) is made with respect to the accuracy of the computation. The proposed approach uses symmetry of a matrix, partitioning the matrix into blocks and data structures for storage of the sparse matrix. The experiments are performed for synthetic and real datasets.

Flexible Approximation Model Approach for Bi-Level Integrated System Synthesis

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw; Kim, Hongman; Ragon, Scott; Soremekun, Grant; Malone, Brett

2004-01-01

Bi-Level Integrated System Synthesis (BLISS) is an approach that allows design problems to be naturally decomposed into a set of subsystem optimizations and a single system optimization. In the BLISS approach, approximate mathematical models are used to transfer information from the subsystem optimizations to the system optimization. Accurate approximation models are therefore critical to the success of the BLISS procedure. In this paper, new capabilities that are being developed to generate accurate approximation models for BLISS procedure will be described. The benefits of using flexible approximation models such as Kriging will be demonstrated in terms of convergence characteristics and computational cost. An approach of dealing with cases where subsystem optimization cannot find a feasible design will be investigated by using the new flexible approximation models for the violated local constraints.

Combination of the pair density approximation and the Takahashi–Imada approximation for path integral Monte Carlo simulations

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

Zillich, Robert E., E-mail: robert.zillich@jku.at

2015-11-15

We construct an accurate imaginary time propagator for path integral Monte Carlo simulations for heterogeneous systems consisting of a mixture of atoms and molecules. We combine the pair density approximation, which is highly accurate but feasible only for the isotropic interactions between atoms, with the Takahashi–Imada approximation for general interactions. We present finite temperature simulations results for energy and structure of molecules–helium clusters X{sup 4}He{sub 20} (X=HCCH and LiH) which show a marked improvement over the Trotter approximation which has a 2nd-order time step bias. We show that the 4th-order corrections of the Takahashi–Imada approximation can also be applied perturbativelymore » to a 2nd-order simulation.« less

Piecewise linear approximation for hereditary control problems

NASA Technical Reports Server (NTRS)

Propst, Georg

1987-01-01

Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

Limitations of shallow nets approximation.

PubMed

Lin, Shao-Bo

2017-10-01

In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.

High temperature ablative foam

NASA Technical Reports Server (NTRS)

Liu, Matthew T. (Inventor)

1992-01-01

An ablative foam composition is formed of approximately 150 to 250 parts by weight polymeric isocyanate having an isocyanate functionality of 2.6 to 3.2; approximately 15 to 30 parts by weight reactive flame retardant having a hydroxyl number range from 200-260; approximately 10 to 40 parts by weight non-reactive flame retardant; approximately 10 to 40 parts by weight nonhydrolyzable silicone copolymer having a hydroxyl number range from 75-205; and approximately 3 to 16 parts by weight amine initiated polyether resin having an isocyanate functionality greater than or equal to 3.0 and a hydroxyl number range from 400-800.

NE VIII lambda 774 and time variable associated absorption in the QSO UM 675

NASA Technical Reports Server (NTRS)

Hamann, Fred; Barlow, Thomas A.; Beaver, E. A.; Burbidge, E. M.; Cohen, Ross D.; Junkkarinen, Vesa; Lyons, R.

1995-01-01

We discuss measurements of Ne VIII lambda 774 absorption and the time variability of other lines in the z(sub a) approximately equal z(sub e) absorption system of the z(sub e) = 2.15 QSO UM 675 (0150-203). The C IV lambda 1549 and N V 1240 doublets at z(sub a) = 2.1340 (shifted approximately 1500 km/s from z(sub e) strengthened by a factor of approximately 3 between observations by Sargent, Boksenberg and Steidel (1981 November) and our earliest measurements (1990 November and December). We have no information on changes in other z(sub a) approximately equal z(sub e) absorption lines. Continued monitoring since 1990 November shows no clear changes in any of the absorptions between approximately 1100 and 1640 A rest. The short timescale of the variability (less than or approximately equal to 2.9 yr rest) strongly suggests that the clouds are dense, compact, close to the QSO, and photoionized by the QSO continuum. If the line variability is caused by changes in the ionization, the timescale requires densities greater than approximately 4000/cu cm. Photoionization calculations place the absorbing clouds within approximately 200 pc of the continuum source. The full range of line ionizations (from Ne VIII lambda 774 to C III lambda 977) in optically thin gas (no Lyman limit) implies that the absorbing regions span a factor of more than approximately 10 in distance or approximately 100 in density. Across these regions, the total hydrogen (H I + H II) column ranges from a few times 10(exp 18)/sq cm in the low-ionization gas to approximately 10(exp 20)/sq cm where the Ne VIII doublet forms. The metallicity is roughly solar or higher, with nitrogen possibly more enhanced by factors of a few. The clouds might contribute significant line emission if they nearly envelop the QSO. The presence of highly ionized Ne VIII lambda 774 absorption near the QSO supports recent studies that link z(sub a) approximately equal to z(sub e) systems with X-ray 'wamr absorbers. We show that the Ne VIII absorbing gas would itself produce measurable warm absorption -- characterized by bound-free O VII or O VIII edegs near 0.8 keV -- if the column densities were N(sub H) greater than or approximately equal to 10(exp 21)/sq cm (for solar abundances).

NE VIII lambda 774 and time variable associated absorption in the QSO UM 675

NASA Astrophysics Data System (ADS)

Hamann, Fred; Barlow, Thomas A.; Beaver, E. A.; Burbidge, E. M.; Cohen, Ross D.; Junkkarinen, Vesa; Lyons, R.

1995-04-01

We discuss measurements of Ne VIII lambda 774 absorption and the time variability of other lines in the za approximately equal ze absorption system of the ze = 2.15 QSO UM 675 (0150-203). The C IV lambda 1549 and N V 1240 doublets at za = 2.1340 (shifted approximately 1500 km/s from ze strengthened by a factor of approximately 3 between observations by Sargent, Boksenberg and Steidel (1981 November) and our earliest measurements (1990 November and December). We have no information on changes in other za approximately equal ze absorption lines. Continued monitoring since 1990 November shows no clear changes in any of the absorptions between approximately 1100 and 1640 A rest. The short timescale of the variability (less than or approximately equal to 2.9 yr rest) strongly suggests that the clouds are dense, compact, close to the QSO, and photoionized by the QSO continuum. If the line variability is caused by changes in the ionization, the timescale requires densities greater than approximately 4000/cu cm. Photoionization calculations place the absorbing clouds within approximately 200 pc of the continuum source. The full range of line ionizations (from Ne VIII lambda 774 to C III lambda 977) in optically thin gas (no Lyman limit) implies that the absorbing regions span a factor of more than approximately 10 in distance or approximately 100 in density. Across these regions, the total hydrogen (H I + H II) column ranges from a few times 1018/sq cm in the low-ionization gas to approximately 1020/sq cm where the Ne VIII doublet forms. The metallicity is roughly solar or higher, with nitrogen possibly more enhanced by factors of a few. The clouds might contribute significant line emission if they nearly envelop the QSO. The presence of highly ionized Ne VIII lambda 774 absorption near the QSO supports recent studies that link za approximately equal to ze systems with X-ray 'wamr absorbers. We show that the Ne VIII absorbing gas would itself produce measurable warm absorption -- characterized by bound-free O VII or O VIII edegs near 0.8 keV -- if the column densities were NH greater than or approximately equal to 1021/sq cm (for solar abundances).

A parallel offline CFD and closed-form approximation strategy for computationally efficient analysis of complex fluid flows

NASA Astrophysics Data System (ADS)

Allphin, Devin

Computational fluid dynamics (CFD) solution approximations for complex fluid flow problems have become a common and powerful engineering analysis technique. These tools, though qualitatively useful, remain limited in practice by their underlying inverse relationship between simulation accuracy and overall computational expense. While a great volume of research has focused on remedying these issues inherent to CFD, one traditionally overlooked area of resource reduction for engineering analysis concerns the basic definition and determination of functional relationships for the studied fluid flow variables. This artificial relationship-building technique, called meta-modeling or surrogate/offline approximation, uses design of experiments (DOE) theory to efficiently approximate non-physical coupling between the variables of interest in a fluid flow analysis problem. By mathematically approximating these variables, DOE methods can effectively reduce the required quantity of CFD simulations, freeing computational resources for other analytical focuses. An idealized interpretation of a fluid flow problem can also be employed to create suitably accurate approximations of fluid flow variables for the purposes of engineering analysis. When used in parallel with a meta-modeling approximation, a closed-form approximation can provide useful feedback concerning proper construction, suitability, or even necessity of an offline approximation tool. It also provides a short-circuit pathway for further reducing the overall computational demands of a fluid flow analysis, again freeing resources for otherwise unsuitable resource expenditures. To validate these inferences, a design optimization problem was presented requiring the inexpensive estimation of aerodynamic forces applied to a valve operating on a simulated piston-cylinder heat engine. The determination of these forces was to be found using parallel surrogate and exact approximation methods, thus evidencing the comparative benefits of this technique. For the offline approximation, latin hypercube sampling (LHS) was used for design space filling across four (4) independent design variable degrees of freedom (DOF). Flow solutions at the mapped test sites were converged using STAR-CCM+ with aerodynamic forces from the CFD models then functionally approximated using Kriging interpolation. For the closed-form approximation, the problem was interpreted as an ideal 2-D converging-diverging (C-D) nozzle, where aerodynamic forces were directly mapped by application of the Euler equation solutions for isentropic compression/expansion. A cost-weighting procedure was finally established for creating model-selective discretionary logic, with a synthesized parallel simulation resource summary provided.

Biogenesis of the Secretory Granule: Chromogranin a Coiled-Coil Structure Results in Unusual Physical Properties And Suggests a Mechanism for Granule Core Condensation

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

Mosley, C.A.; Taupenot, L.; Biswas, N.

2009-06-03

The secretory pro-hormone chromogranin A (CHGA) is densely packed into storage granules along with catecholamines, playing a catalytic role in granule biogenesis. 3-Dimensional structural data on CHGA are lacking. We found a superfamily structural homology for CHGA in the tropomyosin family of alpha-helical coiled-coils, even in mid-molecule regions where primary sequence identity is only modest. The assignment was confirmed by an independent algorithm, suggesting approximately 6-7 such domains spanning CHGA. We provide additional physiochemical evidence (chromatographic, spectral, microscopic) consistent with this unusual structure. Alpha-helical secondary structure (at up to approximately 45%) was confirmed by circular dichroism. CHGA molecular mass wasmore » estimated by MALDI-TOF mass spectrometry at approximately 50 kDa and by denaturing gel filtration at approximately 50-61 kDa, while its native Stokes radius was approximately 84.8 A, as compared to an expected approximately 30 A; the increase gave rise to an apparent native molecular weight of approximately 578 kDa, also consistent with the extended conformation of a coiled-coil. Small-angle X-ray scattering (SAXS) on CHGA in solution best fit an elongated cylindrical conformation in the monodisperse region with a radius of gyration of the rod cross-section (Rt) of approximately 52 A, compatible with a coiled-coil in the hydrated, aqueous state, or a multimeric coiled-coil. Electron microscopy with negative staining revealed an extended, filamentous CHGA structure with a diameter of approximately 94 +/- 4.5 A. Extended, coiled-coil conformation is likely to permit protein 'packing' in the secretory granule at approximately 50% higher density than a globular/spherical conformation. Natural allelic variation in the catestatin region was predicted to disrupt the coiled-coil. Chromaffin granule ultrastructure revealed a approximately 108 +/- 6.3 A periodicity of electron density, suggesting nucleation of a binding complex by the CHGA core. Inhibition of CHGA expression, by siRNA, disrupted regulated secretory protein traffic by approximately 65%, while targeted ablation of the CHGA gene in the mouse reduced chromaffin granule cotransmitter concentrations by approximately 40-80%. These results suggest new roles for secretory protein tertiary structure in hormone and transmitter storage, with implications for secretory cargo condensation (or dense core 'packing' structure) within the regulated pathway.« less

75 FR 69892 - Final Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2010-11-16

.... Yellow Medicine River Approximately 3,295 feet +1094 Unincorporated Areas of downstream of the county..., Unincorporated Areas of Cass County. Approximately 0.53 mile +1094 downstream of State Highway 50. Approximately...

Pressure broadening of the ((dt. mu. )dee)/sup */ formation resonances

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

Cohen, J.S.; Leon, M.; Padial, N.T.

1988-01-01

The treatment of ((dt..mu..)dee)/sup */ formation at high densities as a pressure broadening process is discussed. The quasistatic approximation is shown to satisfy the usual conditions of muon-catalyzed fusion better than does the impact approximation. Complete accurate results are shown for the impact approximation, and a preliminary rough treatment is presented to illustrate the quasistatic approximation. 13 refs., 8 figs.

19 CFR 12.104g - Specific items or categories designated by agreements or emergency actions.

Code of Federal Regulations, 2012 CFR

2012-04-01

... representing the Byzantine period ranging from approximately the 4th century A.D. through approximately the... Byzantine culture (approximately the 4th century through the 15th century A.D.) CBP Dec. 11-25 Guatemala... periods ranging approximately from the 9th century B.C. to the 4th century A.D. T.D. 01-06 extended by CBP...

CONTRIBUTIONS TO RATIONAL APPROXIMATION,

DTIC Science & Technology

Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

Quaternary borocarbides: New class of intermetallic superconductors

NASA Technical Reports Server (NTRS)

Nagarajan, R.; Gupta, L. C.; Dhar, S. K.; Mazumdar, Chandan; Hossain, Zakir; Godart, C.; Levy-Clement, C.; Padalia, B. D.; Vijayaraghavan, R.

1995-01-01

Our recent discovery of superconductivity (SC) in the four-element multiphase Y-Ni-B-C system at an elevated temperature (TC approximately 12 K) has opened up great possibilities of identifying new superconducting materials and generating new physics. Superconductivity with Tc (greater than 20 K) higher than that known so far in bulk intermetallics has been observed in multiphase Y-Pd-B-C and Th-Pd-B-C systems and a family of single phase materials RENi2B2C (RE= Y, rare earth) have been found. Our investigations show YNi2B2C to be a strong coupling hard type-II SC. HC2(T) exhibits an unconventional temperature dependence. Specific heat and magnetization studies reveal coexistence of SC and magnetism in RNi2B2C (R = Ho, Er, Tm) with magnetic ordering temperatures (Tc approximately 8 K, 10.5 K, 11 K and Tm approximately 5 K, approximately 7K, approximately 4 K respectively) that are remarkably higher than those in known magnetic superconductors . Mu-SR studies suggest the possibility of Ni atoms carrying a moment in TmNi2B2C. Resistivity results suggests a double re-entrant transition (SC-normal-SC) in HoNi2B2C. RENi2B2C (RE = Ce, Nd, Gd) do not show SC down to 4.2 K. The Nd- and Gd-compounds order magnetically at approximately 4.5 K and approximately 19.5 K, respectively. Two SC transitions are observed in Y-Pd-B-C (Tc approximately 22 K, approximately 10 K) and in Th-Pd-B-C (Tc approximately 20 K, approximately 14 K) systems, which indicate that there are at least two structures which support SC in these borocarbides. In our multiphase ThNi2B2C we observe SC at approximately 6 K. No SC was seen in multiphase UNi2B2C, UPd2B2C, UOs2Ge2C and UPd5B3C(0.35) down to 4.2 K. Tc in YNi2B2C is depressed by substitutions (Gd, Th and U at Y-sites and Fe, Co at Ni-sites).

Dynamic Analyses of Result Quality in Energy-Aware Approximate Programs

NASA Astrophysics Data System (ADS)

RIngenburg, Michael F.

Energy efficiency is a key concern in the design of modern computer systems. One promising approach to energy-efficient computation, approximate computing, trades off output precision for energy efficiency. However, this tradeoff can have unexpected effects on computation quality. This thesis presents dynamic analysis tools to study, debug, and monitor the quality and energy efficiency of approximate computations. We propose three styles of tools: prototyping tools that allow developers to experiment with approximation in their applications, online tools that instrument code to determine the key sources of error, and online tools that monitor the quality of deployed applications in real time. Our prototyping tool is based on an extension to the functional language OCaml. We add approximation constructs to the language, an approximation simulator to the runtime, and profiling and auto-tuning tools for studying and experimenting with energy-quality tradeoffs. We also present two online debugging tools and three online monitoring tools. The first online tool identifies correlations between output quality and the total number of executions of, and errors in, individual approximate operations. The second tracks the number of approximate operations that flow into a particular value. Our online tools comprise three low-cost approaches to dynamic quality monitoring. They are designed to monitor quality in deployed applications without spending more energy than is saved by approximation. Online monitors can be used to perform real time adjustments to energy usage in order to meet specific quality goals. We present prototype implementations of all of these tools and describe their usage with several applications. Our prototyping, profiling, and autotuning tools allow us to experiment with approximation strategies and identify new strategies, our online tools succeed in providing new insights into the effects of approximation on output quality, and our monitors succeed in controlling output quality while still maintaining significant energy efficiency gains.

Interaction of hydrated electron with dietary flavonoids and phenolic acids: rate constants and transient spectra studied by pulse radiolysis.

PubMed

Cai, Z; Li, X; Katsumura, Y

1999-10-01

The reaction rate constants and transient spectra of 11 flavonoids and 4 phenolic acids reacting with e(aq)- at neutral pH were measured. Absorption bands of the transients of e(aq)- reacting with the above compounds all located at a wavelength shorter than 400 nm. The e(aq)- scavenging abilities were divided into three groups: (+)catechin ((1.2 +/-0.1) x 10(8) M(-1)s(-1)) < 4-chromanol ((4.4 +/- 0.4) x 10(8) M(-1)s(-1)) < genistein ((6.2+/-0.4) x 10(9) M (-1) s(-1) approximately genistin ((8 +/- 1) x 10(9) M(-1)s(-1)) approximately rutin ((7.6 +/- 0.4) x M(-1)s(-1) approximately caffeic acid ((8.3 +/- 0.5) x 10(9)M(-1)s(-1)) < transcinnamic acid((1.1 +/- 0.1) x 10(10) M(-1)s(-1)) approximately p-coumaric acid ((1.1 +/- 0.1) x 10(10) M(-1)s(-1) approximately 2,4,6-trihydroxylbenzoic acid((1.1 +/- 0.1) x 10(10) M(-1)s(-1)) approximately baicalein ((1.1 +/- 0.5) x 10(10) M(-1)s(-1)) approximately baicalin((1.3 + 0.1) X 10(10) M(-1)s(-1)) approximately naringenin ((1.2 +/- 0.1) x 10(10) M(-1)s(-1)) approximately naringin ((1.0 +/- 0.1) x 10(10) M(-1)s(-1)) approximately gossypin((1.2 +/- 0.1) x 10(10) M(-1)s(-1)) approximately quercetin((1.3 +/- 0.5) x 10(10) M(-1)s(-1)). These results suggested that C4 keto group is the active site for e(aq)- to attack on flavonoids and phenolic acids, whereas the o-dihydroxy structure in B ring, the C2,3 double bond, the C3-OH group, and glucosylation, which are key structures that influence the antioxidant activities of flavonoids and phenolic acids, have little effects on the e(aq)- scavenging activities.

Review: correlations between oxygen affinity and sequence classifications of plant hemoglobins.

PubMed

Smagghe, Benoit J; Hoy, Julie A; Percifield, Ryan; Kundu, Suman; Hargrove, Mark S; Sarath, Gautam; Hilbert, Jean-Louis; Watts, Richard A; Dennis, Elizabeth S; Peacock, W James; Dewilde, Sylvia; Moens, Luc; Blouin, George C; Olson, John S; Appleby, Cyril A

2009-12-01

Plants express three phylogenetic classes of hemoglobins (Hb) based on sequence analyses. Class 1 and 2 Hbs are full-length globins with the classical eight helix Mb-like fold, whereas Class 3 plant Hbs resemble the truncated globins found in bacteria. With the exception of the specialized leghemoglobins, the physiological functions of these plant hemoglobins remain unknown. We have reviewed and, in some cases, measured new oxygen binding properties of a large number of Class 1 and 2 plant nonsymbiotic Hbs and leghemoglobins. We found that sequence classification correlates with distinct extents of hexacoordination with the distal histidine and markedly different overall oxygen affinities and association and dissociation rate constants. These results suggest strong selective pressure for the evolution of distinct physiological functions. The leghemoglobins evolved from the Class 2 globins and show no hexacoordination, very high rates of O(2) binding ( approximately 250 muM(-1) s(-1)), moderately high rates of O(2) dissociation ( approximately 5-15 s(-1)), and high oxygen affinity (K(d) or P(50) approximately 50 nM). These properties both facilitate O(2) diffusion to respiring N(2) fixing bacteria and reduce O(2) tension in the root nodules of legumes. The Class 1 plant Hbs show weak hexacoordination (K(HisE7) approximately 2), moderate rates of O(2) binding ( approximately 25 muM(-1) s(-1)), very small rates of O(2) dissociation ( approximately 0.16 s(-1)), and remarkably high O(2) affinities (P(50) approximately 2 nM), suggesting a function involving O(2) and nitric oxide (NO) scavenging. The Class 2 Hbs exhibit strong hexacoordination (K(HisE7) approximately 100), low rates of O(2) binding ( approximately 1 muM(-1) s(-1)), moderately low O(2) dissociation rate constants ( approximately 1 s(-1)), and moderate, Mb-like O(2) affinities (P(50) approximately 340 nM), perhaps suggesting a sensing role for sustained low, micromolar levels of oxygen.

Comparison of dynamical approximation schemes for non-linear gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of approximation by truncation, i.e., smoothing the initial conditions by various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was crosscorrelation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(exp 2, sub G)) where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. All other schemes, including those proposed as generalizations of the Zel'dovich approximation created by adding forces, were in fact generally worse by this measure. By explicitly checking, we verified that the success of our best-choice was a result of the best treatment of the phases of nonlinear Fourier components. Of all schemes tested, the adhesion approximation produced the most accurate nonlinear power spectrum and density distribution, but its phase errors suggest mass condensations were moved to slightly the wrong location. Due to its better reproduction of the mass density distribution function and power spectrum, it might be preferred for some uses. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present.

Electromyographic activity and 6RM strength in bench press on stable and unstable surfaces.

PubMed

Saeterbakken, Atle H; Fimland, Marius S

2013-04-01

The purpose of the study was to compare 6-repetition maximum (6RM) loads and muscle activity in bench press on 3 surfaces, namely, stable bench, balance cushion, and Swiss ball. Sixteen healthy, resistance-trained men (age 22.5 ± 2.0 years, stature 1.82 ± 6.6 m, and body mass 82.0 ± 7.8 kg) volunteered for 3 habituation/strength testing sessions and 1 experimental session. In randomized order on the 3 surfaces, 6RM strength and electromyographic activity of pectoralis major, deltoid anterior, biceps brachii, triceps brachii, rectus abdominis, oblique external and erector spinae were assessed. Relative to stable bench, the 6RM strength was approximately 93% for balance cushion (p ≤ 0.001) and approximately 92% for Swiss ball (p = 0.008); the pectoralis major electromyographic (EMG) activity was approximately 90% using the balance cushion (p = 0.080) and approximately 81% using Swiss ball (p = 0.006); the triceps EMG was approximately 79% using the balance cushion (p = 0.028) and approximately 69% using the Swiss ball (p = 0.002). Relative to balance cushion, the EMG activity in pectoralis, triceps, and erector spinae using Swiss ball was approximately 89% (p = 0.016), approximately 88% (p = 0.014) and approximately 80% (p = 0.020), respectively. In rectus abdominis, the EMG activity relative to Swiss ball was approximately 69% using stable bench (p = 0.042) and approximately 65% using the balance cushion (p = 0.046). Similar EMG activities between stable and unstable surfaces were observed for deltoid anterior, biceps brachii, and oblique external. In conclusion, stable bench press had greater 6RM strength and triceps and pectoralis EMG activity compared with the unstable surfaces. These findings have implications for athletic training and rehabilitation, because they demonstrate an inferior effect of unstable surfaces on muscle activation of prime movers and strength in bench press. If an unstable surface in bench press is desirable, a balance cushion should be chosen instead of a Swiss ball.

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. I. Semi-infinite slab approximations

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

Berkel, M. van; Fellow of the Japan Society for the Promotion of Science; FOM Institute DIFFER-Dutch Institute for Fundamental Energy Research, Association EURATOM- FOM, Trilateral Euregio Cluster, PO Box 1207, 3430 BE Nieuwegein

2014-11-15

In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on semi-infinite slab approximations of the heat equation. The main result is the approximation of χ under the influence of V and τ based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate χ well in cylindrical geometry, the relationships betweenmore » heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate χ, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which χ, V, and τ can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and τ in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and τ based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated.« less

Temperature and abundances in the Jovian auroral stratosphere. 1: Ethane as a probe of the millibar region

NASA Technical Reports Server (NTRS)

Livengood, Timothy A.; Kostiuk, Theodor; Espenak, Fred

1993-01-01

We report infrared heterodyne spectroscopy (lambda/delta lambda is approximately 10(exp 6)) of C2H6 emission at 11.9 microns from the northern Jovian auroral region, in observations conducted over December 2-7, 1989. Accurately measured line shapes provide information on C2H6 abundance as well as temperature and permit retrieval of the source pressure region. Enhanced emission was observed in the longitude range approximately 150-180 deg at approximately 60 deg north latitude, approximately corresponding to the CH4 7.8 micron hot spot and the region of brightest UV aurora. Significant brightness variations were observed in the hot spot emissions on a time scale of approximately 20 hours. Analysis of the brightest hot spot spectra indicates C2H6 mole fractions of approximately (6.3-6.8) x 10(exp -6) at temperatures of approximately 182-184 K at 1 mbar, compared to mole fractions of (3.8 +/- 1.4) x 10(exp -6) averaged over spectra outside the hot spot at a temperature of approximately 172 K at the same pressure. Fixing the mole fraction to the lower limit retrieved in the quiescent (non-hot spot) region allows the temperature at 1 mbar to be as high as approximately 200 K within the hot spot. These results provide upper limits to the temperature increase near the source of the C2H6 thermal infrared emission. Combined with results from similar measurements of ethylene emission probing the approximately 10-microbar region (Kostiuk et al., this issue), altitude information on the thermal structure of the Jovian auroral stratosphere can be obtained for the first time.

Dynamic Approximate Entropy Electroanatomic Maps Detect Rotors in a Simulated Atrial Fibrillation Model

PubMed Central

Ugarte, Juan P.; Orozco-Duque, Andrés; Tobón, Catalina; Kremen, Vaclav; Novak, Daniel; Saiz, Javier; Oesterlein, Tobias; Schmitt, Clauss; Luik, Armin; Bustamante, John

2014-01-01

There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multi-center databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping. PMID:25489858

Heisenberg-Langevin versus quantum master equation

NASA Astrophysics Data System (ADS)

Boyanovsky, Daniel; Jasnow, David

2017-12-01

The quantum master equation is an important tool in the study of quantum open systems. It is often derived under a set of approximations, chief among them the Born (factorization) and Markov (neglect of memory effects) approximations. In this article we study the paradigmatic model of quantum Brownian motion of a harmonic oscillator coupled to a bath of oscillators with a Drude-Ohmic spectral density. We obtain analytically the exact solution of the Heisenberg-Langevin equations, with which we study correlation functions in the asymptotic stationary state. We compare the exact correlation functions to those obtained in the asymptotic long time limit with the quantum master equation in the Born approximation with and without the Markov approximation. In the latter case we implement a systematic derivative expansion that yields the exact asymptotic limit under the factorization approximation only. We find discrepancies that could be significant when the bandwidth of the bath Λ is much larger than the typical scales of the system. We study the exact interaction energy as a proxy for the correlations missed by the Born approximation and find that its dependence on Λ is similar to the discrepancy between the exact solution and that of the quantum master equation in the Born approximation. We quantify the regime of validity of the quantum master equation in the Born approximation with or without the Markov approximation in terms of the system's relaxation rate γ , its unrenormalized natural frequency Ω and Λ : γ /Ω ≪1 and also γ Λ /Ω2≪1 . The reliability of the Born approximation is discussed within the context of recent experimental settings and more general environments.

Numerical cognition is resilient to dramatic changes in early sensory experience.

PubMed

Kanjlia, Shipra; Feigenson, Lisa; Bedny, Marina

2018-06-20

Humans and non-human animals can approximate large visual quantities without counting. The approximate number representations underlying this ability are noisy, with the amount of noise proportional to the quantity being represented. Numerate humans also have access to a separate system for representing exact quantities using number symbols and words; it is this second, exact system that supports most of formal mathematics. Although numerical approximation abilities and symbolic number abilities are distinct in representational format and in their phylogenetic and ontogenetic histories, they appear to be linked throughout development--individuals who can more precisely discriminate quantities without counting are better at math. The origins of this relationship are debated. On the one hand, symbolic number abilities may be directly linked to, perhaps even rooted in, numerical approximation abilities. On the other hand, the relationship between the two systems may simply reflect their independent relationships with visual abilities. To test this possibility, we asked whether approximate number and symbolic math abilities are linked in congenitally blind individuals who have never experienced visual sets or used visual strategies to learn math. Congenitally blind and blind-folded sighted participants completed an auditory numerical approximation task, as well as a symbolic arithmetic task and non-math control tasks. We found that the precision of approximate number representations was identical across congenitally blind and sighted groups, suggesting that the development of the Approximate Number System (ANS) does not depend on visual experience. Crucially, the relationship between numerical approximation and symbolic math abilities is preserved in congenitally blind individuals. These data support the idea that the Approximate Number System and symbolic number abilities are intrinsically linked, rather than indirectly linked through visual abilities. Copyright © 2018. Published by Elsevier B.V.

40 CFR 92.204 - Designation of engine families.

Code of Federal Regulations, 2010 CFR

2010-07-01

... stroke dimensions; (4) The approximate intake and exhaust event timing and duration (valve or port); (5... shutters, etc.); (3) The approximate bore and stroke dimensions; (4) The approximate location of the intake...

40 CFR 92.204 - Designation of engine families.

Code of Federal Regulations, 2013 CFR

2013-07-01

... stroke dimensions; (4) The approximate intake and exhaust event timing and duration (valve or port); (5... shutters, etc.); (3) The approximate bore and stroke dimensions; (4) The approximate location of the intake...

40 CFR 1033.230 - Grouping locomotives into engine families.

Code of Federal Regulations, 2013 CFR

2013-07-01

... nominal bore and stroke dimensions. (4) The approximate intake and exhaust event timing and duration... approximate bore and stroke dimensions. (4) The approximate location of the intake and exhaust valves (or...

40 CFR 92.204 - Designation of engine families.

Code of Federal Regulations, 2012 CFR

2012-07-01

... stroke dimensions; (4) The approximate intake and exhaust event timing and duration (valve or port); (5... shutters, etc.); (3) The approximate bore and stroke dimensions; (4) The approximate location of the intake...

40 CFR 92.204 - Designation of engine families.

Code of Federal Regulations, 2014 CFR

2014-07-01

... stroke dimensions; (4) The approximate intake and exhaust event timing and duration (valve or port); (5... shutters, etc.); (3) The approximate bore and stroke dimensions; (4) The approximate location of the intake...

40 CFR 92.204 - Designation of engine families.

Code of Federal Regulations, 2011 CFR

2011-07-01

... stroke dimensions; (4) The approximate intake and exhaust event timing and duration (valve or port); (5... shutters, etc.); (3) The approximate bore and stroke dimensions; (4) The approximate location of the intake...

Approximation methods for combined thermal/structural design

NASA Technical Reports Server (NTRS)

Haftka, R. T.; Shore, C. P.

1979-01-01

Two approximation concepts for combined thermal/structural design are evaluated. The first concept is an approximate thermal analysis based on the first derivatives of structural temperatures with respect to design variables. Two commonly used first-order Taylor series expansions are examined. The direct and reciprocal expansions are special members of a general family of approximations, and for some conditions other members of that family of approximations are more accurate. Several examples are used to compare the accuracy of the different expansions. The second approximation concept is the use of critical time points for combined thermal and stress analyses of structures with transient loading conditions. Significant time savings are realized by identifying critical time points and performing the stress analysis for those points only. The design of an insulated panel which is exposed to transient heating conditions is discussed.

Parameter estimation in nonlinear distributed systems - Approximation theory and convergence results

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.

Superconductor-to-insulator transition and transport properties of underdoped YBa2Cu3O(y) crystals.

PubMed

Semba, K; Matsuda, A

2001-01-15

The carrier-concentration-driven superconductor-to-insulator (SI) transition as well as transport properties in underdoped YBa2Cu3O(y) twinned crystals is studied. The SI transition takes place at y approximately 6.3, carrier concentration n(SI)H approximately 3x10(20) cm(-3), anisotropy rho(c)/rho(ab) approximately 10(3), and the threshold resistivity rho(SI)ab approximately 0.8 mOmega cm which corresponds to a critical sheet resistance h/4e2 approximately 6.5 kOmega per CuO2 bilayer. The evolution of a carrier, nH infiniti y - 6.2, is clearly observed in the underdoped region. The resistivity and Hall coefficient abruptly acquire strong temperature dependence at y approximately 6.5 indicating a radical change in the electronic state.

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

NASA Technical Reports Server (NTRS)

Smith, Andrew M.; Davis, Robert Ben; LaVerde, Bruce T.; Jones, Douglas C.; Band, Jonathon L.

2012-01-01

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

Best uniform approximation to a class of rational functions

NASA Astrophysics Data System (ADS)

Zheng, Zhitong; Yong, Jun-Hai

2007-10-01

We explicitly determine the best uniform polynomial approximation to a class of rational functions of the form 1/(x-c)2+K(a,b,c,n)/(x-c) on [a,b] represented by their Chebyshev expansion, where a, b, and c are real numbers, n-1 denotes the degree of the best approximating polynomial, and K is a constant determined by a, b, c, and n. Our result is based on the explicit determination of a phase angle [eta] in the representation of the approximation error by a trigonometric function. Moreover, we formulate an ansatz which offers a heuristic strategies to determine the best approximating polynomial to a function represented by its Chebyshev expansion. Combined with the phase angle method, this ansatz can be used to find the best uniform approximation to some more functions.

Approximate error conjugation gradient minimization methods

DOEpatents

Kallman, Jeffrey S

2013-05-21

In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.

Spacecraft attitude control using neuro-fuzzy approximation of the optimal controllers

NASA Astrophysics Data System (ADS)

Kim, Sung-Woo; Park, Sang-Young; Park, Chandeok

2016-01-01

In this study, a neuro-fuzzy controller (NFC) was developed for spacecraft attitude control to mitigate large computational load of the state-dependent Riccati equation (SDRE) controller. The NFC was developed by training a neuro-fuzzy network to approximate the SDRE controller. The stability of the NFC was numerically verified using a Lyapunov-based method, and the performance of the controller was analyzed in terms of approximation ability, steady-state error, cost, and execution time. The simulations and test results indicate that the developed NFC efficiently approximates the SDRE controller, with asymptotic stability in a bounded region of angular velocity encompassing the operational range of rapid-attitude maneuvers. In addition, it was shown that an approximated optimal feedback controller can be designed successfully through neuro-fuzzy approximation of the optimal open-loop controller.

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

DOE PAGES

Jakeman, J. D.; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity. We show that utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this papermore » we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less

Including fluid shear viscosity in a structural acoustic finite element model using a scalar fluid representation

PubMed Central

Cheng, Lei; Li, Yizeng; Grosh, Karl

2013-01-01

An approximate boundary condition is developed in this paper to model fluid shear viscosity at boundaries of coupled fluid-structure system. The effect of shear viscosity is approximated by a correction term to the inviscid boundary condition, written in terms of second order in-plane derivatives of pressure. Both thin and thick viscous boundary layer approximations are formulated; the latter subsumes the former. These approximations are used to develop a variational formation, upon which a viscous finite element method (FEM) model is based, requiring only minor modifications to the boundary integral contributions of an existing inviscid FEM model. Since this FEM formulation has only one degree of freedom for pressure, it holds a great computational advantage over the conventional viscous FEM formulation which requires discretization of the full set of linearized Navier-Stokes equations. The results from thick viscous boundary layer approximation are found to be in good agreement with the prediction from a Navier-Stokes model. When applicable, thin viscous boundary layer approximation also gives accurate results with computational simplicity compared to the thick boundary layer formulation. Direct comparison of simulation results using the boundary layer approximations and a full, linearized Navier-Stokes model are made and used to evaluate the accuracy of the approximate technique. Guidelines are given for the parameter ranges over which the accurate application of the thick and thin boundary approximations can be used for a fluid-structure interaction problem. PMID:23729844

On Nash-Equilibria of Approximation-Stable Games

NASA Astrophysics Data System (ADS)

Awasthi, Pranjal; Balcan, Maria-Florina; Blum, Avrim; Sheffet, Or; Vempala, Santosh

One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ɛ-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ɛ-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximation-stable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ɛ,Δ) approximation-stable games must have an ɛ-equilibrium of support O(Δ^{2-o(1)}/ɛ2{log n}), yielding an immediate n^{O(Δ^{2-o(1)}/ɛ^2log n)}-time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ɛ are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.

Including fluid shear viscosity in a structural acoustic finite element model using a scalar fluid representation.

PubMed

Cheng, Lei; Li, Yizeng; Grosh, Karl

2013-08-15

An approximate boundary condition is developed in this paper to model fluid shear viscosity at boundaries of coupled fluid-structure system. The effect of shear viscosity is approximated by a correction term to the inviscid boundary condition, written in terms of second order in-plane derivatives of pressure. Both thin and thick viscous boundary layer approximations are formulated; the latter subsumes the former. These approximations are used to develop a variational formation, upon which a viscous finite element method (FEM) model is based, requiring only minor modifications to the boundary integral contributions of an existing inviscid FEM model. Since this FEM formulation has only one degree of freedom for pressure, it holds a great computational advantage over the conventional viscous FEM formulation which requires discretization of the full set of linearized Navier-Stokes equations. The results from thick viscous boundary layer approximation are found to be in good agreement with the prediction from a Navier-Stokes model. When applicable, thin viscous boundary layer approximation also gives accurate results with computational simplicity compared to the thick boundary layer formulation. Direct comparison of simulation results using the boundary layer approximations and a full, linearized Navier-Stokes model are made and used to evaluate the accuracy of the approximate technique. Guidelines are given for the parameter ranges over which the accurate application of the thick and thin boundary approximations can be used for a fluid-structure interaction problem.

An approximation theory for nonlinear partial differential equations with applications to identification and control

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1982-01-01

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

A Reduced Dimension Static, Linearized Kalman Filter and Smoother

NASA Technical Reports Server (NTRS)

Fukumori, I.

1995-01-01

An approximate Kalman filter and smoother, based on approximations of the state estimation error covariance matrix, is described. Approximations include a reduction of the effective state dimension, use of a static asymptotic error limit, and a time-invariant linearization of the dynamic model for error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. Examples of use come from TOPEX/POSEIDON.

Locality of correlation in density functional theory.

PubMed

Burke, Kieron; Cancio, Antonio; Gould, Tim; Pittalis, Stefano

2016-08-07

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that EC → -AC ZlnZ + BCZ as Z → ∞, where Z is the atomic number, AC is known, and we estimate BC to be about 37 mhartree. The local density approximation yields AC exactly, but a very incorrect value for BC, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with BC a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.

Approximate formulas for elasticity of the Tornquist functions and some their advantages

NASA Astrophysics Data System (ADS)

Issin, Meyram

2017-09-01

In this article functions of demand for prime necessity, second necessity and luxury goods depending on the income are considered. These functions are called Tornquist functions. By means of the return model the demand for prime necessity goods and second necessity goods are approximately described. Then on the basis of a method of the smallest squares approximate formulas for elasticity of these Tornquist functions are received. To receive an approximate formula for elasticity of function of demand for luxury goods, the linear asymptotic formula is constructed for this function. Some benefits of approximate formulas for elasticity of Tornquist functions are specified.

A modified Rayleigh-Gans-Debye formula for small angle X-ray scattering by interstellar dust grains

NASA Astrophysics Data System (ADS)

Sharma, Subodh K.

2015-05-01

A widely used approximation in studies relating to small angle differential scattering cross-section of X-rays scattered by interstellar dust grains is the well known Rayleigh-Gans-Debye approximation (RGDA). The validity of this approximation, however, is limited only to X-ray energies greater than about 1 keV. At lower energies, this approximation overestimates the exact results. In this paper a modification to the RGDA is suggested. It is shown that a combination of the RGDA with Ramsauer approximation retains the formal simplicity of the RGDA and also yields good agreement with Mie computations at all X-ray energies.

Risk approximation in decision making: approximative numeric abilities predict advantageous decisions under objective risk.

PubMed

Mueller, Silke M; Schiebener, Johannes; Delazer, Margarete; Brand, Matthias

2018-01-22

Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.

Automatic Aircraft Collision Avoidance System and Method

NASA Technical Reports Server (NTRS)

Skoog, Mark (Inventor); Hook, Loyd (Inventor); McWherter, Shaun (Inventor); Willhite, Jaimie (Inventor)

2014-01-01

The invention is a system and method of compressing a DTM to be used in an Auto-GCAS system using a semi-regular geometric compression algorithm. In general, the invention operates by first selecting the boundaries of the three dimensional map to be compressed and dividing the three dimensional map data into regular areas. Next, a type of free-edged, flat geometric surface is selected which will be used to approximate terrain data of the three dimensional map data. The flat geometric surface is used to approximate terrain data for each regular area. The approximations are checked to determine if they fall within selected tolerances. If the approximation for a specific regular area is within specified tolerance, the data is saved for that specific regular area. If the approximation for a specific area falls outside the specified tolerances, the regular area is divided and a flat geometric surface approximation is made for each of the divided areas. This process is recursively repeated until all of the regular areas are approximated by flat geometric surfaces. Finally, the compressed three dimensional map data is provided to the automatic ground collision system for an aircraft.

Structural Reliability Analysis and Optimization: Use of Approximations

NASA Technical Reports Server (NTRS)

Grandhi, Ramana V.; Wang, Liping

1999-01-01

This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different approximations including the higher-order reliability methods (HORM) for representing the failure surface. This report is divided into several parts to emphasize different segments of the structural reliability analysis and design. Broadly, it consists of mathematical foundations, methods and applications. Chapter I discusses the fundamental definitions of the probability theory, which are mostly available in standard text books. Probability density function descriptions relevant to this work are addressed. In Chapter 2, the concept and utility of function approximation are discussed for a general application in engineering analysis. Various forms of function representations and the latest developments in nonlinear adaptive approximations are presented with comparison studies. Research work accomplished in reliability analysis is presented in Chapter 3. First, the definition of safety index and most probable point of failure are introduced. Efficient ways of computing the safety index with a fewer number of iterations is emphasized. In chapter 4, the probability of failure prediction is presented using first-order, second-order and higher-order methods. System reliability methods are discussed in chapter 5. Chapter 6 presents optimization techniques for the modification and redistribution of structural sizes for improving the structural reliability. The report also contains several appendices on probability parameters.

Optimal approximations for risk measures of sums of lognormals based on conditional expectations

NASA Astrophysics Data System (ADS)

Vanduffel, S.; Chen, X.; Dhaene, J.; Goovaerts, M.; Henrard, L.; Kaas, R.

2008-11-01

In this paper we investigate the approximations for the distribution function of a sum S of lognormal random variables. These approximations are obtained by considering the conditional expectation E[S|[Lambda

Analytical approximate solutions for a general class of nonlinear delay differential equations.

PubMed

Căruntu, Bogdan; Bota, Constantin

2014-01-01

We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

Combining global and local approximations

NASA Technical Reports Server (NTRS)

Haftka, Raphael T.

1991-01-01

A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model.

Approximations of Two-Attribute Utility Functions

DTIC Science & Technology

1976-09-01

preferred to") be a bina-zy relation on the set • of simple probability measures or ’gambles’ defined on a set T of consequences. Throughout this study it...simplifying independence assumptions. Although there are several approaches to this problem, the21 present study will focus on approximations of u... study will elicit additional interest in the topic. 2. REMARKS ON APPROXIMATION THEORY This section outlines a few basic ideas of approximation theory

Light scattering by cylindrical nanoparticles: Limits of applicability of the Rayleigh-Gans-Debye approximation

NASA Astrophysics Data System (ADS)

Kanevskii, V. I.; Rozenbaum, V. M.

2014-08-01

Applicability of the Rayleigh-Gans-Debye (RGD) approximation for describing light scattering by nanoparticles with large dielectric losses (such as carbon nanotubes) is analyzed. By a comparison of the approximate results with exact ones, it is shown that the presence of dielectric losses expands the range of applicability of the RGD approximation. This conclusion is illustrated by a differential cross-section diagram of scattering by a multiwall carbon nanotube.

Microeconomic analysis of military aircraft bearing restoration

NASA Technical Reports Server (NTRS)

Hein, G. F.

1976-01-01

The risk and cost of a bearing restoration by grinding program was analyzed. A microeconomic impact analysis was performed. The annual cost savings to U.S. Army aviation is approximately $950,000.00 for three engines and three transmissions. The capital value over an indefinite life is approximately ten million dollars. The annual cost savings for U.S. Air Force engines are approximately $313,000.00 with a capital value of approximately 3.1 million dollars.

Synthesis and characterization of Cu nanotubes and nanothreads by electrical arc evaporation.

PubMed

Yadav, Ram Manohar; Singh, A K; Srivastava, O N

2003-06-01

We report the formation and characterization of copper nanostructures, nanotubules and nanothreads, which were obtained by electrical arc evaporation of Cu electrodes under varied conditions of He ambience. Electrical arc evaporation was done with approximately 10 V and (approximately 50-100 A) DC current. The current was used in a pulse mode. The evaporated material was condensed on a formvar-coated Cu grid mounted on a liquid N2-cooled specimen holder. Transmission electron microscopy was employed to characterize the condensed materials. These investigations revealed that the condensed materials consisted of the mentioned nanostructures. Nanotubes and nanothreads are formed for a He pressure in the chamber corresponding to approximately 140 and approximately 500 torr, respectively. Extensive electron microscopic investigations showed that the diameter of the nanotubes varied from approximately 5 nm to approximately 50 nm and their length from 2 microns to 3 microns.

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

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

Jakeman, J.D., E-mail: jdjakem@sandia.gov; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchicalmore » surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less

Localization-delocalization transition in a system of quantum kicked rotors.

PubMed

Creffield, C E; Hur, G; Monteiro, T S

2006-01-20

The quantum dynamics of atoms subjected to pairs of closely spaced delta kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the single delta-kick system. We find the unitary matrix has a new oscillating band structure corresponding to a cellular structure of phase space and observe a spectral signature of a localization-delocalization transition from one cell to several. We find that the eigenstates have localization lengths which scale with a fractional power L approximately h(-0.75) and obtain a regime of near-linear spectral variances which approximate the "critical statistics" relation summation2(L) approximately or equal to chi(L) approximately 1/2 (1-nu)L, where nu approximately 0.75 is related to the fractal classical phase-space structure. The origin of the nu approximately 0.75 exponent is analyzed.

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Analytical Derivation and Experimental Evaluation of Short-Bearing Approximation for Full Journal Bearing

NASA Technical Reports Server (NTRS)

Dubois, George B; Ocvirk, Fred W

1953-01-01

An approximate analytical solution including the effect of end leakage from the oil film of short plain bearings is presented because of the importance of endwise flow in sleeve bearings of the short lengths commonly used. The analytical approximation is supported by experimental data, resulting in charts which facilitate analysis of short plain bearings. The analytical approximation includes the endwise flow and that part of the circumferential flow which is related to surface velocity and film thickness but neglects the effect of film pressure on the circumferential flow. In practical use, this approximation applies best to bearings having a length-diameter ratio up to 1, and the effects of elastic deflection, inlet oil pressure, and changes of clearance with temperature minimize the relative importance of the neglected term. The analytical approximation was found to be an extension of a little-known pressure-distribution function originally proposed by Michell and Cardullo.

Radiative properties of flame-generated soot

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

Koeylue, U.O.; Faeth, G.M.

1993-05-01

Approximate methods for estimating the optical properties of flame-generated soot aggregates were evaluated using existing computer simulations and measurements in the visible and near-infrared portions of the spectrum. The following approximate methods were evaluated for both individual aggregates and polydisperse aggregate populations: the Rayleigh scattering approximation, Mie scattering for an equivalent sphere, and Rayleigh-Debye-Gans (R-D-G) scattering for both given and fractal aggregates. Results of computer simulations involved both prescribed aggregate geometry and numerically generated aggregates by cluster-cluster aggregation; multiple scattering was considered exactly using the mean-field approximation, and ignored using the R-D-G approximation. Measurements involved the angular scattering properties ofmore » soot in the postflame regions of both premixed and nonpremixed flames. The results show that available computer simulations and measurements of soot aggregate optical properties are not adequate to provide a definitive evaluation of the approximate prediction methods. 40 refs., 7 figs., 1 tab.« less

Representation of Ice Geometry by Parametric Functions: Construction of Approximating NURBS Curves and Quantification of Ice Roughness--Year 1: Approximating NURBS Curves

NASA Technical Reports Server (NTRS)

Dill, Loren H.; Choo, Yung K. (Technical Monitor)

2004-01-01

Software was developed to construct approximating NURBS curves for iced airfoil geometries. Users specify a tolerance that determines the extent to which the approximating curve follows the rough ice. The user can therefore smooth the ice geometry in a controlled manner, thereby enabling the generation of grids suitable for numerical aerodynamic simulations. Ultimately, this ability to smooth the ice geometry will permit studies of the effects of smoothing upon the aerodynamics of iced airfoils. The software was applied to several different types of iced airfoil data collected in the Icing Research Tunnel at NASA Glenn Research Center, and in all cases was found to efficiently generate suitable approximating NURBS curves. This method is an improvement over the current "control point formulation" of Smaggice (v.1.2). In this report, we present the relevant theory of approximating NURBS curves and discuss typical results of the software.

On the validity of the use of a localized approximation for helical beams. I. Formal aspects

NASA Astrophysics Data System (ADS)

Gouesbet, Gérard; André Ambrosio, Leonardo

2018-03-01

The description of an electromagnetic beam for use in light scattering theories may be carried out by using an expansion over vector spherical wave functions with expansion coefficients expressed in terms of Beam Shape Coefficients (BSCs). A celebrated method to evaluate these BSCs has been the use of localized approximations (with several existing variants). We recently established that the use of any existing localized approximation is of limited validity in the case of Bessel and Mathieu beams. In the present paper, we address a warning against the use of any existing localized approximation in the case of helical beams. More specifically, we demonstrate that a procedure used to validate any existing localized approximation fails in the case of helical beams. Numerical computations in a companion paper will confirm that existing localized approximations are of limited validity in the case of helical beams.

Approximate circuits for increased reliability

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

Hamlet, Jason R.; Mayo, Jackson R.

2015-08-18

Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the referencemore » circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.« less

Error bounds of adaptive dynamic programming algorithms for solving undiscounted optimal control problems.

PubMed

Liu, Derong; Li, Hongliang; Wang, Ding

2015-06-01

In this paper, we establish error bounds of adaptive dynamic programming algorithms for solving undiscounted infinite-horizon optimal control problems of discrete-time deterministic nonlinear systems. We consider approximation errors in the update equations of both value function and control policy. We utilize a new assumption instead of the contraction assumption in discounted optimal control problems. We establish the error bounds for approximate value iteration based on a new error condition. Furthermore, we also establish the error bounds for approximate policy iteration and approximate optimistic policy iteration algorithms. It is shown that the iterative approximate value function can converge to a finite neighborhood of the optimal value function under some conditions. To implement the developed algorithms, critic and action neural networks are used to approximate the value function and control policy, respectively. Finally, a simulation example is given to demonstrate the effectiveness of the developed algorithms.

Imaging the host galaxies of high-redshift radio-quiet QSOs

NASA Technical Reports Server (NTRS)

Lowenthal, James D.; Heckman, Timothy M.; Lehnert, Matthew, D.; Elias, J. H.

1995-01-01

We present new deep K-band and optical images of four radio-quiet QSOs at z approximately = 1 and six radio-quiet QSOs at z approximately = 2.5, as well as optical images only of six more at z approximately = 2.5. We have examined the images carefully for evidence of extended 'fuzz' from any putative QSO host galaxy. None of the z approximately = 2.5 QSOs shows any extended emission, and only two of the z approximately = 1 QSOs show marginal evidence for extended emission. Our 3 sigma detection limits in the K images, m(sub K) approximately = 21 for an isolated source, would correspond approximately to an unevolved L(sup star) elliptical galaxy at z = 2.5 or 2-3 mag fainter than an L(sup star) elliptical at z = 1, although our limits on host galaxy light are weaker than this due to the difficulty of separating galaxy light from QSO light. We simulate simple models of disk and elliptical host galaxies, and find that the marginal emission around the two z approximately = 1 QSOs can be explained by disks or bulges that are approximately 1-2 mag brighter than an unevolved L(sup star) galaxy in one case and approximately 1.5-2.5 mag brighter than L(sub star) in the other. For two other z approximately = 1 QSOs, we have only upper limits (L approximately = L(sup star)). The hosts of the high-redshift sample must be no brighter than about 3 mag above an unevolved L(sup star) galaxy, and are at least 1 magnitude fainter than the hosts of radio-loud QSOs at the same redshift. If the easily detected K-band light surrounding a previous sample of otherwise similar but radio-loud QSOs is starlight, then it must evolve on timescales of greater than or approximately equal to 10(exp 8) yr (e.g., Chambers & Charlot 1990); therefore our non-detection of host galaxy fuzz around radio-quiet QSOs supports the view that high-redshift radio-quiet and radio-loud QSOs inhabit different host objects, rather than being single types of objects that turn their radio emission on and off over short timescales. This is consistent with the general trend at low redshifts that radio-loud QSOs are found in giant elliptical galaxies while radio-quiet QSOs are found in less luminous disk galaxies. It also suggests that the processes responsible for the spectacular properties of radio-loud AGNs at high redshifts might not be generally relevent to the (far more numerous) radio-quiet population.

Glacier loss on Kilimanjaro continues unabated.

PubMed

Thompson, L G; Brecher, H H; Mosley-Thompson, E; Hardy, D R; Mark, B G

2009-11-24

The dramatic loss of Kilimanjaro's ice cover has attracted global attention. The three remaining ice fields on the plateau and the slopes are both shrinking laterally and rapidly thinning. Summit ice cover (areal extent) decreased approximately 1% per year from 1912 to 1953 and approximately 2.5% per year from 1989 to 2007. Of the ice cover present in 1912, 85% has disappeared and 26% of that present in 2000 is now gone. From 2000 to 2007 thinning (surface lowering) at the summits of the Northern and Southern Ice Fields was approximately 1.9 and approximately 5.1 m, respectively, which based on ice thicknesses at the summit drill sites in 2000 represents a thinning of approximately 3.6% and approximately 24%, respectively. Furtwängler Glacier thinned approximately 50% at the drill site between 2000 and 2009. Ice volume changes (2000-2007) calculated for two ice fields reveal that nearly equivalent ice volumes are now being lost to thinning and lateral shrinking. The relative importance of different climatological drivers remains an area of active inquiry, yet several points bear consideration. Kilimanjaro's ice loss is contemporaneous with widespread glacier retreat in mid to low latitudes. The Northern Ice Field has persisted at least 11,700 years and survived a widespread drought approximately 4,200 years ago that lasted approximately 300 years. We present additional evidence that the combination of processes driving the current shrinking and thinning of Kilimanjaro's ice fields is unique within an 11,700-year perspective. If current climatological conditions are sustained, the ice fields atop Kilimanjaro and on its flanks will likely disappear within several decades.

The Anisotropy of the Microwave Background to l=3500: Mosaic Observations with the Cosmic Background Imager

NASA Technical Reports Server (NTRS)

Pearson, T. J.; Mason, B. S.; Readhead, A. C. S.; Shepherd, M. C.; Sievers, J. L.; Udomprasert, P. S.; Cartwright, J. K.; Farmer, A. J.; Padin, S.; Myers, S. T.;

SMM observations of gamma-ray transients. 3: A search for a broadened, redshifted positron annihilation line from the direction of the Galactic center

NASA Technical Reports Server (NTRS)

Harris, Michael J.; Share, Gerald H.; Leising, Mark D.

1994-01-01

We have searched for 1980-1988 Solar Maximum Mission gamma-ray spectrometer data for transient emission on timescales from hours to approximately 12 days of broad gamma-ray lines at energies approximately 400 keV, which were reported by the High Energy Astronomy Observatory (HEAO) 1 and SIGMA experiments from two sources lying toward the Galactic center. The lines have been interpreted as the product of the annihilation of positrons in pair plasmas surrounding the black hole candidate 1E 1740.7-2942 and the X-ray binary 1H 1822-371. Our results from a combined exposure of approximately 1.5 x 10(exp 7)s provide no convincing evidence for transient emission of this line on any timescale between approximately 9 hr and approximately 1 yr. Our 3 sigma upper limits on the line flux during approximately 12 day intervals are characteristically 4.8 x 10(exp -3) photon/sq cm/s, while for approximately 1 day intervals our 3 sigma upper limits are characteristically 4.9 x 10(exp -3) photon/sq cm/s. These results imply a duty cycle of less than 1.3% for the transient line measured from 1H 1822-371 during a approximately 3 week interval in 1977 by HEAO 1, and a duty cycle of less than or = 0.8% for the transient line detected in 1990 and 1992 from 1E 1740.7-2942 on approximately 1 day timescales by SIGMA.

Geometrical-optics approximation of forward scattering by coated particles.

PubMed

Xu, Feng; Cai, Xiaoshu; Ren, Kuanfang

2004-03-20

By means of geometrical optics we present an approximation algorithm with which to accelerate the computation of scattering intensity distribution within a forward angular range (0 degrees-60 degrees) for coated particles illuminated by a collimated incident beam. Phases of emerging rays are exactly calculated to improve the approximation precision. This method proves effective for transparent and tiny absorbent particles with size parameters larger than 75 but fails to give good approximation results at scattering angles at which refractive rays are absent. When the absorption coefficient of a particle is greater than 0.01, the geometrical optics approximation is effective only for forward small angles, typically less than 10 degrees or so.

Fundamentals and Recent Developments in Approximate Bayesian Computation

PubMed Central

Lintusaari, Jarno; Gutmann, Michael U.; Dutta, Ritabrata; Kaski, Samuel; Corander, Jukka

2017-01-01

Abstract Bayesian inference plays an important role in phylogenetics, evolutionary biology, and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtainable. Approximate Bayesian computation (ABC) refers to a family of algorithms for approximate inference that makes a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of ABC, review the classical algorithms, and highlight recent developments. [ABC; approximate Bayesian computation; Bayesian inference; likelihood-free inference; phylogenetics; simulator-based models; stochastic simulation models; tree-based models.] PMID:28175922

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Facial approximation-from facial reconstruction synonym to face prediction paradigm.

PubMed

Stephan, Carl N

2015-05-01

Facial approximation was first proposed as a synonym for facial reconstruction in 1987 due to dissatisfaction with the connotations the latter label held. Since its debut, facial approximation's identity has morphed as anomalies in face prediction have accumulated. Now underpinned by differences in what problems are thought to count as legitimate, facial approximation can no longer be considered a synonym for, or subclass of, facial reconstruction. Instead, two competing paradigms of face prediction have emerged, namely: facial approximation and facial reconstruction. This paper shines a Kuhnian lens across the discipline of face prediction to comprehensively review these developments and outlines the distinguishing features between the two paradigms. © 2015 American Academy of Forensic Sciences.

High Performance Composite Dielectric Ink for Ultracapacitors

NASA Technical Reports Server (NTRS)

Rolin, Terry D. (Inventor); Hill, Curtis W. (Inventor)

2017-01-01

The present invention is a dielectric ink and means for printing using said ink. Approximately 10-20% of the ink is a custom organic vehicle made of a polar solvent and a binder. Approximately 30-70% of the ink is a dielectric powder having an average particle diameter of approximately 10-750 nm. Approximately 5-15% of the ink is a dielectric constant glass. Approximately 10-35% of the ink is an additional amount of solvent. The ink is deposited on a printing substrate to form at least one printed product, which is then dried and cured to remove the solvent and binder, respectively. The printed product then undergoes sintering in an inert gas atmosphere.

Approximation for discrete Fourier transform and application in study of three-dimensional interacting electron gas.

PubMed

Yan, Xin-Zhong

2011-07-01

The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation efficiency with several orders without losing accuracy. As an example, we apply the algorithm to study the three-dimensional interacting electron gas under the renormalized-ring-diagram approximation where the Green's function needs to be self-consistently solved. We present the results for the chemical potential, compressibility, free energy, entropy, and specific heat of the system. The ground-state energy obtained by the present calculation is compared with the existing results of Monte Carlo simulation and random-phase approximation.

Mean-field approximation for spacing distribution functions in classical systems

NASA Astrophysics Data System (ADS)

González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.

2012-01-01

We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.

Local thermodynamic mapping for effective liquid density-functional theory

NASA Technical Reports Server (NTRS)

Kyrlidis, Agathagelos; Brown, Robert A.

1992-01-01

The structural-mapping approximation introduced by Lutsko and Baus (1990) in the generalized effective-liquid approximation is extended to include a local thermodynamic mapping based on a spatially dependent effective density for approximating the solid phase in terms of the uniform liquid. This latter approximation, called the local generalized effective-liquid approximation (LGELA) yields excellent predictions for the free energy of hard-sphere solids and for the conditions of coexistence of a hard-sphere fcc solid with a liquid. Moreover, the predicted free energy remains single valued for calculations with more loosely packed crystalline structures, such as the diamond lattice. The spatial dependence of the weighted density makes the LGELA useful in the study of inhomogeneous solids.

On the integration of reinforcement learning and approximate reasoning for control

NASA Technical Reports Server (NTRS)

Berenji, Hamid R.

1991-01-01

The author discusses the importance of strengthening the knowledge representation characteristic of reinforcement learning techniques using methods such as approximate reasoning. The ARIC (approximate reasoning-based intelligent control) architecture is an example of such a hybrid approach in which the fuzzy control rules are modified (fine-tuned) using reinforcement learning. ARIC also demonstrates that it is possible to start with an approximately correct control knowledge base and learn to refine this knowledge through further experience. On the other hand, techniques such as the TD (temporal difference) algorithm and Q-learning establish stronger theoretical foundations for their use in adaptive control and also in stability analysis of hybrid reinforcement learning and approximate reasoning-based controllers.

Variationally consistent approximation scheme for charge transfer

NASA Technical Reports Server (NTRS)

Halpern, A. M.

1978-01-01

The author has developed a technique for testing various charge-transfer approximation schemes for consistency with the requirements of the Kohn variational principle for the amplitude to guarantee that the amplitude is correct to second order in the scattering wave functions. Applied to Born-type approximations for charge transfer it allows the selection of particular groups of first-, second-, and higher-Born-type terms that obey the consistency requirement, and hence yield more reliable approximation to the amplitude.

A simple approximation for the current-voltage characteristics of high-power, relativistic diodes

DOE PAGES

Ekdahl, Carl

2016-06-10

A simple approximation for the current-voltage characteristics of a relativistic electron diode is presented. The approximation is accurate from non-relativistic through relativistic electron energies. Although it is empirically developed, it has many of the fundamental properties of the exact diode solutions. Lastly, the approximation is simple enough to be remembered and worked on almost any pocket calculator, so it has proven to be quite useful on the laboratory floor.

Uniform analytic approximation of Wigner rotation matrices

NASA Astrophysics Data System (ADS)

Hoffmann, Scott E.

2018-02-01

We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.

Method of forming pointed structures

NASA Technical Reports Server (NTRS)

Pugel, Diane E. (Inventor)

2011-01-01

A method of forming an array of pointed structures comprises depositing a ferrofluid on a substrate, applying a magnetic field to the ferrofluid to generate an array of surface protrusions, and solidifying the surface protrusions to form the array of pointed structures. The pointed structures may have a tip radius ranging from approximately 10 nm to approximately 25 micron. Solidifying the surface protrusions may be carried out at a temperature ranging from approximately 10 degrees C. to approximately 30 degrees C.

Locality of correlation in density functional theory

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

Burke, Kieron; Cancio, Antonio; Gould, Tim

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that E{sub C} → −A{sub C} ZlnZ +more » B{sub C}Z as Z → ∞, where Z is the atomic number, A{sub C} is known, and we estimate B{sub C} to be about 37 mhartree. The local density approximation yields A{sub C} exactly, but a very incorrect value for B{sub C}, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with B{sub C} a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.« less

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

Taylor, J.A.; Brasseur, G.P.; Zimmerman, P.R.

Using the hydroxyl radical field calibrated to the methyl chloroform observations, the globally averaged release of methane and its spatial and temporal distribution were investigated. Two source function models of the spatial and temporal distribution of the flux of methane to the atmosphere were developed. The first model was based on the assumption that methane is emitted as a proportion of net primary productivity (NPP). With the average hydroxyl radical concentration fixed, the methane source term was computed as {approximately}623 Tg CH{sub 4}, giving an atmospheric lifetime for methane {approximately}8.3 years. The second model identified source regions for methane frommore » rice paddies, wetlands, enteric fermentation, termites, and biomass burning based on high-resolution land use data. This methane source distribution resulted in an estimate of the global total methane source of {approximately}611 Tg CH{sub 4}, giving an atmospheric lifetime for methane {approximately}8.5 years. The most significant difference between the two models were predictions of methane fluxes over China and South East Asia, the location of most of the world's rice paddies. Using a recent measurement of the reaction rate of hydroxyl radical and methane leads to estimates of the global total methane source for SF1 of {approximately}524 Tg CH{sub 4} giving an atmospheric lifetime of {approximately}10.0 years and for SF2{approximately}514 Tg CH{sub 4} yielding a lifetime of {approximately}10.2 years.« less

Structure and thermodynamics of a simple fluid

NASA Astrophysics Data System (ADS)

Stell, G.; Weis, J. J.

1980-02-01

Monte Carlo results are found for a simple fluid with a pair potential consisting of a hard-sphere core and a Lennard-Jones attractive tail. They are compared with several of the most promising recent theoretical treatments of simple fluids, all of which involve the decomposition of the pair potential into a hard-sphere-core term and an attractive-tail term. This direct comparison avoids the use of a second perturbation scheme associated with softening the core, which would introduce an ambiguity in the significance of the differences found between the theoretical and Monte Carlo results. The study includes the optimized random-phase approximation (ORPA) and exponential (EXP) approximations of Andersen and Chandler, an extension of the latter approximation to nodal order three (the N3 approximation), the linear-plus-square (LIN + SQ) approximation of Høye and Stell, the renormalized hypernetted chain (RHNC) approximation of Lado, and the quadratic (QUAD) approximation suggested by second-order self-consistent Γ ordering, the lowest order of which is identical to the ORPA. As anticipated on the basis of earlier studies, it is found that the EXP approximation yields radial distribution functions and structure factors of excellent overall accuracy in the liquid state, where the RHNC results are also excellent and the EXP, QUAD, and LIN + SQ results prove to be virtually indistinguishable from one another. For all the approximations, however, the thermodynamics from the compressibility relation are poor and the virial-theorem results are not uniformly reliable. Somewhat more surprisingly, it is found that the EXP results yield a negative structure factor S(k) for very small k in the liquid state and poor radial distribution functions at low densities. The RHNC results are nowhere worse than the EXP results and in some states (e.g., at low densities) much better. In contrast, the N3 results are better in some respects than the EXP results but worse in others. The authors briefly comment on the RHNC and EXP approximations applied to the full Lennard-Jones potential, for which the EXP approximation appears somewhat improved in the liquid state as a result of the softening of the potential core.

libFLASM: a software library for fixed-length approximate string matching.

PubMed

Ayad, Lorraine A K; Pissis, Solon P P; Retha, Ahmad

2016-11-10

Approximate string matching is the problem of finding all factors of a given text that are at a distance at most k from a given pattern. Fixed-length approximate string matching is the problem of finding all factors of a text of length n that are at a distance at most k from any factor of length ℓ of a pattern of length m. There exist bit-vector techniques to solve the fixed-length approximate string matching problem in time [Formula: see text] and space [Formula: see text] under the edit and Hamming distance models, where w is the size of the computer word; as such these techniques are independent of the distance threshold k or the alphabet size. Fixed-length approximate string matching is a generalisation of approximate string matching and, hence, has numerous direct applications in computational molecular biology and elsewhere. We present and make available libFLASM, a free open-source C++ software library for solving fixed-length approximate string matching under both the edit and the Hamming distance models. Moreover we describe how fixed-length approximate string matching is applied to solve real problems by incorporating libFLASM into established applications for multiple circular sequence alignment as well as single and structured motif extraction. Specifically, we describe how it can be used to improve the accuracy of multiple circular sequence alignment in terms of the inferred likelihood-based phylogenies; and we also describe how it is used to efficiently find motifs in molecular sequences representing regulatory or functional regions. The comparison of the performance of the library to other algorithms show how it is competitive, especially with increasing distance thresholds. Fixed-length approximate string matching is a generalisation of the classic approximate string matching problem. We present libFLASM, a free open-source C++ software library for solving fixed-length approximate string matching. The extensive experimental results presented here suggest that other applications could benefit from using libFLASM, and thus further maintenance and development of libFLASM is desirable.

Baryonic dark clusters in galactic halos and their observable consequences

NASA Technical Reports Server (NTRS)

Wasserman, Ira; Salpeter, Edwin E.

1994-01-01

We consider the possibility that approximately 10% of the mass of a typical galaxy halo is in the form of massive (approximately 10(exp 7) solar masses), compact (escape speeds approximately 100 km/s) baryonic clusters made of neutron stars (approximately 10% by mass), black holes (less than or approximately equal to 1%) and brown dwarfs, asteroids, and other low-mass debris (approximately 90%). These general properties are consistent with several different observational and phenomenological constraints on cluster properties subject to the condition that neutron stars comprise approximately 1% of the total halo mass. Such compact, dark clusters could be the sites of a variety of collisional phenomena involving neutron stars. We find that integrated out to the Hubble distance approximately one neutron star-neutron star or neutron star-black hole collision occurs daily. Of order 0.1-1 asteroid-neutron star collisions may also happen daily in the halo of the Milky Way if there is roughly equal cluster mass per logarithmic particle mass interval between asteroids and brown dwarfs. These event rates are comparable to the frequency of gamma-ray burst detections by the Burst and Transient Source Experiment (BATSE) on the Compton Observatory, implying that if dark halo clusters are the sites of most gamma-ray bursts, perhaps approximately 90% of all bursts are extragalactic, but approximately 10% are galactic. It is possible that dark clusters of the kind discussed here could be detected directly by the Infrared Space Observatory (ISO) or Space Infrared Telescope Facility (SIRTF). If the clusters considered in this paper exist, they should produce spatially correlated gravitational microlensing of stars in the Large Magellanic Cloud (LMC). If 10% of the halo is in the form of dark baryonic clusters, and the remaining 90% is in brown dwarfs and other dark objects which are either unclustered or collected into low-mass clusters, then we expect that two events within approximately 1 min of one another are likely to be seen after a total of order 20-30 microlenses have been detected.

Integrating flood modelling in a hydrological catchment model: flow approximations and spatial resolution.

NASA Astrophysics Data System (ADS)

van den Bout, Bastian; Jetten, Victor

2017-04-01

Within hydrological models, flow approximations are commonly used to reduce computation time. The validity of these approximations is strongly determined by flow height, flow velocity, the spatial resolution of the model, and by the manner in which flow routing is implemented. The assumptions of these approximations can furthermore limit emergent behavior, and influence flow behavior under space-time scaling. In this presentation, the validity and performance of the kinematic, diffusive and dynamic flow approximations are investigated for use in a catchment-based flood model. Particularly, the validity during flood events and for varying spatial resolutions is investigated. The OpenLISEM hydrological model is extended to implement these flow approximations and channel flooding based on dynamic flow. The kinematic routing uses a predefined converging flow network, the diffusive and dynamic routing uses a 2D flow solution over a DEM. The channel flow in all cases is a 1D kinematic wave approximation. The flow approximations are used to recreate measured discharge in three catchments of different size in China, Spain and Italy, among which is the hydrograph of the 2003 flood event in the Fella river basin (Italy). Furthermore, spatial resolutions are varied for the flood simulation in order to investigate the influence of spatial resolution on these flow approximations. Results show that the kinematic, diffusive and dynamic flow approximation provide least to highest accuracy, respectively, in recreating measured temporal variation of the discharge. Kinematic flow, which is commonly used in hydrological modelling, substantially over-estimates hydrological connectivity in the simulations with a spatial resolution of below 30 meters. Since spatial resolutions of models have strongly increased over the past decades, usage of routed kinematic flow should be reconsidered. In the case of flood events, spatial modelling of kinematic flow substantially over-estimates hydrological connectivity and flow concentration, leading to significant errors. The combination of diffusive or dynamic overland flow and dynamic channel flooding provides high accuracy in recreating the 2003 Fella river flood event. Finally, flow approximations substantially influenced the predictive potential of the (flash) flood model.

Multifrequency observations of the radio continuum emission from NGC 253. 1: Magnetic fields and rotation measures in the bar and halo

NASA Astrophysics Data System (ADS)

Beck, R.; Carilli, C. L.; Holdaway, M. A.; Klein, U.

1994-12-01

Radio continuum observations of the spiral galaxy NGC 253 with the Effelsberg and Very Large Array (VLA) telescopes reveal polarized emission from the bar and halo regions. Within the bar Faraday depolarization is strong at 1.5 and 5 GHz, due to ionized gas with ne approximately equal 0.1 - 3/cu cm which is mixed with turbulent magnetic fields of approximately equal 17 microG estimated strength. Even at 10 GHz the degree of polarization in the bar is low (only approximately equal 5% east and approximately equal 2% west of the nucleus) due to beam depolarization by unresolved tangled fields. In contrast, the magnetic fields in the halo are highly uniform, as indicated by fractional polarizations up to 40% at 10 GHz. Faraday depolarization in the halo at 1.5 GHz calls for a warm, clumpy gas component with ne approximately equal 0.02/cu cm and approximately equal 6 microG turbulent fields. We detected Faraday rotation in the bar, with rotation measures absolute value of RM approximately equal 100 rad/sq m (between 10 and 5 GHz) having different signs east and west of the nucleus. Below 5 GHz Faraday rotation is strongly reduced by the limited transparency for polarized emission in the bar. Faraday rotation in the halo in two regions at approximately 5 kpc above and below the plane with RM approximately equal -7 rad/sq m between 10 and 1.5 GHz can be ascribed to hot gas with mean value of ne approximately equal 0.002/cu cm and uniform fields along the line of sight of mean value of Bu parallel approximately equal -2 microG. The magnetic field structure in the bar and halo of NGC 253 is best described by the quadrupole-type dynamo mode SO, with a ring-like field in the bar and a field mainly parallel to the plane in a co-rotating halo. A major perturbation occurs in the east where the field is perpendicular to the plane and follows a 'spur'. The galactic wind is suppressed by the dominating plane-parallel field, except along the spur.

Rational approximation to e to the -x power with negative poles

NASA Technical Reports Server (NTRS)

Cuthill, E.

1977-01-01

MACSYMA was applied to the generation of an expansion in terms of Laguerre polynomials to obtain approximations to e to the -x power on 0, infinity. These approximations are compared with those developed by Saff, Schonhage, and Varga.

Flexibility of "polyunsaturated fatty acid chains" and peptide backbones: A comparative ab initio study.

PubMed

Law, Jacqueline M S; Setiadi, David H; Chass, Gregory A; Csizmadia, Imre G; Viskolcz, Béla

2005-01-27

The conformational properties of omega-3 type of polyunsaturated fatty acid (PUFA) chains and their fragments were studied using Hartree-Fock (RHF/3-21G) and DFT (B3LYP/6-31G(d)) methods. Comparisons between a unit (U) fragment of the PUFA chain and a mono N-Ac-glycine-NHMe residue show that both structures have the same sequence of sp2-sp3-sp2 atoms. The flexibility of PUFA originates in the internal rotation about the above pairs of sigma bonds. Therefore, potential energy surfaces (PESs) were generated by a scan around the terminal dihedral angles (phi t1 and phi t2) as well as the phi 1 and psi 1 dihedrals of both 1U congeners (Me-CHCH-CH2-CHCHMe and MeCONH-CH2-CONHMe) at the RHF/3-21G level of theory. An interesting similarity was found in the flexibility between the cis allylic structure and the trans peptide models. A flat landscape can be seen in the cis 1U (hepta-2,5-diene) surface, implying that several conformations are expected to be found in this (PES). An exhaustive search carried out on the 1U and 2U models revealed that straight chain structures such as trans and cis beta (phi 1 approximately psi 1 approximately 120 degrees; phi 2 approximately psi 2 approximately -120 degrees) or trans and cis extended (phi 1 approximately psi 1 approximately phi 2 approximately psi 2 approximately 120 degrees) can be formed at the lowest energy of both isomers. However, forming helical structures, such as trans helix (phi 1 approximately -120 degrees, psi 1 approximately 12 degrees; phi 2 approximately -120 degrees, psi 2 approximately 12 degrees) or cis helix (phi 1 approximately -130 degrees, psi 1 approximately 90 degrees; phi 2 approximately -145 degrees, psi 2 approximately 90 degrees) will require more energy. These six conformations, found in 2U, were selected to construct longer chains such as 3U, 4U, 5U, and 6U to obtain the thermochemistry of secondary structures. The variation in the extension or compression of the chain length turned out to be a factor of 2 between the helical and nonhelical structures. The inside diameter of the "tube" of cis helix turned out to be 3.5 A after discounting the internal H atoms. Thermodynamic functions were computed at the B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d). The cis-trans isomerization energy of 1.7 +/- 0.2 kcal mol(-1) unit(-1) for all structure pairs indicates that the conformer selection was consistent. A folding energy of 0.5 +/- 0.1 kcal mol(-1) unit(-1) has been extracted from the energy comparison of the helices and most extended nonhelical structures. The entropy change associated with the folding (Delta S(folding)) is decreases faster with the degree of polymerization (n) for the cis than for the trans isomer. As a consequence, the linear relationships between (Delta G(folding)) and n for the cis and trans isomer crossed at about n = 3. This suggested that the naturally occurring cis isomer less ready to fold than the trans isomer since a greater degree of organization is exhibited by the cis isomer during the folding process. The result of this work leads to the question within the group additivity rule: could the method applied in our study of the folding of polyallylic hydrocarbons be useful in investigating the thermochemistry of protein folding?

Deep HST imaging of distant weak radio and field galaxies

NASA Technical Reports Server (NTRS)

Windhorst, R. A.; Gordon, J. M.; Pascarelle, S. M.; Schmidtke, P. C.; Keel, W. C.; Burkey, J. M.; Dunlop, J. S.

1994-01-01

We present deep Hubble Space Telescope (HST) Wide-Field Camera (WFC) V- and I-band images of three distant weak radio galaxies with z = 0.311-2.390 and seven field galaxies with z = 0.131-0.58. The images were deconvolved with both the Lucy and multiresolution CLEAN methods, which yield a restoring Full Width at Half Maximum (FWHM) of less than or equal to 0.2 sec, (nearly) preserve photons and signal-to-noise ratio at low spatial frequencies, and produce consistent light profiles down to our 2 sigma surface brightness sensitivity limit of V approximately 27.2 and I approximately 25.9 mag/sq arcsec. Multi-component image modeling was used to provide deconvolution-independent estimates of structural parameters for symmetric galaxies. We present 12-band (m(sub 2750) UBVRIgriJHK) photometry for a subset of the galaxies and bootstrap the unknown FOC/48 zero point at 2750 A in three independent ways (yielding m(sub 2750) = 21.34 +/- 0.09 mag for 1.0 e(-)/s). Two radio galaxies with z = 0.311 and 0.528, as well as one field galaxy with z = 0.58, have the colors and spectra of early-type galaxies, and a(exp 1/4)-like light profiles in the HST images. The two at z greater than 0.5 have little or no color gradients in V - I and are likely giant ellipticals, while the z = 0.311 radio galaxy has a dim exponential disk and is likely an S0. Six of the seven field galaxies have light profiles that indicate (small) inner bulges following a(exp 1/4) laws and outer exponential disks, both with little or no color gradients. These are (early-type) spiral galaxies with z = 0.131-0.528. About half have faint companions or bars. One shows lumpy structure, possibly a merger. The compact narrow-line galaxy 53W002 at z = 2.390 has less than or = 30% +/- 10% of its HST V and I flux in the central kiloparsec (due to its weak Active Galactic Nucleus (AGN)). Most of its light (V approximately equal to 23.3) occurs in a symmetric envelope with a regular a(exp 1/4)-like profile of effective radius a approximately equal to 1.1 sec (approximately equal to 12 kpc for H(sub 0) = 50, q(sub 0) = 0.1. Its (HST) V - I color varies at most from approximately 0.3 mag at a approximately equal to 0.2 sec to approximately 1.2 mag at a approximately greater than 0.4 sec, and possibly to approximately greater than 2.2 mag at a approximately greater than 1.2 sec. Together with its I - K color (approximately equal to 2.5 mag for a approximately greater than 1.0 sec-2.0 sec), this is consistent with an aging stellar population approximately 0.3-0.5 Gyr old in the galaxy center (a approx. less than 2 kpc radius), and possibly approximately 0.5-1.0 Gyr old at a approximately greater than 10 kpc radius. While its outer part may thus have started to collapse at z = 2.5-4, its inner part still is aligned with its redshifted Ly(alpha) cloud and its radio axis, possibly caused by star formation associated with the radio jet, or by reflection from its AGN cone.

Extension of many-body theory and approximate density functionals to fractional charges and fractional spins.

PubMed

Yang, Weitao; Mori-Sánchez, Paula; Cohen, Aron J

2013-09-14

The exact conditions for density functionals and density matrix functionals in terms of fractional charges and fractional spins are known, and their violation in commonly used functionals has been shown to be the root of many major failures in practical applications. However, approximate functionals are designed for physical systems with integer charges and spins, not in terms of the fractional variables. Here we develop a general framework for extending approximate density functionals and many-electron theory to fractional-charge and fractional-spin systems. Our development allows for the fractional extension of any approximate theory that is a functional of G(0), the one-electron Green's function of the non-interacting reference system. The extension to fractional charge and fractional spin systems is based on the ensemble average of the basic variable, G(0). We demonstrate the fractional extension for the following theories: (1) any explicit functional of the one-electron density, such as the local density approximation and generalized gradient approximations; (2) any explicit functional of the one-electron density matrix of the non-interacting reference system, such as the exact exchange functional (or Hartree-Fock theory) and hybrid functionals; (3) many-body perturbation theory; and (4) random-phase approximations. A general rule for such an extension has also been derived through scaling the orbitals and should be useful for functionals where the link to the Green's function is not obvious. The development thus enables the examination of approximate theories against known exact conditions on the fractional variables and the analysis of their failures in chemical and physical applications in terms of violations of exact conditions of the energy functionals. The present work should facilitate the calculation of chemical potentials and fundamental bandgaps with approximate functionals and many-electron theories through the energy derivatives with respect to the fractional charge. It should play an important role in developing accurate approximate density functionals and many-body theory.

Transport of Biomass Burning Emissions from Southern Africa

NASA Technical Reports Server (NTRS)

Sinha, Parikhit; Jaegle,Lyatt; Hobbs, Peter V.; Liang, Qing

2004-01-01

The transport of biomass burning emissions from southern Africa to the neighboring Atlantic and Indian Oceans during the dry season (May-October) of 2000 is characterized using ground, ozonesonde, and aircraft measurements of carbon monoxide (CO) and ozone (O3) in and around southern Africa, together with the GEOS-CHEM global model of tropospheric chemistry. The model shows a positive bias of approximately 20% for CO and a negative bias of approximately 10-25% for O3 at oceanic sites downwind of fire emissions. Near areas of active fire emissions the model shows a negative bias of approximately 60% and approximately 30% for CO and O3, respectively, likely due to the coarse spatial (2 deg. x 2.5 deg.) and temporal (monthly) resolution of the model compared to that of active fires. On average, from 1994 to 2000, approximately 60 Tg of carbon monoxide (CO) from biomass burning in southern Africa was transported eastward to the Indian Ocean across the latitude band 0 deg. -60 S during the 6 months of the dry season. Over the same time period, approximately 40 Tg of CO from southern African biomass burning was transported westward to the Atlantic Ocean over the latitudes 0 deg. -20 S during the 6-month dry season, but most of that amount was transported back eastward over higher latitudes to the south (21 deg. -60 S). Eastward transport of biomass burning emissions from southern Africa enhances CO concentrations by approximately 4- 13 ppbv per month over the southern subtropical Indian Ocean during the dry season, with peak enhancements in September. Carbon monoxide from southern African and South American biomass burning is seen in the model simulations as far away as Australia, contributing approximately 8 ppbv and approximately 12-15 ppbv CO, respectively, and thus explaining the approximately 20- 25 ppbv observed enhancement of CO over Melbourne in mid-September 2000.

Femtosecond/picosecond time-resolved fluorescence study of hydrophilic polymer fine particles.

PubMed

Nanjo, Daisuke; Hosoi, Haruko; Fujino, Tatsuya; Tahara, Tahei; Korenaga, Takashi

2007-03-22

Femtosecond/picosecond time-resolved fluorescence study of hydrophilic polymer fine particles (polyacrylamide, PAAm) was reported. Ultrafast fluorescence dynamics of polymer/water solution was monitored using a fluorescent probe molecule (C153). In the femtosecond time-resolved fluorescence measurement at 480 nm, slowly decay components having lifetimes of tau(1) approximately 53 ps and tau(2) approximately 5 ns were observed in addition to rapid fluorescence decay. Picosecond time-resolved fluorescence spectra of C153/PAAm/H2O solution were also measured. In the time-resolved fluorescence spectra of C153/PAAm/H2O, a peak shift from 490 to 515 nm was measured, which can be assigned to the solvation dynamics of polymer fine particles. The fluorescence peak shift was related to the solvation response function and two time constants were determined (tau(3) approximately 50 ps and tau(4) approximately 467 ps). Therefore, the tau(1) component observed in the femtosecond time-resolved fluorescence measurement was assigned to the solvation dynamics that was observed only in the presence of polymer fine particles. Rotational diffusion measurements were also carried out on the basis of the picosecond time-resolved fluorescence spectra. In the C153/PAAm/H2O solution, anisotropy decay having two different time constants was also derived (tau(6) approximately 76 ps and tau(7) approximately 676 ps), indicating the presence of two different microscopic molecular environments around the polymer surface. Using the Stokes-Einstein-Debye (SED) equation, microscopic viscosity around the polymer surface was evaluated. For the area that gave a rotational diffusion time of tau(6) approximately 76 ps, the calculated viscosity is approximately 1.1 cP and for tau(7) approximately 676 ps, it is approximately 10 cP. The calculated viscosity values clearly revealed that there are two different molecular environments around the polyacrylamide fine particles.

Extinction efficiencies from DDA calculations solved for finite circular cylinders and disks

NASA Technical Reports Server (NTRS)

Withrow, J. R.; Cox, S. K.

1993-01-01

One of the most commonly noted uncertainties with respect to the modeling of cirrus clouds and their effect upon the planetary radiation balance is the disputed validity of the use of Mie scattering results as an approximation to the scattering results of the hexagonal plates and columns found in cirrus clouds. This approximation has historically been a kind of default, a result of the lack of an appropriate analytical solution of Maxwell's equations to particles other than infinite cylinders and spheroids. Recently, however, the use of such approximate techniques as the Discrete Dipole Approximation has made scattering solutions on such particles a computationally intensive but feasible possibility. In this study, the Discrete Dipole Approximation (DDA) developed by Flatau (1992) is used to find such solutions for homogeneous, circular cylinders and disks. This can serve to not only assess the validity of the current radiative transfer schemes which are available for the study of cirrus but also to extend the current approximation of equivalent spheres to an approximation of second order, homogeneous finite circular cylinders and disks. The results will be presented in the form of a single variable, the extinction efficiency.

Quasi-CW diode-pumped self-starting adaptive laser with self-Q-switched output.

PubMed

Smith, G; Damzen, M J

2007-05-14

An investigation is made into a quasi-CW (QCW) diode-pumped holographic adaptive laser utilising an ultra high gain (approximately 10(4)) Nd:YVO(4) bounce amplifier. The laser produces pulses at 1064 nm with energy approximately 0.6 mJ, duration <3 ns and peak power approximately 200 kW, with high stability, via self-Q-switching effects due to the transient dynamics of the writing and replay of the gain hologram for each pump pulse. The system produces a near-diffraction-limited output with M(2)<1.3 and operates with a single longitudinal mode. In a further adaptive laser configuration, the output was amplified to obtain pulses of approximately 5.6 mJ energy, approximately 7 ns duration and approximately 1 MW peak power. The output spatial quality is also M(2)<1.3 with SLM operation. Up to 2.9 mJ pulse energy of frequency doubled green (532 nm) radiation is obtained, using an LBO crystal, representing approximately 61% conversion efficiency. This work shows that QCW diode-pumped self-adaptive holographic lasers can provide a useful source of high peak power, short duration pulses with excellent spatial quality and narrow linewidth spectrum.

Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

NASA Astrophysics Data System (ADS)

Kilcrease, D. P.; Brookes, S.

2013-12-01

The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. A simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure for the Born cross-sections that employs the Elwert-Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. We also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.

Minimal-Approximation-Based Decentralized Backstepping Control of Interconnected Time-Delay Systems.

PubMed

Choi, Yun Ho; Yoo, Sung Jin

2016-12-01

A decentralized adaptive backstepping control design using minimal function approximators is proposed for nonlinear large-scale systems with unknown unmatched time-varying delayed interactions and unknown backlash-like hysteresis nonlinearities. Compared with existing decentralized backstepping methods, the contribution of this paper is to design a simple local control law for each subsystem, consisting of an actual control with one adaptive function approximator, without requiring the use of multiple function approximators and regardless of the order of each subsystem. The virtual controllers for each subsystem are used as intermediate signals for designing a local actual control at the last step. For each subsystem, a lumped unknown function including the unknown nonlinear terms and the hysteresis nonlinearities is derived at the last step and is estimated by one function approximator. Thus, the proposed approach only uses one function approximator to implement each local controller, while existing decentralized backstepping control methods require the number of function approximators equal to the order of each subsystem and a calculation of virtual controllers to implement each local actual controller. The stability of the total controlled closed-loop system is analyzed using the Lyapunov stability theorem.

Pair and triplet approximation of a spatial lattice population model with multiscale dispersal using Markov chains for estimating spatial autocorrelation.

PubMed

Hiebeler, David E; Millett, Nicholas E

2011-06-21

We investigate a spatial lattice model of a population employing dispersal to nearest and second-nearest neighbors, as well as long-distance dispersal across the landscape. The model is studied via stochastic spatial simulations, ordinary pair approximation, and triplet approximation. The latter method, which uses the probabilities of state configurations of contiguous blocks of three sites as its state variables, is demonstrated to be greatly superior to pair approximations for estimating spatial correlation information at various scales. Correlations between pairs of sites separated by arbitrary distances are estimated by constructing spatial Markov processes using the information from both approximations. These correlations demonstrate why pair approximation misses basic qualitative features of the model, such as decreasing population density as a large proportion of offspring are dropped on second-nearest neighbors, and why triplet approximation is able to include them. Analytical and numerical results show that, excluding long-distance dispersal, the initial growth rate of an invading population is maximized and the equilibrium population density is also roughly maximized when the population spreads its offspring evenly over nearest and second-nearest neighboring sites. Copyright © 2011 Elsevier Ltd. All rights reserved.

Approximate l-fold cross-validation with Least Squares SVM and Kernel Ridge Regression

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

Edwards, Richard E; Zhang, Hao; Parker, Lynne Edwards

2013-01-01

Kernel methods have difficulties scaling to large modern data sets. The scalability issues are based on computational and memory requirements for working with a large matrix. These requirements have been addressed over the years by using low-rank kernel approximations or by improving the solvers scalability. However, Least Squares Support VectorMachines (LS-SVM), a popular SVM variant, and Kernel Ridge Regression still have several scalability issues. In particular, the O(n^3) computational complexity for solving a single model, and the overall computational complexity associated with tuning hyperparameters are still major problems. We address these problems by introducing an O(n log n) approximate l-foldmore » cross-validation method that uses a multi-level circulant matrix to approximate the kernel. In addition, we prove our algorithm s computational complexity and present empirical runtimes on data sets with approximately 1 million data points. We also validate our approximate method s effectiveness at selecting hyperparameters on real world and standard benchmark data sets. Lastly, we provide experimental results on using a multi-level circulant kernel approximation to solve LS-SVM problems with hyperparameters selected using our method.« less

Revealing the face of an ancient Egyptian: synthesis of current and traditional approaches to evidence-based facial approximation.

PubMed

Lindsay, Kaitlin E; Rühli, Frank J; Deleon, Valerie Burke

2015-06-01

The technique of forensic facial approximation, or reconstruction, is one of many facets of the field of mummy studies. Although far from a rigorous scientific technique, evidence-based visualization of antemortem appearance may supplement radiological, chemical, histological, and epidemiological studies of ancient remains. Published guidelines exist for creating facial approximations, but few approximations are published with documentation of the specific process and references used. Additionally, significant new research has taken place in recent years which helps define best practices in the field. This case study records the facial approximation of a 3,000-year-old ancient Egyptian woman using medical imaging data and the digital sculpting program, ZBrush. It represents a synthesis of current published techniques based on the most solid anatomical and/or statistical evidence. Through this study, it was found that although certain improvements have been made in developing repeatable, evidence-based guidelines for facial approximation, there are many proposed methods still awaiting confirmation from comprehensive studies. This study attempts to assist artists, anthropologists, and forensic investigators working in facial approximation by presenting the recommended methods in a chronological and usable format. © 2015 Wiley Periodicals, Inc.

Approximations of e and ?: An Exploration

ERIC Educational Resources Information Center

Brown, Philip R.

2017-01-01

Fractional approximations of e and p are discovered by searching for repetitions or partial repetitions of digit strings in their expansions in different number bases. The discovery of such fractional approximations is suggested for students and teachers as an entry point into mathematics research.

Modification of Surface Energy via Direct Laser Ablative Surface Patterning

NASA Technical Reports Server (NTRS)

Wohl, Christopher J., Jr. (Inventor); Belcher, Marcus A. (Inventor); Connell, John W. (Inventor); Hopkins, John W. (Inventor)

2015-01-01

Surface energy of a substrate is changed without the need for any template, mask, or additional coating medium applied to the substrate. At least one beam of energy directly ablates a substrate surface to form a predefined topographical pattern at the surface. Each beam of energy has a width of approximately 25 micrometers and an energy of approximately 1-500 microJoules. Features in the topographical pattern have a width of approximately 1-500 micrometers and a height of approximately 1.4-100 micrometers.

Interpretation of ES, CS, and IOS approximations within a translational--internal coupling scheme. IV. ES and IOS molecule--molecule cross sections

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

Snider, R.F.; Parvatiyar, M.G.

1981-05-15

Properties of energy sudden and infinite order sudden translational--internal reduced S matrices are given for general molecule--molecule collisions. Formal similarities with the distorted wave Born approximation are discussed. Structural simplifications of energy dependent and kinetic cross sections associated with making the ES approximation are described. Conceptual difficulties associated with applying the ES and IOS approximations to kinetic processes dominated by energetically inelastic collisions are pointed out.

Comparison of techniques for approximating ocean bottom topography in a wave-refraction computer model

NASA Technical Reports Server (NTRS)

Poole, L. R.

1975-01-01

A study of the effects of using different methods for approximating bottom topography in a wave-refraction computer model was conducted. Approximation techniques involving quadratic least squares, cubic least squares, and constrained bicubic polynomial interpolation were compared for computed wave patterns and parameters in the region of Saco Bay, Maine. Although substantial local differences can be attributed to use of the different approximation techniques, results indicated that overall computed wave patterns and parameter distributions were quite similar.

On prediction of genetic values in marker-assisted selection.

PubMed Central

Lange, C; Whittaker, J C

2001-01-01

We suggest a new approximation for the prediction of genetic values in marker-assisted selection. The new approximation is compared to the standard approach. It is shown that the new approach will often provide substantially better prediction of genetic values; furthermore the new approximation avoids some of the known statistical problems of the standard approach. The advantages of the new approach are illustrated by a simulation study in which the new approximation outperforms both the standard approach and phenotypic selection. PMID:11729177

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

NASA Astrophysics Data System (ADS)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

Self-consistent approximation beyond the CPA: Part II

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

Kaplan, T.; Gray, L.J.

1981-08-01

In Part I, Professor Leath has described the substantial efforts to generalize the CPA. In this second part, a particular self-consistent approximation for random alloys developed by Kaplan, Leath, Gray, and Diehl is described. This approximation is applicable to diagonal, off-diagonal and environmental disorder, includes cluster scattering, and yields a translationally invariant and analytic (Herglotz) average Green's function. Furthermore Gray and Kaplan have shown that an approximation for alloys with short-range order can be constructed from this theory.

Partially Coherent Scattering in Stellar Chromospheres. Part 4; Analytic Wing Approximations

NASA Technical Reports Server (NTRS)

Gayley, K. G.

1993-01-01

Simple analytic expressions are derived to understand resonance-line wings in stellar chromospheres and similar astrophysical plasmas. The results are approximate, but compare well with accurate numerical simulations. The redistribution is modeled using an extension of the partially coherent scattering approximation (PCS) which we term the comoving-frame partially coherent scattering approximation (CPCS). The distinction is made here because Doppler diffusion is included in the coherent/noncoherent decomposition, in a form slightly improved from the earlier papers in this series.

The Development and Design of a Prototype Ultra High Pressure P-19 Firefighting Vehicle

DTIC Science & Technology

2007-02-03

the energizing affects of a delivery pressure 4 times (approximately 1200 psi) the magnitude of the standard system at the bumper turret nozzle...permanently extinguish a fire. The onboard CAF system is capable of 300 gpm delivery of foam at approximately 165 psi out of the bumper turret, and a...hand line flowing 45 gpm at approximately 165 psi also. The dry chemical system is designed to flow approximately 7 pps from the bumper turret, and 5

Statistical significance approximation in local trend analysis of high-throughput time-series data using the theory of Markov chains.

PubMed

Xia, Li C; Ai, Dongmei; Cram, Jacob A; Liang, Xiaoyi; Fuhrman, Jed A; Sun, Fengzhu

2015-09-21

Local trend (i.e. shape) analysis of time series data reveals co-changing patterns in dynamics of biological systems. However, slow permutation procedures to evaluate the statistical significance of local trend scores have limited its applications to high-throughput time series data analysis, e.g., data from the next generation sequencing technology based studies. By extending the theories for the tail probability of the range of sum of Markovian random variables, we propose formulae for approximating the statistical significance of local trend scores. Using simulations and real data, we show that the approximate p-value is close to that obtained using a large number of permutations (starting at time points >20 with no delay and >30 with delay of at most three time steps) in that the non-zero decimals of the p-values obtained by the approximation and the permutations are mostly the same when the approximate p-value is less than 0.05. In addition, the approximate p-value is slightly larger than that based on permutations making hypothesis testing based on the approximate p-value conservative. The approximation enables efficient calculation of p-values for pairwise local trend analysis, making large scale all-versus-all comparisons possible. We also propose a hybrid approach by integrating the approximation and permutations to obtain accurate p-values for significantly associated pairs. We further demonstrate its use with the analysis of the Polymouth Marine Laboratory (PML) microbial community time series from high-throughput sequencing data and found interesting organism co-occurrence dynamic patterns. The software tool is integrated into the eLSA software package that now provides accelerated local trend and similarity analysis pipelines for time series data. The package is freely available from the eLSA website: http://bitbucket.org/charade/elsa.

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

NASA Astrophysics Data System (ADS)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

5-10 GeV neutrinos from gamma-Ray burst fireballs

PubMed

Bahcall; Meszaros

2000-08-14

A gamma-ray burst fireball is likely to contain an admixture of neutrons. Inelastic collisions between differentially streaming protons and neutrons in the fireball produce nu(&mgr;) (nu;(&mgr;)) of approximately 10 GeV as well as nu(e) (nu;(e)) of approximately 5 GeV, which could produce approximately 7 events/year in km(3) detectors, if the neutron abundance is comparable to that of protons. Photons of approximately 10 GeV from pi(0) decay and approximately 100 MeV nu;(e) from neutron decay are also produced, but will be difficult to detect. Photons with energies less, similar1 MeV from shocks following neutron decay produce a characteristic signal which may be distinguishable from the proton-related MeV photons.

Forward multiple scattering corrections as function of detector field of view

NASA Astrophysics Data System (ADS)

Zardecki, A.; Deepak, A.

1983-06-01

The theoretical formulations are given for an approximate method based on the solution of the radiative transfer equation in the small angle approximation. The method is approximate in the sense that an approximation is made in addition to the small angle approximation. Numerical results were obtained for multiple scattering effects as functions of the detector field of view, as well as the size of the detector's aperture for three different values of the optical depth tau (=1.0, 4.0 and 10.0). Three cases of aperture size were considered--namely, equal to or smaller or larger than the laser beam diameter. The contrast between the on-axis intensity and the received power for the last three cases is clearly evident.

Mean-field approximation for spacing distribution functions in classical systems.

PubMed

González, Diego Luis; Pimpinelli, Alberto; Einstein, T L

2012-01-01

We propose a mean-field method to calculate approximately the spacing distribution functions p((n))(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p((n))(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed. © 2012 American Physical Society

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1987-01-01

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation

NASA Astrophysics Data System (ADS)

Bervillier, C.; Boisseau, B.; Giacomini, H.

2008-02-01

The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).

Approximate supernova remnant dynamics with cosmic ray production

NASA Technical Reports Server (NTRS)

Voelk, H. J.; Drury, L. O.; Dorfi, E. A.

1985-01-01

Supernova explosions are the most violent and energetic events in the galaxy and have long been considered probably sources of Cosmic Rays. Recent shock acceleration models treating the Cosmic Rays (CR's) as test particles nb a prescribed Supernova Remnant (SNR) evolution, indeed indicate an approximate power law momentum distribution f sub source (p) approximation p(-a) for the particles ultimately injected into the Interstellar Medium (ISM). This spectrum extends almost to the momentum p = 1 million GeV/c, where the break in the observed spectrum occurs. The calculated power law index approximately less than 4.2 agrees with that inferred for the galactic CR sources. The absolute CR intensity can however not be well determined in such a test particle approximation.

The blind leading the blind: Mutual refinement of approximate theories

NASA Technical Reports Server (NTRS)

Kedar, Smadar T.; Bresina, John L.; Dent, C. Lisa

1991-01-01

The mutual refinement theory, a method for refining world models in a reactive system, is described. The method detects failures, explains their causes, and repairs the approximate models which cause the failures. The approach focuses on using one approximate model to refine another.

Practical approximations to quantify the impact of time windows and delivery sizes on VMT multi-stop tours.

DOT National Transportation Integrated Search

2009-04-01

This paper studies approximations to the average length of Vehicle Routing Problems (VRP). The approximations are valuable for strategic and : planning analysis of transportation and logistics problems. The research focus is on VRP with varying numbe...

Reply to Steele & Ferrer: Modeling Oscillation, Approximately or Exactly?

ERIC Educational Resources Information Center

Oud, Johan H. L.; Folmer, Henk

2011-01-01

This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure…

Two-parametric {\\delta'} -interactions: approximation by Schrödinger operators with localized rank-two perturbations

NASA Astrophysics Data System (ADS)

Golovaty, Yuriy

2018-06-01

We construct a norm resolvent approximation to the family of point interactions , by Schrödinger operators with localized rank-two perturbations coupled with short range potentials. In particular, a new approximation to the -interactions is obtained.

Memory Efficient Ranking.

ERIC Educational Resources Information Center

Moffat, Alistair; And Others

1994-01-01

Describes an approximate document ranking process that uses a compact array of in-memory, low-precision approximations for document length. Combined with another rule for reducing the memory required by partial similarity accumulators, the approximation heuristic allows the ranking of large document collections using less than one byte of memory…

A Gaussian-based rank approximation for subspace clustering

NASA Astrophysics Data System (ADS)

Xu, Fei; Peng, Chong; Hu, Yunhong; He, Guoping

2018-04-01

Low-rank representation (LRR) has been shown successful in seeking low-rank structures of data relationships in a union of subspaces. Generally, LRR and LRR-based variants need to solve the nuclear norm-based minimization problems. Beyond the success of such methods, it has been widely noted that the nuclear norm may not be a good rank approximation because it simply adds all singular values of a matrix together and thus large singular values may dominant the weight. This results in far from satisfactory rank approximation and may degrade the performance of lowrank models based on the nuclear norm. In this paper, we propose a novel nonconvex rank approximation based on the Gaussian distribution function, which has demanding properties to be a better rank approximation than the nuclear norm. Then a low-rank model is proposed based on the new rank approximation with application to motion segmentation. Experimental results have shown significant improvements and verified the effectiveness of our method.

A refinement of the combination equations for evaporation

USGS Publications Warehouse

Milly, P.C.D.

1991-01-01

Most combination equations for evaporation rely on a linear expansion of the saturation vapor-pressure curve around the air temperature. Because the temperature at the surface may differ from this temperature by several degrees, and because the saturation vapor-pressure curve is nonlinear, this approximation leads to a certain degree of error in those evaporation equations. It is possible, however, to introduce higher-order polynomial approximations for the saturation vapor-pressure curve and to derive a family of explicit equations for evaporation, having any desired degree of accuracy. Under the linear approximation, the new family of equations for evaporation reduces, in particular cases, to the combination equations of H. L. Penman (Natural evaporation from open water, bare soil and grass, Proc. R. Soc. London, Ser. A193, 120-145, 1948) and of subsequent workers. Comparison of the linear and quadratic approximations leads to a simple approximate expression for the error associated with the linear case. Equations based on the conventional linear approximation consistently underestimate evaporation, sometimes by a substantial amount. ?? 1991 Kluwer Academic Publishers.

Discovery of a Jupiter/Saturn analog with gravitational microlensing.

PubMed

Gaudi, B S; Bennett, D P; Udalski, A; Gould, A; Christie, G W; Maoz, D; Dong, S; McCormick, J; Szymanski, M K; Tristram, P J; Nikolaev, S; Paczynski, B; Kubiak, M; Pietrzynski, G; Soszynski, I; Szewczyk, O; Ulaczyk, K; Wyrzykowski, L; Depoy, D L; Han, C; Kaspi, S; Lee, C-U; Mallia, F; Natusch, T; Pogge, R W; Park, B-G; Abe, F; Bond, I A; Botzler, C S; Fukui, A; Hearnshaw, J B; Itow, Y; Kamiya, K; Korpela, A V; Kilmartin, P M; Lin, W; Masuda, K; Matsubara, Y; Motomura, M; Muraki, Y; Nakamura, S; Okumura, T; Ohnishi, K; Rattenbury, N J; Sako, T; Saito, To; Sato, S; Skuljan, L; Sullivan, D J; Sumi, T; Sweatman, W L; Yock, P C M; Albrow, M D; Allan, A; Beaulieu, J-P; Burgdorf, M J; Cook, K H; Coutures, C; Dominik, M; Dieters, S; Fouqué, P; Greenhill, J; Horne, K; Steele, I; Tsapras, Y; Chaboyer, B; Crocker, A; Frank, S; Macintosh, B

2008-02-15

Searches for extrasolar planets have uncovered an astonishing diversity of planetary systems, yet the frequency of solar system analogs remains unknown. The gravitational microlensing planet search method is potentially sensitive to multiple-planet systems containing analogs of all the solar system planets except Mercury. We report the detection of a multiple-planet system with microlensing. We identify two planets with masses of approximately 0.71 and approximately 0.27 times the mass of Jupiter and orbital separations of approximately 2.3 and approximately 4.6 astronomical units orbiting a primary star of mass approximately 0.50 solar mass at a distance of approximately 1.5 kiloparsecs. This system resembles a scaled version of our solar system in that the mass ratio, separation ratio, and equilibrium temperatures of the planets are similar to those of Jupiter and Saturn. These planets could not have been detected with other techniques; their discovery from only six confirmed microlensing planet detections suggests that solar system analogs may be common.

Metaheuristic optimisation methods for approximate solving of singular boundary value problems

NASA Astrophysics Data System (ADS)

Sadollah, Ali; Yadav, Neha; Gao, Kaizhou; Su, Rong

2017-07-01

This paper presents a novel approximation technique based on metaheuristics and weighted residual function (WRF) for tackling singular boundary value problems (BVPs) arising in engineering and science. With the aid of certain fundamental concepts of mathematics, Fourier series expansion, and metaheuristic optimisation algorithms, singular BVPs can be approximated as an optimisation problem with boundary conditions as constraints. The target is to minimise the WRF (i.e. error function) constructed in approximation of BVPs. The scheme involves generational distance metric for quality evaluation of the approximate solutions against exact solutions (i.e. error evaluator metric). Four test problems including two linear and two non-linear singular BVPs are considered in this paper to check the efficiency and accuracy of the proposed algorithm. The optimisation task is performed using three different optimisers including the particle swarm optimisation, the water cycle algorithm, and the harmony search algorithm. Optimisation results obtained show that the suggested technique can be successfully applied for approximate solving of singular BVPs.

Light propagation and the distance-redshift relation in a realistic inhomogeneous universe

NASA Technical Reports Server (NTRS)

Futamase, Toshifumi; Sasaki, Misao

1989-01-01

The propagation of light rays in a clumpy universe constructed by cosmological version of the post-Newtonian approximation was investigated. It is shown that linear approximation to the propagation equations is valid in the region where zeta is approximately less than 1 even if the density contrast is much larger than unity. Based on a gerneral order-of-magnitude statistical consideration, it is argued that the linear approximation is still valid where zeta is approximately greater than 1. A general formula for the distance-redshift relation in a clumpy universe is given. An explicit expression is derived for a simplified situation in which the effect of the gravitational potential of inhomogeneities dominates. In the light of the derived relation, the validity of the Dyer-Roeder distance is discussed. Also, statistical properties of light rays are investigated for a simple model of an inhomogeneous universe. The result of this example supports the validity of the linear approximation.

Efficient solution of parabolic equations by Krylov approximation methods

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Y.

1990-01-01

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

Padé Approximant and Minimax Rational Approximation in Standard Cosmology

NASA Astrophysics Data System (ADS)

Zaninetti, Lorenzo

2016-02-01

The luminosity distance in the standard cosmology as given by $\\Lambda$CDM and consequently the distance modulus for supernovae can be defined by the Pad\\'e approximant. A comparison with a known analytical solution shows that the Pad\\'e approximant for the luminosity distance has an error of $4\\%$ at redshift $= 10$. A similar procedure for the Taylor expansion of the luminosity distance gives an error of $4\\%$ at redshift $=0.7 $; this means that for the luminosity distance, the Pad\\'e approximation is superior to the Taylor series. The availability of an analytical expression for the distance modulus allows applying the Levenberg--Marquardt method to derive the fundamental parameters from the available compilations for supernovae. A new luminosity function for galaxies derived from the truncated gamma probability density function models the observed luminosity function for galaxies when the observed range in absolute magnitude is modeled by the Pad\\'e approximant. A comparison of $\\Lambda$CDM with other cosmologies is done adopting a statistical point of view.

Unanticipated benefits of automotive emission control: reduction in fatalities by motor vehicle exhaust gas.

PubMed

Shelef, M

1994-05-23

In 1970, before the implementation of strict controls on emissions in motor vehicle exhaust gas (MVEG), the annual USA incidence of fatal accidents by carbon monoxide in the MVEG was approximately 800 and that of suicides approximately 2000 (somewhat less than 10% of total suicides). In 1987, there were approximately 400 fatal accidents and approximately 2700 suicides by MVEG. Accounting for the growth in population and vehicle registration, the yearly lives saved in accidents by MVEG were approximately 1200 in 1987 and avoided suicides approximately 1400. The decrease in accidents continues unabated while the decrease in expected suicides by MVEG reached a plateau in 1981-1983. The reasons for this disparity are discussed. Juxtaposition of these results with the projected cancer risk avoidance of less than 500 annually in 2005 (as compared with 1986) plainly shows that, in terms of mortality, the unanticipated benefits of emission control far overshadow the intended benefits. With the spread of MVEG control these benefits will accrue worldwide.

A comparison of transport algorithms for premixed, laminar steady state flames

NASA Technical Reports Server (NTRS)

Coffee, T. P.; Heimerl, J. M.

1980-01-01

The effects of different methods of approximating multispecies transport phenomena in models of premixed, laminar, steady state flames were studied. Five approximation methods that span a wide range of computational complexity were developed. Identical data for individual species properties were used for each method. Each approximation method is employed in the numerical solution of a set of five H2-02-N2 flames. For each flame the computed species and temperature profiles, as well as the computed flame speeds, are found to be very nearly independent of the approximation method used. This does not indicate that transport phenomena are unimportant, but rather that the selection of the input values for the individual species transport properties is more important than the selection of the method used to approximate the multispecies transport. Based on these results, a sixth approximation method was developed that is computationally efficient and provides results extremely close to the most sophisticated and precise method used.

Kernel K-Means Sampling for Nyström Approximation.

PubMed

He, Li; Zhang, Hong

2018-05-01

A fundamental problem in Nyström-based kernel matrix approximation is the sampling method by which training set is built. In this paper, we suggest to use kernel -means sampling, which is shown in our works to minimize the upper bound of a matrix approximation error. We first propose a unified kernel matrix approximation framework, which is able to describe most existing Nyström approximations under many popular kernels, including Gaussian kernel and polynomial kernel. We then show that, the matrix approximation error upper bound, in terms of the Frobenius norm, is equal to the -means error of data points in kernel space plus a constant. Thus, the -means centers of data in kernel space, or the kernel -means centers, are the optimal representative points with respect to the Frobenius norm error upper bound. Experimental results, with both Gaussian kernel and polynomial kernel, on real-world data sets and image segmentation tasks show the superiority of the proposed method over the state-of-the-art methods.

Uplift, thermal unrest and magma intrusion at Yellowstone caldera.

PubMed

Wicks, Charles W; Thatcher, Wayne; Dzurisin, Daniel; Svarc, Jerry

2006-03-02

The Yellowstone caldera, in the western United States, formed approximately 640,000 years ago when an explosive eruption ejected approximately 1,000 km3 of material. It is the youngest of a series of large calderas that formed during sequential cataclysmic eruptions that began approximately 16 million years ago in eastern Oregon and northern Nevada. The Yellowstone caldera was largely buried by rhyolite lava flows during eruptions that occurred from approximately 150,000 to approximately 70,000 years ago. Since the last eruption, Yellowstone has remained restless, with high seismicity, continuing uplift/subsidence episodes with movements of approximately 70 cm historically to several metres since the Pleistocene epoch, and intense hydrothermal activity. Here we present observations of a new mode of surface deformation in Yellowstone, based on radar interferometry observations from the European Space Agency ERS-2 satellite. We infer that the observed pattern of uplift and subsidence results from variations in the movement of molten basalt into and out of the Yellowstone volcanic system.

Electrolytes for Low Impedance, Wide Operating Temperature Range Lithium-Ion Battery Module

NASA Technical Reports Server (NTRS)

Hallac, Boutros (Inventor); Krause, Frederick C. (Inventor); Jiang, Junwei (Inventor); Smart, Marshall C. (Inventor); Metz, Bernhard M. (Inventor); Bugga, Ratnakumar V. (Inventor)

2018-01-01

A lithium ion battery cell includes a housing, a cathode disposed within the housing, wherein the cathode comprises a cathode active material, an anode disposed within the housing, wherein the anode comprises an anode active material, and an electrolyte disposed within the housing and in contact with the cathode and anode. The electrolyte consists essentially of a solvent mixture, a lithium salt in a concentration ranging from approximately 1.0 molar (M) to approximately 1.6 M, and an additive mixture. The solvent mixture includes a cyclic carbonate, an non-cyclic carbonate, and a linear ester. The additive mixture consists essentially of lithium difluoro(oxalato)borate (LiDFOB) in an amount ranging from approximately 0.5 weight percent to approximately 2.0 weight percent based on the weight of the electrolyte, and vinylene carbonate (VC) in an amount ranging from approximately 0.5 weight percent to approximately 2.0 weight percent based on the weight of the electrolyte.

New cosmic microwave background constraint to primordial gravitational waves.

PubMed

Smith, Tristan L; Pierpaoli, Elena; Kamionkowski, Marc

2006-07-14

Primordial gravitational waves (GWs) with frequencies > or approximately equal to 10(-15) Hz contribute to the radiation density of the Universe at the time of decoupling of the cosmic microwave background (CMB). This affects the CMB and matter power spectra in a manner identical to massless neutrinos, unless the initial density perturbation for the GWs is nonadiabatic, as may occur if such GWs are produced during inflation or some post-inflation phase transition. In either case, current observations provide a constraint to the GW amplitude that competes with that from big-bang nucleosynthesis (BBN), although it extends to much lower frequencies (approximately 10(-15) Hz rather than the approximately 10(-10) Hz from BBN): at 95% confidence level, omega(gw)h(2)

Neural Network and Regression Approximations in High Speed Civil Transport Aircraft Design Optimization

NASA Technical Reports Server (NTRS)

Patniak, Surya N.; Guptill, James D.; Hopkins, Dale A.; Lavelle, Thomas M.

1998-01-01

Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

Surface expression of the Chicxulub crater

PubMed

Pope, K O; Ocampo, A C; Kinsland, G L; Smith, R

1996-06-01

Analyses of geomorphic, soil, and topographic data from the northern Yucatan Peninsula, Mexico, confirm that the buried Chicxulub impact crater has a distinct surface expression and that carbonate sedimentation throughout the Cenozoic has been influenced by the crater. Late Tertiary sedimentation was mostly restricted to the region within the buried crater, and a semicircular moat existed until at least Pliocene time. The topographic expression of the crater is a series of features concentric with the crater. The most prominent is an approximately 83-km-radius trough or moat containing sinkholes (the Cenote ring). Early Tertiary surfaces rise abruptly outside the moat and form a stepped topography with an outer trough and ridge crest at radii of approximately 103 and approximately 129 km, respectively. Two discontinuous troughs lie within the moat at radii of approximately 41 and approximately 62 km. The low ridge between the inner troughs corresponds to the buried peak ring. The moat corresponds to the outer edge of the crater floor demarcated by a major ring fault. The outer trough and the approximately 62-km-radius inner trough also mark buried ring faults. The ridge crest corresponds to the topographic rim of the crater as modified by postimpact processes. These interpretations support previous findings that the principal impact basin has a diameter of approximately 180 km, but concentric, low-relief slumping extends well beyond this diameter and the eroded crater rim may extend to a diameter of approximately 260 km.

Construction and accuracy of partial differential equation approximations to the chemical master equation.

PubMed

Grima, Ramon

2011-11-01

The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.

Computational Modeling of Proteins based on Cellular Automata: A Method of HP Folding Approximation.

PubMed

Madain, Alia; Abu Dalhoum, Abdel Latif; Sleit, Azzam

2018-06-01

The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primary structures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic-hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H-H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H's at even positions and the other side ignores H's at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one half approximation minus the H-H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences.

Comparison of approximate solutions to the phonon Boltzmann transport equation with the relaxation time approximation: Spherical harmonics expansions and the discrete ordinates method

NASA Astrophysics Data System (ADS)

Christenson, J. G.; Austin, R. A.; Phillips, R. J.

2018-05-01

The phonon Boltzmann transport equation is used to analyze model problems in one and two spatial dimensions, under transient and steady-state conditions. New, explicit solutions are obtained by using the P1 and P3 approximations, based on expansions in spherical harmonics, and are compared with solutions from the discrete ordinates method. For steady-state energy transfer, it is shown that analytic expressions derived using the P1 and P3 approximations agree quantitatively with the discrete ordinates method, in some cases for large Knudsen numbers, and always for Knudsen numbers less than unity. However, for time-dependent energy transfer, the PN solutions differ qualitatively from converged solutions obtained by the discrete ordinates method. Although they correctly capture the wave-like behavior of energy transfer at short times, the P1 and P3 approximations rely on one or two wave velocities, respectively, yielding abrupt, step-changes in temperature profiles that are absent when the angular dependence of the phonon velocities is captured more completely. It is shown that, with the gray approximation, the P1 approximation is formally equivalent to the so-called "hyperbolic heat equation." Overall, these results support the use of the PN approximation to find solutions to the phonon Boltzmann transport equation for steady-state conditions. Such solutions can be useful in the design and analysis of devices that involve heat transfer at nanometer length scales, where continuum-scale approaches become inaccurate.

The X-Ray Weakness of GPS Radio Galaxies: A Volume-Limited Complete Sample

NASA Technical Reports Server (NTRS)

Mushotzky, Richard F. (Technical Monitor); Siemiginowska, Aneta (Principal Investigator)

2004-01-01

The XMM observations of Mkn 668 have been analyzed. We found soft X-ray signatures of a hot plasma (kT approximately 10^7 approximately K) and a hard X-ray emission from the nucleus. The X-ray spectrum above 2.5 approximately keV is characterized by a very flat (observed photon index, Gamma approximately 0.5) power-law continuum, alongside with a strong Fe-K-alpha neutral iron fluorescent line (EW approximately 600 approximately eV). The best explanation for the origin of this high energy X-ray emission is in terms of the Compton-reflection of the nuclear emission. The primary X-ray emission is obscured by a Compton-thick (N_H approximately 10^24 approximately cm-2) matter which becomes transparent at higher energies. The observed above 2.5-keV X-rays are mostly due to reflection which is indicated by a strong Fe-K-alpha line. This represents the second hard X-ray detection of the GPS galaxy ever (the first one being 1345+125; O Dea et al. 2000). Interestingly, the both such trend is confirmed by our on going XMM-Newton observations of a larger GPS sample, it would lead us to looking into the question on how the dense nuclear environment impacts the nature and evolution of a GPS source, and more generally, on the history of radio power in the universe. The paper summarizing the results has been submitted to Astronomy and Astrophysics in December 2003.

76 FR 79098 - Final Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2011-12-21

... County. Approximately 0.9 mile +3089 downstream of Black Angus Lane. Redwater River Approximately 1,200... Crosse County, Wisconsin, and Incorporated Areas Docket No. FEMA-B-1155 Black River Approximately 0.5... Federal Domestic Assistance No. 97.022, ``Flood Insurance.'') Dated: December 5, 2011. Sandra K. Knight...

Quirks of Stirling's Approximation

ERIC Educational Resources Information Center

Macrae, Roderick M.; Allgeier, Benjamin M.

2013-01-01

Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…

Evaluation of Jacobian determinants by Monte Carlo methods: Application to the quasiclassical approximation in molecular scattering

NASA Technical Reports Server (NTRS)

Labudde, R. A.

1971-01-01

A technique is described which can be used to evaluate Jacobian determinants which occur in classical mechanical and quasiclassical approximation descriptions of molecular scattering. The method may be valuable in the study of reactive scattering using the quasiclassical approximation.

Sulfur, Chlorine and Fluorine Degassing and Atmospheric Loading by the Roza eruption, Columbia River Basalt Group, Washington

NASA Technical Reports Server (NTRS)

Thordarson, Th.; Self, S

1996-01-01

In this study we attempt to quantify the amount of S, Cl and F released by the 1300 cu km Roza member (approximately 14.7 Ma) of the Columbia River Basalt Group, which was produced by a moderate-size flood basalt eruption in the mid-Miocene. Our results are the first indication of the potential atmospheric SO2 yield from a flood basalt eruption, and indicate the mechanism by which flood basalt eruptions may have seriously affected the environment. Glass inclusions in phenocrysts and quenched glass in products from various stages of the eruption were analyzed for concentrations of S, Cl and F and major elements. Glass inclusions contain 1965 +/- 110 ppm S, 295 +/- 65 ppm Cl and 1310 +/- 110 ppm F. Groundmass glass of Roza dike selvages contains considerably lower concentrations: 1110 +/- 90 ppm S, 245 +/- 30 ppm Cl and 1020 +/- 25 ppm F. Scoria clasts from near vent deposits contain 665 +/- 75 ppm S, 175 +/- 5 ppm Cl and 950 +/- 20 ppm F, and the groundmass glass of lava selvages contains 520 +/- 30 ppm S, 190 +/- 30 ppm Cl and 890 +/- 55 ppm F. In crystalline lava, the concentrations are 195 ppm S, 100 ppm Cl and 830 ppm F. Volatile element concentrations in these samples represent the progress of degassing through the eruption and can be used to estimate the potential amount of the volatiles S, Cl and F released by the magma into the atmosphere, as well as to evaluate the amount liberated by various phases of the eruption. The total amount of volatiles released by the Roza eruption is estimated to have been approximately 12,420 MtSO2, approximately 710 MtHCI and approximately 1780 MtHF. The Roza magma liberated approximately 9620 MtSO, (77% of the total volatile mass released), approximately 400 MtHCI (56%) and approximately 1450 MtHF (81%) at the vents and lofted by the eruption columns to altitudes of 7-13 km. Degassing of the lava is estimated to have released an additional approximately 2810 MtSO2, approximately 310 MtHCI and approximately 330 MtHF. The Roza eruption is likely to have lasted for approximately 10 years, indicating an annual H2SO4-mass loading of approximately 1800 Mt. Thus, the atmospheric perturbations associated with the Roza eruption may have been of the magnitude predicted for a severe "nuclear" or "volcanic" winter, but lasting up to a decade or more.

The Pendulum Equation

ERIC Educational Resources Information Center

Fay, Temple H.

2002-01-01

We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…

27 CFR 9.225 - Middleburg Virginia.

Code of Federal Regulations, 2013 CFR

2013-04-01

... (downstream) for approximately 8.2 miles, crossing onto the Point of Rocks map, to the mouth of Catoctin Creek; then (2) Proceed southwesterly (upstream) along the meandering Catoctin Creek for approximately 4 miles... State Route 663 for approximately 0.1 mile to State Route 665 (locally known as Loyalty Road) in...

27 CFR 9.71 - Hermann.

Code of Federal Regulations, 2011 CFR

2011-04-01

... northeast approximately 16.5 miles along the Missouri River Pacific Railroad, as it parallels the Missouri... southeast approximately 8.5 miles to the intersection Big Berger Creek. (4) Then southwest along the winding course of Big Berger Creek for approximately 20 miles (eight miles due southwest) to Township line T.44...

27 CFR 9.71 - Hermann.

Code of Federal Regulations, 2014 CFR

2014-04-01

... northeast approximately 16.5 miles along the Missouri River Pacific Railroad, as it parallels the Missouri... southeast approximately 8.5 miles to the intersection Big Berger Creek. (4) Then southwest along the winding course of Big Berger Creek for approximately 20 miles (eight miles due southwest) to Township line T.44...

27 CFR 9.71 - Hermann.

Code of Federal Regulations, 2012 CFR

2012-04-01

... northeast approximately 16.5 miles along the Missouri River Pacific Railroad, as it parallels the Missouri... southeast approximately 8.5 miles to the intersection Big Berger Creek. (4) Then southwest along the winding course of Big Berger Creek for approximately 20 miles (eight miles due southwest) to Township line T.44...

27 CFR 9.71 - Hermann.

Code of Federal Regulations, 2013 CFR

2013-04-01

... northeast approximately 16.5 miles along the Missouri River Pacific Railroad, as it parallels the Missouri... southeast approximately 8.5 miles to the intersection Big Berger Creek. (4) Then southwest along the winding course of Big Berger Creek for approximately 20 miles (eight miles due southwest) to Township line T.44...

27 CFR 9.129 - Arroyo Grande Valley.

Code of Federal Regulations, 2014 CFR

2014-04-01

... boundary proceeds approximately 0.1 mile, in a northwesterly direction, along the roadway of State Route... Manuela land grant; (2) Then northwesterly, approximately 1.5 miles, along Printz Road to its intersection with Noyes Road in the Santa Manuela land grant; (3) Then northerly, approximately 1.5 miles, along...

27 CFR 9.225 - Middleburg Virginia.

Code of Federal Regulations, 2014 CFR

2014-04-01

... (downstream) for approximately 8.2 miles, crossing onto the Point of Rocks map, to the mouth of Catoctin Creek; then (2) Proceed southwesterly (upstream) along the meandering Catoctin Creek for approximately 4 miles... State Route 663 for approximately 0.1 mile to State Route 665 (locally known as Loyalty Road) in...

27 CFR 9.141 - Escondido Valley.

Code of Federal Regulations, 2012 CFR

2012-04-01

... westerly direction approximately 17 miles; (5) The boundary continues to follow the 3000 foot contour line... intermittent stream approximately 18 miles east of the city of Fort Stockton (standard reference GE3317 on the... easterly direction approximately 9 miles until a southbound trail diverges from I-10 just past the point...

27 CFR 9.141 - Escondido Valley.

Code of Federal Regulations, 2010 CFR

2010-04-01

... westerly direction approximately 17 miles; (5) The boundary continues to follow the 3000 foot contour line... intermittent stream approximately 18 miles east of the city of Fort Stockton (standard reference GE3317 on the... easterly direction approximately 9 miles until a southbound trail diverges from I-10 just past the point...

27 CFR 9.139 - Santa Lucia Highlands.

Code of Federal Regulations, 2014 CFR

2014-04-01

... boundary follows Limekiln Creek for approximately 1.25 miles northeast to the 100 foot elevation. (2) Then following the 100 foot contour in a southeasterly direction for approximately 1 mile, where the boundary... approximately 6.50 miles, to the point where the 160 foot elevation crosses River Road. (6) Then following River...

27 CFR 9.141 - Escondido Valley.

Code of Federal Regulations, 2014 CFR

2014-04-01

... westerly direction approximately 17 miles; (5) The boundary continues to follow the 3000 foot contour line... intermittent stream approximately 18 miles east of the city of Fort Stockton (standard reference GE3317 on the... easterly direction approximately 9 miles until a southbound trail diverges from I-10 just past the point...

27 CFR 9.141 - Escondido Valley.

Code of Federal Regulations, 2013 CFR

2013-04-01

... westerly direction approximately 17 miles; (5) The boundary continues to follow the 3000 foot contour line... intermittent stream approximately 18 miles east of the city of Fort Stockton (standard reference GE3317 on the... easterly direction approximately 9 miles until a southbound trail diverges from I-10 just past the point...

27 CFR 9.139 - Santa Lucia Highlands.

Code of Federal Regulations, 2012 CFR

2012-04-01

... boundary follows Limekiln Creek for approximately 1.25 miles northeast to the 100 foot elevation. (2) Then following the 100 foot contour in a southeasterly direction for approximately 1 mile, where the boundary... approximately 6.50 miles, to the point where the 160 foot elevation crosses River Road. (6) Then following River...

27 CFR 9.141 - Escondido Valley.

Code of Federal Regulations, 2011 CFR

2011-04-01

... westerly direction approximately 17 miles; (5) The boundary continues to follow the 3000 foot contour line... intermittent stream approximately 18 miles east of the city of Fort Stockton (standard reference GE3317 on the... easterly direction approximately 9 miles until a southbound trail diverges from I-10 just past the point...

27 CFR 9.139 - Santa Lucia Highlands.

Code of Federal Regulations, 2013 CFR

2013-04-01

... boundary follows Limekiln Creek for approximately 1.25 miles northeast to the 100 foot elevation. (2) Then following the 100 foot contour in a southeasterly direction for approximately 1 mile, where the boundary... approximately 6.50 miles, to the point where the 160 foot elevation crosses River Road. (6) Then following River...

75 FR 23642 - Proposed Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2010-05-04

... Flat River Approximately 375 feet None +683 City of Desloge, City downstream of the of Park Hills... confluence with Flat of St. Francois Creek. County. Approximately 2,000 None +767 feet upstream of City of... of the St. Francois County. confluence with the Flat River. Approximately 7,000 None +783 feet...

26 CFR 1.985-3 - United States dollar approximate separate transactions method.

Code of Federal Regulations, 2010 CFR

2010-04-01

... transactions method. 1.985-3 Section 1.985-3 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE... dollar approximate separate transactions method. (a) Scope and effective date—(1) Scope. This section describes the United States dollar (dollar) approximate separate transactions method of accounting (DASTM...

Application of the Parabolic Approximation to Predict Acoustical Propagation in the Ocean.

ERIC Educational Resources Information Center

McDaniel, Suzanne T.

1979-01-01

A simplified derivation of the parabolic approximation to the acoustical wave equation is presented. Exact solutions to this approximate equation are compared with solutions to the wave equation to demonstrate the applicability of this method to the study of underwater sound propagation. (Author/BB)

The use of neural networks for approximation of nuclear data

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

Korovin, Yu. A.; Maksimushkina, A. V., E-mail: AVMaksimushkina@mephi.ru

2015-12-15

The article discusses the possibility of using neural networks for approximation or reconstruction of data such as the reaction cross sections. The quality of the approximation using fitting criteria is also evaluated. The activity of materials under irradiation is calculated from data obtained using neural networks.

Approximate spatial reasoning

NASA Technical Reports Server (NTRS)

Dutta, Soumitra

1988-01-01

A model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment is presented. Algorithms are developed which can be used to reason about spatial information expressed in the form of approximate linguistic descriptions similar to the kind of spatial information processed by humans. Particular attention is given to static spatial reasoning.

75 FR 62061 - Proposed Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2010-10-07

... railroad bridge. Mahanoy Creek Approximately 0.71 mile None +781 Township of Butler. upstream of Rice Road... Unincorporated Areas of Black Creek. Darlington County. Approximately 0.7 mile None +189 upstream of Bobo Newsom Highway. Black Creek (DS) Approximately 0.5 mile None +77 City of Darlington, downstream of Muses...

Communicating Professional Noticing through Animations as a Transformational Approximation of Practice

ERIC Educational Resources Information Center

Amador, Julie M.; Estapa, Anna; Weston, Tracy; Kosko, Karl

2016-01-01

This paper explores the use of animations as an approximation of practice to provide a transformational technology experience for elementary mathematics preservice teachers. Preservice teachers in mathematics methods courses at six universities (n = 126) engaged in a practice of decomposing and approximating components of a fraction lesson. Data…

Unified Approximations: A New Approach for Monoprotic Weak Acid-Base Equilibria

ERIC Educational Resources Information Center

Pardue, Harry; Odeh, Ihab N.; Tesfai, Teweldemedhin M.

2004-01-01

The unified approximations reduce the conceptual complexity by combining solutions for a relatively large number of different situations into just two similar sets of processes. Processes used to solve problems by either the unified or classical approximations require similar degrees of understanding of the underlying chemical processes.

78 FR 48813 - Final Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2013-08-12

... Unincorporated Areas of Green River). the Green River to Butler County. approximately 0.6 mile upstream of the... with +428 Unincorporated Areas of Green River). the Green River to Butler County. approximately 0.5... with +433 Unincorporated Areas of Green River). the Green River to Butler County. approximately 1,202...

75 FR 69619 - East Reservoir Project; Kootenai National Forest, Lincoln County, MT

Federal Register 2010, 2011, 2012, 2013, 2014

2010-11-15

... harvest. Vegetation treatments total approximately 13,000 acres of treated area. (2) Road management includes new road construction, road storage and adding existing, undetermined roads to the National Forest Service road system. Approximately 2.04 miles of new road construction is proposed. Approximately 40 miles...

36 CFR 254.11 - Exchanges at approximately equal value.

Code of Federal Regulations, 2010 CFR

2010-07-01

... equal value. 254.11 Section 254.11 Parks, Forests, and Public Property FOREST SERVICE, DEPARTMENT OF AGRICULTURE LANDOWNERSHIP ADJUSTMENTS Land Exchanges § 254.11 Exchanges at approximately equal value. (a) The authorized officer may exchange lands which are of approximately equal value upon a determination that: (1...

Approximate isotropic cloak for the Maxwell equations

NASA Astrophysics Data System (ADS)

Ghosh, Tuhin; Tarikere, Ashwin

2018-05-01

We construct a regular isotropic approximate cloak for the Maxwell system of equations. The method of transformation optics has enabled the design of electromagnetic parameters that cloak a region from external observation. However, these constructions are singular and anisotropic, making practical implementation difficult. Thus, regular approximations to these cloaks have been constructed that cloak a given region to any desired degree of accuracy. In this paper, we show how to construct isotropic approximations to these regularized cloaks using homogenization techniques so that one obtains cloaking of arbitrary accuracy with regular and isotropic parameters.

Two Point Exponential Approximation Method for structural optimization of problems with frequency constraints

NASA Technical Reports Server (NTRS)

Fadel, G. M.

1991-01-01

The point exponential approximation method was introduced by Fadel et al. (Fadel, 1990), and tested on structural optimization problems with stress and displacement constraints. The reports in earlier papers were promising, and the method, which consists of correcting Taylor series approximations using previous design history, is tested in this paper on optimization problems with frequency constraints. The aim of the research is to verify the robustness and speed of convergence of the two point exponential approximation method when highly non-linear constraints are used.

Efficient High-Order Accurate Methods using Unstructured Grids for Hydrodynamics and Acoustics

DTIC Science & Technology

2007-08-31

Leer. On upstream differencing and godunov-type schemes for hyperbolic conservation laws. SIAM Review, 25(1):35-61, 1983. [46] F . Eleuterio Toro ...early stage [4-61. The basic idea can be surmised from simple approximation theory. If a continuous function f is to be approximated over a set of...a2f 4h4 a4ff(x+eh) = f (x)+-- + _ •-+• e +0 +... (1) where 0 < e < 1 for approximations inside the interval of width h. For a second-order approximation

Reliability of the pair-defect-sum approximation for the strength of valence-bond orbitals

PubMed Central

Pauling, Linus; Herman, Zelek S.; Kamb, Barclay J.

1982-01-01

The pair-defect-sum approximation to the bond strength of a hybrid orbital (angular wave functions only) is compared to the rigorous value as a function of bond angle for seven types of bonding situations, with between three and eight bond directions equivalent by geometrical symmetry operations and with only one independent bond angle. The approximation is seen to be an excellent one in all cases, and the results provide a rationale for the application of this approximation to a variety of problems. PMID:16593167

On singlet s-wave electron-hydrogen scattering.

NASA Technical Reports Server (NTRS)

Madan, R. N.

1973-01-01

Discussion of various zeroth-order approximations to s-wave scattering of electrons by hydrogen atoms below the first excitation threshold. The formalism previously developed by the author (1967, 1968) is applied to Feshbach operators to derive integro-differential equations, with the optical-potential set equal to zero, for the singlet and triplet cases. Phase shifts of s-wave scattering are computed in the zeroth-order approximation of the Feshbach operator method and in the static-exchange approximation. It is found that the convergence of numerical computations is faster in the former approximation than in the latter.

Rational positive real approximations for LQG optimal compensators arising in active stabilization of flexible structures

NASA Technical Reports Server (NTRS)

Desantis, A.

1994-01-01

In this paper the approximation problem for a class of optimal compensators for flexible structures is considered. The particular case of a simply supported truss with an offset antenna is dealt with. The nonrational positive real optimal compensator transfer function is determined, and it is proposed that an approximation scheme based on a continued fraction expansion method be used. Comparison with the more popular modal expansion technique is performed in terms of stability margin and parameters sensitivity of the relative approximated closed loop transfer functions.

Blind Backscattering Experimental Data Collected in the Field and an Approximately Globally Convergent Inverse Algorithm

DTIC Science & Technology

2012-01-01

unknown functions q and V . To approximate both of them, we use a predictor / corrector -like scheme. First, given an approximation for V , we update q via...coefficient εr(x). This is our predictor -like step. On the corrector -like step we update the tail function V (x, s) via (5.7). Consider a partition of...10] and figures 5.13–5.16 in [6]. We point out that the adaptivity has used the solution of the approximately globally convergent algorithm as the

Finite-dimensional compensators for infinite-dimensional systems via Galerkin-type approximation

NASA Technical Reports Server (NTRS)

Ito, Kazufumi

1990-01-01

In this paper existence and construction of stabilizing compensators for linear time-invariant systems defined on Hilbert spaces are discussed. An existence result is established using Galkerin-type approximations in which independent basis elements are used instead of the complete set of eigenvectors. A design procedure based on approximate solutions of the optimal regulator and optimal observer via Galerkin-type approximation is given and the Schumacher approach is used to reduce the dimension of compensators. A detailed discussion for parabolic and hereditary differential systems is included.

Rover Takes a Sunday Drive

NASA Technical Reports Server (NTRS)

2004-01-01

This animation, made with images from the Mars Exploration Rover Spirit hazard-identification camera, shows the rover's perspective of its first post-egress drive on Mars Sunday. Engineers drove Spirit approximately 3 meters (10 feet) toward its first rock target, a football-sized, mountain-shaped rock called Adirondack. The drive took approximately 30 minutes to complete, including time stopped to take images. Spirit first made a series of arcing turns totaling approximately 1 meter (3 feet). It then turned in place and made a series of short, straightforward movements totaling approximately 2 meters (6.5 feet).

Polynomial approximation of the Lense-Thirring rigid precession frequency

NASA Astrophysics Data System (ADS)

De Falco, Vittorio; Motta, Sara

2018-05-01

We propose a polynomial approximation of the global Lense-Thirring rigid precession frequency to study low-frequency quasi-periodic oscillations around spinning black holes. This high-performing approximation allows to determine the expected frequencies of a precessing thick accretion disc with fixed inner radius and variable outer radius around a black hole with given mass and spin. We discuss the accuracy and the applicability regions of our polynomial approximation, showing that the computational times are reduced by a factor of ≈70 in the range of minutes.

Minimax rational approximation of the Fermi-Dirac distribution.

PubMed

Moussa, Jonathan E

2016-10-28

Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ -1 )) poles to achieve an error tolerance ϵ at temperature β -1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δ occ , the occupied energy interval. This is particularly beneficial when Δ ≫ Δ occ , such as in electronic structure calculations that use a large basis set.

Solution of linear systems by a singular perturbation technique

NASA Technical Reports Server (NTRS)

Ardema, M. D.

1976-01-01

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation.

Minimax rational approximation of the Fermi-Dirac distribution

NASA Astrophysics Data System (ADS)

Moussa, Jonathan E.

2016-10-01

Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ɛ-1)) poles to achieve an error tolerance ɛ at temperature β-1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. This is particularly beneficial when Δ ≫ Δocc, such as in electronic structure calculations that use a large basis set.

The application of Legendre-tau approximation to parameter identification for delay and partial differential equations

NASA Technical Reports Server (NTRS)

Ito, K.

1983-01-01

Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.

The simultaneous integration of many trajectories using nilpotent normal forms

NASA Technical Reports Server (NTRS)

Grayson, Matthew A.; Grossman, Robert

1990-01-01

Taylor's formula shows how to approximate a certain class of functions by polynomials. The approximations are arbitrarily good in some neighborhood whenever the function is analytic and they are easy to compute. The main goal is to give an efficient algorithm to approximate a neighborhood of the configuration space of a dynamical system by a nilpotent, explicitly integrable dynamical system. The major areas covered include: an approximating map; the generalized Baker-Campbell-Hausdorff formula; the Picard-Taylor method; the main theorem; simultaneous integration of trajectories; and examples.

Fast and low power Michelson interferometer thermo-optical switch on SOI.

PubMed

Song, Junfeng; Fang, Q; Tao, S H; Liow, T Y; Yu, M B; Lo, G Q; Kwong, D L

2008-09-29

We designed and fabricated silicon-on-insulator based Michelson interferometer (MI) thermo-optical switches with deep etched trenches for heat-isolation. Switch power was reduced approximately 20% for the switch with deep etched trenches, and the MI saved approximately 50% power than that of the Mach-Zehnder interferometer. 10.6 mW switch power, approximately 42 micros switch time for the MI with deep trenches, 13.14 mW switch power and approximately 34 micros switch time for the MI without deep trenches were achieved.

A Survey of Techniques for Approximate Computing

DOE PAGES

Mittal, Sparsh

2016-03-18

Approximate computing trades off computation quality with the effort expended and as rising performance demands confront with plateauing resource budgets, approximate computing has become, not merely attractive, but even imperative. Here, we present a survey of techniques for approximate computing (AC). We discuss strategies for finding approximable program portions and monitoring output quality, techniques for using AC in different processing units (e.g., CPU, GPU and FPGA), processor components, memory technologies etc., and programming frameworks for AC. Moreover, we classify these techniques based on several key characteristics to emphasize their similarities and differences. Finally, the aim of this paper is tomore » provide insights to researchers into working of AC techniques and inspire more efforts in this area to make AC the mainstream computing approach in future systems.« less

Approximate analysis for repeated eigenvalue problems with applications to controls-structure integrated design

NASA Technical Reports Server (NTRS)

Kenny, Sean P.; Hou, Gene J. W.

1994-01-01

A method for eigenvalue and eigenvector approximate analysis for the case of repeated eigenvalues with distinct first derivatives is presented. The approximate analysis method developed involves a reparameterization of the multivariable structural eigenvalue problem in terms of a single positive-valued parameter. The resulting equations yield first-order approximations to changes in the eigenvalues and the eigenvectors associated with the repeated eigenvalue problem. This work also presents a numerical technique that facilitates the definition of an eigenvector derivative for the case of repeated eigenvalues with repeated eigenvalue derivatives (of all orders). Examples are given which demonstrate the application of such equations for sensitivity and approximate analysis. Emphasis is placed on the application of sensitivity analysis to large-scale structural and controls-structures optimization problems.

Approximation Of Multi-Valued Inverse Functions Using Clustering And Sugeno Fuzzy Inference

NASA Technical Reports Server (NTRS)

Walden, Maria A.; Bikdash, Marwan; Homaifar, Abdollah

1998-01-01

Finding the inverse of a continuous function can be challenging and computationally expensive when the inverse function is multi-valued. Difficulties may be compounded when the function itself is difficult to evaluate. We show that we can use fuzzy-logic approximators such as Sugeno inference systems to compute the inverse on-line. To do so, a fuzzy clustering algorithm can be used in conjunction with a discriminating function to split the function data into branches for the different values of the forward function. These data sets are then fed into a recursive least-squares learning algorithm that finds the proper coefficients of the Sugeno approximators; each Sugeno approximator finds one value of the inverse function. Discussions about the accuracy of the approximation will be included.

Correlation energy functional within the GW -RPA: Exact forms, approximate forms, and challenges

NASA Astrophysics Data System (ADS)

Ismail-Beigi, Sohrab

2010-05-01

In principle, the Luttinger-Ward Green’s-function formalism allows one to compute simultaneously the total energy and the quasiparticle band structure of a many-body electronic system from first principles. We present approximate and exact expressions for the correlation energy within the GW -random-phase approximation that are more amenable to computation and allow for developing efficient approximations to the self-energy operator and correlation energy. The exact form is a sum over differences between plasmon and interband energies. The approximate forms are based on summing over screened interband transitions. We also demonstrate that blind extremization of such functionals leads to unphysical results: imposing physical constraints on the allowed solutions (Green’s functions) is necessary. Finally, we present some relevant numerical results for atomic systems.

An analytical technique for approximating unsteady aerodynamics in the time domain

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1980-01-01

An analytical technique is presented for approximating unsteady aerodynamic forces in the time domain. The order of elements of a matrix Pade approximation was postulated, and the resulting polynomial coefficients were determined through a combination of least squares estimates for the numerator coefficients and a constrained gradient search for the denominator coefficients which insures stable approximating functions. The number of differential equations required to represent the aerodynamic forces to a given accuracy tends to be smaller than that employed in certain existing techniques where the denominator coefficients are chosen a priori. Results are shown for an aeroelastic, cantilevered, semispan wing which indicate a good fit to the aerodynamic forces for oscillatory motion can be achieved with a matrix Pade approximation having fourth order numerator and second order denominator polynomials.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces

NASA Technical Reports Server (NTRS)

Ito, Kazufumi

1987-01-01

The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization

NASA Technical Reports Server (NTRS)

Simpson, Timothy W.; Korte, John J.; Mauery, Timothy M.; Mistree, Farrokh

1998-01-01

In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems m formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.

Spitzer Photometry of Approximately 1 Million Stars in M31 and 15 Other Galaxies

NASA Technical Reports Server (NTRS)

Khan, Rubab

2017-01-01

We present Spitzer IRAC 3.6-8 micrometer and Multiband Imaging Photometer 24 micrometer point-source catalogs for M31 and 15 other mostly large, star-forming galaxies at distances approximately 3.5-14 Mpc, including M51, M83, M101, and NGC 6946. These catalogs contain approximately 1 million sources including approximately 859,000 in M31 and approximately 116,000 in the other galaxies. They were created following the procedures described in Khan et al. through a combination of pointspread function (PSF) fitting and aperture photometry. These data products constitute a resource to improve our understanding of the IR-bright (3.6-24 micrometer) point-source populations in crowded extragalactic stellar fields and to plan observations with the James Webb Space Telescope.

Thermal and suprathermal protons and alpha particles in the earth's plasma sheet

NASA Technical Reports Server (NTRS)

Ipavich, F. M.; Scholer, M.

1983-01-01

Detailed proton energy spectra in the quasi-stable distant plasma sheet over the energy range from approximately 13 keV to approximately 130 keV are presented. These spectra are compared with spectra of simultaneously measured alpha particles in the energy range from approximately 30 keV/Q to approximately 130 keV/Q. The proton spectra are then extended into the higher energy range up to approximately 1 MeV, thereby supplementing the study of Sarris et al. (1981). The temporal behavior of the spectra in the higher energy range is discussed. It is found that below about 16 keV the proton spectra can be represented by a Maxwellian distribution; above this level, a suprathermal tail is found that cannot be represented by a single power law.

Analytical approximations to the Hotelling trace for digital x-ray detectors

NASA Astrophysics Data System (ADS)

Clarkson, Eric; Pineda, Angel R.; Barrett, Harrison H.

2001-06-01

The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.

Time and Memory Efficient Online Piecewise Linear Approximation of Sensor Signals.

PubMed

Grützmacher, Florian; Beichler, Benjamin; Hein, Albert; Kirste, Thomas; Haubelt, Christian

2018-05-23

Piecewise linear approximation of sensor signals is a well-known technique in the fields of Data Mining and Activity Recognition. In this context, several algorithms have been developed, some of them with the purpose to be performed on resource constrained microcontroller architectures of wireless sensor nodes. While microcontrollers are usually constrained in computational power and memory resources, all state-of-the-art piecewise linear approximation techniques either need to buffer sensor data or have an execution time depending on the segment’s length. In the paper at hand, we propose a novel piecewise linear approximation algorithm, with a constant computational complexity as well as a constant memory complexity. Our proposed algorithm’s worst-case execution time is one to three orders of magnitude smaller and its average execution time is three to seventy times smaller compared to the state-of-the-art Piecewise Linear Approximation (PLA) algorithms in our experiments. In our evaluations, we show that our algorithm is time and memory efficient without sacrificing the approximation quality compared to other state-of-the-art piecewise linear approximation techniques, while providing a maximum error guarantee per segment, a small parameter space of only one parameter, and a maximum latency of one sample period plus its worst-case execution time.

Polynomial approximation of functions of matrices and its application to the solution of a general system of linear equations

NASA Technical Reports Server (NTRS)

Tal-Ezer, Hillel

1987-01-01

During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described.

Polymerization shrinkage and hygroscopic expansion of contemporary posterior resin-based filling materials--a comparative study.

PubMed

Rüttermann, Stefan; Krüger, Sören; Raab, Wolfgang H-M; Janda, Ralf

2007-10-01

To investigate the polymerization shrinkage and hygroscopic expansion of contemporary posterior resin-based filling materials. The densities of SureFil (SU), CeramXMono (CM), Clearfil AP-X (CF), Solitaire 2 (SO), TetricEvoCeram (TE), and Filtek P60 (FT) were measured using the Archimedes' principle prior to and 15min after curing for 20, 40 and 60s and after 1h, 24h, 7 d, and 30 d storage at 37 degrees C in water. Volumetric changes (DeltaV) in percent after polymerization and after each storage period in water were calculated from the changes of densities. Water sorption and solubility were determined after 30 d for all specimens and their curing times. Two-way ANOVA was calculated for shrinkage and repeated measures ANOVA was calculated for hygroscopic expansion (p<0.05). DeltaV depended on filler load but not on curing time (SU approximately -2.0%, CM approximately -2.6%, CF approximately -2.1%, SO approximately -3.3%, TE approximately -1.7%, FT approximately -1.8%). Hygroscopic expansion depended on water sorption and solubility. Except for SU, all materials showed DeltaV approximately +1% after water storage. Polymerization shrinkage depended on the type of resin-based filling material but not on curing time. Shrinkage was not compensated by hygroscopic expansion.

A rotor optimization using regression analysis

NASA Technical Reports Server (NTRS)

Giansante, N.

1984-01-01

The design and development of helicopter rotors is subject to the many design variables and their interactions that effect rotor operation. Until recently, selection of rotor design variables to achieve specified rotor operational qualities has been a costly, time consuming, repetitive task. For the past several years, Kaman Aerospace Corporation has successfully applied multiple linear regression analysis, coupled with optimization and sensitivity procedures, in the analytical design of rotor systems. It is concluded that approximating equations can be developed rapidly for a multiplicity of objective and constraint functions and optimizations can be performed in a rapid and cost effective manner; the number and/or range of design variables can be increased by expanding the data base and developing approximating functions to reflect the expanded design space; the order of the approximating equations can be expanded easily to improve correlation between analyzer results and the approximating equations; gradients of the approximating equations can be calculated easily and these gradients are smooth functions reducing the risk of numerical problems in the optimization; the use of approximating functions allows the problem to be started easily and rapidly from various initial designs to enhance the probability of finding a global optimum; and the approximating equations are independent of the analysis or optimization codes used.

Approximate kernel competitive learning.

PubMed

Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang

2015-03-01

Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.

Testing the Ginzburg-Landau approximation for three-flavor crystalline color superconductivity

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

Mannarelli, Massimo; Sharma, Rishi; Rajagopal, Krishna

2006-06-01

It is an open challenge to analyze the crystalline color superconducting phases that may arise in cold dense, but not asymptotically dense, three-flavor quark matter. At present the only approximation within which it seems possible to compare the free energies of the myriad possible crystal structures is the Ginzburg-Landau approximation. Here, we test this approximation on a particularly simple 'crystal' structure in which there are only two condensates {approx}{delta}exp(iq{sub 2}{center_dot}r) and {approx}{delta}exp(iq{sub 3}{center_dot}r) whose position-space dependence is that of two plane waves with wave vectors q{sub 2} and q{sub 3} at arbitrary angles. For this case, we are able tomore » solve the mean-field gap equation without making a Ginzburg-Landau approximation. We find that the Ginzburg-Landau approximation works in the {delta}{yields}0 limit as expected, find that it correctly predicts that {delta} decreases with increasing angle between q{sub 2} and q{sub 3} meaning that the phase with q{sub 2} parallel q{sub 3} has the lowest free energy, and find that the Ginzburg-Landau approximation is conservative in the sense that it underestimates {delta} at all values of the angle between q{sub 2} and q{sub 3}.« less

Energetics of the magnetosphere

NASA Technical Reports Server (NTRS)

Stern, D. P.

1980-01-01

The approximate magnitudes of several power inputs and energies associated with the Earth's magnetosphere will be derived. They include: Solar wind power impinging on the dayside magnetopause approximately 1.4 10 to the 13th power watt; power input to cross tail current approximately 3 10 to the 11th power watt; energy of moderate magnetic storm approximately 2 10 to the 15th power joule; power related to the flow of j approximately 1 to 3 10 to the 11th power watt; average power deposited by the aurora approximately 2 10 to the 10th power watt. Stored magnetic energy: released in a substorm approximately 1.5 10 to the 14th power joule. Compared to the above, the rate at which energy is released locally in magnetospheric regions where magnetic merging occurs is probably small. Merging is essential, however, for the existence of open field lines, which provide the most likely explanation for some major energy inputs listed here. Merging is also required if part of the open flux of the tail lobes is converted into closed flux, as seems to happen during substorms. Again, most of the energy release becomes evident only beyond the merging region, though some particles may gain appreciable energy in that region itself, if the plasma sheet is completely squeezed out and the high latitude lobes interact directly.

Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

DOE PAGES

Kilcrease, D. P.; Brookes, S.

2013-08-19

The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. Additionally, a simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure formore » the Born cross-sections that employs the Elwert–Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. Furthermore, we also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.« less

Sources of sedimentary PAHs in tropical Asian waters: differentiation between pyrogenic and petrogenic sources by alkyl homolog abundance.

PubMed

Saha, Mahua; Togo, Ayako; Mizukawa, Kaoruko; Murakami, Michio; Takada, Hideshige; Zakaria, Mohamad P; Chiem, Nguyen H; Tuyen, Bui Cach; Prudente, Maricar; Boonyatumanond, Ruchaya; Sarkar, Santosh Kumar; Bhattacharya, Badal; Mishra, Pravakar; Tana, Touch Seang

2009-02-01

We collected surface sediment samples from 174 locations in India, Indonesia, Malaysia, Thailand, Vietnam, Cambodia, Laos, and the Philippines and analyzed them for polycyclic aromatic hydrocarbons (PAHs) and hopanes. PAHs were widely distributed in the sediments, with comparatively higher concentrations in urban areas (Sigma PAHs: approximately 1000 to approximately 100,000 ng/g-dry) than in rural areas ( approximately 10 to approximately 100g-dry), indicating large sources of PAHs in urban areas. To distinguish petrogenic and pyrogenic sources of PAHs, we calculated the ratios of alkyl PAHs to parent PAHs: methylphenanthrenes to phenanthrene (MP/P), methylpyrenes+methylfluoranthenes to pyrene+fluoranthene (MPy/Py), and methylchrysenes+methylbenz[a]anthracenes to chrysene+benz[a]anthracene (MC/C). Analysis of source materials (crude oil, automobile exhaust, and coal and wood combustion products) gave thresholds of MP/P=0.4, MPy/Py=0.5, and MC/C=1.0 for exclusive combustion origin. All the combustion product samples had the ratios of alkyl PAHs to parent PAHs below these threshold values. Contributions of petrogenic and pyrogenic sources to the sedimentary PAHs were uneven among the homologs: the phenanthrene series had a greater petrogenic contribution, whereas the chrysene series had a greater pyrogenic contribution. All the Indian sediments showed a strong pyrogenic signature with MP/P approximately 0.5, MPy/Py approximately 0.1, and MC/C approximately 0.2, together with depletion of hopanes indicating intensive inputs of combustion products of coal and/or wood, probably due to the heavy dependence on these fuels as sources of energy. In contrast, sedimentary PAHs from all other tropical Asian cities were abundant in alkylated PAHs with MP/P approximately 1-4, MPy/Py approximately 0.3-1, and MC/C approximately 0.2-1.0, suggesting a ubiquitous input of petrogenic PAHs. Petrogenic contributions to PAH homologs varied among the countries: largest in Malaysia whereas inferior in Laos. The higher abundance of alkylated PAHs together with constant hopane profiles suggests widespread inputs of automobile-derived petrogenic PAHs to Asian waters.

The validity of flow approximations when simulating catchment-integrated flash floods

NASA Astrophysics Data System (ADS)

Bout, B.; Jetten, V. G.

2018-01-01

Within hydrological models, flow approximations are commonly used to reduce computation time. The validity of these approximations is strongly determined by flow height, flow velocity and the spatial resolution of the model. In this presentation, the validity and performance of the kinematic, diffusive and dynamic flow approximations are investigated for use in a catchment-based flood model. Particularly, the validity during flood events and for varying spatial resolutions is investigated. The OpenLISEM hydrological model is extended to implement both these flow approximations and channel flooding based on dynamic flow. The flow approximations are used to recreate measured discharge in three catchments, among which is the hydrograph of the 2003 flood event in the Fella river basin. Furthermore, spatial resolutions are varied for the flood simulation in order to investigate the influence of spatial resolution on these flow approximations. Results show that the kinematic, diffusive and dynamic flow approximation provide least to highest accuracy, respectively, in recreating measured discharge. Kinematic flow, which is commonly used in hydrological modelling, substantially over-estimates hydrological connectivity in the simulations with a spatial resolution of below 30 m. Since spatial resolutions of models have strongly increased over the past decades, usage of routed kinematic flow should be reconsidered. The combination of diffusive or dynamic overland flow and dynamic channel flooding provides high accuracy in recreating the 2003 Fella river flood event. Finally, in the case of flood events, spatial modelling of kinematic flow substantially over-estimates hydrological connectivity and flow concentration since pressure forces are removed, leading to significant errors.

Approximate likelihood calculation on a phylogeny for Bayesian estimation of divergence times.

PubMed

dos Reis, Mario; Yang, Ziheng

2011-07-01

The molecular clock provides a powerful way to estimate species divergence times. If information on some species divergence times is available from the fossil or geological record, it can be used to calibrate a phylogeny and estimate divergence times for all nodes in the tree. The Bayesian method provides a natural framework to incorporate different sources of information concerning divergence times, such as information in the fossil and molecular data. Current models of sequence evolution are intractable in a Bayesian setting, and Markov chain Monte Carlo (MCMC) is used to generate the posterior distribution of divergence times and evolutionary rates. This method is computationally expensive, as it involves the repeated calculation of the likelihood function. Here, we explore the use of Taylor expansion to approximate the likelihood during MCMC iteration. The approximation is much faster than conventional likelihood calculation. However, the approximation is expected to be poor when the proposed parameters are far from the likelihood peak. We explore the use of parameter transforms (square root, logarithm, and arcsine) to improve the approximation to the likelihood curve. We found that the new methods, particularly the arcsine-based transform, provided very good approximations under relaxed clock models and also under the global clock model when the global clock is not seriously violated. The approximation is poorer for analysis under the global clock when the global clock is seriously wrong and should thus not be used. The results suggest that the approximate method may be useful for Bayesian dating analysis using large data sets.

MRO's High Resolution Imaging Science Experiment (HiRISE): Polar Science Expectations

NASA Technical Reports Server (NTRS)

McEwen, A.; Herkenhoff, K.; Hansen, C.; Bridges, N.; Delamere, W. A.; Eliason, E.; Grant, J.; Gulick, V.; Keszthelyi, L.; Kirk, R.

2003-01-01

The Mars Reconnaissance Orbiter (MRO) is expected to launch in August 2005, arrive at Mars in March 2006, and begin the primary science phase in November 2006. MRO will carry a suite of remote-sensing instruments and is designed to routinely point off-nadir to precisely target locations on Mars for high-resolution observations. The mission will have a much higher data return than any previous planetary mission, with 34 Tbits of returned data expected in the first Mars year in the mapping orbit (255 x 320 km). The HiRISE camera features a 0.5 m telescope, 12 m focal length, and 14 CCDs. We expect to acquire approximately 10,000 observations in the primary science phase (approximately 1 Mars year), including approximately 2,000 images for 1,000 stereo targets. Each observation will be accompanied by a approximately 6 m/pixel image over a 30 x 45 km region acquired by MRO s context imager. Many HiRISE images will be full resolution in the center portion of the swath width and binned (typically 4x4) on the sides. This provides two levels of context, so we step out from 0.3 m/pixel to 1.2 m/pixel to 6 m/pixel (at 300 km altitude). We expect to cover approximately 1% of Mars at better than 1.2 m/pixel, approximately 0.1% at 0.3 m/pixel, approximately 0.1% in 3 colors, and approximately 0.05% in stereo. Our major challenge is to find the dey contacts, exposures and type morphologies to observe.

Simulation of water-table aquifers using specified saturated thickness

USGS Publications Warehouse

Sheets, Rodney A.; Hill, Mary C.; Haitjema, Henk M.; Provost, Alden M.; Masterson, John P.

2014-01-01

Simulating groundwater flow in a water-table (unconfined) aquifer can be difficult because the saturated thickness available for flow depends on model-calculated hydraulic heads. It is often possible to realize substantial time savings and still obtain accurate head and flow solutions by specifying an approximate saturated thickness a priori, thus linearizing this aspect of the model. This specified-thickness approximation often relies on the use of the “confined” option in numerical models, which has led to confusion and criticism of the method. This article reviews the theoretical basis for the specified-thickness approximation, derives an error analysis for relatively ideal problems, and illustrates the utility of the approximation with a complex test problem. In the transient version of our complex test problem, the specified-thickness approximation produced maximum errors in computed drawdown of about 4% of initial aquifer saturated thickness even when maximum drawdowns were nearly 20% of initial saturated thickness. In the final steady-state version, the approximation produced maximum errors in computed drawdown of about 20% of initial aquifer saturated thickness (mean errors of about 5%) when maximum drawdowns were about 35% of initial saturated thickness. In early phases of model development, such as during initial model calibration efforts, the specified-thickness approximation can be a very effective tool to facilitate convergence. The reduced execution time and increased stability obtained through the approximation can be especially useful when many model runs are required, such as during inverse model calibration, sensitivity and uncertainty analyses, multimodel analysis, and development of optimal resource management scenarios.

Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Yang, Yajun

2017-01-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

Finding the Best Quadratic Approximation of a Function

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2011-01-01

This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

27 CFR 9.128 - Seneca Lake.

Code of Federal Regulations, 2012 CFR

2012-04-01

... bridge over the New York State Barge Canal, follow the Canal south approximately 0.2 miles to the mouth... the Reading Center, N.Y. map; (5) Proceed west approximately 0.7 miles on County Road 23 to its... Yan, N.Y. and Dresden, N.Y. maps, for approximately 18 miles to its junction with an unnamed light...

27 CFR 9.128 - Seneca Lake.

Code of Federal Regulations, 2013 CFR

2013-04-01

... bridge over the New York State Barge Canal, follow the Canal south approximately 0.2 miles to the mouth... the Reading Center, N.Y. map; (5) Proceed west approximately 0.7 miles on County Road 23 to its... Yan, N.Y. and Dresden, N.Y. maps, for approximately 18 miles to its junction with an unnamed light...

27 CFR 9.128 - Seneca Lake.

Code of Federal Regulations, 2010 CFR

2010-04-01

... bridge over the New York State Barge Canal, follow the Canal south approximately 0.2 miles to the mouth... the Reading Center, N.Y. map; (5) Proceed west approximately 0.7 miles on County Road 23 to its... Yan, N.Y. and Dresden, N.Y. maps, for approximately 18 miles to its junction with an unnamed light...

27 CFR 9.128 - Seneca Lake.

Code of Federal Regulations, 2011 CFR

2011-04-01

... bridge over the New York State Barge Canal, follow the Canal south approximately 0.2 miles to the mouth... the Reading Center, N.Y. map; (5) Proceed west approximately 0.7 miles on County Road 23 to its... Yan, N.Y. and Dresden, N.Y. maps, for approximately 18 miles to its junction with an unnamed light...

27 CFR 9.41 - Lancaster Valley.

Code of Federal Regulations, 2013 CFR

2013-04-01

... boundary for approximately 0.9 mile to the 500 foot contour line immediately south of the Conestoga River... Township boundary. (3) Then south approximately 0.1 mile following the Caernarvon-East Earl Township boundary to U.S. Highway 322. (4) Then west following U.S. Highway 322 for approximately 1.7 miles to the...

27 CFR 9.41 - Lancaster Valley.

Code of Federal Regulations, 2014 CFR

2014-04-01

... boundary for approximately 0.9 mile to the 500 foot contour line immediately south of the Conestoga River... Township boundary. (3) Then south approximately 0.1 mile following the Caernarvon-East Earl Township boundary to U.S. Highway 322. (4) Then west following U.S. Highway 322 for approximately 1.7 miles to the...

27 CFR 9.128 - Seneca Lake.

Code of Federal Regulations, 2014 CFR

2014-04-01

... bridge over the New York State Barge Canal, follow the Canal south approximately 0.2 miles to the mouth... the Reading Center, N.Y. map; (5) Proceed west approximately 0.7 miles on County Road 23 to its... Yan, N.Y. and Dresden, N.Y. maps, for approximately 18 miles to its junction with an unnamed light...

27 CFR 9.41 - Lancaster Valley.

Code of Federal Regulations, 2012 CFR

2012-04-01

... boundary for approximately 0.9 mile to the 500 foot contour line immediately south of the Conestoga River... Township boundary. (3) Then south approximately 0.1 mile following the Caernarvon-East Earl Township boundary to U.S. Highway 322. (4) Then west following U.S. Highway 322 for approximately 1.7 miles to the...

27 CFR 9.124 - Wild Horse Valley.

Code of Federal Regulations, 2014 CFR

2014-04-01

... direction approximately .9 mile to the summit of an unnamed hill having a marked elevation of 1,804 feet; (3... 1,824 feet; (4) Then south-southeasterly approximately .6 mile to the summit of an unnamed hill having a marked elevation of 1,866 feet; (5) Then south-southeasterly approximately .5 mile to the summit...

27 CFR 9.194 - San Antonio Valley.

Code of Federal Regulations, 2014 CFR

2014-04-01

... southeast in a straight line for approximately 5 miles across sections 24 and 25, T23S, R9E, and sections 30... Tierra Redonda Mountain map; then (3) Continue southeast in a straight line for approximately 3.25 miles... the Bradley map; then (4) Proceed straight south for approximately 2.5 miles along the eastern...

27 CFR 9.124 - Wild Horse Valley.

Code of Federal Regulations, 2013 CFR

2013-04-01

... direction approximately .9 mile to the summit of an unnamed hill having a marked elevation of 1,804 feet; (3... 1,824 feet; (4) Then south-southeasterly approximately .6 mile to the summit of an unnamed hill having a marked elevation of 1,866 feet; (5) Then south-southeasterly approximately .5 mile to the summit...

27 CFR 9.124 - Wild Horse Valley.

Code of Federal Regulations, 2012 CFR

2012-04-01

... direction approximately .9 mile to the summit of an unnamed hill having a marked elevation of 1,804 feet; (3... 1,824 feet; (4) Then south-southeasterly approximately .6 mile to the summit of an unnamed hill having a marked elevation of 1,866 feet; (5) Then south-southeasterly approximately .5 mile to the summit...

27 CFR 9.106 - North Yuba.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 1,900-foot contour line, approximately 0.75 mile north of Finley Ranch; (11) Then north along said... indiana Creek, approximately 0.87 mile, to the point where Indiana Creek meets the 2,000-foot contour line.... 17 N., R. 6 E., the boundary proceeds northeasterly in a meandering line approximately 1.5 miles...

27 CFR 9.106 - North Yuba.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 1,900-foot contour line, approximately 0.75 mile north of Finley Ranch; (11) Then north along said... indiana Creek, approximately 0.87 mile, to the point where Indiana Creek meets the 2,000-foot contour line.... 17 N., R. 6 E., the boundary proceeds northeasterly in a meandering line approximately 1.5 miles...

27 CFR 9.134 - Oakville.

Code of Federal Regulations, 2014 CFR

2014-04-01

... Highway 29, then continuing in a straight line approximately .1 mile to the peak of the 320+ foot hill... direction in a straight line approximately 1.7 miles along Skellenger Lane, past its intersection with Conn... quadrangle map); (2) Then south along the center of the river bed approximately .4 miles to the point where...

27 CFR 9.134 - Oakville.

Code of Federal Regulations, 2012 CFR

2012-04-01

... Highway 29, then continuing in a straight line approximately .1 mile to the peak of the 320+ foot hill... direction in a straight line approximately 1.7 miles along Skellenger Lane, past its intersection with Conn... quadrangle map); (2) Then south along the center of the river bed approximately .4 miles to the point where...

27 CFR 9.106 - North Yuba.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 1,900-foot contour line, approximately 0.75 mile north of Finley Ranch; (11) Then north along said... indiana Creek, approximately 0.87 mile, to the point where Indiana Creek meets the 2,000-foot contour line.... 17 N., R. 6 E., the boundary proceeds northeasterly in a meandering line approximately 1.5 miles...

An Evaluation of Three Approximate Item Response Theory Models for Equating Test Scores.

ERIC Educational Resources Information Center

Marco, Gary L.; And Others

Three item response models were evaluated for estimating item parameters and equating test scores. The models, which approximated the traditional three-parameter model, included: (1) the Rasch one-parameter model, operationalized in the BICAL computer program; (2) an approximate three-parameter logistic model based on coarse group data divided…

76 FR 39063 - Proposed Flood Elevation Determinations

Federal Register 2010, 2011, 2012, 2013, 2014

2011-07-05

...,000 None +6802 feet upstream of Rodeo Road. Arroyo De La Piedra Approximately 300 feet +7099 +7103... +7043 City of Santa Fe. upstream of the Arroyo De La Piedra confluence. Approximately 600 feet None.... Approximately 0.3 mile None +7780 upstream of La Entrada. East Arroyo De La Piedra At the Arroyo De La None...

A Monte Carlo Study on the Performance of a Corrected Formula for Epsilon Approximate Suggested by Lecoutre.

ERIC Educational Resources Information Center

Chen, Ru San; Dunlap, William P.

1994-01-01

The present simulation study confirms that the corrected epsilon approximate test of B. Lecoutre yields a less biased estimation of population epsilon and reduces Type I error rates when compared to the epsilon approximate test of H. Huynh and L. S. Feldt. (SLD)

77 FR 60114 - Agency Information Collection Activities Under OMB Review

Federal Register 2010, 2011, 2012, 2013, 2014

2012-10-02

... approximately 100 entities on a daily basis. The recordkeeping requirement of section 22.5 is expected to apply to approximately 100 entities on an approximately annual basis. Based on experience with analogous... required by section 22.2(g) is expected to require about 100 hours annually per entity, for a total burden...

Animations as a Transformational Approximation of Practice for Preservice Teachers to Communicate Professional Noticing

ERIC Educational Resources Information Center

Amador, Julie; Weston, Tracy; Estapa, Anne; Kosko, Karl; De Araujo, Zandra

2016-01-01

This paper explores the use of animations as an approximation of practice to provide a transformational technology experience for elementary mathematics preservice teachers. Preservice teachers in mathematics methods courses at six universities (n = 126) engaged in a practice of decomposing and approximating components of a fraction lesson. Data…

Techniques for assessing the environmental outcomes of conservation practices applied to rangeland watersheds

USDA-ARS?s Scientific Manuscript database

Grazing lands are the most dominate land cover type in the United States with approximately 311.7 Mha being defined as rangelands. Approximately 53% of the Nation’s rangelands are owned and managed by the private sector while the Federal government manages approximately 43% of the Nation’s rangelan...

75 FR 1401 - Notice of Intent To Prepare a Draft Environmental Impact Statement for the Baldwin Hills Crenshaw...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-01-11

... approximately 535,000 square feet), two grocery stores (totaling approximately 85,000 square feet), restaurants (both in mall and as stand-alone restaurants totaling approximately 156,000 square feet), a movie... with meeting rooms and two restaurants, and 551 condominium units, and 410 apartment units...

Model Program: Brillion High School, Brillion, Wisconsin

ERIC Educational Resources Information Center

Meyer, Steve

2007-01-01

The Brillion School District is located in Brillion, Wisconsin, approximately 20 miles south of Green Bay in the heart of the Fox Valley. Brillion High School (BHS) has approximately 330 students in Grades 9-12. Brillion is home to approximately 3000 residents. Interestingly, Brillion also serves as the headquarters of three major manufacturing…

75 FR 69089 - Guidance for Industry and Food and Drug Administration Staff; Class II Special Controls Guidance...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-11-10

...: Tissue Adhesive With Adjunct Wound Closure Device Intended for the Topical Approximation of Skin... Document: Tissue Adhesive with Adjunct Wound Closure Device Intended for the Topical Approximation of Skin... intended for the topical approximation of skin may comply with the requirement of special controls for...

Computational methods for estimation of parameters in hyperbolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.; Murphy, K. A.

1983-01-01

Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized.

The Role of Intuitive Approximation Skills for School Math Abilities

ERIC Educational Resources Information Center

Libertus, Melissa E.

2015-01-01

Research has shown that educated children and adults have access to two ways of representing numerical information: an approximate number system (ANS) that is present from birth and allows for quick approximations of numbers of objects encountered in one's environment, and an exact number system (ENS) that is acquired through experience and…

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1988-01-01

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

Is approximated de-epithelized glanuloplasty beneficial for hypospadiologist?

PubMed

ZakiEldahshoury, M; Gamal, W; Salem, E; Rashed, E; Mamdouh, A

2016-05-01

Further evaluation of the cosmetic and functional results of approximated de-epithelized glanuloplasty in different degree of hypospadias. This study included 96 male patients (DPH=68 & MPH=28). Patients selected for repair with glans approximation should have wide urethral plate & grooved glans. All cases were repaired with the classic TIP and glans approximation technique. Follow up was for one year by clinical examination of the meatal shape, size & site, glans shape, skin covering, suture line, urethral catheter, edema & fistula in addition to parent satisfaction. Mean operative time was 49±9minutes. As regards the functional and cosmetic outcomes, success was reported in 95.8%, while failure was in 4.16% in the form of glanular disruption in two patients and subcoronal urethrocutaneous fistula in another two patients. Glans approximation has many advantages, good cosmetic and functional results, short operative time, less blood loss, no need for tourniquet. Study of a large number of cases and comparing glans approximation with the classic TIP technique. Copyright © 2015 AEU. Publicado por Elsevier España, S.L.U. All rights reserved.

A walk through the approximations of ab initio multiple spawning

NASA Astrophysics Data System (ADS)

Mignolet, Benoit; Curchod, Basile F. E.

2018-04-01

Full multiple spawning offers an in principle exact framework for excited-state dynamics, where nuclear wavefunctions in different electronic states are represented by a set of coupled trajectory basis functions that follow classical trajectories. The couplings between trajectory basis functions can be approximated to treat molecular systems, leading to the ab initio multiple spawning method which has been successfully employed to study the photochemistry and photophysics of several molecules. However, a detailed investigation of its approximations and their consequences is currently missing in the literature. In this work, we simulate the explicit photoexcitation and subsequent excited-state dynamics of a simple system, LiH, and we analyze (i) the effect of the ab initio multiple spawning approximations on different observables and (ii) the convergence of the ab initio multiple spawning results towards numerically exact quantum dynamics upon a progressive relaxation of these approximations. We show that, despite the crude character of the approximations underlying ab initio multiple spawning for this low-dimensional system, the qualitative excited-state dynamics is adequately captured, and affordable corrections can further be applied to ameliorate the coupling between trajectory basis functions.

Accuracy of the adiabatic-impulse approximation for closed and open quantum systems

NASA Astrophysics Data System (ADS)

Tomka, Michael; Campos Venuti, Lorenzo; Zanardi, Paolo

2018-03-01

We study the adiabatic-impulse approximation (AIA) as a tool to approximate the time evolution of quantum states when driven through a region of small gap. Such small-gap regions are a common situation in adiabatic quantum computing and having reliable approximations is important in this context. The AIA originates from the Kibble-Zurek theory applied to continuous quantum phase transitions. The Kibble-Zurek mechanism was developed to predict the power-law scaling of the defect density across a continuous quantum phase transition. Instead, here we quantify the accuracy of the AIA via the trace norm distance with respect to the exact evolved state. As expected, we find that for short times or fast protocols, the AIA outperforms the simple adiabatic approximation. However, for large times or slow protocols, the situation is actually reversed and the AIA provides a worse approximation. Nevertheless, we found a variation of the AIA that can perform better than the adiabatic one. This counterintuitive modification consists in crossing the region of small gap twice. Our findings are illustrated by several examples of driven closed and open quantum systems.

Course 4: Density Functional Theory, Methods, Techniques, and Applications

NASA Astrophysics Data System (ADS)

Chrétien, S.; Salahub, D. R.

Contents 1 Introduction 2 Density functional theory 2.1 Hohenberg and Kohn theorems 2.2 Levy's constrained search 2.3 Kohn-Sham method 3 Density matrices and pair correlation functions 4 Adiabatic connection or coupling strength integration 5 Comparing and constrasting KS-DFT and HF-CI 6 Preparing new functionals 7 Approximate exchange and correlation functionals 7.1 The Local Spin Density Approximation (LSDA) 7.2 Gradient Expansion Approximation (GEA) 7.3 Generalized Gradient Approximation (GGA) 7.4 meta-Generalized Gradient Approximation (meta-GGA) 7.5 Hybrid functionals 7.6 The Optimized Effective Potential method (OEP) 7.7 Comparison between various approximate functionals 8 LAP correlation functional 9 Solving the Kohn-Sham equations 9.1 The Kohn-Sham orbitals 9.2 Coulomb potential 9.3 Exchange-correlation potential 9.4 Core potential 9.5 Other choices and sources of error 9.6 Functionality 10 Applications 10.1 Ab initio molecular dynamics for an alanine dipeptide model 10.2 Transition metal clusters: The ecstasy, and the agony... 10.3 The conversion of acetylene to benzene on Fe clusters 11 Conclusions

Using radiance predicted by the P3 approximation in a spherical geometry to predict tissue optical properties

NASA Astrophysics Data System (ADS)

Dickey, Dwayne J.; Moore, Ronald B.; Tulip, John

2001-01-01

For photodynamic therapy of solid tumors, such as prostatic carcinoma, to be achieved, an accurate model to predict tissue parameters and light dose must be found. Presently, most analytical light dosimetry models are fluence based and are not clinically viable for tissue characterization. Other methods of predicting optical properties, such as Monet Carlo, are accurate but far too time consuming for clinical application. However, radiance predicted by the P3-Approximation, an anaylitical solution to the transport equation, may be a viable and accurate alternative. The P3-Approximation accurately predicts optical parameters in intralipid/methylene blue based phantoms in a spherical geometry. The optical parameters furnished by the radiance, when introduced into fluence predicted by both P3- Approximation and Grosjean Theory, correlate well with experimental data. The P3-Approximation also predicts the optical properties of prostate tissue, agreeing with documented optical parameters. The P3-Approximation could be the clinical tool necessary to facilitate PDT of solid tumors because of the limited number of invasive measurements required and the speed in which accurate calculations can be performed.

Einstein Observatory solid state spectrometer observations of M87 and the Virgo cluster

NASA Technical Reports Server (NTRS)

Lea, S. M.; Mushotzky, R. F.; Holt, S. S.

1982-01-01

X-ray observations of the galaxy M87 and of a region in the Virgo cluster displaced 7 minutes from the center of M87 are presented. X-ray spectra are obtained at these two locations with the slid state spectrometer onboard the Einstein Observatory. Emission lines were observed in both locations, indicating the presence of heavy elements at abundances approximately solar (to within a factor of 2). A temperature gradient, T increases from approximately 1.4 keV at the position of M87 to T approximately 3.35 keV 7' away, was detected. There is lower temperature thermal emission at the center of M87 with T approximately 0.6 keV, consistent with models for cooling flows in this cluster. In addition to the thermal emission, a power law component in the spectrum of M87, was detected consistent with that observed by HEAO-1, indicating that this component probably originates in the galaxy itself. The presence of intracluster gas having density approximately .001 cu cm and temperature approximately 30 million K is indicated.

Second order nonlinear QED processes in ultra-strong laser fields

NASA Astrophysics Data System (ADS)

Mackenroth, Felix

2017-10-01

In the interaction of ultra-intense laser fields with matter the ever increasing peak laser intensities render nonlinear QED effects ever more important. For long, ultra-intense laser pulses scattering large systems, like a macroscopic plasma, the interaction time can be longer than the scattering time, leading to multiple scatterings. These are usually approximated as incoherent cascades of single-vertex processes. Under certain conditions, however, this common cascade approximation may be insufficient, as it disregards several effects such as coherent processes, quantum interferences or pulse shape effects. Quantifying deviations of the full amplitude of multiple scatterings from the commonly employed cascade approximations is a formidable, yet unaccomplished task. In this talk we are going to discuss how to compute second order nonlinear QED amplitudes and relate them to the conventional cascade approximation. We present examples for typical second order processes and benchmark the full result against common approximations. We demonstrate that the approximation of multiple nonlinear QED scatterings as a cascade of single interactions has certain limitations and discuss these limits in light of upcoming experimental tests.

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Gottlieb, David; Tadmor, Eitan

1991-01-01

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Gottlieb, David; Tadmor, Eitan

1990-01-01

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks

NASA Astrophysics Data System (ADS)

Bronstein, Leo; Koeppl, Heinz

2018-01-01

Approximate solutions of the chemical master equation and the chemical Fokker-Planck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the moment-closure approach used to obtain such approximations, calling it an ad hoc method. In this article, we give a new variational derivation of moment-closure equations which provides us with an intuitive understanding of their properties and failure modes and allows us to correct some of these problems. We use mixtures of product-Poisson distributions to obtain a flexible parametric family which solves the commonly observed problem of divergences at low system sizes. We also extend the recently introduced entropic matching approach to arbitrary ansatz distributions and Markov processes, demonstrating that it is a special case of variational moment closure. This provides us with a particularly principled approximation method. Finally, we extend the above approaches to cover the approximation of multi-time joint distributions, resulting in a viable alternative to process-level approximations which are often intractable.

A walk through the approximations of ab initio multiple spawning.

PubMed

Mignolet, Benoit; Curchod, Basile F E

2018-04-07

Full multiple spawning offers an in principle exact framework for excited-state dynamics, where nuclear wavefunctions in different electronic states are represented by a set of coupled trajectory basis functions that follow classical trajectories. The couplings between trajectory basis functions can be approximated to treat molecular systems, leading to the ab initio multiple spawning method which has been successfully employed to study the photochemistry and photophysics of several molecules. However, a detailed investigation of its approximations and their consequences is currently missing in the literature. In this work, we simulate the explicit photoexcitation and subsequent excited-state dynamics of a simple system, LiH, and we analyze (i) the effect of the ab initio multiple spawning approximations on different observables and (ii) the convergence of the ab initio multiple spawning results towards numerically exact quantum dynamics upon a progressive relaxation of these approximations. We show that, despite the crude character of the approximations underlying ab initio multiple spawning for this low-dimensional system, the qualitative excited-state dynamics is adequately captured, and affordable corrections can further be applied to ameliorate the coupling between trajectory basis functions.

Rational trigonometric approximations using Fourier series partial sums

NASA Technical Reports Server (NTRS)

Geer, James F.

1993-01-01

A class of approximations (S(sub N,M)) to a periodic function f which uses the ideas of Pade, or rational function, approximations based on the Fourier series representation of f, rather than on the Taylor series representation of f, is introduced and studied. Each approximation S(sub N,M) is the quotient of a trigonometric polynomial of degree N and a trigonometric polynomial of degree M. The coefficients in these polynomials are determined by requiring that an appropriate number of the Fourier coefficients of S(sub N,M) agree with those of f. Explicit expressions are derived for these coefficients in terms of the Fourier coefficients of f. It is proven that these 'Fourier-Pade' approximations converge point-wise to (f(x(exp +))+f(x(exp -)))/2 more rapidly (in some cases by a factor of 1/k(exp 2M)) than the Fourier series partial sums on which they are based. The approximations are illustrated by several examples and an application to the solution of an initial, boundary value problem for the simple heat equation is presented.

Formal properties of the probability of fixation: identities, inequalities and approximations.

PubMed

McCandlish, David M; Epstein, Charles L; Plotkin, Joshua B

2015-02-01

The formula for the probability of fixation of a new mutation is widely used in theoretical population genetics and molecular evolution. Here we derive a series of identities, inequalities and approximations for the exact probability of fixation of a new mutation under the Moran process (equivalent results hold for the approximate probability of fixation under the Wright-Fisher process, after an appropriate change of variables). We show that the logarithm of the fixation probability has particularly simple behavior when the selection coefficient is measured as a difference of Malthusian fitnesses, and we exploit this simplicity to derive inequalities and approximations. We also present a comprehensive comparison of both existing and new approximations for the fixation probability, highlighting those approximations that induce a reversible Markov chain when used to describe the dynamics of evolution under weak mutation. To demonstrate the power of these results, we consider the classical problem of determining the total substitution rate across an ensemble of biallelic loci and prove that, at equilibrium, a strict majority of substitutions are due to drift rather than selection. Copyright © 2014 Elsevier Inc. All rights reserved.

Conformational equilibria of alkanes in aqueous solution: relationship to water structure near hydrophobic solutes.

PubMed Central

Ashbaugh, H S; Garde, S; Hummer, G; Kaler, E W; Paulaitis, M E

1999-01-01

Conformational free energies of butane, pentane, and hexane in water are calculated from molecular simulations with explicit waters and from a simple molecular theory in which the local hydration structure is estimated based on a proximity approximation. This proximity approximation uses only the two nearest carbon atoms on the alkane to predict the local water density at a given point in space. Conformational free energies of hydration are subsequently calculated using a free energy perturbation method. Quantitative agreement is found between the free energies obtained from simulations and theory. Moreover, free energy calculations using this proximity approximation are approximately four orders of magnitude faster than those based on explicit water simulations. Our results demonstrate the accuracy and utility of the proximity approximation for predicting water structure as the basis for a quantitative description of n-alkane conformational equilibria in water. In addition, the proximity approximation provides a molecular foundation for extending predictions of water structure and hydration thermodynamic properties of simple hydrophobic solutes to larger clusters or assemblies of hydrophobic solutes. PMID:10423414

Towards syntactic characterizations of approximation schemes via predicate and graph decompositions

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

Hunt, H.B. III; Stearns, R.E.; Jacob, R.

1998-12-01

The authors present a simple extensible theoretical framework for devising polynomial time approximation schemes for problems represented using natural syntactic (algebraic) specifications endowed with natural graph theoretic restrictions on input instances. Direct application of the technique yields polynomial time approximation schemes for all the problems studied in [LT80, NC88, KM96, Ba83, DTS93, HM+94a, HM+94] as well as the first known approximation schemes for a number of additional combinatorial problems. One notable aspect of the work is that it provides insights into the structure of the syntactic specifications and the corresponding algorithms considered in [KM96, HM+94]. The understanding allows them tomore » extend the class of syntactic specifications for which generic approximation schemes can be developed. The results can be shown to be tight in many cases, i.e. natural extensions of the specifications can be shown to yield non-approximable problems. The results provide a non-trivial characterization of a class of problems having a PTAS and extend the earlier work on this topic by [KM96, HM+94].« less

ɛ-connectedness, finite approximations, shape theory and coarse graining in hyperspaces

NASA Astrophysics Data System (ADS)

Alonso-Morón, Manuel; Cuchillo-Ibanez, Eduardo; Luzón, Ana

2008-12-01

We use upper semifinite hyperspaces of compacta to describe ε-connectedness and to compute homology from finite approximations. We find a new connection between ε-connectedness and the so-called Shape Theory. We construct a geodesically complete R-tree, by means of ε-components at different resolutions, whose behavior at infinite captures the topological structure of the space of components of a given compact metric space. We also construct inverse sequences of finite spaces using internal finite approximations of compact metric spaces. These sequences can be converted into inverse sequences of polyhedra and simplicial maps by means of what we call the Alexandroff-McCord correspondence. This correspondence allows us to relate upper semifinite hyperspaces of finite approximation with the Vietoris-Rips complexes of such approximations at different resolutions. Two motivating examples are included in the introduction. We propose this procedure as a different mathematical foundation for problems on data analysis. This process is intrinsically related to the methodology of shape theory. This paper reinforces Robins’s idea of using methods from shape theory to compute homology from finite approximations.

Effects of fluorescent dyes, quenchers, and dangling ends on DNA duplex stability.

PubMed

Moreira, Bernardo G; You, Yong; Behlke, Mark A; Owczarzy, Richard

2005-02-11

Single and dual-labeled fluorescent oligodeoxynucleotides are used in many molecular biology applications. We investigated the effects of commonly used fluorescent dyes and quenchers on the thermodynamic stability of a model probe-target DNA duplex. We demonstrate that those effects can be significant. Fluorescent dyes and quenchers were attached to the probe ends. In certain combinations, these groups stabilized the duplex up to 1.8kcal/mol and increased T(m) up to 4.3 degrees C. None of the groups tested significantly destabilized the duplex. Rank order of potency was, starting with the most stabilizing group: Iowa Black RQ approximately Black Hole 2>Cy5 approximately Cy3>Black Hole 1>QSY7 approximately Iowa Black FQ>Texas Red approximately TAMRA>FAM approximately HEX approximately Dabcyl>TET. Longer linkers decreased stabilizing effects. Hybridizations to targets with various dangling ends were also studied and were found to have only minor effects on thermodynamic stability. Depending on the dye/quencher combination employed, it can be important to include thermodynamic contributions from fluorophore and quencher when designing oligonucleotide probe assays.

Adaptive control using neural networks and approximate models.

PubMed

Narendra, K S; Mukhopadhyay, S

1997-01-01

The NARMA model is an exact representation of the input-output behavior of finite-dimensional nonlinear discrete-time dynamical systems in a neighborhood of the equilibrium state. However, it is not convenient for purposes of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate methods are used for realizing the neural controllers to overcome computational complexity. In this paper, we introduce two classes of models which are approximations to the NARMA model, and which are linear in the control input. The latter fact substantially simplifies both the theoretical analysis as well as the practical implementation of the controller. Extensive simulation studies have shown that the neural controllers designed using the proposed approximate models perform very well, and in many cases even better than an approximate controller designed using the exact NARMA model. In view of their mathematical tractability as well as their success in simulation studies, a case is made in this paper that such approximate input-output models warrant a detailed study in their own right.

An approximate generalized linear model with random effects for informative missing data.

PubMed

Follmann, D; Wu, M

1995-03-01

This paper develops a class of models to deal with missing data from longitudinal studies. We assume that separate models for the primary response and missingness (e.g., number of missed visits) are linked by a common random parameter. Such models have been developed in the econometrics (Heckman, 1979, Econometrica 47, 153-161) and biostatistics (Wu and Carroll, 1988, Biometrics 44, 175-188) literature for a Gaussian primary response. We allow the primary response, conditional on the random parameter, to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness. The resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects. An example is given to illustrate the approximate approach, and simulations are performed to critique the adequacy of the approximation for repeated binary data.

Two types of electron events in solar flares

NASA Technical Reports Server (NTRS)

Daibog, E. I.; Kurt, V. G.; Logachev, Y. I.; Stolpovsky, V. G.

1985-01-01

The fluxes and spectra of the flare electrons measured on board Venera-I3 and I4 space probes are compared with the parameters of the hard (E sub x approximately 55 keV) and thermal X-ray bursts. The electron flux amplitude has been found to correlate with flare importance in the thermal X-ray range (r approximately 0.8). The following two types of flare events have been found in the electron component of SCR. The electron flux increase is accompanied by a hard X-ray burst and the electron spectrum index in the approximately 25 to 200 keV energy range is gamma approximately 2 to 3. The electron flux increase is not accompanied by a hard X-ray burst and the electron spectrum is softer (Delta gamma approximately 0.7 to 1.0).

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

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

Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less

Approximations used in calculating many-body effects in resonant ((dt. mu. )dee) formation

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

Cohen, J.S.; Leon, M.

1989-02-01

The approximations needed to treat the resonant formation of the compound molecule ((dt..mu..)dee)/sup */ as a line-broadening process are examined. The necessary criteria for applying the impact (Lorentzian) approximation are shown to be seriously violated under the usual conditions of muon-catalyzed fusion. Neither the condition for binary collisions nor the requirement that the detuning not be too large holds. A much more appropriate description is the many-body quasistatic approximation, which is valid for large detunings at any density and for practically the whole profile at high densities. The convenient factorization of the three-body rate into a convolution of a two-bodymore » rate with a broadening factor is shown to hold within some approximations, but the broadening factor itself depends on the transition being considered.« less

Approximating the Helium Wavefunction in Positronium-Helium Scattering

NASA Technical Reports Server (NTRS)

DiRienzi, Joseph; Drachman, Richard J.

2003-01-01

In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.

Approximation concepts for efficient structural synthesis

NASA Technical Reports Server (NTRS)

Schmit, L. A., Jr.; Miura, H.

1976-01-01

It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role.

Approximations to the exact exchange potential: KLI versus semilocal

NASA Astrophysics Data System (ADS)

Tran, Fabien; Blaha, Peter; Betzinger, Markus; Blügel, Stefan

2016-10-01

In the search for an accurate and computationally efficient approximation to the exact exchange potential of Kohn-Sham density functional theory, we recently compared various semilocal exchange potentials to the exact one [F. Tran et al., Phys. Rev. B 91, 165121 (2015), 10.1103/PhysRevB.91.165121]. It was concluded that the Becke-Johnson (BJ) potential is a very good starting point, but requires the use of empirical parameters to obtain good agreement with the exact exchange potential. In this work, we extend the comparison by considering the Krieger-Li-Iafrate (KLI) approximation, which is a beyond-semilocal approximation. It is shown that overall the KLI- and BJ-based potentials are the most reliable approximations to the exact exchange potential, however, sizable differences, especially for the antiferromagnetic transition-metal oxides, can be obtained.

Analysis of iodide and iodate in Lake Mead, Nevada using a headspace derivatization gas chromatography-mass spectrometry.

PubMed

Dorman, James W; Steinberg, Spencer M

2010-02-01

We report here a derivatization headspace method for the analysis of inorganic iodine in water. Samples from Lake Mead, the Las Vegas Wash, and from Las Vegas tap water were examined. Lake Mead and the Las Vegas Wash contained a mixture of both iodide and iodate. The average concentration of total inorganic iodine (TII) for Lake Mead was approximately 90 nM with an iodide-to-iodate ratio of approximately 1. The TII concentration (approximately 160 nM) and the ratio of iodide to iodate were higher for the Las Vegas Wash (approximately 2). The TII concentration for tap water was close to that of Lake Mead (approximately 90 nM); however, tap water contained no detectable iodide as a result of ozonation and chlorine treatment which converts all of the iodide to iodate.

Behavior of endocrine disrupting chemicals in Johkasou improved septic tank in Japan.

PubMed

Nakagawa, S; Matsuo, H; Motoyama, M; Nomiyama, K; Shinohara, R

2009-09-01

The behavior of estrogens (estrone: E1, 17beta-estradiol: E2, estriol: E3 and ethinylestradiol: EE2) and an androgen (testosterone) in the water and sludge from Johkasou in Japan was investigated. The concentrations of E1, E2, E3 and testosterone in water samples from the Johkasou were 33-500, N.D. approximately 150, N.D. approximately 6,700 and 500 ng/L, respectively. In sludge samples, the concentrations of E1, E2, E3, and testostrerone were N.D. approximately 39, N.D. approximately 6.7, N.D. approximately 60 and 0.2-9.0 ng/L, respectively. EE2 was not detected in all samples. The removal rates of E1, E2, E3 and testosterone in Johkasou were 45%-91%, 66%-100%, 90%-100%, and about 90%, respectively.

Comparison of universal approximators incorporating partial monotonicity by structure.

PubMed

Minin, Alexey; Velikova, Marina; Lang, Bernhard; Daniels, Hennie

2010-05-01

Neural networks applied in control loops and safety-critical domains have to meet more requirements than just the overall best function approximation. On the one hand, a small approximation error is required; on the other hand, the smoothness and the monotonicity of selected input-output relations have to be guaranteed. Otherwise, the stability of most of the control laws is lost. In this article we compare two neural network-based approaches incorporating partial monotonicity by structure, namely the Monotonic Multi-Layer Perceptron (MONMLP) network and the Monotonic MIN-MAX (MONMM) network. We show the universal approximation capabilities of both types of network for partially monotone functions. On a number of datasets, we investigate the advantages and disadvantages of these approaches related to approximation performance, training of the model and convergence. 2009 Elsevier Ltd. All rights reserved.

Integral approximations to classical diffusion and smoothed particle hydrodynamics

DOE PAGES

Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

2014-12-31

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.more » The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.« less

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

Hamlet, Jason R.; Mayo, Jackson R.

Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the referencemore » circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.« less

Stochastic approximation methods-Powerful tools for simulation and optimization: A survey of some recent work on multi-agent systems and cyber-physical systems

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

Yin, George; Wang, Le Yi; Zhang, Hongwei

2014-12-10

Stochastic approximation methods have found extensive and diversified applications. Recent emergence of networked systems and cyber-physical systems has generated renewed interest in advancing stochastic approximation into a general framework to support algorithm development for information processing and decisions in such systems. This paper presents a survey on some recent developments in stochastic approximation methods and their applications. Using connected vehicles in platoon formation and coordination as a platform, we highlight some traditional and new methodologies of stochastic approximation algorithms and explain how they can be used to capture essential features in networked systems. Distinct features of networked systems with randomlymore » switching topologies, dynamically evolving parameters, and unknown delays are presented, and control strategies are provided.« less

Linear Approximation SAR Azimuth Processing Study

NASA Technical Reports Server (NTRS)

Lindquist, R. B.; Masnaghetti, R. K.; Belland, E.; Hance, H. V.; Weis, W. G.

1979-01-01

A segmented linear approximation of the quadratic phase function that is used to focus the synthetic antenna of a SAR was studied. Ideal focusing, using a quadratic varying phase focusing function during the time radar target histories are gathered, requires a large number of complex multiplications. These can be largely eliminated by using linear approximation techniques. The result is a reduced processor size and chip count relative to ideally focussed processing and a correspondingly increased feasibility for spaceworthy implementation. A preliminary design and sizing for a spaceworthy linear approximation SAR azimuth processor meeting requirements similar to those of the SEASAT-A SAR was developed. The study resulted in a design with approximately 1500 IC's, 1.2 cubic feet of volume, and 350 watts of power for a single look, 4000 range cell azimuth processor with 25 meters resolution.

An Assessment of Helium Evolution from Helium-Saturated Propellant Depressurization in Space

NASA Technical Reports Server (NTRS)

Nguyen, Bich N.; Best, Frederick; Wong, Tony; Kurwitz, Cable; McConnaughey, H. (Technical Monitor)

2001-01-01

Helium evolution from the transfer of helium-saturated propellant in space is quantified to assess its impacts from creating two-phase gas/liquid flow from the supply tank, gas injection into the receiving tank, and liquid discharge from the receiving tank. Propellant transfer takes place between two similar tanks whose maximum storage capacity is approximately 2.55 cubic meters each. The maximum on-orbit propellants transfer capability is 9000 lbm (fuel and oxidizer). The transfer line is approximately 1.27 cm in diameter and 6096 cm in length and comprised of the fluid interconnect system (FICS), the orbiter propellant transfer system (OPTS), and the International Space Station (ISS) propulsion module (ISSPM). The propellant transfer rate begins at approximately 11 liter per minute (lpm) and subsequently drops to approximately 0.5 lpm. The tank nominal operating pressure is approximately 1827 kPa (absolute). The line pressure drops for Monomethy1hydrazine (MMH) and Nitrogen tetroxide (NTO) at 11.3 lpm are approximately 202 kPa and 302 kPa, respectively. The pressure-drop results are based on a single-phase flow. The receiving tank is required to vent from approximately 1827 kPa to a lower pressure to affect propellant transfer. These pressure-drop scenarios cause the helium-saturated propellants to release excess helium. For tank ullage venting, the maximum volumes of helium evolved at tank pressure are approximately 0.5 ft3 for MMH and 2 ft3 for NTO. In microgravity environment, due to lack of body force, the helium evolution from a liquid body acts to propel it, which influences its fluid dynamics. For propellant transfer, the volume fractions of helium evolved at line pressure are 0.1% by volume for MMH and 0.6 % by volume for NTO at 11.3 lpm. The void fraction of helium evolved varies as an approximate second order power function of flow rate.

Comparison of infrared thermometer with thermocouple for monitoring skin temperature.

PubMed

Matsukawa, T; Ozaki, M; Nishiyama, T; Imamura, M; Kumazawa, T

2000-02-01

To test the hypothesis that the infrared thermometer (Genius) is comparably useful with thermocouples that are routinely used for skin temperature monitoring. Prospective, controlled, not blinded study. Operating room of a university hospital. Ten healthy male volunteers. Volunteers were minimally clothed and were initially warmed by a forced air warmer until they became vasodilated at the finger and the foot for approximately 30 mins. Subsequently, they were kept in the room with no blanket. Skin temperatures were measured continuously with the Mon-a-Therm thermocouple and were also measured with the Genius thermometer just before and after the warming and subsequently every 10 mins for 70 mins. Forearm and finger-tip skin temperatures and skin-surface temperature gradients (from arm to finger and from calf to toe) measured by the Genius thermometer were compared with those measured by the Mon-a-Therm thermocouple using linear regression and Bland and Altman statistics. Forearm temperature and finger-tip temperature ranged from approximately 31 degrees to approximately 36.5 degrees C (87.8-97.7 degrees F) and approximately 22.5 degrees to approximately 36 degrees C (72.5-96.8 degrees F), respectively. Gradients (from arm to finger and from calf to toe) ranged from approximately -3 degrees to approximately 10 degrees C (26.6-50.0 degrees F) and approximately -3 degrees to approximately 11 degrees C (26.6-51.8 degrees F), respectively. Correlations between the temperatures measured by the Genius thermometer and those by the Mon-a-Therm thermocouple were similar and reliable. The correlation coefficients were as follows: 0.78 at forearm, 0.97 at finger-tip, and 0.97 at skin-surface temperature gradients. The infrared thermometer with a special probe is useful to measure the change of skin-surface temperatures and to evaluate the severity of shock in patients.

Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models

NASA Astrophysics Data System (ADS)

Vakilzadeh, Majid K.; Huang, Yong; Beck, James L.; Abrahamsson, Thomas

2017-02-01

A new multi-level Markov Chain Monte Carlo algorithm for Approximate Bayesian Computation, ABC-SubSim, has recently appeared that exploits the Subset Simulation method for efficient rare-event simulation. ABC-SubSim adaptively creates a nested decreasing sequence of data-approximating regions in the output space that correspond to increasingly closer approximations of the observed output vector in this output space. At each level, multiple samples of the model parameter vector are generated by a component-wise Metropolis algorithm so that the predicted output corresponding to each parameter value falls in the current data-approximating region. Theoretically, if continued to the limit, the sequence of data-approximating regions would converge on to the observed output vector and the approximate posterior distributions, which are conditional on the data-approximation region, would become exact, but this is not practically feasible. In this paper we study the performance of the ABC-SubSim algorithm for Bayesian updating of the parameters of dynamical systems using a general hierarchical state-space model. We note that the ABC methodology gives an approximate posterior distribution that actually corresponds to an exact posterior where a uniformly distributed combined measurement and modeling error is added. We also note that ABC algorithms have a problem with learning the uncertain error variances in a stochastic state-space model and so we treat them as nuisance parameters and analytically integrate them out of the posterior distribution. In addition, the statistical efficiency of the original ABC-SubSim algorithm is improved by developing a novel strategy to regulate the proposal variance for the component-wise Metropolis algorithm at each level. We demonstrate that Self-regulated ABC-SubSim is well suited for Bayesian system identification by first applying it successfully to model updating of a two degree-of-freedom linear structure for three cases: globally, locally and un-identifiable model classes, and then to model updating of a two degree-of-freedom nonlinear structure with Duffing nonlinearities in its interstory force-deflection relationship.

Quantum mean-field approximation for lattice quantum models: Truncating quantum correlations and retaining classical ones

NASA Astrophysics Data System (ADS)

Malpetti, Daniele; Roscilde, Tommaso

2017-02-01

The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical approaches based on an approximate, yet systematically improved account of quantum correlations.

mtDNA variation predicts population size in humans and reveals a major Southern Asian chapter in human prehistory.

PubMed

Atkinson, Quentin D; Gray, Russell D; Drummond, Alexei J

2008-02-01

The relative timing and size of regional human population growth following our expansion from Africa remain unknown. Human mitochondrial DNA (mtDNA) diversity carries a legacy of our population history. Given a set of sequences, we can use coalescent theory to estimate past population size through time and draw inferences about human population history. However, recent work has challenged the validity of using mtDNA diversity to infer species population sizes. Here we use Bayesian coalescent inference methods, together with a global data set of 357 human mtDNA coding-region sequences, to infer human population sizes through time across 8 major geographic regions. Our estimates of relative population sizes show remarkable concordance with the contemporary regional distribution of humans across Africa, Eurasia, and the Americas, indicating that mtDNA diversity is a good predictor of population size in humans. Plots of population size through time show slow growth in sub-Saharan Africa beginning 143-193 kya, followed by a rapid expansion into Eurasia after the emergence of the first non-African mtDNA lineages 50-70 kya. Outside Africa, the earliest and fastest growth is inferred in Southern Asia approximately 52 kya, followed by a succession of growth phases in Northern and Central Asia (approximately 49 kya), Australia (approximately 48 kya), Europe (approximately 42 kya), the Middle East and North Africa (approximately 40 kya), New Guinea (approximately 39 kya), the Americas (approximately 18 kya), and a second expansion in Europe (approximately 10-15 kya). Comparisons of relative regional population sizes through time suggest that between approximately 45 and 20 kya most of humanity lived in Southern Asia. These findings not only support the use of mtDNA data for estimating human population size but also provide a unique picture of human prehistory and demonstrate the importance of Southern Asia to our recent evolutionary past.

Comparison of radiographic and clinical diagnosis of approximal and occlusal dental caries in a young adult population.

PubMed

Hopcraft, Matthew S; Morgan, Michael V

2005-06-01

The aims of the study were: (1) to determine if bitewing radiographs provided additional diagnostic yield for occlusal and approximal dental caries in adults aged between 17 and 30 years of age when compared with a clinical examination only, (2) how this translated into the measurement of dental caries experience, and (3) to determine the influence of water fluoridation on the diagnosis of dental caries in occlusal and approximal surfaces by clinical examination alone and by radiographic examination. Between November 2002 and March 2003 a total of 879 subjects aged 17-30 years had a clinical examination using visual and tactile criteria. Subsequent to this examination, bitewing radiographs were taken and viewed separately and blind. Approximal and occlusal surfaces of molars and premolars were examined on the radiographs. Between 22.9-32.9% of approximal caries and 75.9-82.9% of occlusal caries was detected by clinical examination, while 93.1-97.1% of approximal caries and 33.1-42.6% of occlusal caries was detected by radiographic examination. In addition, while only 0.97% of clinically sound approximal surfaces and 0.83% of clinically sound occlusal surfaces were diagnosed with dentine caries on the radiographs, 67.1-77.1% of approximal caries was detected by radiographs alone, an additional diagnostic yield of 204-336%. The DS score increased 45-46% and the DMFS score increased 6-11% from the clinical examination with the addition of the radiographic information (P<0.001). The prevalence of approximal and occlusal caries was underestimated when clinical means only were employed. There was a significant increase in DS and DMFS scores from the clinical examination only when radiographic information was added across all age groups (P<0.001). This study confirms the value of bitewing radiographs in caries diagnosis.

High-current, relativistic electron-beam transport in metals and the role of magnetic collimation.

PubMed

Storm, M; Solodov, A A; Myatt, J F; Meyerhofer, D D; Stoeckl, C; Mileham, C; Betti, R; Nilson, P M; Sangster, T C; Theobald, W; Guo, Chunlei

2009-06-12

High-resolution coherent transition radiation (CTR) imaging diagnoses electrons accelerated in laser-solid interactions with intensities of approximately 10;{19} W/cm;{2}. The CTR images indicate electron-beam filamentation and annular propagation. The beam temperature and half-angle divergence are inferred to be approximately 1.4 MeV and approximately 16 degrees , respectively. Three-dimensional hybrid-particle-in-cell code simulations reproduce the details of the CTR images assuming an initial half-angle divergence of approximately 56 degrees . Self-generated resistive magnetic fields are responsible for the difference between the initial and measured divergence.

The Investigation of Optimal Discrete Approximations for Real Time Flight Simulations

NASA Technical Reports Server (NTRS)

Parrish, E. A.; Mcvey, E. S.; Cook, G.; Henderson, K. C.

1976-01-01

The results are presented of an investigation of discrete approximations for real time flight simulation. Major topics discussed include: (1) consideration of the particular problem of approximation of continuous autopilots by digital autopilots; (2) use of Bode plots and synthesis of transfer functions by asymptotic fits in a warped frequency domain; (3) an investigation of the various substitution formulas, including the effects of nonlinearities; (4) use of pade approximation to the solution of the matrix exponential arising from the discrete state equations; and (5) an analytical integration of the state equation using interpolated input.

Process for epoxy foam production

DOEpatents

Celina, Mathias C [Albuquerque, NM

2011-08-23

An epoxy resin mixture with at least one epoxy resin of between approximately 60 wt % and 90 wt %, a maleic anhydride of between approximately 1 wt % and approximately 30 wt %, and an imidazole catalyst of less than approximately 2 wt % where the resin mixture is formed from at least one epoxy resin with a 1-30 wt % maleic anhydride compound and an imidazole catalyst at a temperature sufficient to keep the maleic anhydride compound molten, the resin mixture reacting to form a foaming resin which can then be cured at a temperature greater than 50.degree. C. to form an epoxy foam.

Mean-trajectory approximation for electronic and vibrational-electronic nonlinear spectroscopy

NASA Astrophysics Data System (ADS)

Loring, Roger F.

2017-04-01

Mean-trajectory approximations permit the calculation of nonlinear vibrational spectra from semiclassically quantized trajectories on a single electronically adiabatic potential surface. By describing electronic degrees of freedom with classical phase-space variables and subjecting these to semiclassical quantization, mean-trajectory approximations may be extended to compute both nonlinear electronic spectra and vibrational-electronic spectra. A general mean-trajectory approximation for both electronic and nuclear degrees of freedom is presented, and the results for purely electronic and for vibrational-electronic four-wave mixing experiments are quantitatively assessed for harmonic surfaces with linear electronic-nuclear coupling.

Modeling boundary measurements of scattered light using the corrected diffusion approximation

PubMed Central

Lehtikangas, Ossi; Tarvainen, Tanja; Kim, Arnold D.

2012-01-01

We study the modeling and simulation of steady-state measurements of light scattered by a turbid medium taken at the boundary. In particular, we implement the recently introduced corrected diffusion approximation in two spatial dimensions to model these boundary measurements. This implementation uses expansions in plane wave solutions to compute boundary conditions and the additive boundary layer correction, and a finite element method to solve the diffusion equation. We show that this corrected diffusion approximation models boundary measurements substantially better than the standard diffusion approximation in comparison to numerical solutions of the radiative transport equation. PMID:22435102

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

NASA Technical Reports Server (NTRS)

Skollermo, G.

1979-01-01

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

Boson expansions based on the random phase approximation representation

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

Pedrocchi, V.G.; Tamura, T.

1984-04-01

A new boson expansion theory based on the random phase approximation is presented. The boson expansions are derived here directly in the random phase approximation representation with the help of a technique that combines the use of the Usui operator with that of a new bosonization procedure, called the term-by-term bosonization method. The present boson expansion theory is constructed by retaining a single collective quadrupole random phase approximation component, a truncation that allows for a perturbative treatment of the whole problem. Both Hermitian, as well as non-Hermitian boson expansions, valid for even nuclei, are obtained.

Heats of Segregation of BCC Binaries from Ab Initio and Quantum Approximate Calculations

NASA Technical Reports Server (NTRS)

Good, Brian S.

2003-01-01

We compare dilute-limit segregation energies for selected BCC transition metal binaries computed using ab initio and quantum approximate energy methods. Ab initio calculations are carried out using the CASTEP plane-wave pseudopotential computer code, while quantum approximate results are computed using the Bozzolo-Ferrante-Smith (BFS) method with the most recent parameters. Quantum approximate segregation energies are computed with and without atomistic relaxation. Results are discussed within the context of segregation models driven by strain and bond-breaking effects. We compare our results with full-potential quantum calculations and with available experimental results.

Application of the probabilistic approximate analysis method to a turbopump blade analysis. [for Space Shuttle Main Engine

NASA Technical Reports Server (NTRS)

Thacker, B. H.; Mcclung, R. C.; Millwater, H. R.

1990-01-01

An eigenvalue analysis of a typical space propulsion system turbopump blade is presented using an approximate probabilistic analysis methodology. The methodology was developed originally to investigate the feasibility of computing probabilistic structural response using closed-form approximate models. This paper extends the methodology to structures for which simple closed-form solutions do not exist. The finite element method will be used for this demonstration, but the concepts apply to any numerical method. The results agree with detailed analysis results and indicate the usefulness of using a probabilistic approximate analysis in determining efficient solution strategies.

The TSP-approach to approximate solving the m-Cycles Cover Problem

NASA Astrophysics Data System (ADS)

Gimadi, Edward Kh.; Rykov, Ivan; Tsidulko, Oxana

2016-10-01

In the m-Cycles Cover problem it is required to find a collection of m vertex-disjoint cycles that covers all vertices of the graph and the total weight of edges in the cover is minimum (or maximum). The problem is a generalization of the Traveling salesmen problem. It is strongly NP-hard. We discuss a TSP-approach that gives polynomial approximate solutions for this problem. It transforms an approximation TSP algorithm into an approximation m-CCP algorithm. In this paper we present a number of successful transformations with proven performance guarantees for the obtained solutions.

Experiment-specific cosmic microwave background calculations made easier - Approximation formula for smoothed delta T/T windows

NASA Technical Reports Server (NTRS)

Gorski, Krzysztof M.

1993-01-01

Simple and easy to implement elementary function approximations are introduced to the spectral window functions needed in calculations of model predictions of the cosmic microwave backgrond (CMB) anisotropy. These approximations allow the investigator to obtain model delta T/T predictions in terms of single integrals over the power spectrum of cosmological perturbations and to avoid the necessity of performing the additional integrations. The high accuracy of these approximations is demonstrated here for the CDM theory-based calculations of the expected delta T/T signal in several experiments searching for the CMB anisotropy.

Minimax rational approximation of the Fermi-Dirac distribution

DOE PAGES

Moussa, Jonathan E.

2016-10-27

Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ –1)) poles to achieve an error tolerance ϵ at temperature β –1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δ occ, the occupied energy interval. Furthermore, this is particularly beneficial when Δ >> Δ occ, such as in electronic structure calculations that use a large basis set.

Approximate dynamic programming for optimal stationary control with control-dependent noise.

PubMed

Jiang, Yu; Jiang, Zhong-Ping

2011-12-01

This brief studies the stochastic optimal control problem via reinforcement learning and approximate/adaptive dynamic programming (ADP). A policy iteration algorithm is derived in the presence of both additive and multiplicative noise using Itô calculus. The expectation of the approximated cost matrix is guaranteed to converge to the solution of some algebraic Riccati equation that gives rise to the optimal cost value. Moreover, the covariance of the approximated cost matrix can be reduced by increasing the length of time interval between two consecutive iterations. Finally, a numerical example is given to illustrate the efficiency of the proposed ADP methodology.

Automated facial recognition and candidate list rank change of computer generated facial approximations generated with multiple eye orb positions.

PubMed

Parks, Connie L; Monson, Keith L

2016-09-01

Expanding on research previously reported by the authors, this study further examines the recognizability of ReFace facial approximations generated with the following eye orb positions: (i) centrally within the bony eye socket, (ii) 1.0mm superior and 2.0mm lateral relative to center, and (iii) 1.0mm superior and 2.5mm lateral relative to center. Overall, 81% of the test subjects' approximation ranks improved with the use of either of the two supero-lateral eye orbs. Highly significant performance differences (p<0.01) were observed between the approximations with centrally positioned eye orbs (i) and approximations with the eye orbs placed in the supero-laterally positions (ii and iii). Noteworthy was the observation that in all cases when the best rank for an approximation was obtained with the eye orbs in position (iii), the second best rank was achieved with the eye orbs in position (ii). A similar pattern was also observed when the best rank was obtained with the eye orbs in position (ii), with 60% of the second best ranks observed in position (iii). It is argued, therefore, that an approximation constructed with the eye orbs placed in either of the two supero-lateral positions may be more effective and operationally informative than centrally positioned orbs. Copyright © 2016. Published by Elsevier Ireland Ltd.

Assimilation of elements and digestion in grass shrimp pre-exposed to dietary mercury.

PubMed

Seebaugh, David R; Wallace, William G; L'amoreaux, William J; Stewart, Gillian M

2012-08-01

Grass shrimp Palaemonetes pugio were fed mercury (Hg)-contaminated oligochaetes for 15 days and analyzed for Hg, cadmium (Cd), and carbon assimilation efficiencies (AE) as well as toxicological end points related to digestion. Disproportionate increases in stable Hg concentrations in shrimp did not appear to be related to partitioning to trophically available Hg in worms. Hg AE by pre-exposed shrimp reached a plateau (approximately 53 %), whereas Cd AE varied (approximately 40-60 %) in a manner that was not dose-dependent. Carbon AE did not differ among treatments (approximately 69 %). Gut residence time was not impacted significantly by Hg pre-exposure (grand median approximately 465 min), however, there was a trend between curves showing percentages of individuals with markers in feces over time versus treatment. Feces-elimination rate did not vary with dietary pre-exposure. Extracellular protease activity varied approximately 1.9-fold but did not exhibit dose-dependency. pH increased over the range of Hg pre-exposures within the anterior (pH approximately 5.33-6.51) and posterior (pH approximately 5.29-6.25) regions of the cardiac proventriculus and Hg assimilation exhibited a negative relationship to hydrogen ion concentrations. The results of this study indicate that previous Hg ingestion can elicit post-assimilatory impacts on grass shrimp digestive physiology, which may, in turn, influence Hg assimilation during subsequent digestive cycles.

Approximate spatial reasoning

NASA Technical Reports Server (NTRS)

Dutta, Soumitra

1988-01-01

Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.

Approximating Matsubara dynamics using the planetary model: Tests on liquid water and ice

NASA Astrophysics Data System (ADS)

Willatt, Michael J.; Ceriotti, Michele; Althorpe, Stuart C.

2018-03-01

Matsubara dynamics is the quantum-Boltzmann-conserving classical dynamics which remains when real-time coherences are taken out of the exact quantum Liouvillian [T. J. H. Hele et al., J. Chem. Phys. 142, 134103 (2015)]; because of a phase-term, it cannot be used as a practical method without further approximation. Recently, Smith et al. [J. Chem. Phys. 142, 244112 (2015)] developed a "planetary" model dynamics which conserves the Feynman-Kleinert (FK) approximation to the quantum-Boltzmann distribution. Here, we show that for moderately anharmonic potentials, the planetary dynamics gives a good approximation to Matsubara trajectories on the FK potential surface by decoupling the centroid trajectory from the locally harmonic Matsubara fluctuations, which reduce to a single phase-less fluctuation particle (the "planet"). We also show that the FK effective frequency can be approximated by a direct integral over these fluctuations, obviating the need to solve iterative equations. This modification, together with use of thermostatted ring-polymer molecular dynamics, allows us to test the planetary model on water (gas-phase, liquid, and ice) using the q-TIP4P/F potential surface. The "planetary" fluctuations give a poor approximation to the rotational/librational bands in the infrared spectrum, but a good approximation to the bend and stretch bands, where the fluctuation lineshape is found to be motionally narrowed by the vibrations of the centroid.

Symmetric rotating-wave approximation for the generalized single-mode spin-boson system

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

Albert, Victor V.; Scholes, Gregory D.; Brumer, Paul

2011-10-15

The single-mode spin-boson model exhibits behavior not included in the rotating-wave approximation (RWA) in the ultra and deep-strong coupling regimes, where counter-rotating contributions become important. We introduce a symmetric rotating-wave approximation that treats rotating and counter-rotating terms equally, preserves the invariances of the Hamiltonian with respect to its parameters, and reproduces several qualitative features of the spin-boson spectrum not present in the original rotating-wave approximation both off-resonance and at deep-strong coupling. The symmetric rotating-wave approximation allows for the treatment of certain ultra- and deep-strong coupling regimes with similar accuracy and mathematical simplicity as does the RWA in the weak-coupling regime.more » Additionally, we symmetrize the generalized form of the rotating-wave approximation to obtain the same qualitative correspondence with the addition of improved quantitative agreement with the exact numerical results. The method is readily extended to higher accuracy if needed. Finally, we introduce the two-photon parity operator for the two-photon Rabi Hamiltonian and obtain its generalized symmetric rotating-wave approximation. The existence of this operator reveals a parity symmetry similar to that in the Rabi Hamiltonian as well as another symmetry that is unique to the two-photon case, providing insight into the mathematical structure of the two-photon spectrum, significantly simplifying the numerics, and revealing some interesting dynamical properties.« less

Construction of exchange-correlation functionals through interpolation between the non-interacting and the strong-correlation limit

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

Zhou, Yongxi; Ernzerhof, Matthias, E-mail: Matthias.Ernzerhof@UMontreal.ca; Bahmann, Hilke

Drawing on the adiabatic connection of density functional theory, exchange-correlation functionals of Kohn-Sham density functional theory are constructed which interpolate between the extreme limits of the electron-electron interaction strength. The first limit is the non-interacting one, where there is only exchange. The second limit is the strong correlated one, characterized as the minimum of the electron-electron repulsion energy. The exchange-correlation energy in the strong-correlation limit is approximated through a model for the exchange-correlation hole that is referred to as nonlocal-radius model [L. O. Wagner and P. Gori-Giorgi, Phys. Rev. A 90, 052512 (2014)]. Using the non-interacting and strong-correlated extremes, variousmore » interpolation schemes are presented that yield new approximations to the adiabatic connection and thus to the exchange-correlation energy. Some of them rely on empiricism while others do not. Several of the proposed approximations yield the exact exchange-correlation energy for one-electron systems where local and semi-local approximations often fail badly. Other proposed approximations generalize existing global hybrids by using a fraction of the exchange-correlation energy in the strong-correlation limit to replace an equal fraction of the semi-local approximation to the exchange-correlation energy in the strong-correlation limit. The performance of the proposed approximations is evaluated for molecular atomization energies, total atomic energies, and ionization potentials.« less

Approximating Matsubara dynamics using the planetary model: Tests on liquid water and ice.

PubMed

Willatt, Michael J; Ceriotti, Michele; Althorpe, Stuart C

2018-03-14

Matsubara dynamics is the quantum-Boltzmann-conserving classical dynamics which remains when real-time coherences are taken out of the exact quantum Liouvillian [T. J. H. Hele et al., J. Chem. Phys. 142, 134103 (2015)]; because of a phase-term, it cannot be used as a practical method without further approximation. Recently, Smith et al. [J. Chem. Phys. 142, 244112 (2015)] developed a "planetary" model dynamics which conserves the Feynman-Kleinert (FK) approximation to the quantum-Boltzmann distribution. Here, we show that for moderately anharmonic potentials, the planetary dynamics gives a good approximation to Matsubara trajectories on the FK potential surface by decoupling the centroid trajectory from the locally harmonic Matsubara fluctuations, which reduce to a single phase-less fluctuation particle (the "planet"). We also show that the FK effective frequency can be approximated by a direct integral over these fluctuations, obviating the need to solve iterative equations. This modification, together with use of thermostatted ring-polymer molecular dynamics, allows us to test the planetary model on water (gas-phase, liquid, and ice) using the q-TIP4P/F potential surface. The "planetary" fluctuations give a poor approximation to the rotational/librational bands in the infrared spectrum, but a good approximation to the bend and stretch bands, where the fluctuation lineshape is found to be motionally narrowed by the vibrations of the centroid.

Vertical and horizontal fluxes of plutonium and americium in the western Mediterranean and the Strait of Gibraltar.

PubMed

León Vintró, L; Mitchell, P I; Condren, O M; Downes, A B; Papucci, C; Delfanti, R

1999-09-30

New data on the vertical distributions of plutonium and americium in the waters of the western Mediterranean and the Strait of Gibraltar are examined in terms of the processes governing their delivery to, transport in and removal from the water column within the basin. Residence times for plutonium and americium in surface waters of approximately 15 and approximately 3 years, respectively, are deduced, and it is shown that by the mid 1990s only approximately 35% of the 239,240Pu and approximately 5% of the 241Am deposited as weapons fallout still resided in the water column. Present 239,240Pu inventories in the water column and the underlying sediments are estimated to be approximately 25 TBq and approximately 40 TBq, respectively, which reconcile well with the time-integrated fallout deposition in this zone, taken to be approximately 69 TBq. The data show that there are significant net outward fluxes of plutonium and americium from the basin through the Strait of Gibraltar at the present time. These appear to be compensated by net inward fluxes of similar magnitude through the Strait of Sicily. Thus, the time-integrated fallout deposition in the western basin can be accounted for satisfactorily in terms of present water column and sediment inventories. Enhanced scavenging on the continental shelves, as evidenced by the appreciably higher transuranic concentrations in shelf sediments, supports this contention.

27 CFR 9.30 - North Coast.

Code of Federal Regulations, 2012 CFR

2012-04-01

... Valley Ford; (2) Then southeast in a straight line for approximately 22.0 miles to the peak of Barnabe Mountain (elevation 1466 feet); (3) Then southeast in a straight line for approximately 10.0 miles to the... approximately 5.8 miles to the confluence of San Rafael Creek and San Rafael Bay in San Rafael; (5) Then north...

27 CFR 9.30 - North Coast.

Code of Federal Regulations, 2013 CFR

2013-04-01

... Valley Ford; (2) Then southeast in a straight line for approximately 22.0 miles to the peak of Barnabe Mountain (elevation 1466 feet); (3) Then southeast in a straight line for approximately 10.0 miles to the... approximately 5.8 miles to the confluence of San Rafael Creek and San Rafael Bay in San Rafael; (5) Then north...

27 CFR 9.30 - North Coast.

Code of Federal Regulations, 2011 CFR

2011-04-01

... Valley Ford; (2) Then southeast in a straight line for approximately 22.0 miles to the peak of Barnabe Mountain (elevation 1466 feet); (3) Then southeast in a straight line for approximately 10.0 miles to the... approximately 5.8 miles to the confluence of San Rafael Creek and San Rafael Bay in San Rafael; (5) Then north...

27 CFR 9.30 - North Coast.

Code of Federal Regulations, 2014 CFR

2014-04-01

... Valley Ford; (2) Then southeast in a straight line for approximately 22.0 miles to the peak of Barnabe Mountain (elevation 1466 feet); (3) Then southeast in a straight line for approximately 10.0 miles to the... approximately 5.8 miles to the confluence of San Rafael Creek and San Rafael Bay in San Rafael; (5) Then north...

27 CFR 9.30 - North Coast.

Code of Federal Regulations, 2010 CFR

2010-04-01

... Valley Ford; (2) Then southeast in a straight line for approximately 22.0 miles to the peak of Barnabe Mountain (elevation 1466 feet); (3) Then southeast in a straight line for approximately 10.0 miles to the... approximately 5.8 miles to the confluence of San Rafael Creek and San Rafael Bay in San Rafael; (5) Then north...

27 CFR 9.179 - Southern Oregon.

Code of Federal Regulations, 2013 CFR

2013-04-01

... approximately 0.5 miles to the 1,000-foot contour line; then (2) Proceed northwest along the 1,000-foot contour... approximately 8 miles to its intersection with the 1,000-foot contour line; then in a southeasterly direction in... approximately 0.33 mile, rejoining the 1,000-foot contour line; then in a northerly and eventually a southerly...

27 CFR 9.129 - Arroyo Grande Valley.

Code of Federal Regulations, 2013 CFR

2013-04-01

... of 626 feet in the Santa Manuela land grant; (7) Then easterly, approximately 0.46 mile in a straight..., approximately 1.8 miles, to the summit of an unnamed peak identified as having an elevation of 1,182 feet, in... of 1,308 feet, in the Huasna land grant; (20) Then west northwesterly, approximately 1.50 miles in a...

27 CFR 9.129 - Arroyo Grande Valley.

Code of Federal Regulations, 2012 CFR

2012-04-01

... of 626 feet in the Santa Manuela land grant; (7) Then easterly, approximately 0.46 mile in a straight..., approximately 1.8 miles, to the summit of an unnamed peak identified as having an elevation of 1,182 feet, in... of 1,308 feet, in the Huasna land grant; (20) Then west northwesterly, approximately 1.50 miles in a...

27 CFR 9.179 - Southern Oregon.

Code of Federal Regulations, 2012 CFR

2012-04-01

... approximately 0.5 miles to the 1,000-foot contour line; then (2) Proceed northwest along the 1,000-foot contour... approximately 8 miles to its intersection with the 1,000-foot contour line; then in a southeasterly direction in... approximately 0.33 mile, rejoining the 1,000-foot contour line; then in a northerly and eventually a southerly...

27 CFR 9.179 - Southern Oregon.

Code of Federal Regulations, 2014 CFR

2014-04-01

... approximately 0.5 miles to the 1,000-foot contour line; then (2) Proceed northwest along the 1,000-foot contour... approximately 8 miles to its intersection with the 1,000-foot contour line; then in a southeasterly direction in... approximately 0.33 mile, rejoining the 1,000-foot contour line; then in a northerly and eventually a southerly...

Spline approximations for nonlinear hereditary control systems

NASA Technical Reports Server (NTRS)

Daniel, P. L.

1982-01-01

A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.

Computing Functions by Approximating the Input

ERIC Educational Resources Information Center

Goldberg, Mayer

2012-01-01

In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…

Inversion and approximation of Laplace transforms

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

A method of inverting Laplace transforms by using a set of orthonormal functions is reported. As a byproduct of the inversion, approximation of complicated Laplace transforms by a transform with a series of simple poles along the left half plane real axis is shown. The inversion and approximation process is simple enough to be put on a programmable hand calculator.

75 FR 16732 - Action Affecting Export Privileges; Aqua-Loop Cooling Towers, Co.

Federal Register 2010, 2011, 2012, 2013, 2014

2010-04-02

... Regulations by facilitating or coordinating the export of approximately 174 rolls of hog hair filter media... about September 28, 2004, Aqua-Loop ordered or financed approximately 174 rolls of hog hair filter media... coordinating the export of approximately 185 rolls of hog hair filter media, part number HHB6O 130 and valued...

Vibration Damping Circuit Card Assembly

NASA Technical Reports Server (NTRS)

Hunt, Ronald Allen (Inventor)

2016-01-01

A vibration damping circuit card assembly includes a populated circuit card having a mass M. A closed metal container is coupled to a surface of the populated circuit card at approximately a geometric center of the populated circuit card. Tungsten balls fill approximately 90% of the metal container with a collective mass of the tungsten balls being approximately (0.07) M.

A Monte Carlo Application to Approximate the Integral from a to b of e Raised to the x Squared.

ERIC Educational Resources Information Center

Easterday, Kenneth; Smith, Tommy

1992-01-01

Proposes an alternative means of approximating the value of complex integrals, the Monte Carlo procedure. Incorporating a discrete approach and probability, an approximation is obtained from the ratio of computer-generated points falling under the curve to the number of points generated in a predetermined rectangle. (MDH)

Quality Out-of-School Care in Aotearoa/New Zealand

ERIC Educational Resources Information Center

Walter, Christine

2007-01-01

Research shows that New Zealand has an approximate population of 600,000 children between the ages of five and fourteen years, and that approximately 80,000 of those children attend an out-of-school-care service each year. The New Zealand government allocates approximately $20 million to suitably approved programs, funding for families of lower…

The Approximate Number System and Its Relation to Early Math Achievement: Evidence from the Preschool Years

ERIC Educational Resources Information Center

Bonny, Justin W.; Lourenco, Stella F.

2013-01-01

Humans rely on two main systems of quantification; one is nonsymbolic and involves approximate number representations (known as the approximate number system or ANS), and the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and school-aged…

Viète's Formula and an Error Bound without Taylor's Theorem

ERIC Educational Resources Information Center

Boucher, Chris

2018-01-01

This note presents a derivation of Viète's classic product approximation of pi that relies on only the Pythagorean Theorem. We also give a simple error bound for the approximation that, while not optimal, still reveals the exponential convergence of the approximation and whose derivation does not require Taylor's Theorem.

An approximation formula for a class of fault-tolerant computers

NASA Technical Reports Server (NTRS)

White, A. L.

1986-01-01

An approximation formula is derived for the probability of failure for fault-tolerant process-control computers. These computers use redundancy and reconfiguration to achieve high reliability. Finite-state Markov models capture the dynamic behavior of component failure and system recovery, and the approximation formula permits an estimation of system reliability by an easy examination of the model.

Developmental Change in the Acuity of Approximate Number and Area Representations

ERIC Educational Resources Information Center

Odic, Darko; Libertus, Melissa E.; Feigenson, Lisa; Halberda, Justin

2013-01-01

From very early in life, humans can approximate the number and surface area of objects in a scene. The ability to discriminate between 2 approximate quantities, whether number or area, critically depends on the ratio between the quantities, with the most difficult ratio that a participant can reliably discriminate known as the Weber fraction.…

Emission-line studies of young stars. 4: The optical forbidden lines

NASA Astrophysics Data System (ADS)

Hamann, Fred

1994-08-01

Optical forbidden line strengths and profiles are discussed for a sample of 30 T Tauri stars and 12 Herbig Ae-Be stars. Transitions of (C I), (N II), (O I), (O II), (S II), (Ca II), (Cr II), (Fe II), and (Ni II) are detected. Profile variability occurred in DG Tau and probably other sources. The ensemble profiles can be divided into four generic components that may represent distinct emitting regions; (1) narrow rest-velocity lines, (2) 'low'-velocity lines (peaking at less than or approximately +/- 50 km s-1), (3) 'high'-velocity (usually greater than or approximately +/- 100 km s-1) blueshifted peaks or wings, and (4) high-velocity redshifted peaks. Among T Tauri stars, the rest-velocity lines appear most often in sources with weak and narrow permitted lines, such as the Ca II triplet. The low- and high-velocity blueshifted components usually appear together in sources with strong and broad Ca II triplet lines. If the velocity-shifted lines form in jets, the smallest (full) opening angles required by the profiles are less than or approximately 20 deg for the narrow, blueshifted (Ca II) lines of DG Tau and HL Tau. Other lines in DG Tau are much broader, implying larger opening angles or greater velocity dispersions. The variability in DG Tau also implies significant changes in the collimation or velocity coherence on timescales of a few years. RW Aur and AS 353A have blue- and redshifted line peaks that could form in oppositely directed jets. The strong (S II) lambda 6716 and lambda 6731 lines in RW Aur are exclusively redshifted and require opening angles less than or approximately 60 deg. Measurements of different profiles in the same spectrum show that the physical conditions change with the line-of-sight velocities. The most persistent trends are for more (N II) and (O II) and less (O I) lambda 5577 flux at high velocities. Constraints on the physical conditions are derived by modeling the emission lines via multilevel ions in 'coronal ionization equilibrium.' A single temperature and density cannot fully describe the line spectra in any velocity interval. Temperatures in the (O I) region are 9000 less than or approximately Te less than 14,000 K, and the ionization fraction (of H) is less than 35%. The densities derived from (O I) include ne less than or approximately 5 x 105 to approximately 107 cm-3, but ne greater than or approximately 106 cm-3 obtains only at low velocities. In the (S II) regions the densities are lower, 103 less than or approximately ne less than or approximately 7 x 104 cm-3, and the temperatures are probably higher, Te greater than or approximately 13,000 K. At high velocities (only) there is additional hot gas that produces (N II) and (O II), possibly most of the (S II), and little (O I). This region is characterized by Te greater than or approximately 15,000 K, ne less than or approximately 105 cm-3, and an ionization fraction greater than or approximately 50%.

Emission-line studies of young stars. 4: The optical forbidden lines

NASA Technical Reports Server (NTRS)

Hamann, Fred

1994-01-01

Optical forbidden line strengths and profiles are discussed for a sample of 30 T Tauri stars and 12 Herbig Ae-Be stars. Transitions of (C I), (N II), (O I), (O II), (S II), (Ca II), (Cr II), (Fe II), and (Ni II) are detected. Profile variability occurred in DG Tau and probably other sources. The ensemble profiles can be divided into four generic components that may represent distinct emitting regions; (1) narrow rest-velocity lines, (2) 'low'-velocity lines (peaking at less than or approximately +/- 50 km s(exp -1)), (3) 'high'-velocity (usually greater than or approximately +/- 100 km s(exp -1)) blueshifted peaks or wings, and (4) high-velocity redshifted peaks. Among T Tauri stars, the rest-velocity lines appear most often in sources with weak and narrow permitted lines, such as the Ca II triplet. The low- and high-velocity blueshifted components usually appear together in sources with strong and broad Ca II triplet lines. If the velocity-shifted lines form in jets, the smallest (full) opening angles required by the profiles are less than or approximately 20 deg for the narrow, blueshifted (Ca II) lines of DG Tau and HL Tau. Other lines in DG Tau are much broader, implying larger opening angles or greater velocity dispersions. The variability in DG Tau also implies significant changes in the collimation or velocity coherence on timescales of a few years. RW Aur and AS 353A have blue- and redshifted line peaks that could form in oppositely directed jets. The strong (S II) lambda 6716 and lambda 6731 lines in RW Aur are exclusively redshifted and require opening angles less than or approximately 60 deg. Measurements of different profiles in the same spectrum show that the physical conditions change with the line-of-sight velocities. The most persistent trends are for more (N II) and (O II) and less (O I) lambda 5577 flux at high velocities. Constraints on the physical conditions are derived by modeling the emission lines via multilevel ions in 'coronal ionization equilibrium.' A single temperature and density cannot fully describe the line spectra in any velocity interval. Temperatures in the (O I) region are 9000 less than or approximately T(sub e) less than 14,000 K, and the ionization fraction (of H) is less than 35%. The densities derived from (O I) include n(sub e) less than or approximately 5 x 10(exp 5) to approximately 10(exp 7) cm(exp -3), but n(sub e) greater than or approximately 10(exp 6) cm(exp -3) obtains only at low velocities. In the (S II) regions the densities are lower, 10(exp 3) less than or approximately n(sub e) less than or approximately 7 x 10(exp 4) cm(exp -3), and the temperatures are probably higher, T(sub e) greater than or approximately 13,000 K. At high velocities (only) there is additional hot gas that produces (N II) and (O II), possibly most of the (S II), and little (O I). This region is characterized by T(sub e) greater than or approximately 15,000 K, n(sub e) less than or approximately 10(exp 5) cm(exp -3), and an ionization fraction greater than or approximately 50%. When combined with the spatially segregated emitting regions observed by others by spectral imaging, these results suggest decreasing n(sub e) and increasing T(sub e) away from the star in at least the high velocity gas.

Blue lobes in the Hydra A cluster central galaxy

NASA Technical Reports Server (NTRS)

Mcnamara, Brian R.

1995-01-01

We present new U- and I-band images of the centrally dominant galaxy in the Hydra A cluster, obtained with the 2.5 m Isaac Newton Telescope at La Palma. The galaxy is centered in a poor, X-ray-luminous cluster whose gaseous intracluster medium is apparently cooling at a rate of m-dot(sub CF) approximately 3000 solar masses/yr. The galaxy's structure is that of a normal giant elliptical galaxy, apart from the central approximately 8 x 6 arcsec (approximately 12 x 9 kpc) region which contains an unusually blue, lobelike structure that is spatially coincident with a luminous emission-line nebula in rotation about the nucleus. Based on near spatial coincidence of the central continuum structure and the emission-line nebula, we suggest that the blue continuum is due to a warm stellar population in a central disk. In order to isolate and study the structure of the disk, we have subtracted a smooth galactic background model from the U-band image. The disk's surface brightness profiles along its major and minor axes decline roughly exponentially with radius. The disk's axial ratio is consistent with a nearly edge-on thick disk or a thin disk that is inclined with respect to the line of sight. The bluest regions, located a few arcsec on either side of the nucleus (giving the lobelike appearance), may be due to locally enhanced star formation or a seeing-blurred ring of young stars embedded in the disk observed nearly edge-on. If star-formation is occurring with the local initial mass function, the central color, surface brightness, and dynamical mass would be consistent with models for star formation at a rate of less than and approximately 1 solar masses/yr which has persisted for the past approximately 10(exp 9) yr, a short burst (10(exp 7) yr) of star formation at a rate of approximately 30 solar masses/yr which occurred less than and approximately 10(exp 8) yr ago, or an instantaneous burst of star formation which occurred approximately 5 x 10(exp 7) yr ago. While the young population contributes approximately 30%-40% of the central U-band luminosity, its mass would be less than and approximately 1% to less than and approximately 10% (10(exp 8) solar masses - 2 x 10(exp 9) solar masses of the galaxy's central dynamical mass. We consider a number of possible origins for the disk material.

Connection between the regular approximation and the normalized elimination of the small component in relativistic quantum theory

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2005-02-01

The regular approximation to the normalized elimination of the small component (NESC) in the modified Dirac equation has been developed and presented in matrix form. The matrix form of the infinite-order regular approximation (IORA) expressions, obtained in [Filatov and Cremer, J. Chem. Phys. 118, 6741 (2003)] using the resolution of the identity, is the exact matrix representation and corresponds to the zeroth-order regular approximation to NESC (NESC-ZORA). Because IORA (=NESC-ZORA) is a variationally stable method, it was used as a suitable starting point for the development of the second-order regular approximation to NESC (NESC-SORA). As shown for hydrogenlike ions, NESC-SORA energies are closer to the exact Dirac energies than the energies from the fifth-order Douglas-Kroll approximation, which is much more computationally demanding than NESC-SORA. For the application of IORA (=NESC-ZORA) and NESC-SORA to many-electron systems, the number of the two-electron integrals that need to be evaluated (identical to the number of the two-electron integrals of a full Dirac-Hartree-Fock calculation) was drastically reduced by using the resolution of the identity technique. An approximation was derived, which requires only the two-electron integrals of a nonrelativistic calculation. The accuracy of this approach was demonstrated for heliumlike ions. The total energy based on the approximate integrals deviates from the energy calculated with the exact integrals by less than 5×10-9hartree units. NESC-ZORA and NESC-SORA can easily be implemented in any nonrelativistic quantum chemical program. Their application is comparable in cost with that of nonrelativistic methods. The methods can be run with density functional theory and any wave function method. NESC-SORA has the advantage that it does not imply a picture change.

Chemical association in simple models of molecular and ionic fluids. III. The cavity function

NASA Astrophysics Data System (ADS)

Zhou, Yaoqi; Stell, George

1992-01-01

Exact equations which relate the cavity function to excess solvation free energies and equilibrium association constants are rederived by using a thermodynamic cycle. A zeroth-order approximation, derived previously by us as a simple interpolation scheme, is found to be very accurate if the associative bonding occurs on or near the surface of the repulsive core of the interaction potential. If the bonding radius is substantially less than the core radius, the approximation overestimates the association degree and the association constant. For binary association, the zeroth-order approximation is equivalent to the first-order thermodynamic perturbation theory (TPT) of Wertheim. For n-particle association, the combination of the zeroth-order approximation with a ``linear'' approximation (for n-particle distribution functions in terms of the two-particle function) yields the first-order TPT result. Using our exact equations to go beyond TPT, near-exact analytic results for binary hard-sphere association are obtained. Solvent effects on binary hard-sphere association and ionic association are also investigated. A new rule which generalizes Le Chatelier's principle is used to describe the three distinct forms of behaviors involving solvent effects that we find. The replacement of the dielectric-continuum solvent model by a dipolar hard-sphere model leads to improved agreement with an experimental observation. Finally, equation of state for an n-particle flexible linear-chain fluid is derived on the basis of a one-parameter approximation that interpolates between the generalized Kirkwood superposition approximation and the linear approximation. A value of the parameter that appears to be near optimal in the context of this application is obtained from comparison with computer-simulation data.

Approximating a DSM-5 Diagnosis of PTSD Using DSM-IV Criteria

PubMed Central

Rosellini, Anthony J.; Stein, Murray B.; Colpe, Lisa J.; Heeringa, Steven G.; Petukhova, Maria V.; Sampson, Nancy A.; Schoenbaum, Michael; Ursano, Robert J.; Kessler, Ronald C.

2015-01-01

Background Diagnostic criteria for DSM-5 posttraumatic stress disorder (PTSD) are in many ways similar to DSM-IV criteria, raising the possibility that it might be possible to closely approximate DSM-5 diagnoses using DSM-IV symptoms. If so, the resulting transformation rules could be used to pool research data based on the two criteria sets. Methods The Pre-Post Deployment Study (PPDS) of the Army Study to Assess Risk and Resilience in Servicemembers (Army STARRS) administered a blended 30-day DSM-IV and DSM-5 PTSD symptom assessment based on the civilian PTSD Checklist for DSM-IV (PCL-C) and the PTSD Checklist for DSM-5 (PCL-5). This assessment was completed by 9,193 soldiers from three US Army Brigade Combat Teams approximately three months after returning from Afghanistan. PCL-C items were used to operationalize conservative and broad approximations of DSM-5 PTSD diagnoses. The operating characteristics of these approximations were examined compared to diagnoses based on actual DSM-5 criteria. Results The estimated 30-day prevalence of DSM-5 PTSD based on conservative (4.3%) and broad (4.7%) approximations of DSM-5 criteria using DSM-IV symptom assessments were similar to estimates based on actual DSM-5 criteria (4.6%). Both approximations had excellent sensitivity (92.6-95.5%), specificity (99.6-99.9%), total classification accuracy (99.4-99.6%), and area under the receiver operating characteristic curve (0.96-0.98). Conclusions DSM-IV symptoms can be used to approximate DSM-5 diagnoses of PTSD among recently-deployed soldiers, making it possible to recode symptom-level data from earlier DSM-IV studies to draw inferences about DSM-5 PTSD. However, replication is needed in broader trauma-exposed samples to evaluate the external validity of this finding. PMID:25845710

[Effects of a benzodiazepine derivative, MS4101, on emotional behaviour of untamed cats].

PubMed

Anezaki, K; Sakurada, S; Ando, R; Kisara, K; Nakahama, H

1976-09-01

Effects of MS4101 on emotional behaviour in untamed cats were studied and compared with those of diazepam. Offensive behaviour, i.e., whine response to a rod presented in front of the snout and blowing air on back hair was markedly observed, and whine, attacking and biting responses to tapping with a rod on the back in these cats were marked. Defensive behaviour, i.e., hissing, crouching body, ear flattening to blowing air on back hair, a rod presented and tapping was markedly observed. From 30 min after MS4101 and diazepam in doses of 2 approximately 4 mg/kg i.p., offensive behaviour in untamed cats was depressed. ID50 (50% of inhibition dose) of offensive behaviour for MS4101 and diazepam was 2.40 (1.95 approximately 2.95) mg/kg i.p. and 0.96 (0.69 approximately 1.34) mg/kg i.p., respectively. MS4101 and diazepam in doses of 2 approximately 4 mg/kg i.p. decreased the offensive behaviour. ID50 of defensive behaviour for MS4101 and diazepam was 3.00 (2.46 approximately 3.66) mg/kg i.p. and 1.45 (1.14 approximately 1.84) mg/kg i.p., respectively. Both MS4101 and diazepam exhibited muscle relaxant effects. Here, diazepam was more effective than MS4101. ED50 of muscle relaxant activity for MS4101 and diazepam was 4.30 (3.03 approximately 6.11) mg/kg i.p., 7.40 (5.04 approximately 10.66) mg/kg i.p., respectively. A single administration of MS4101 and of diazepam in doses 2 mg/kg i.p. enhanced food intake.

The Size Evolution of Passive Galaxies: Observations From the Wide-Field Camera 3 Early Release Science Program

NASA Technical Reports Server (NTRS)

Ryan, R. E., Jr.; Mccarthy, P.J.; Cohen, S. H.; Yan, H.; Hathi, N. P.; Koekemoer, A. M.; Rutkowski, M. J.; Mechtley, M. R.; Windhorst, R. A.; O’Connell, R. W.;

Different forms of soluble cytoplasmic mRNA binding proteins and particles in Xenopus laevis oocytes and embryos

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

Murray, M.T.; Krohne, G.; Franke, W.W.

1991-01-01

To gain insight into the mechanisms involved in the formation of maternally stored mRNPs during Xenopus laevis development, we searched for soluble cytoplasmic proteins of the oocyte that are able to selectively bind mRNAs, using as substrate radiolabeled mRNA. In vitro mRNP assembly in solution was followed by UV-cross-linking and RNase digestion, resulting in covalent tagging of polypeptides by nucleotide transfer. Five polypeptides of approximately 54, 56 60, 70, and 100 kD (p54, p56, p60, p70, and p100) have been found to selectively bind mRNA and assemble into mRNPs. These polypeptides, which correspond to previously described native mRNP components, occurmore » in three different particle classes of approximately 4.5S, approximately 6S, and approximately 15S, as also determined by their reactions with antibodies against p54 and p56. Whereas the approximately 4.5S class contains p42, p60, and p70, probably each in the form of individual molecules or small complexes, the approximately 6S particles appears to consist only of p54 and p56, which occur in a near-stoichiometric ratio suggestive of a heterodimer complex. The approximately 15S particles contain, in addition to p54 and p56, p60 and p100 and this is the single occurring form of RNA-binding p100. We have also observed changes in the in vitro mRNA binding properties of these polypeptides during oogenesis and early embryonic development, in relation to their phosphorylation state and to the activity of an approximately 15S particle-associated protein kinase, suggesting that these proteins are involved in the developmental translational regulation of maternal mRNAs.« less

Na(+) transport, and the E(1)P-E(2)P conformational transition of the Na(+)/K(+)-ATPase.

PubMed Central

Babes, A; Fendler, K

2000-01-01

We have used admittance analysis together with the black lipid membrane technique to analyze electrogenic reactions within the Na(+) branch of the reaction cycle of the Na(+)/K(+)-ATPase. ATP release by flash photolysis of caged ATP induced changes in the admittance of the compound membrane system that are associated with partial reactions of the Na(+)/K(+)-ATPase. Frequency spectra and the Na(+) dependence of the capacitive signal are consistent with an electrogenic or electroneutral E(1)P <--> E(2)P conformational transition which is rate limiting for a faster electrogenic Na(+) dissociation reaction. We determine the relaxation rate of the rate-limiting reaction and the equilibrium constants for both reactions at pH 6.2-8.5. The relaxation rate has a maximum value at pH 7.4 (approximately 320 s(-1)), which drops to acidic (approximately 190 s(-1)) and basic (approximately 110 s(-1)) pH. The E(1)P <--> E(2)P equilibrium is approximately at a midpoint position at pH 6.2 (equilibrium constant approximately 0.8) but moves more to the E(1)P side at basic pH 8.5 (equilibrium constant approximately 0.4). The Na(+) affinity at the extracellular binding site decreases from approximately 900 mM at pH 6.2 to approximately 200 mM at pH 8.5. The results suggest that during Na(+) transport the free energy supplied by the hydrolysis of ATP is mainly used for the generation of a low-affinity extracellular Na(+) discharge site. Ionic strength and lyotropic anions both decrease the relaxation rate. However, while ionic strength does not change the position of the conformational equilibrium E(1)P <--> E(2)P, lyotropic anions shift it to E(1)P. PMID:11053130

Comparing methods for modelling spreading cell fronts.

PubMed

Markham, Deborah C; Simpson, Matthew J; Maini, Philip K; Gaffney, Eamonn A; Baker, Ruth E

2014-07-21

Spreading cell fronts play an essential role in many physiological processes. Classically, models of this process are based on the Fisher-Kolmogorov equation; however, such continuum representations are not always suitable as they do not explicitly represent behaviour at the level of individual cells. Additionally, many models examine only the large time asymptotic behaviour, where a travelling wave front with a constant speed has been established. Many experiments, such as a scratch assay, never display this asymptotic behaviour, and in these cases the transient behaviour must be taken into account. We examine the transient and the asymptotic behaviour of moving cell fronts using techniques that go beyond the continuum approximation via a volume-excluding birth-migration process on a regular one-dimensional lattice. We approximate the averaged discrete results using three methods: (i) mean-field, (ii) pair-wise, and (iii) one-hole approximations. We discuss the performance of these methods, in comparison to the averaged discrete results, for a range of parameter space, examining both the transient and asymptotic behaviours. The one-hole approximation, based on techniques from statistical physics, is not capable of predicting transient behaviour but provides excellent agreement with the asymptotic behaviour of the averaged discrete results, provided that cells are proliferating fast enough relative to their rate of migration. The mean-field and pair-wise approximations give indistinguishable asymptotic results, which agree with the averaged discrete results when cells are migrating much more rapidly than they are proliferating. The pair-wise approximation performs better in the transient region than does the mean-field, despite having the same asymptotic behaviour. Our results show that each approximation only works in specific situations, thus we must be careful to use a suitable approximation for a given system, otherwise inaccurate predictions could be made. Copyright © 2014 Elsevier Ltd. All rights reserved.

On the dynamics of approximating schemes for dissipative nonlinear equations

NASA Technical Reports Server (NTRS)

Jones, Donald A.

1993-01-01

Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.

Guidelines for Use of the Approximate Beta-Poisson Dose-Response Model.

PubMed

Xie, Gang; Roiko, Anne; Stratton, Helen; Lemckert, Charles; Dunn, Peter K; Mengersen, Kerrie

2017-07-01

For dose-response analysis in quantitative microbial risk assessment (QMRA), the exact beta-Poisson model is a two-parameter mechanistic dose-response model with parameters α>0 and β>0, which involves the Kummer confluent hypergeometric function. Evaluation of a hypergeometric function is a computational challenge. Denoting PI(d) as the probability of infection at a given mean dose d, the widely used dose-response model PI(d)=1-(1+dβ)-α is an approximate formula for the exact beta-Poisson model. Notwithstanding the required conditions α<β and β>1, issues related to the validity and approximation accuracy of this approximate formula have remained largely ignored in practice, partly because these conditions are too general to provide clear guidance. Consequently, this study proposes a probability measure Pr(0 < r < 1 | α̂, β̂) as a validity measure (r is a random variable that follows a gamma distribution; α̂ and β̂ are the maximum likelihood estimates of α and β in the approximate model); and the constraint conditions β̂>(22α̂)0.50 for 0.02<α̂<2 as a rule of thumb to ensure an accurate approximation (e.g., Pr(0 < r < 1 | α̂, β̂) >0.99) . This validity measure and rule of thumb were validated by application to all the completed beta-Poisson models (related to 85 data sets) from the QMRA community portal (QMRA Wiki). The results showed that the higher the probability Pr(0 < r < 1 | α̂, β̂), the better the approximation. The results further showed that, among the total 85 models examined, 68 models were identified as valid approximate model applications, which all had a near perfect match to the corresponding exact beta-Poisson model dose-response curve. © 2016 Society for Risk Analysis.

Evidence of a possible NNE-trending fault zone in the Summerville, South Carolina, area from shallow seismic reflection surveys

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

Marple, R.T.; Talwani, P.

1994-03-01

Five high-resolution seismic-reflection surveys trending approximately WNW-ESE and totaling about 31 km were acquired in the Summerville, South Carolina, area. The surveys trend across the postulated Woodstock fault zone. These newly acquired data together with earlier data revealed the existence of an [approximately]50-km-long feature associated with gentle warping of the shallow sediments that lies along a recently described zone of river anomalies (ZRA). The first ([approximately]5.9-km-long) seismic reflection profile located about 14 km NNE of Summerville revealed that the J reflector (basalt) at about 670 m depth is offset about 30--40 m with the west side up. The overlying sedimentsmore » displayed upwarping rather than brittle offset. A second ([approximately]6.7-km-long) survey located along interstate Highway 26 revealed as much as 30--40 m of upwarping of the sediments above about 450 m depth. A third ([approximately]7.3-km-long) profile acquired through the town of Summerville revealed four, [approximately]200--300 m wide, nearly vertical zones in which the reflectors are noncoherent. Away from these zones the reflectors are relatively flat and are slightly higher on the west side of each zone. The fourth (3-km-long) survey was located about 5 km SW of Middleton Gardens and indicated minor faulting at about 500 m depth. The fifth ([approximately]6.4-km-long) seismic survey acquired just north of Ravenel revealed an [approximately]0.5-km-wide zone in which the reflectors in the top 350 m displayed as much as 20 m of upwarping. On all the surveys, except for the first, the basalt was at too great a depth to be resolved.« less

Insight into organic reactions from the direct random phase approximation and its corrections

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

Ruzsinszky, Adrienn; Zhang, Igor Ying; Scheffler, Matthias

2015-10-14

The performance of the random phase approximation (RPA) and beyond-RPA approximations for the treatment of electron correlation is benchmarked on three different molecular test sets. The test sets are chosen to represent three typical sources of error which can contribute to the failure of most density functional approximations in chemical reactions. The first test set (atomization and n-homodesmotic reactions) offers a gradually increasing balance of error from the chemical environment. The second test set (Diels-Alder reaction cycloaddition = DARC) reflects more the effect of weak dispersion interactions in chemical reactions. Finally, the third test set (self-interaction error 11 = SIE11)more » represents reactions which are exposed to noticeable self-interaction errors. This work seeks to answer whether any one of the many-body approximations considered here successfully addresses all these challenges.« less

Real-time dynamics of matrix quantum mechanics beyond the classical approximation

NASA Astrophysics Data System (ADS)

Buividovich, Pavel; Hanada, Masanori; Schäfer, Andreas

2018-03-01

We describe a numerical method which allows to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state approximation is accurate for significantly smaller field strengths and longer times than the classical one. Applying this approximation to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound λL < 2πT, which inevitably happens for classical dynamics at sufficiently small temperatures.

Properties of gamma-ray burst progenitor stars.

PubMed

Kumar, Pawan; Narayan, Ramesh; Johnson, Jarrett L

2008-07-18

We determined some basic properties of stars that produce spectacular gamma-ray bursts at the end of their lives. We assumed that accretion of the outer portion of the stellar core by a central black hole fuels the prompt emission and that fall-back and accretion of the stellar envelope later produce the plateau in the x-ray light curve seen in some bursts. Using x-ray data for three bursts, we estimated the radius of the stellar core to be approximately (1 - 3) x 10(10) cm and that of the stellar envelope to be approximately (1 - 2) x 10(11) cm. The density profile in the envelope is fairly shallow, with rho approximately r(-2) (where rho is density and r is distance from the center of the explosion). The rotation speeds of the core and envelope are approximately 0.05 and approximately 0.2 of the local Keplerian speed, respectively.

On the Accuracy of Double Scattering Approximation for Atmospheric Polarization Computations

NASA Technical Reports Server (NTRS)

Korkin, Sergey V.; Lyapustin, Alexei I.; Marshak, Alexander L.

2011-01-01

Interpretation of multi-angle spectro-polarimetric data in remote sensing of atmospheric aerosols require fast and accurate methods of solving the vector radiative transfer equation (VRTE). The single and double scattering approximations could provide an analytical framework for the inversion algorithms and are relatively fast, however accuracy assessments of these approximations for the aerosol atmospheres in the atmospheric window channels have been missing. This paper provides such analysis for a vertically homogeneous aerosol atmosphere with weak and strong asymmetry of scattering. In both cases, the double scattering approximation gives a high accuracy result (relative error approximately 0.2%) only for the low optical path - 10(sup -2) As the error rapidly grows with optical thickness, a full VRTE solution is required for the practical remote sensing analysis. It is shown that the scattering anisotropy is not important at low optical thicknesses neither for reflected nor for transmitted polarization components of radiation.

Approximate Computing Techniques for Iterative Graph Algorithms

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

Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh

Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with lowmore » impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.« less

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1988-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Zero-sum two-player game theoretic formulation of affine nonlinear discrete-time systems using neural networks.

PubMed

Mehraeen, Shahab; Dierks, Travis; Jagannathan, S; Crow, Mariesa L

2013-12-01

In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control and disturbance inputs for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. A numerical example is provided illustrating the effectiveness of the approach.

Sediment and water discharge rates of Turkish Black Sea rivers before and after hydropower dam construction

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

Hay, B.J.

1994-06-01

Presently, the water discharge rate to the Black Sea by Turkish rivers is approximately 41 km[sup 3]/yr. The sediment discharge rate of Turkish rivers to the Black Sea is 28 x 10[sup 6] t/yr. Before construction of the hydroelectric dams, the sediment discharge rate was approximately 70 x 10[sup 6] t/yr. The sharp reduction in sediment load is largely a result of the dams near the mouths of the Yesil Irmak and Kizil Irmak rivers. Before the construction of dams, Turkish rivers contributed approximately one third of the total amount of sediment received by the Black Sea from all surroundingmore » rivers. The life-span of the major reservoirs varies from approximately only one century (Yesil Irmak river reservoirs) to several thousand years (Sakarya river reservoirs). Life-span for the large Altinkaya Dam reservoir is estimated with approximately 500 yr.« less

Onsets of hierarchy truncation and self–consistent Born approximation with quantum mechanics prescriptions invariance

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

Zhang, Hou-Dao; Yan, YiJing, E-mail: yyan@ust.hk; iChEM and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026

2015-12-07

The issue of efficient hierarchy truncation is related to many approximate theories. In this paper, we revisit this issue from both the numerical efficiency and quantum mechanics prescription invariance aspects. The latter requires that the truncation approximation made in Schrödinger picture, such as the quantum master equations and their self–consistent–Born–approximation improvements, should be transferable to their Heisenberg–picture correspondences, without further approximations. We address this issue with the dissipaton equation of motion (DEOM), which is a unique theory for the dynamics of not only reduced systems but also hybrid bath environments. We also highlight the DEOM theory is not only aboutmore » how its dynamical variables evolve in time, but also the underlying dissipaton algebra. We demonstrate this unique feature of DEOM with model systems and report some intriguing nonlinear Fano interferences characteristics that are experimentally measurable.« less

The Evolution and Discharge of Electric Fields within a Thunderstorm

NASA Astrophysics Data System (ADS)

Hager, William W.; Nisbet, John S.; Kasha, John R.

1989-05-01

A 3-dimensional electrical model for a thunderstorm is developed and finite difference approximations to the model are analyzed. If the spatial derivatives are approximated by a method akin to the ☐ scheme and if the temporal derivative is approximated by either a backward difference or the Crank-Nicholson scheme, we show that the resulting discretization is unconditionally stable. The forward difference approximation to the time derivative is stable when the time step is sufficiently small relative to the ratio between the permittivity and the conductivity. Max-norm error estimates for the discrete approximations are established. To handle the propagation of lightning, special numerical techniques are devised based on the Inverse Matrix Modification Formula and Cholesky updates. Numerical comparisons between the model and theoretical results of Wilson and Holzer-Saxon are presented. We also apply our model to a storm observed at the Kennedy Space Center on July 11, 1978.

An approximation theory for the identification of nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Monte Carlo turbulence simulation using rational approximations to von Karman spectra

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1986-01-01

Turbulence simulation is computationally much simpler using rational spectra, but turbulence falls off as f exp -5/3 in frequency ranges of interest to aircraft response and as predicted by von Karman's model. Rational approximations to von Karman spectra should satisfy three requirements: (1) the rational spectra should provide a good approximation to the von Karman spectra in the frequency range of interest; (2) for stability, the resulting rational transfer function should have all its poles in the left half-plane; and (3) at high frequencies, the rational spectra must fall off as an integer power of frequency, and since the -2 power is closest to the -5/3 power, the rational approximation should roll off as the -2 power at high frequencies. Rational approximations to von Karman spectra that satisfy these three criteria are presented, along with spectra from simulated turbulence. Agreement between the spectra of the simulated turbulence and von Karman spectra is excellent.

Stable finite element approximations of two-phase flow with soluble surfactant

NASA Astrophysics Data System (ADS)

Barrett, John W.; Garcke, Harald; Nürnberg, Robert

2015-09-01

A parametric finite element approximation of incompressible two-phase flow with soluble surfactants is presented. The Navier-Stokes equations are coupled to bulk and surfaces PDEs for the surfactant concentrations. At the interface adsorption, desorption and stress balances involving curvature effects and Marangoni forces have to be considered. A parametric finite element approximation for the advection of the interface, which maintains good mesh properties, is coupled to the evolving surface finite element method, which is used to discretize the surface PDE for the interface surfactant concentration. The resulting system is solved together with standard finite element approximations of the Navier-Stokes equations and of the bulk parabolic PDE for the surfactant concentration. Semidiscrete and fully discrete approximations are analyzed with respect to stability, conservation and existence/uniqueness issues. The approach is validated for simple test cases and for complex scenarios, including colliding drops in a shear flow, which are computed in two and three space dimensions.

A faster 1.375-approximation algorithm for sorting by transpositions.

PubMed

Cunha, Luís Felipe I; Kowada, Luis Antonio B; Hausen, Rodrigo de A; de Figueiredo, Celina M H

2015-11-01

Sorting by Transpositions is an NP-hard problem for which several polynomial-time approximation algorithms have been developed. Hartman and Shamir (2006) developed a 1.5-approximation [Formula: see text] algorithm, whose running time was improved to O(nlogn) by Feng and Zhu (2007) with a data structure they defined, the permutation tree. Elias and Hartman (2006) developed a 1.375-approximation O(n(2)) algorithm, and Firoz et al. (2011) claimed an improvement to the running time, from O(n(2)) to O(nlogn), by using the permutation tree. We provide counter-examples to the correctness of Firoz et al.'s strategy, showing that it is not possible to reach a component by sufficient extensions using the method proposed by them. In addition, we propose a 1.375-approximation algorithm, modifying Elias and Hartman's approach with the use of permutation trees and achieving O(nlogn) time.

The effect of Limber and flat-sky approximations on galaxy weak lensing

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

Lemos, Pablo; Challinor, Anthony; Efstathiou, George, E-mail: pl411@cam.ac.uk, E-mail: a.d.challinor@ast.cam.ac.uk, E-mail: gpe@ast.cam.ac.uk

We review the effect of the commonly-used Limber and flat-sky approximations on the calculation of shear power spectra and correlation functions for galaxy weak lensing. These approximations are accurate at small scales, but it has been claimed recently that their impact on low multipoles could lead to an increase in the amplitude of the mass fluctuations inferred from surveys such as CFHTLenS, reducing the tension between galaxy weak lensing and the amplitude determined by Planck from observations of the cosmic microwave background. Here, we explore the impact of these approximations on cosmological parameters derived from weak lensing surveys, using themore » CFHTLenS data as a test case. We conclude that the use of small-angle approximations for cosmological parameter estimation is negligible for current data, and does not contribute to the tension between current weak lensing surveys and Planck.« less

An Approximate Dissipation Function for Large Strain Rubber Thermo-Mechanical Analyses

NASA Technical Reports Server (NTRS)

Johnson, Arthur R.; Chen, Tzi-Kang

2003-01-01

Mechanically induced viscoelastic dissipation is difficult to compute. When the constitutive model is defined by history integrals, the formula for dissipation is a double convolution integral. Since double convolution integrals are difficult to approximate, coupled thermo-mechanical analyses of highly viscous rubber-like materials cannot be made with most commercial finite element software. In this study, we present a method to approximate the dissipation for history integral constitutive models that represent Maxwell-like materials without approximating the double convolution integral. The method requires that the total stress can be separated into elastic and viscous components, and that the relaxation form of the constitutive law is defined with a Prony series. Numerical data is provided to demonstrate the limitations of this approximate method for determining dissipation. Rubber cylinders with imbedded steel disks and with an imbedded steel ball are dynamically loaded, and the nonuniform heating within the cylinders is computed.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

An hp-adaptivity and error estimation for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Bey, Kim S.

1995-01-01

This paper presents an hp-adaptive discontinuous Galerkin method for linear hyperbolic conservation laws. A priori and a posteriori error estimates are derived in mesh-dependent norms which reflect the dependence of the approximate solution on the element size (h) and the degree (p) of the local polynomial approximation. The a posteriori error estimate, based on the element residual method, provides bounds on the actual global error in the approximate solution. The adaptive strategy is designed to deliver an approximate solution with the specified level of error in three steps. The a posteriori estimate is used to assess the accuracy of a given approximate solution and the a priori estimate is used to predict the mesh refinements and polynomial enrichment needed to deliver the desired solution. Numerical examples demonstrate the reliability of the a posteriori error estimates and the effectiveness of the hp-adaptive strategy.

Flexible scheme to truncate the hierarchy of pure states.

PubMed

Zhang, P-P; Bentley, C D B; Eisfeld, A

2018-04-07

The hierarchy of pure states (HOPS) is a wavefunction-based method that can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However, truncation of the hierarchy is required to numerically implement HOPS. We want to choose a "good" truncation method, where by "good" we mean that it is numerically feasible to check convergence of the results. For the truncation approximation used in previous applications of HOPS, convergence checks are numerically challenging. In this work, we demonstrate the application of the "n-particle approximation" to HOPS. We also introduce a new approximation, which we call the "n-mode approximation." We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy in two exemplary problems: absorption and energy transfer of molecular aggregates.

Stochastic resonance-enhanced laser-based particle detector.

PubMed

Dutta, A; Werner, C

2009-01-01

This paper presents a Laser-based particle detector whose response was enhanced by modulating the Laser diode with a white-noise generator. A Laser sheet was generated to cast a shadow of the object on a 200 dots per inch, 512 x 1 pixels linear sensor array. The Laser diode was modulated with a white-noise generator to achieve stochastic resonance. The white-noise generator essentially amplified the wide-bandwidth (several hundred MHz) noise produced by a reverse-biased zener diode operating in junction-breakdown mode. The gain in the amplifier in the white-noise generator was set such that the Receiver Operating Characteristics plot provided the best discriminability. A monofiber 40 AWG (approximately 80 microm) wire was detected with approximately 88% True Positive rate and approximately 19% False Positive rate in presence of white-noise modulation and with approximately 71% True Positive rate and approximately 15% False Positive rate in absence of white-noise modulation.

An intensity map of hydrogen 21-cm emission at redshift z approximately 0.8.

PubMed

Chang, Tzu-Ching; Pen, Ue-Li; Bandura, Kevin; Peterson, Jeffrey B

2010-07-22

Observations of 21-cm radio emission by neutral hydrogen at redshifts z approximately 0.5 to approximately 2.5 are expected to provide a sensitive probe of cosmic dark energy. This is particularly true around the onset of acceleration at z approximately 1, where traditional optical cosmology becomes very difficult because of the infrared opacity of the atmosphere. Hitherto, 21-cm emission has been detected only to z = 0.24. More distant galaxies generally are too faint for individual detections but it is possible to measure the aggregate emission from many unresolved galaxies in the 'cosmic web'. Here we report a three-dimensional 21-cm intensity field at z = 0.53 to 1.12. We then co-add neutral-hydrogen (H i) emission from the volumes surrounding about 10,000 galaxies (from the DEEP2 optical galaxy redshift survey). We detect the aggregate 21-cm glow at a significance of approximately 4sigma.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1990-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Flexible scheme to truncate the hierarchy of pure states

NASA Astrophysics Data System (ADS)

Zhang, P.-P.; Bentley, C. D. B.; Eisfeld, A.

2018-04-01

The hierarchy of pure states (HOPS) is a wavefunction-based method that can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However, truncation of the hierarchy is required to numerically implement HOPS. We want to choose a "good" truncation method, where by "good" we mean that it is numerically feasible to check convergence of the results. For the truncation approximation used in previous applications of HOPS, convergence checks are numerically challenging. In this work, we demonstrate the application of the "n-particle approximation" to HOPS. We also introduce a new approximation, which we call the "n-mode approximation." We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy in two exemplary problems: absorption and energy transfer of molecular aggregates.

NMR signal analysis to characterize solid, aqueous, and lipid phases in baked cakes.

PubMed

Le Grand, F; Cambert, M; Mariette, F

2007-12-26

Proton mobility was studied in molecular fractions of some model systems and of cake using a 1H nuclear magnetic resonance (NMR) relaxation technique. For cake, five spin-spin relaxation times (T2) were obtained from transverse relaxation curves: T2 (1) approximately 20 micros, T2 (2) approximately 0.2 ms, T2 (3) approximately 3 ms, T2 (4) approximately 50 ms, and T2 (2) approximately 165 ms. The faster component was attributed to the solid phase, components 2 and 3 were associated with the aqueous phase, and the two slowest components were linked to the lipid phase. After cooking, the crust contained more fat but less water than the center part of the cake. The amount of gelatinized starch was lower in the crust, and water was more mobile due to less interaction with macromolecules. This preliminary study revealed different effects of storage on the center and crust.

27 CFR 9.46 - Livermore Valley.

Code of Federal Regulations, 2014 CFR

2014-04-01

... straight line approximately 4.2 miles, passing onto the Cedar Mtn. map, to BM 1878, 40 feet north of Mines..., R1E; then (18) Continue northwest in a straight line approximately 1.1 miles to an unnamed, 1,291-foot..., 840-foot peak, T3S, R2W; then (24) Proceed north-northeast in a straight line approximately 3.4 miles...

27 CFR 9.46 - Livermore Valley.

Code of Federal Regulations, 2012 CFR

2012-04-01

... straight line approximately 4.2 miles, passing onto the Cedar Mtn. map, to BM 1878, 40 feet north of Mines..., R1E; then (18) Continue northwest in a straight line approximately 1.1 miles to an unnamed, 1,291-foot..., 840-foot peak, T3S, R2W; then (24) Proceed north-northeast in a straight line approximately 3.4 miles...

27 CFR 9.46 - Livermore Valley.

Code of Federal Regulations, 2013 CFR

2013-04-01

... straight line approximately 4.2 miles, passing onto the Cedar Mtn. map, to BM 1878, 40 feet north of Mines..., R1E; then (18) Continue northwest in a straight line approximately 1.1 miles to an unnamed, 1,291-foot..., 840-foot peak, T3S, R2W; then (24) Proceed north-northeast in a straight line approximately 3.4 miles...

Exponential approximations in optimal design

NASA Technical Reports Server (NTRS)

Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.

1990-01-01

One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.

Robustness of controllers designed using Galerkin type approximations

NASA Technical Reports Server (NTRS)

Morris, K. A.

1990-01-01

One of the difficulties in designing controllers for infinite-dimensional systems arises from attempting to calculate a state for the system. It is shown that Galerkin type approximations can be used to design controllers which will perform as designed when implemented on the original infinite-dimensional system. No assumptions, other than those typically employed in numerical analysis, are made on the approximating scheme.

A DEIM Induced CUR Factorization

DTIC Science & Technology

2015-09-18

CUR approximate matrix factorization based on the Discrete Empirical Interpolation Method (DEIM). For a given matrix A, such a factorization provides a...CUR approximations based on leverage scores. 1 Introduction This work presents a new CUR matrix factorization based upon the Discrete Empirical...SUPPLEMENTARY NOTES 14. ABSTRACT We derive a CUR approximate matrix factorization based on the Discrete Empirical Interpolation Method (DEIM). For a given